id	sid	tid	token	lemma	pos
ap-610	1	1	ap04-bittnar1.vp	ap04-bittnar1.vp	PROPN
ap-610	1	2	1	1	NUM
ap-610	1	3	introduction	introduction	NOUN
ap-610	1	4	in	in	ADP
ap-610	1	5	standard	standard	ADJ
ap-610	1	6	continuum	continuum	ADJ
ap-610	1	7	mechanics	mechanic	NOUN
ap-610	1	8	,	,	PUNCT
ap-610	1	9	a	a	DET
ap-610	1	10	solid	solid	ADJ
ap-610	1	11	body	body	NOUN
ap-610	1	12	is	be	AUX
ap-610	1	13	decomposed	decompose	VERB
ap-610	1	14	into	into	ADP
ap-610	1	15	a	a	DET
ap-610	1	16	set	set	NOUN
ap-610	1	17	of	of	ADP
ap-610	1	18	idealized	idealized	ADJ
ap-610	1	19	,	,	PUNCT
ap-610	1	20	infinitesimal	infinitesimal	ADJ
ap-610	1	21	material	material	NOUN
ap-610	1	22	volumes	volume	NOUN
ap-610	1	23	,	,	PUNCT
ap-610	1	24	each	each	PRON
ap-610	1	25	of	of	ADP
ap-610	1	26	which	which	PRON
ap-610	1	27	can	can	AUX
ap-610	1	28	be	be	AUX
ap-610	1	29	described	describe	VERB
ap-610	1	30	independently	independently	ADV
ap-610	1	31	as	as	ADV
ap-610	1	32	far	far	ADV
ap-610	1	33	as	as	SCONJ
ap-610	1	34	the	the	DET
ap-610	1	35	constitutive	constitutive	ADJ
ap-610	1	36	behavior	behavior	NOUN
ap-610	1	37	is	be	AUX
ap-610	1	38	concerned	concern	VERB
ap-610	1	39	.	.	PUNCT
ap-610	2	1	of	of	ADP
ap-610	2	2	course	course	NOUN
ap-610	2	3	,	,	PUNCT
ap-610	2	4	this	this	PRON
ap-610	2	5	does	do	AUX
ap-610	2	6	not	not	PART
ap-610	2	7	mean	mean	VERB
ap-610	2	8	that	that	SCONJ
ap-610	2	9	the	the	DET
ap-610	2	10	individual	individual	ADJ
ap-610	2	11	material	material	NOUN
ap-610	2	12	points	point	NOUN
ap-610	2	13	are	be	AUX
ap-610	2	14	completely	completely	ADV
ap-610	2	15	isolated	isolate	VERB
ap-610	2	16	,	,	PUNCT
ap-610	2	17	but	but	CCONJ
ap-610	2	18	their	their	PRON
ap-610	2	19	interaction	interaction	NOUN
ap-610	2	20	can	can	AUX
ap-610	2	21	take	take	VERB
ap-610	2	22	place	place	NOUN
ap-610	2	23	only	only	ADV
ap-610	2	24	on	on	ADP
ap-610	2	25	the	the	DET
ap-610	2	26	level	level	NOUN
ap-610	2	27	of	of	ADP
ap-610	2	28	balance	balance	NOUN
ap-610	2	29	equations	equation	NOUN
ap-610	2	30	,	,	PUNCT
ap-610	2	31	through	through	ADP
ap-610	2	32	the	the	DET
ap-610	2	33	exchange	exchange	NOUN
ap-610	2	34	of	of	ADP
ap-610	2	35	mass	mass	PROPN
ap-610	2	36	,	,	PUNCT
ap-610	2	37	momentum	momentum	NOUN
ap-610	2	38	,	,	PUNCT
ap-610	2	39	energy	energy	NOUN
ap-610	2	40	and	and	CCONJ
ap-610	2	41	entropy	entropy	NOUN
ap-610	2	42	.	.	PUNCT
ap-610	3	1	in	in	ADP
ap-610	3	2	reality	reality	NOUN
ap-610	3	3	,	,	PUNCT
ap-610	3	4	however	however	ADV
ap-610	3	5	,	,	PUNCT
ap-610	3	6	no	no	DET
ap-610	3	7	material	material	NOUN
ap-610	3	8	is	be	AUX
ap-610	3	9	an	an	DET
ap-610	3	10	ideal	ideal	ADJ
ap-610	3	11	continuum	continuum	ADJ
ap-610	3	12	.	.	PUNCT
ap-610	4	1	both	both	DET
ap-610	4	2	natural	natural	ADJ
ap-610	4	3	and	and	CCONJ
ap-610	4	4	man	man	NOUN
ap-610	4	5	-	-	PUNCT
ap-610	4	6	made	make	VERB
ap-610	4	7	materials	material	NOUN
ap-610	4	8	have	have	VERB
ap-610	4	9	a	a	DET
ap-610	4	10	complicated	complicated	ADJ
ap-610	4	11	internal	internal	ADJ
ap-610	4	12	structure	structure	NOUN
ap-610	4	13	,	,	PUNCT
ap-610	4	14	characterized	characterize	VERB
ap-610	4	15	by	by	ADP
ap-610	4	16	microstructural	microstructural	ADJ
ap-610	4	17	details	detail	NOUN
ap-610	4	18	whose	whose	DET
ap-610	4	19	size	size	NOUN
ap-610	4	20	typically	typically	ADV
ap-610	4	21	ranges	range	VERB
ap-610	4	22	over	over	ADP
ap-610	4	23	many	many	ADJ
ap-610	4	24	orders	order	NOUN
ap-610	4	25	of	of	ADP
ap-610	4	26	magnitude	magnitude	NOUN
ap-610	4	27	.	.	PUNCT
ap-610	5	1	the	the	DET
ap-610	5	2	expression	expression	NOUN
ap-610	5	3	“	"	PUNCT
ap-610	5	4	microstructure	microstructure	NOUN
ap-610	5	5	”	"	PUNCT
ap-610	5	6	will	will	AUX
ap-610	5	7	be	be	AUX
ap-610	5	8	used	use	VERB
ap-610	5	9	as	as	ADP
ap-610	5	10	a	a	DET
ap-610	5	11	generic	generic	ADJ
ap-610	5	12	denomination	denomination	NOUN
ap-610	5	13	for	for	ADP
ap-610	5	14	any	any	DET
ap-610	5	15	type	type	NOUN
ap-610	5	16	of	of	ADP
ap-610	5	17	internal	internal	ADJ
ap-610	5	18	material	material	NOUN
ap-610	5	19	structure	structure	NOUN
ap-610	5	20	,	,	PUNCT
ap-610	5	21	not	not	PART
ap-610	5	22	necessarily	necessarily	ADV
ap-610	5	23	on	on	ADP
ap-610	5	24	the	the	DET
ap-610	5	25	level	level	NOUN
ap-610	5	26	of	of	ADP
ap-610	5	27	micrometers	micrometer	NOUN
ap-610	5	28	.	.	PUNCT
ap-610	6	1	some	some	PRON
ap-610	6	2	of	of	ADP
ap-610	6	3	these	these	DET
ap-610	6	4	details	detail	NOUN
ap-610	6	5	can	can	AUX
ap-610	6	6	be	be	AUX
ap-610	6	7	described	describe	VERB
ap-610	6	8	explicitly	explicitly	ADV
ap-610	6	9	by	by	ADP
ap-610	6	10	spatial	spatial	ADJ
ap-610	6	11	variation	variation	NOUN
ap-610	6	12	of	of	ADP
ap-610	6	13	the	the	DET
ap-610	6	14	material	material	NOUN
ap-610	6	15	properties	property	NOUN
ap-610	6	16	.	.	PUNCT
ap-610	7	1	but	but	CCONJ
ap-610	7	2	this	this	PRON
ap-610	7	3	can	can	AUX
ap-610	7	4	never	never	ADV
ap-610	7	5	be	be	AUX
ap-610	7	6	done	do	VERB
ap-610	7	7	simultaneously	simultaneously	ADV
ap-610	7	8	over	over	ADP
ap-610	7	9	the	the	DET
ap-610	7	10	entire	entire	ADJ
ap-610	7	11	range	range	NOUN
ap-610	7	12	of	of	ADP
ap-610	7	13	scales	scale	NOUN
ap-610	7	14	.	.	PUNCT
ap-610	8	1	one	one	NUM
ap-610	8	2	reason	reason	NOUN
ap-610	8	3	is	be	AUX
ap-610	8	4	that	that	SCONJ
ap-610	8	5	such	such	DET
ap-610	8	6	a	a	DET
ap-610	8	7	model	model	NOUN
ap-610	8	8	would	would	AUX
ap-610	8	9	be	be	AUX
ap-610	8	10	prohibitively	prohibitively	ADV
ap-610	8	11	expensive	expensive	ADJ
ap-610	8	12	for	for	ADP
ap-610	8	13	practical	practical	ADJ
ap-610	8	14	applications	application	NOUN
ap-610	8	15	.	.	PUNCT
ap-610	9	1	another	another	PRON
ap-610	9	2	,	,	PUNCT
ap-610	9	3	more	more	ADV
ap-610	9	4	fundamental	fundamental	ADJ
ap-610	9	5	,	,	PUNCT
ap-610	9	6	reason	reason	NOUN
ap-610	9	7	is	be	AUX
ap-610	9	8	that	that	SCONJ
ap-610	9	9	,	,	PUNCT
ap-610	9	10	on	on	ADP
ap-610	9	11	a	a	DET
ap-610	9	12	small	small	ADJ
ap-610	9	13	enough	enough	ADJ
ap-610	9	14	scale	scale	NOUN
ap-610	9	15	,	,	PUNCT
ap-610	9	16	the	the	DET
ap-610	9	17	continuum	continuum	ADJ
ap-610	9	18	description	description	NOUN
ap-610	9	19	per	per	ADP
ap-610	9	20	se	se	X
ap-610	9	21	is	be	AUX
ap-610	9	22	no	no	ADV
ap-610	9	23	longer	long	ADV
ap-610	9	24	adequate	adequate	ADJ
ap-610	9	25	and	and	CCONJ
ap-610	9	26	needs	need	VERB
ap-610	9	27	to	to	PART
ap-610	9	28	be	be	AUX
ap-610	9	29	replaced	replace	VERB
ap-610	9	30	by	by	ADP
ap-610	9	31	a	a	DET
ap-610	9	32	discrete	discrete	ADJ
ap-610	9	33	model	model	NOUN
ap-610	9	34	(	(	PUNCT
ap-610	9	35	or	or	CCONJ
ap-610	9	36	,	,	PUNCT
ap-610	9	37	ultimately	ultimately	ADV
ap-610	9	38	,	,	PUNCT
ap-610	9	39	by	by	ADP
ap-610	9	40	interatomic	interatomic	ADJ
ap-610	9	41	potentials	potential	NOUN
ap-610	9	42	based	base	VERB
ap-610	9	43	on	on	ADP
ap-610	9	44	quantum	quantum	ADJ
ap-610	9	45	mechanics	mechanic	NOUN
ap-610	9	46	)	)	PUNCT
ap-610	9	47	.	.	PUNCT
ap-610	10	1	constructing	construct	VERB
ap-610	10	2	a	a	DET
ap-610	10	3	material	material	NOUN
ap-610	10	4	model	model	NOUN
ap-610	10	5	,	,	PUNCT
ap-610	10	6	one	one	PRON
ap-610	10	7	must	must	AUX
ap-610	10	8	select	select	VERB
ap-610	10	9	a	a	DET
ap-610	10	10	certain	certain	ADJ
ap-610	10	11	resolution	resolution	NOUN
ap-610	10	12	level	level	NOUN
ap-610	10	13	below	below	ADP
ap-610	10	14	which	which	PRON
ap-610	10	15	the	the	DET
ap-610	10	16	microstructural	microstructural	ADJ
ap-610	10	17	details	detail	NOUN
ap-610	10	18	are	be	AUX
ap-610	10	19	not	not	PART
ap-610	10	20	explicitly	explicitly	ADV
ap-610	10	21	“	"	PUNCT
ap-610	10	22	visible	visible	ADJ
ap-610	10	23	”	"	PUNCT
ap-610	10	24	to	to	ADP
ap-610	10	25	the	the	DET
ap-610	10	26	model	model	NOUN
ap-610	10	27	and	and	CCONJ
ap-610	10	28	need	need	VERB
ap-610	10	29	to	to	PART
ap-610	10	30	be	be	AUX
ap-610	10	31	taken	take	VERB
ap-610	10	32	into	into	ADP
ap-610	10	33	account	account	NOUN
ap-610	10	34	approximately	approximately	ADV
ap-610	10	35	and	and	CCONJ
ap-610	10	36	indirectly	indirectly	ADV
ap-610	10	37	,	,	PUNCT
ap-610	10	38	by	by	ADP
ap-610	10	39	an	an	DET
ap-610	10	40	appropriate	appropriate	ADJ
ap-610	10	41	definition	definition	NOUN
ap-610	10	42	of	of	ADP
ap-610	10	43	“	"	PUNCT
ap-610	10	44	effective	effective	ADJ
ap-610	10	45	”	"	PUNCT
ap-610	10	46	material	material	NOUN
ap-610	10	47	properties	property	NOUN
ap-610	10	48	.	.	PUNCT
ap-610	11	1	also	also	ADV
ap-610	11	2	,	,	PUNCT
ap-610	11	3	one	one	PRON
ap-610	11	4	should	should	AUX
ap-610	11	5	specify	specify	VERB
ap-610	11	6	the	the	DET
ap-610	11	7	characteristic	characteristic	ADJ
ap-610	11	8	wavelength	wavelength	NOUN
ap-610	11	9	of	of	ADP
ap-610	11	10	the	the	DET
ap-610	11	11	imposed	impose	VERB
ap-610	11	12	deformation	deformation	NOUN
ap-610	11	13	fields	field	NOUN
ap-610	11	14	that	that	PRON
ap-610	11	15	can	can	AUX
ap-610	11	16	be	be	AUX
ap-610	11	17	expected	expect	VERB
ap-610	11	18	for	for	ADP
ap-610	11	19	the	the	DET
ap-610	11	20	given	give	VERB
ap-610	11	21	type	type	NOUN
ap-610	11	22	of	of	ADP
ap-610	11	23	geometry	geometry	NOUN
ap-610	11	24	and	and	CCONJ
ap-610	11	25	loading	loading	NOUN
ap-610	11	26	.	.	PUNCT
ap-610	12	1	here	here	ADV
ap-610	12	2	,	,	PUNCT
ap-610	12	3	the	the	DET
ap-610	12	4	notion	notion	NOUN
ap-610	12	5	of	of	ADP
ap-610	12	6	characteristic	characteristic	ADJ
ap-610	12	7	wavelength	wavelength	NOUN
ap-610	12	8	has	have	VERB
ap-610	12	9	to	to	PART
ap-610	12	10	be	be	AUX
ap-610	12	11	understood	understand	VERB
ap-610	12	12	in	in	ADP
ap-610	12	13	a	a	DET
ap-610	12	14	broad	broad	ADJ
ap-610	12	15	sense	sense	NOUN
ap-610	12	16	,	,	PUNCT
ap-610	12	17	not	not	PART
ap-610	12	18	only	only	ADV
ap-610	12	19	as	as	ADP
ap-610	12	20	the	the	DET
ap-610	12	21	spatial	spatial	ADJ
ap-610	12	22	period	period	NOUN
ap-610	12	23	of	of	ADP
ap-610	12	24	a	a	DET
ap-610	12	25	dynamic	dynamic	ADJ
ap-610	12	26	phenomenon	phenomenon	NOUN
ap-610	12	27	but	but	CCONJ
ap-610	12	28	also	also	ADV
ap-610	12	29	as	as	ADP
ap-610	12	30	the	the	DET
ap-610	12	31	length	length	NOUN
ap-610	12	32	on	on	ADP
ap-610	12	33	which	which	PRON
ap-610	12	34	the	the	DET
ap-610	12	35	value	value	NOUN
ap-610	12	36	of	of	ADP
ap-610	12	37	strain	strain	NOUN
ap-610	12	38	changes	change	NOUN
ap-610	12	39	substantially	substantially	ADV
ap-610	12	40	in	in	ADP
ap-610	12	41	static	static	ADJ
ap-610	12	42	problems	problem	NOUN
ap-610	12	43	.	.	PUNCT
ap-610	13	1	if	if	SCONJ
ap-610	13	2	the	the	DET
ap-610	13	3	characteristic	characteristic	ADJ
ap-610	13	4	wavelength	wavelength	NOUN
ap-610	13	5	of	of	ADP
ap-610	13	6	the	the	DET
ap-610	13	7	deformation	deformation	NOUN
ap-610	13	8	field	field	NOUN
ap-610	13	9	remains	remain	VERB
ap-610	13	10	above	above	ADP
ap-610	13	11	the	the	DET
ap-610	13	12	resolution	resolution	NOUN
ap-610	13	13	level	level	NOUN
ap-610	13	14	of	of	ADP
ap-610	13	15	the	the	DET
ap-610	13	16	material	material	NOUN
ap-610	13	17	model	model	NOUN
ap-610	13	18	,	,	PUNCT
ap-610	13	19	a	a	DET
ap-610	13	20	conventional	conventional	ADJ
ap-610	13	21	continuum	continuum	ADJ
ap-610	13	22	description	description	NOUN
ap-610	13	23	can	can	AUX
ap-610	13	24	be	be	AUX
ap-610	13	25	adequate	adequate	ADJ
ap-610	13	26	.	.	PUNCT
ap-610	14	1	on	on	ADP
ap-610	14	2	the	the	DET
ap-610	14	3	other	other	ADJ
ap-610	14	4	hand	hand	NOUN
ap-610	14	5	,	,	PUNCT
ap-610	14	6	if	if	SCONJ
ap-610	14	7	the	the	DET
ap-610	14	8	deformation	deformation	NOUN
ap-610	14	9	field	field	NOUN
ap-610	14	10	is	be	AUX
ap-610	14	11	expected	expect	VERB
ap-610	14	12	to	to	PART
ap-610	14	13	have	have	VERB
ap-610	14	14	important	important	ADJ
ap-610	14	15	components	component	NOUN
ap-610	14	16	with	with	ADP
ap-610	14	17	wavelengths	wavelength	NOUN
ap-610	14	18	below	below	ADP
ap-610	14	19	the	the	DET
ap-610	14	20	resolution	resolution	NOUN
ap-610	14	21	level	level	NOUN
ap-610	14	22	,	,	PUNCT
ap-610	14	23	the	the	DET
ap-610	14	24	model	model	NOUN
ap-610	14	25	needs	need	VERB
ap-610	14	26	to	to	PART
ap-610	14	27	be	be	AUX
ap-610	14	28	enriched	enrich	VERB
ap-610	14	29	so	so	ADV
ap-610	14	30	as	as	SCONJ
ap-610	14	31	to	to	PART
ap-610	14	32	capture	capture	VERB
ap-610	14	33	the	the	DET
ap-610	14	34	real	real	ADJ
ap-610	14	35	processes	process	NOUN
ap-610	14	36	more	more	ADV
ap-610	14	37	adequately	adequately	ADV
ap-610	14	38	.	.	PUNCT
ap-610	15	1	instead	instead	ADV
ap-610	15	2	of	of	ADP
ap-610	15	3	refining	refine	VERB
ap-610	15	4	the	the	DET
ap-610	15	5	explicit	explicit	ADJ
ap-610	15	6	resolution	resolution	NOUN
ap-610	15	7	level	level	NOUN
ap-610	15	8	,	,	PUNCT
ap-610	15	9	it	it	PRON
ap-610	15	10	is	be	AUX
ap-610	15	11	often	often	ADV
ap-610	15	12	more	more	ADV
ap-610	15	13	effective	effective	ADJ
ap-610	15	14	to	to	PART
ap-610	15	15	use	use	VERB
ap-610	15	16	various	various	ADJ
ap-610	15	17	forms	form	NOUN
ap-610	15	18	of	of	ADP
ap-610	15	19	the	the	DET
ap-610	15	20	so	so	ADV
ap-610	15	21	-	-	PUNCT
ap-610	15	22	called	call	VERB
ap-610	15	23	enriched	enriched	ADJ
ap-610	15	24	or	or	CCONJ
ap-610	15	25	generalized	generalized	ADJ
ap-610	15	26	continuum	continuum	ADJ
ap-610	15	27	formulations	formulation	NOUN
ap-610	15	28	.	.	PUNCT
ap-610	16	1	a	a	DET
ap-610	16	2	systematic	systematic	ADJ
ap-610	16	3	overview	overview	NOUN
ap-610	16	4	and	and	CCONJ
ap-610	16	5	detailed	detailed	ADJ
ap-610	16	6	discussion	discussion	NOUN
ap-610	16	7	of	of	ADP
ap-610	16	8	generalized	generalized	ADJ
ap-610	16	9	continuum	continuum	ADJ
ap-610	16	10	theories	theory	NOUN
ap-610	16	11	has	have	AUX
ap-610	16	12	been	be	AUX
ap-610	16	13	given	give	VERB
ap-610	16	14	e.g.	e.g.	ADV
ap-610	16	15	in	in	ADP
ap-610	16	16	the	the	DET
ap-610	16	17	recent	recent	ADJ
ap-610	16	18	review	review	NOUN
ap-610	16	19	paper	paper	NOUN
ap-610	16	20	by	by	ADP
ap-610	16	21	bažant	bažant	NOUN
ap-610	16	22	and	and	CCONJ
ap-610	16	23	jirásek	jirásek	NOUN
ap-610	16	24	(	(	PUNCT
ap-610	16	25	2002	2002	NUM
ap-610	16	26	)	)	PUNCT
ap-610	16	27	.	.	PUNCT
ap-610	17	1	the	the	DET
ap-610	17	2	aim	aim	NOUN
ap-610	17	3	of	of	ADP
ap-610	17	4	the	the	DET
ap-610	17	5	present	present	ADJ
ap-610	17	6	study	study	NOUN
ap-610	17	7	is	be	AUX
ap-610	17	8	to	to	PART
ap-610	17	9	demonstrate	demonstrate	VERB
ap-610	17	10	by	by	ADP
ap-610	17	11	specific	specific	ADJ
ap-610	17	12	examples	example	NOUN
ap-610	17	13	how	how	SCONJ
ap-610	17	14	the	the	DET
ap-610	17	15	need	need	NOUN
ap-610	17	16	for	for	ADP
ap-610	17	17	enriched	enriched	ADJ
ap-610	17	18	continuum	continuum	ADJ
ap-610	17	19	formulations	formulation	NOUN
ap-610	17	20	arises	arise	VERB
ap-610	17	21	from	from	ADP
ap-610	17	22	discrepancies	discrepancy	NOUN
ap-610	17	23	between	between	ADP
ap-610	17	24	experimental	experimental	ADJ
ap-610	17	25	observations	observation	NOUN
ap-610	17	26	and	and	CCONJ
ap-610	17	27	theoretical	theoretical	ADJ
ap-610	17	28	predictions	prediction	NOUN
ap-610	17	29	based	base	VERB
ap-610	17	30	on	on	ADP
ap-610	17	31	the	the	DET
ap-610	17	32	standard	standard	ADJ
ap-610	17	33	theories	theory	NOUN
ap-610	17	34	,	,	PUNCT
ap-610	17	35	and	and	CCONJ
ap-610	17	36	also	also	ADV
ap-610	17	37	how	how	SCONJ
ap-610	17	38	the	the	DET
ap-610	17	39	model	model	NOUN
ap-610	17	40	performance	performance	NOUN
ap-610	17	41	can	can	AUX
ap-610	17	42	be	be	AUX
ap-610	17	43	improved	improve	VERB
ap-610	17	44	by	by	ADP
ap-610	17	45	adding	add	VERB
ap-610	17	46	carefully	carefully	ADV
ap-610	17	47	selected	select	VERB
ap-610	17	48	enrichment	enrichment	NOUN
ap-610	17	49	terms	term	NOUN
ap-610	17	50	.	.	PUNCT
ap-610	18	1	the	the	DET
ap-610	18	2	enrichments	enrichment	NOUN
ap-610	18	3	to	to	PART
ap-610	18	4	be	be	AUX
ap-610	18	5	discussed	discuss	VERB
ap-610	18	6	here	here	ADV
ap-610	18	7	are	be	AUX
ap-610	18	8	in	in	ADP
ap-610	18	9	general	general	ADJ
ap-610	18	10	referred	refer	VERB
ap-610	18	11	to	to	ADP
ap-610	18	12	as	as	ADP
ap-610	18	13	nonlocal	nonlocal	ADJ
ap-610	18	14	,	,	PUNCT
ap-610	18	15	but	but	CCONJ
ap-610	18	16	this	this	DET
ap-610	18	17	adjective	adjective	NOUN
ap-610	18	18	must	must	AUX
ap-610	18	19	be	be	AUX
ap-610	18	20	understood	understand	VERB
ap-610	18	21	in	in	ADP
ap-610	18	22	the	the	DET
ap-610	18	23	broad	broad	ADJ
ap-610	18	24	sense	sense	NOUN
ap-610	18	25	,	,	PUNCT
ap-610	18	26	covering	cover	VERB
ap-610	18	27	both	both	DET
ap-610	18	28	strongly	strongly	ADV
ap-610	18	29	nonlocal	nonlocal	ADJ
ap-610	18	30	and	and	CCONJ
ap-610	18	31	weakly	weakly	ADJ
ap-610	18	32	nonlocal	nonlocal	ADJ
ap-610	18	33	formulations	formulation	NOUN
ap-610	18	34	.	.	PUNCT
ap-610	19	1	precise	precise	ADJ
ap-610	19	2	mathematical	mathematical	ADJ
ap-610	19	3	definitions	definition	NOUN
ap-610	19	4	of	of	ADP
ap-610	19	5	strong	strong	ADJ
ap-610	19	6	and	and	CCONJ
ap-610	19	7	weak	weak	ADJ
ap-610	19	8	nonlocality	nonlocality	NOUN
ap-610	19	9	were	be	AUX
ap-610	19	10	given	give	VERB
ap-610	19	11	by	by	ADP
ap-610	19	12	rogula	rogula	NOUN
ap-610	19	13	(	(	PUNCT
ap-610	19	14	1982	1982	NUM
ap-610	19	15	)	)	PUNCT
ap-610	19	16	and	and	CCONJ
ap-610	19	17	are	be	AUX
ap-610	19	18	also	also	ADV
ap-610	19	19	explained	explain	VERB
ap-610	19	20	in	in	ADP
ap-610	19	21	bažant	bažant	NOUN
ap-610	19	22	and	and	CCONJ
ap-610	19	23	jirásek	jirásek	NOUN
ap-610	19	24	(	(	PUNCT
ap-610	19	25	2002	2002	NUM
ap-610	19	26	)	)	PUNCT
ap-610	19	27	.	.	PUNCT
ap-610	20	1	here	here	ADV
ap-610	20	2	we	we	PRON
ap-610	20	3	only	only	ADV
ap-610	20	4	note	note	VERB
ap-610	20	5	that	that	SCONJ
ap-610	20	6	strongly	strongly	ADV
ap-610	20	7	nonlocal	nonlocal	ADJ
ap-610	20	8	theories	theory	NOUN
ap-610	20	9	are	be	AUX
ap-610	20	10	exemplified	exemplify	VERB
ap-610	20	11	by	by	ADP
ap-610	20	12	integral	integral	ADJ
ap-610	20	13	-	-	PUNCT
ap-610	20	14	type	type	NOUN
ap-610	20	15	formulations	formulation	NOUN
ap-610	20	16	with	with	ADP
ap-610	20	17	weighted	weight	VERB
ap-610	20	18	spatial	spatial	ADJ
ap-610	20	19	averaging	averaging	NOUN
ap-610	20	20	or	or	CCONJ
ap-610	20	21	by	by	ADP
ap-610	20	22	implicit	implicit	ADJ
ap-610	20	23	gradient	gradient	NOUN
ap-610	20	24	models	model	NOUN
ap-610	20	25	,	,	PUNCT
ap-610	20	26	while	while	SCONJ
ap-610	20	27	weakly	weakly	ADJ
ap-610	20	28	nonlocal	nonlocal	ADJ
ap-610	20	29	theories	theory	NOUN
ap-610	20	30	include	include	VERB
ap-610	20	31	for	for	ADP
ap-610	20	32	instance	instance	NOUN
ap-610	20	33	explicit	explicit	ADJ
ap-610	20	34	gradient	gradient	NOUN
ap-610	20	35	models	model	NOUN
ap-610	20	36	.	.	PUNCT
ap-610	21	1	the	the	DET
ap-610	21	2	meaning	meaning	NOUN
ap-610	21	3	of	of	ADP
ap-610	21	4	these	these	DET
ap-610	21	5	expressions	expression	NOUN
ap-610	21	6	will	will	AUX
ap-610	21	7	become	become	VERB
ap-610	21	8	clear	clear	ADJ
ap-610	21	9	from	from	ADP
ap-610	21	10	the	the	DET
ap-610	21	11	examples	example	NOUN
ap-610	21	12	to	to	PART
ap-610	21	13	follow	follow	VERB
ap-610	21	14	.	.	PUNCT
ap-610	22	1	we	we	PRON
ap-610	22	2	will	will	AUX
ap-610	22	3	start	start	VERB
ap-610	22	4	from	from	ADP
ap-610	22	5	enriched	enriched	ADJ
ap-610	22	6	formulations	formulation	NOUN
ap-610	22	7	of	of	ADP
ap-610	22	8	the	the	DET
ap-610	22	9	theory	theory	NOUN
ap-610	22	10	of	of	ADP
ap-610	22	11	elasticity	elasticity	NOUN
ap-610	22	12	,	,	PUNCT
ap-610	22	13	and	and	CCONJ
ap-610	22	14	then	then	ADV
ap-610	22	15	proceed	proceed	VERB
ap-610	22	16	to	to	ADP
ap-610	22	17	elastoplasticity	elastoplasticity	NOUN
ap-610	22	18	and	and	CCONJ
ap-610	22	19	damage	damage	NOUN
ap-610	22	20	mechanics	mechanic	NOUN
ap-610	22	21	.	.	PUNCT
ap-610	23	1	the	the	DET
ap-610	23	2	paper	paper	NOUN
ap-610	23	3	is	be	AUX
ap-610	23	4	organized	organize	VERB
ap-610	23	5	as	as	SCONJ
ap-610	23	6	follows	follow	VERB
ap-610	23	7	.	.	PUNCT
ap-610	24	1	section	section	NOUN
ap-610	24	2	2	2	NUM
ap-610	24	3	treats	treat	VERB
ap-610	24	4	the	the	DET
ap-610	24	5	dispersion	dispersion	NOUN
ap-610	24	6	of	of	ADP
ap-610	24	7	short	short	ADJ
ap-610	24	8	elastic	elastic	ADJ
ap-610	24	9	waves	wave	NOUN
ap-610	24	10	in	in	ADP
ap-610	24	11	heterogeneous	heterogeneous	ADJ
ap-610	24	12	or	or	CCONJ
ap-610	24	13	discrete	discrete	ADJ
ap-610	24	14	media	medium	NOUN
ap-610	24	15	.	.	PUNCT
ap-610	25	1	it	it	PRON
ap-610	25	2	is	be	AUX
ap-610	25	3	shown	show	VERB
ap-610	25	4	that	that	SCONJ
ap-610	25	5	the	the	DET
ap-610	25	6	standard	standard	ADJ
ap-610	25	7	homogenization	homogenization	NOUN
ap-610	25	8	procedure	procedure	NOUN
ap-610	25	9	erases	erase	VERB
ap-610	25	10	the	the	DET
ap-610	25	11	information	information	NOUN
ap-610	25	12	on	on	ADP
ap-610	25	13	dispersive	dispersive	ADJ
ap-610	25	14	properties	property	NOUN
ap-610	25	15	.	.	PUNCT
ap-610	26	1	dispersion	dispersion	NOUN
ap-610	26	2	laws	law	NOUN
ap-610	26	3	are	be	AUX
ap-610	26	4	then	then	ADV
ap-610	26	5	derived	derive	VERB
ap-610	26	6	for	for	ADP
ap-610	26	7	a	a	DET
ap-610	26	8	host	host	NOUN
ap-610	26	9	of	of	ADP
ap-610	26	10	generalized	generalized	ADJ
ap-610	26	11	continuum	continuum	ADJ
ap-610	26	12	models	model	NOUN
ap-610	26	13	,	,	PUNCT
ap-610	26	14	including	include	VERB
ap-610	26	15	strain	strain	NOUN
ap-610	26	16	-	-	PUNCT
ap-610	26	17	gradient	gradient	NOUN
ap-610	26	18	elasticity	elasticity	NOUN
ap-610	26	19	,	,	PUNCT
ap-610	26	20	models	model	NOUN
ap-610	26	21	with	with	ADP
ap-610	26	22	mixed	mixed	ADJ
ap-610	26	23	spatial	spatial	ADJ
ap-610	26	24	-	-	PUNCT
ap-610	26	25	temporal	temporal	ADJ
ap-610	26	26	derivatives	derivative	NOUN
ap-610	26	27	,	,	PUNCT
ap-610	26	28	and	and	CCONJ
ap-610	26	29	integral	integral	ADJ
ap-610	26	30	-	-	PUNCT
ap-610	26	31	type	type	NOUN
ap-610	26	32	nonlocal	nonlocal	ADJ
ap-610	26	33	elasticity	elasticity	NOUN
ap-610	26	34	.	.	PUNCT
ap-610	27	1	advantages	advantage	NOUN
ap-610	27	2	and	and	CCONJ
ap-610	27	3	drawbacks	drawback	NOUN
ap-610	27	4	of	of	ADP
ap-610	27	5	individual	individual	ADJ
ap-610	27	6	formulations	formulation	NOUN
ap-610	27	7	are	be	AUX
ap-610	27	8	discussed	discuss	VERB
ap-610	27	9	,	,	PUNCT
ap-610	27	10	and	and	CCONJ
ap-610	27	11	a	a	DET
ap-610	27	12	general	general	ADJ
ap-610	27	13	framework	framework	NOUN
ap-610	27	14	of	of	ADP
ap-610	27	15	nonlocal	nonlocal	ADJ
ap-610	27	16	strain	strain	NOUN
ap-610	27	17	-	-	PUNCT
ap-610	27	18	gradient	gradient	NOUN
ap-610	27	19	elasticity	elasticity	NOUN
ap-610	27	20	is	be	AUX
ap-610	27	21	outlined	outline	VERB
ap-610	27	22	.	.	PUNCT
ap-610	28	1	section	section	NOUN
ap-610	28	2	3	3	NUM
ap-610	28	3	deals	deal	NOUN
ap-610	28	4	with	with	ADP
ap-610	28	5	size	size	NOUN
ap-610	28	6	effects	effect	NOUN
ap-610	28	7	in	in	ADP
ap-610	28	8	microscale	microscale	ADJ
ap-610	28	9	elastoplasticity	elastoplasticity	NOUN
ap-610	28	10	,	,	PUNCT
ap-610	28	11	in	in	ADP
ap-610	28	12	particular	particular	ADJ
ap-610	28	13	with	with	ADP
ap-610	28	14	the	the	DET
ap-610	28	15	size	size	NOUN
ap-610	28	16	dependence	dependence	NOUN
ap-610	28	17	of	of	ADP
ap-610	28	18	the	the	DET
ap-610	28	19	apparent	apparent	ADJ
ap-610	28	20	hardening	harden	VERB
ap-610	28	21	modulus	modulus	NOUN
ap-610	28	22	.	.	PUNCT
ap-610	29	1	using	use	VERB
ap-610	29	2	the	the	DET
ap-610	29	3	academic	academic	ADJ
ap-610	29	4	example	example	NOUN
ap-610	29	5	of	of	ADP
ap-610	29	6	a	a	DET
ap-610	29	7	16	16	NUM
ap-610	29	8	©	©	PROPN
ap-610	29	9	czech	czech	PROPN
ap-610	29	10	technical	technical	PROPN
ap-610	29	11	university	university	PROPN
ap-610	29	12	publishing	publishing	NOUN
ap-610	29	13	house	house	NOUN
ap-610	29	14	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	29	15	acta	acta	PROPN
ap-610	29	16	polytechnica	polytechnica	PROPN
ap-610	29	17	vol	vol	NOUN
ap-610	29	18	.	.	PROPN
ap-610	30	1	44	44	NUM
ap-610	30	2	no	no	NOUN
ap-610	30	3	.	.	PUNCT
ap-610	31	1	5–6/2004	5–6/2004	NUM
ap-610	31	2	nonlocal	nonlocal	ADJ
ap-610	31	3	theories	theory	NOUN
ap-610	31	4	in	in	ADP
ap-610	31	5	continuum	continuum	ADJ
ap-610	31	6	mechanics	mechanic	NOUN
ap-610	31	7	m.	m.	NOUN
ap-610	31	8	jirásek	jirásek	VERB
ap-610	31	9	the	the	DET
ap-610	31	10	purpose	purpose	NOUN
ap-610	31	11	of	of	ADP
ap-610	31	12	this	this	DET
ap-610	31	13	paper	paper	NOUN
ap-610	31	14	is	be	AUX
ap-610	31	15	to	to	PART
ap-610	31	16	explain	explain	VERB
ap-610	31	17	why	why	SCONJ
ap-610	31	18	the	the	DET
ap-610	31	19	standard	standard	ADJ
ap-610	31	20	continuum	continuum	ADJ
ap-610	31	21	theory	theory	NOUN
ap-610	31	22	fails	fail	VERB
ap-610	31	23	to	to	PART
ap-610	31	24	properly	properly	ADV
ap-610	31	25	describe	describe	VERB
ap-610	31	26	certain	certain	ADJ
ap-610	31	27	mechanical	mechanical	ADJ
ap-610	31	28	phenomena	phenomenon	NOUN
ap-610	31	29	and	and	CCONJ
ap-610	31	30	how	how	SCONJ
ap-610	31	31	the	the	DET
ap-610	31	32	description	description	NOUN
ap-610	31	33	can	can	AUX
ap-610	31	34	be	be	AUX
ap-610	31	35	improved	improve	VERB
ap-610	31	36	by	by	ADP
ap-610	31	37	enrichments	enrichment	NOUN
ap-610	31	38	that	that	PRON
ap-610	31	39	incorporate	incorporate	VERB
ap-610	31	40	the	the	DET
ap-610	31	41	influence	influence	NOUN
ap-610	31	42	of	of	ADP
ap-610	31	43	gradients	gradient	NOUN
ap-610	31	44	or	or	CCONJ
ap-610	31	45	weighted	weight	VERB
ap-610	31	46	spatial	spatial	ADJ
ap-610	31	47	averages	average	NOUN
ap-610	31	48	of	of	ADP
ap-610	31	49	strain	strain	NOUN
ap-610	31	50	or	or	CCONJ
ap-610	31	51	of	of	ADP
ap-610	31	52	an	an	DET
ap-610	31	53	internal	internal	ADJ
ap-610	31	54	variable	variable	NOUN
ap-610	31	55	.	.	PUNCT
ap-610	32	1	three	three	NUM
ap-610	32	2	typical	typical	ADJ
ap-610	32	3	mechanical	mechanical	ADJ
ap-610	32	4	problems	problem	NOUN
ap-610	32	5	that	that	PRON
ap-610	32	6	require	require	VERB
ap-610	32	7	such	such	ADJ
ap-610	32	8	enrichments	enrichment	NOUN
ap-610	32	9	are	be	AUX
ap-610	32	10	presented	present	VERB
ap-610	32	11	:	:	PUNCT
ap-610	32	12	(	(	PUNCT
ap-610	32	13	i	i	NOUN
ap-610	32	14	)	)	PUNCT
ap-610	32	15	dispersion	dispersion	NOUN
ap-610	32	16	of	of	ADP
ap-610	32	17	short	short	ADJ
ap-610	32	18	elastic	elastic	ADJ
ap-610	32	19	waves	wave	NOUN
ap-610	32	20	in	in	ADP
ap-610	32	21	heterogeneous	heterogeneous	ADJ
ap-610	32	22	or	or	CCONJ
ap-610	32	23	discrete	discrete	ADJ
ap-610	32	24	media	medium	NOUN
ap-610	32	25	,	,	PUNCT
ap-610	32	26	(	(	PUNCT
ap-610	32	27	ii	ii	NOUN
ap-610	32	28	)	)	PUNCT
ap-610	32	29	size	size	NOUN
ap-610	32	30	effects	effect	NOUN
ap-610	32	31	in	in	ADP
ap-610	32	32	microscale	microscale	ADJ
ap-610	32	33	elastoplasticity	elastoplasticity	NOUN
ap-610	32	34	,	,	PUNCT
ap-610	32	35	in	in	ADP
ap-610	32	36	particular	particular	ADJ
ap-610	32	37	with	with	ADP
ap-610	32	38	the	the	DET
ap-610	32	39	size	size	NOUN
ap-610	32	40	dependence	dependence	NOUN
ap-610	32	41	of	of	ADP
ap-610	32	42	the	the	DET
ap-610	32	43	apparent	apparent	ADJ
ap-610	32	44	hardening	harden	VERB
ap-610	32	45	modulus	modulus	NOUN
ap-610	32	46	,	,	PUNCT
ap-610	32	47	and	and	CCONJ
ap-610	32	48	(	(	PUNCT
ap-610	32	49	iii	iii	NOUN
ap-610	32	50	)	)	PUNCT
ap-610	32	51	localization	localization	NOUN
ap-610	32	52	of	of	ADP
ap-610	32	53	strain	strain	NOUN
ap-610	32	54	and	and	CCONJ
ap-610	32	55	damage	damage	NOUN
ap-610	32	56	in	in	ADP
ap-610	32	57	quasibrittle	quasibrittle	ADJ
ap-610	32	58	structures	structure	NOUN
ap-610	32	59	and	and	CCONJ
ap-610	32	60	with	with	ADP
ap-610	32	61	the	the	DET
ap-610	32	62	resulting	result	VERB
ap-610	32	63	transitional	transitional	ADJ
ap-610	32	64	size	size	NOUN
ap-610	32	65	effect	effect	NOUN
ap-610	32	66	.	.	PUNCT
ap-610	33	1	problems	problem	NOUN
ap-610	33	2	covered	cover	VERB
ap-610	33	3	in	in	ADP
ap-610	33	4	the	the	DET
ap-610	33	5	examples	example	NOUN
ap-610	33	6	encompass	encompass	VERB
ap-610	33	7	static	static	ADJ
ap-610	33	8	and	and	CCONJ
ap-610	33	9	dynamic	dynamic	ADJ
ap-610	33	10	phenomena	phenomenon	NOUN
ap-610	33	11	,	,	PUNCT
ap-610	33	12	linear	linear	ADJ
ap-610	33	13	and	and	CCONJ
ap-610	33	14	nonlinear	nonlinear	ADJ
ap-610	33	15	behavior	behavior	NOUN
ap-610	33	16	,	,	PUNCT
ap-610	33	17	and	and	CCONJ
ap-610	33	18	three	three	NUM
ap-610	33	19	constitutive	constitutive	ADJ
ap-610	33	20	frameworks	framework	NOUN
ap-610	33	21	,	,	PUNCT
ap-610	33	22	namely	namely	ADV
ap-610	33	23	elasticity	elasticity	NOUN
ap-610	33	24	,	,	PUNCT
ap-610	33	25	plasticity	plasticity	NOUN
ap-610	33	26	and	and	CCONJ
ap-610	33	27	continuum	continuum	ADJ
ap-610	33	28	damage	damage	NOUN
ap-610	33	29	mechanics	mechanic	NOUN
ap-610	33	30	.	.	PUNCT
ap-610	34	1	this	this	PRON
ap-610	34	2	shows	show	VERB
ap-610	34	3	that	that	SCONJ
ap-610	34	4	enrichments	enrichment	NOUN
ap-610	34	5	of	of	ADP
ap-610	34	6	the	the	DET
ap-610	34	7	standard	standard	ADJ
ap-610	34	8	continuum	continuum	ADJ
ap-610	34	9	theory	theory	NOUN
ap-610	34	10	can	can	AUX
ap-610	34	11	be	be	AUX
ap-610	34	12	useful	useful	ADJ
ap-610	34	13	in	in	ADP
ap-610	34	14	a	a	DET
ap-610	34	15	wide	wide	ADJ
ap-610	34	16	range	range	NOUN
ap-610	34	17	of	of	ADP
ap-610	34	18	mechanical	mechanical	ADJ
ap-610	34	19	problems	problem	NOUN
ap-610	34	20	.	.	PUNCT
ap-610	35	1	keywords	keyword	NOUN
ap-610	35	2	:	:	PUNCT
ap-610	35	3	damage	damage	NOUN
ap-610	35	4	mechanics	mechanic	NOUN
ap-610	35	5	,	,	PUNCT
ap-610	35	6	dispersion	dispersion	NOUN
ap-610	35	7	,	,	PUNCT
ap-610	35	8	elasticity	elasticity	NOUN
ap-610	35	9	,	,	PUNCT
ap-610	35	10	enriched	enriched	ADJ
ap-610	35	11	continuum	continuum	ADJ
ap-610	35	12	,	,	PUNCT
ap-610	35	13	gradient	gradient	NOUN
ap-610	35	14	models	model	NOUN
ap-610	35	15	,	,	PUNCT
ap-610	35	16	nonlocal	nonlocal	ADJ
ap-610	35	17	models	model	NOUN
ap-610	35	18	,	,	PUNCT
ap-610	35	19	plasticity	plasticity	NOUN
ap-610	35	20	,	,	PUNCT
ap-610	35	21	quasibrittle	quasibrittle	ADJ
ap-610	35	22	materials	material	NOUN
ap-610	35	23	,	,	PUNCT
ap-610	35	24	size	size	NOUN
ap-610	35	25	effect	effect	NOUN
ap-610	35	26	,	,	PUNCT
ap-610	35	27	strain	strain	NOUN
ap-610	35	28	localization	localization	NOUN
ap-610	35	29	,	,	PUNCT
ap-610	35	30	wave	wave	NOUN
ap-610	35	31	propagation	propagation	NOUN
ap-610	35	32	.	.	PUNCT
ap-610	36	1	semi	semi	ADJ
ap-610	36	2	-	-	ADJ
ap-610	36	3	infinite	infinite	ADJ
ap-610	36	4	shear	shear	NOUN
ap-610	36	5	layer	layer	NOUN
ap-610	36	6	,	,	PUNCT
ap-610	36	7	it	it	PRON
ap-610	36	8	is	be	AUX
ap-610	36	9	shown	show	VERB
ap-610	36	10	that	that	SCONJ
ap-610	36	11	stiffer	stiff	ADJ
ap-610	36	12	behavior	behavior	NOUN
ap-610	36	13	of	of	ADP
ap-610	36	14	smaller	small	ADJ
ap-610	36	15	structures	structure	NOUN
ap-610	36	16	can	can	AUX
ap-610	36	17	be	be	AUX
ap-610	36	18	reproduced	reproduce	VERB
ap-610	36	19	with	with	ADP
ap-610	36	20	explicit	explicit	ADJ
ap-610	36	21	or	or	CCONJ
ap-610	36	22	implicit	implicit	ADJ
ap-610	36	23	gradient	gradient	NOUN
ap-610	36	24	plasticity	plasticity	NOUN
ap-610	36	25	if	if	SCONJ
ap-610	36	26	appropriate	appropriate	ADJ
ap-610	36	27	boundary	boundary	ADJ
ap-610	36	28	conditions	condition	NOUN
ap-610	36	29	are	be	AUX
ap-610	36	30	enforced	enforce	VERB
ap-610	36	31	.	.	PUNCT
ap-610	37	1	the	the	DET
ap-610	37	2	general	general	ADJ
ap-610	37	3	trends	trend	NOUN
ap-610	37	4	are	be	AUX
ap-610	37	5	discussed	discuss	VERB
ap-610	37	6	and	and	CCONJ
ap-610	37	7	compared	compare	VERB
ap-610	37	8	to	to	ADP
ap-610	37	9	experimental	experimental	ADJ
ap-610	37	10	measurements	measurement	NOUN
ap-610	37	11	of	of	ADP
ap-610	37	12	size	size	NOUN
ap-610	37	13	effect	effect	NOUN
ap-610	37	14	in	in	ADP
ap-610	37	15	plastic	plastic	ADJ
ap-610	37	16	torsion	torsion	NOUN
ap-610	37	17	of	of	ADP
ap-610	37	18	thin	thin	ADJ
ap-610	37	19	wires	wire	NOUN
ap-610	37	20	.	.	PUNCT
ap-610	38	1	section	section	NOUN
ap-610	38	2	4	4	NUM
ap-610	38	3	is	be	AUX
ap-610	38	4	concerned	concern	VERB
ap-610	38	5	with	with	ADP
ap-610	38	6	localization	localization	NOUN
ap-610	38	7	of	of	ADP
ap-610	38	8	strain	strain	NOUN
ap-610	38	9	and	and	CCONJ
ap-610	38	10	damage	damage	NOUN
ap-610	38	11	in	in	ADP
ap-610	38	12	quasibrittle	quasibrittle	ADJ
ap-610	38	13	structures	structure	NOUN
ap-610	38	14	and	and	CCONJ
ap-610	38	15	with	with	ADP
ap-610	38	16	the	the	DET
ap-610	38	17	resulting	result	VERB
ap-610	38	18	transitional	transitional	ADJ
ap-610	38	19	size	size	NOUN
ap-610	38	20	effect	effect	NOUN
ap-610	38	21	.	.	PUNCT
ap-610	39	1	mathematical	mathematical	ADJ
ap-610	39	2	and	and	CCONJ
ap-610	39	3	numerical	numerical	ADJ
ap-610	39	4	difficulties	difficulty	NOUN
ap-610	39	5	related	relate	VERB
ap-610	39	6	to	to	ADP
ap-610	39	7	the	the	DET
ap-610	39	8	objective	objective	ADJ
ap-610	39	9	description	description	NOUN
ap-610	39	10	of	of	ADP
ap-610	39	11	strain	strain	NOUN
ap-610	39	12	localization	localization	NOUN
ap-610	39	13	due	due	ADJ
ap-610	39	14	to	to	ADP
ap-610	39	15	softening	soften	VERB
ap-610	39	16	are	be	AUX
ap-610	39	17	explained	explain	VERB
ap-610	39	18	using	use	VERB
ap-610	39	19	the	the	DET
ap-610	39	20	one	one	NUM
ap-610	39	21	-	-	PUNCT
ap-610	39	22	dimensional	dimensional	ADJ
ap-610	39	23	example	example	NOUN
ap-610	39	24	of	of	ADP
ap-610	39	25	a	a	DET
ap-610	39	26	tensile	tensile	NOUN
ap-610	39	27	bar	bar	NOUN
ap-610	39	28	.	.	PUNCT
ap-610	40	1	it	it	PRON
ap-610	40	2	is	be	AUX
ap-610	40	3	shown	show	VERB
ap-610	40	4	that	that	SCONJ
ap-610	40	5	if	if	SCONJ
ap-610	40	6	a	a	DET
ap-610	40	7	stress	stress	NOUN
ap-610	40	8	-	-	PUNCT
ap-610	40	9	strain	strain	NOUN
ap-610	40	10	law	law	NOUN
ap-610	40	11	with	with	ADP
ap-610	40	12	softening	softening	NOUN
ap-610	40	13	is	be	AUX
ap-610	40	14	incorporated	incorporate	VERB
ap-610	40	15	in	in	ADP
ap-610	40	16	the	the	DET
ap-610	40	17	standard	standard	ADJ
ap-610	40	18	continuum	continuum	ADJ
ap-610	40	19	theory	theory	NOUN
ap-610	40	20	,	,	PUNCT
ap-610	40	21	the	the	DET
ap-610	40	22	numerical	numerical	ADJ
ap-610	40	23	results	result	NOUN
ap-610	40	24	suffer	suffer	VERB
ap-610	40	25	from	from	ADP
ap-610	40	26	pathological	pathological	ADJ
ap-610	40	27	sensitivity	sensitivity	NOUN
ap-610	40	28	to	to	ADP
ap-610	40	29	the	the	DET
ap-610	40	30	discretization	discretization	NOUN
ap-610	40	31	parameter	parameter	NOUN
ap-610	40	32	such	such	ADJ
ap-610	40	33	as	as	ADP
ap-610	40	34	the	the	DET
ap-610	40	35	size	size	NOUN
ap-610	40	36	of	of	ADP
ap-610	40	37	finite	finite	ADJ
ap-610	40	38	elements	element	NOUN
ap-610	40	39	.	.	PUNCT
ap-610	41	1	this	this	PRON
ap-610	41	2	can	can	AUX
ap-610	41	3	be	be	AUX
ap-610	41	4	remedied	remedie	VERB
ap-610	41	5	by	by	ADP
ap-610	41	6	special	special	ADJ
ap-610	41	7	enrichments	enrichment	NOUN
ap-610	41	8	acting	act	VERB
ap-610	41	9	as	as	ADP
ap-610	41	10	localization	localization	NOUN
ap-610	41	11	limiters	limiter	NOUN
ap-610	41	12	,	,	PUNCT
ap-610	41	13	e.g.	e.g.	ADV
ap-610	41	14	by	by	ADP
ap-610	41	15	a	a	DET
ap-610	41	16	nonlocal	nonlocal	ADJ
ap-610	41	17	damage	damage	NOUN
ap-610	41	18	formulation	formulation	NOUN
ap-610	41	19	.	.	PUNCT
ap-610	42	1	the	the	DET
ap-610	42	2	onset	onset	NOUN
ap-610	42	3	of	of	ADP
ap-610	42	4	localization	localization	NOUN
ap-610	42	5	is	be	AUX
ap-610	42	6	studied	study	VERB
ap-610	42	7	analytically	analytically	ADV
ap-610	42	8	and	and	CCONJ
ap-610	42	9	relations	relation	NOUN
ap-610	42	10	to	to	PART
ap-610	42	11	dispersion	dispersion	VERB
ap-610	42	12	analysis	analysis	NOUN
ap-610	42	13	are	be	AUX
ap-610	42	14	pointed	point	VERB
ap-610	42	15	out	out	ADP
ap-610	42	16	.	.	PUNCT
ap-610	43	1	it	it	PRON
ap-610	43	2	is	be	AUX
ap-610	43	3	also	also	ADV
ap-610	43	4	shown	show	VERB
ap-610	43	5	that	that	SCONJ
ap-610	43	6	the	the	DET
ap-610	43	7	nonlocal	nonlocal	ADJ
ap-610	43	8	model	model	NOUN
ap-610	43	9	can	can	AUX
ap-610	43	10	correctly	correctly	ADV
ap-610	43	11	reproduce	reproduce	VERB
ap-610	43	12	the	the	DET
ap-610	43	13	transitional	transitional	ADJ
ap-610	43	14	size	size	NOUN
ap-610	43	15	effect	effect	NOUN
ap-610	43	16	on	on	ADP
ap-610	43	17	the	the	DET
ap-610	43	18	nominal	nominal	ADJ
ap-610	43	19	strength	strength	NOUN
ap-610	43	20	of	of	ADP
ap-610	43	21	a	a	DET
ap-610	43	22	quasibrittle	quasibrittle	ADJ
ap-610	43	23	structure	structure	NOUN
ap-610	43	24	.	.	PUNCT
ap-610	44	1	all	all	DET
ap-610	44	2	generalized	generalized	ADJ
ap-610	44	3	theories	theory	NOUN
ap-610	44	4	presented	present	VERB
ap-610	44	5	here	here	ADV
ap-610	44	6	introduce	introduce	VERB
ap-610	44	7	a	a	DET
ap-610	44	8	model	model	NOUN
ap-610	44	9	parameter	parameter	NOUN
ap-610	44	10	with	with	ADP
ap-610	44	11	the	the	DET
ap-610	44	12	dimension	dimension	NOUN
ap-610	44	13	of	of	ADP
ap-610	44	14	length	length	NOUN
ap-610	44	15	that	that	PRON
ap-610	44	16	reflects	reflect	VERB
ap-610	44	17	the	the	DET
ap-610	44	18	intrinsic	intrinsic	ADJ
ap-610	44	19	material	material	NOUN
ap-610	44	20	length	length	NOUN
ap-610	44	21	scale	scale	NOUN
ap-610	44	22	.	.	PUNCT
ap-610	45	1	the	the	DET
ap-610	45	2	response	response	NOUN
ap-610	45	3	of	of	ADP
ap-610	45	4	a	a	DET
ap-610	45	5	material	material	NOUN
ap-610	45	6	point	point	NOUN
ap-610	45	7	depends	depend	VERB
ap-610	45	8	not	not	PART
ap-610	45	9	only	only	ADV
ap-610	45	10	on	on	ADP
ap-610	45	11	the	the	DET
ap-610	45	12	strain	strain	NOUN
ap-610	45	13	and	and	CCONJ
ap-610	45	14	temperature	temperature	NOUN
ap-610	45	15	history	history	NOUN
ap-610	45	16	at	at	ADP
ap-610	45	17	that	that	DET
ap-610	45	18	point	point	NOUN
ap-610	45	19	but	but	CCONJ
ap-610	45	20	also	also	ADV
ap-610	45	21	on	on	ADP
ap-610	45	22	the	the	DET
ap-610	45	23	history	history	NOUN
ap-610	45	24	of	of	ADP
ap-610	45	25	a	a	DET
ap-610	45	26	certain	certain	ADJ
ap-610	45	27	neighborhood	neighborhood	NOUN
ap-610	45	28	of	of	ADP
ap-610	45	29	that	that	DET
ap-610	45	30	point	point	NOUN
ap-610	45	31	or	or	CCONJ
ap-610	45	32	even	even	ADV
ap-610	45	33	of	of	ADP
ap-610	45	34	the	the	DET
ap-610	45	35	entire	entire	ADJ
ap-610	45	36	body	body	NOUN
ap-610	45	37	.	.	PUNCT
ap-610	46	1	for	for	ADP
ap-610	46	2	this	this	DET
ap-610	46	3	reason	reason	NOUN
ap-610	46	4	,	,	PUNCT
ap-610	46	5	such	such	ADJ
ap-610	46	6	theories	theory	NOUN
ap-610	46	7	are	be	AUX
ap-610	46	8	classified	classify	VERB
ap-610	46	9	as	as	ADP
ap-610	46	10	nonlocal	nonlocal	ADJ
ap-610	46	11	in	in	ADP
ap-610	46	12	the	the	DET
ap-610	46	13	broad	broad	ADJ
ap-610	46	14	sense	sense	NOUN
ap-610	46	15	.	.	PUNCT
ap-610	47	1	2	2	NUM
ap-610	47	2	dispersion	dispersion	NOUN
ap-610	47	3	of	of	ADP
ap-610	47	4	elastic	elastic	ADJ
ap-610	47	5	waves	wave	NOUN
ap-610	47	6	2.1	2.1	NUM
ap-610	47	7	continuum	continuum	ADJ
ap-610	47	8	versus	versus	ADP
ap-610	47	9	discrete	discrete	ADJ
ap-610	47	10	models	model	NOUN
ap-610	47	11	in	in	ADP
ap-610	47	12	the	the	DET
ap-610	47	13	standard	standard	ADJ
ap-610	47	14	continuum	continuum	ADJ
ap-610	47	15	theory	theory	NOUN
ap-610	47	16	,	,	PUNCT
ap-610	47	17	propagation	propagation	NOUN
ap-610	47	18	of	of	ADP
ap-610	47	19	waves	wave	NOUN
ap-610	47	20	in	in	ADP
ap-610	47	21	a	a	DET
ap-610	47	22	homogeneous	homogeneous	ADJ
ap-610	47	23	one	one	NUM
ap-610	47	24	-	-	PUNCT
ap-610	47	25	dimensional	dimensional	ADJ
ap-610	47	26	linear	linear	ADJ
ap-610	47	27	elastic	elastic	ADJ
ap-610	47	28	medium	medium	NOUN
ap-610	47	29	is	be	AUX
ap-610	47	30	described	describe	VERB
ap-610	47	31	by	by	ADP
ap-610	47	32	the	the	DET
ap-610	47	33	hyperbolic	hyperbolic	ADJ
ap-610	47	34	partial	partial	ADJ
ap-610	47	35	differential	differential	NOUN
ap-610	47	36	equation	equation	NOUN
ap-610	47	37	�	�	PROPN
ap-610	47	38	�	�	PROPN
ap-610	47	39	�	�	PROPN
ap-610	47	40	u	u	PROPN
ap-610	47	41	eu	eu	PROPN
ap-610	47	42	�	�	PROPN
ap-610	47	43	�	�	PROPN
ap-610	47	44	�	�	PROPN
ap-610	47	45	�	�	PROPN
ap-610	47	46	0	0	NUM
ap-610	47	47	,	,	PUNCT
ap-610	47	48	(	(	PUNCT
ap-610	47	49	1	1	X
ap-610	47	50	)	)	PUNCT
ap-610	47	51	where	where	SCONJ
ap-610	47	52	�	�	PROPN
ap-610	47	53	is	be	AUX
ap-610	47	54	the	the	DET
ap-610	47	55	mass	mass	ADJ
ap-610	47	56	density	density	NOUN
ap-610	47	57	,	,	PUNCT
ap-610	47	58	e	e	X
ap-610	47	59	is	be	AUX
ap-610	47	60	the	the	DET
ap-610	47	61	elastic	elastic	ADJ
ap-610	47	62	modulus	modulus	NOUN
ap-610	47	63	,	,	PUNCT
ap-610	47	64	u(x	u(x	PROPN
ap-610	47	65	,	,	PUNCT
ap-610	47	66	t	t	PROPN
ap-610	47	67	)	)	PUNCT
ap-610	47	68	is	be	AUX
ap-610	47	69	the	the	DET
ap-610	47	70	displacement	displacement	NOUN
ap-610	47	71	and	and	CCONJ
ap-610	47	72	,	,	PUNCT
ap-610	47	73	as	as	ADP
ap-610	47	74	usual	usual	ADJ
ap-610	47	75	,	,	PUNCT
ap-610	47	76	overdots	overdot	NOUN
ap-610	47	77	stand	stand	VERB
ap-610	47	78	for	for	ADP
ap-610	47	79	derivatives	derivative	NOUN
ap-610	47	80	with	with	ADP
ap-610	47	81	respect	respect	NOUN
ap-610	47	82	to	to	ADP
ap-610	47	83	time	time	NOUN
ap-610	47	84	t	t	NOUN
ap-610	47	85	and	and	CCONJ
ap-610	47	86	primes	prime	NOUN
ap-610	47	87	for	for	ADP
ap-610	47	88	derivatives	derivative	NOUN
ap-610	47	89	with	with	ADP
ap-610	47	90	respect	respect	NOUN
ap-610	47	91	to	to	ADP
ap-610	47	92	the	the	DET
ap-610	47	93	spatial	spatial	ADJ
ap-610	47	94	coordinate	coordinate	NOUN
ap-610	47	95	x.	x.	NOUN
ap-610	47	96	since	since	SCONJ
ap-610	47	97	�	�	PROPN
ap-610	47	98	and	and	CCONJ
ap-610	47	99	e	e	NOUN
ap-610	47	100	are	be	AUX
ap-610	47	101	constant	constant	ADJ
ap-610	47	102	coefficients	coefficient	NOUN
ap-610	47	103	,	,	PUNCT
ap-610	47	104	equation	equation	NOUN
ap-610	47	105	(	(	PUNCT
ap-610	47	106	1	1	X
ap-610	47	107	)	)	PUNCT
ap-610	47	108	admits	admit	VERB
ap-610	47	109	solutions	solution	NOUN
ap-610	47	110	of	of	ADP
ap-610	47	111	the	the	DET
ap-610	47	112	form	form	NOUN
ap-610	47	113	u	u	NOUN
ap-610	47	114	x	x	NOUN
ap-610	47	115	t	t	X
ap-610	48	1	i	i	PRON
ap-610	48	2	kx	kx	PROPN
ap-610	49	1	t	t	PROPN
ap-610	49	2	ik	ik	PROPN
ap-610	49	3	x	x	SYM
ap-610	49	4	ct	ct	PROPN
ap-610	49	5	(	(	PUNCT
ap-610	49	6	,	,	PUNCT
ap-610	49	7	)	)	PUNCT
ap-610	49	8	(	(	PUNCT
ap-610	49	9	)	)	PUNCT
ap-610	49	10	(	(	PUNCT
ap-610	49	11	)	)	PUNCT
ap-610	49	12	�	�	PROPN
ap-610	49	13	�	�	PROPN
ap-610	49	14	�	�	PROPN
ap-610	49	15	�	�	PROPN
ap-610	49	16	e	e	PROPN
ap-610	49	17	e	e	NOUN
ap-610	49	18	�	�	PROPN
ap-610	49	19	,	,	PUNCT
ap-610	49	20	(	(	PUNCT
ap-610	49	21	2	2	X
ap-610	49	22	)	)	PUNCT
ap-610	49	23	where	where	SCONJ
ap-610	49	24	i	i	PRON
ap-610	49	25	is	be	AUX
ap-610	49	26	the	the	DET
ap-610	49	27	imaginary	imaginary	ADJ
ap-610	49	28	unit	unit	NOUN
ap-610	49	29	,	,	PUNCT
ap-610	49	30	�	�	PROPN
ap-610	49	31	is	be	AUX
ap-610	49	32	the	the	DET
ap-610	49	33	circular	circular	ADJ
ap-610	49	34	frequency	frequency	NOUN
ap-610	49	35	,	,	PUNCT
ap-610	49	36	k	k	PROPN
ap-610	49	37	is	be	AUX
ap-610	49	38	the	the	DET
ap-610	49	39	wave	wave	NOUN
ap-610	49	40	number	number	NOUN
ap-610	49	41	,	,	PUNCT
ap-610	49	42	and	and	CCONJ
ap-610	49	43	c	c	X
ap-610	49	44	k	k	X
ap-610	49	45	�	�	PROPN
ap-610	49	46	�	�	PROPN
ap-610	49	47	is	be	AUX
ap-610	49	48	the	the	DET
ap-610	49	49	wave	wave	NOUN
ap-610	49	50	velocity	velocity	NOUN
ap-610	49	51	.	.	PUNCT
ap-610	50	1	substituting	substitute	VERB
ap-610	50	2	(	(	PUNCT
ap-610	50	3	2	2	NUM
ap-610	50	4	)	)	PUNCT
ap-610	50	5	into	into	ADP
ap-610	50	6	(	(	PUNCT
ap-610	50	7	1	1	NUM
ap-610	50	8	)	)	PUNCT
ap-610	50	9	,	,	PUNCT
ap-610	50	10	we	we	PRON
ap-610	50	11	find	find	VERB
ap-610	50	12	the	the	DET
ap-610	50	13	condition	condition	NOUN
ap-610	50	14	�	�	PROPN
ap-610	50	15	�	�	PROPN
ap-610	50	16	�	�	PROPN
ap-610	50	17	�	�	PROPN
ap-610	50	18	�	�	PROPN
ap-610	50	19	2	2	NUM
ap-610	50	20	2	2	NUM
ap-610	50	21	0ek	0ek	NOUN
ap-610	50	22	(	(	PUNCT
ap-610	50	23	3	3	NUM
ap-610	50	24	)	)	PUNCT
ap-610	50	25	which	which	PRON
ap-610	50	26	implies	imply	VERB
ap-610	50	27	that	that	SCONJ
ap-610	50	28	the	the	DET
ap-610	50	29	magnitude	magnitude	NOUN
ap-610	50	30	of	of	ADP
ap-610	50	31	the	the	DET
ap-610	50	32	circular	circular	ADJ
ap-610	50	33	frequency	frequency	NOUN
ap-610	50	34	is	be	AUX
ap-610	50	35	proportional	proportional	ADJ
ap-610	50	36	to	to	ADP
ap-610	50	37	the	the	DET
ap-610	50	38	magnitude	magnitude	NOUN
ap-610	50	39	of	of	ADP
ap-610	50	40	the	the	DET
ap-610	50	41	wave	wave	NOUN
ap-610	50	42	number	number	NOUN
ap-610	50	43	.	.	PUNCT
ap-610	51	1	the	the	DET
ap-610	51	2	signs	sign	NOUN
ap-610	51	3	of	of	ADP
ap-610	51	4	�	�	PROPN
ap-610	51	5	and	and	CCONJ
ap-610	51	6	k	k	PROPN
ap-610	51	7	are	be	AUX
ap-610	51	8	irrelevant	irrelevant	ADJ
ap-610	51	9	–	–	PUNCT
ap-610	51	10	if	if	SCONJ
ap-610	51	11	both	both	PRON
ap-610	51	12	change	change	VERB
ap-610	51	13	,	,	PUNCT
ap-610	51	14	the	the	DET
ap-610	51	15	real	real	ADJ
ap-610	51	16	part	part	NOUN
ap-610	51	17	of	of	ADP
ap-610	51	18	(	(	PUNCT
ap-610	51	19	2	2	X
ap-610	51	20	)	)	PUNCT
ap-610	51	21	does	do	AUX
ap-610	51	22	not	not	PART
ap-610	51	23	change	change	VERB
ap-610	51	24	,	,	PUNCT
ap-610	51	25	and	and	CCONJ
ap-610	51	26	if	if	SCONJ
ap-610	51	27	one	one	NUM
ap-610	51	28	of	of	ADP
ap-610	51	29	them	they	PRON
ap-610	51	30	changes	change	VERB
ap-610	51	31	,	,	PUNCT
ap-610	51	32	the	the	DET
ap-610	51	33	wave	wave	NOUN
ap-610	51	34	propagates	propagate	VERB
ap-610	51	35	in	in	ADP
ap-610	51	36	the	the	DET
ap-610	51	37	opposite	opposite	ADJ
ap-610	51	38	direction	direction	NOUN
ap-610	51	39	but	but	CCONJ
ap-610	51	40	otherwise	otherwise	ADV
ap-610	51	41	remains	remain	VERB
ap-610	51	42	the	the	DET
ap-610	51	43	same	same	ADJ
ap-610	51	44	.	.	PUNCT
ap-610	52	1	therefore	therefore	ADV
ap-610	52	2	,	,	PUNCT
ap-610	52	3	we	we	PRON
ap-610	52	4	will	will	AUX
ap-610	52	5	restrict	restrict	VERB
ap-610	52	6	ourselves	ourselves	PRON
ap-610	52	7	to	to	ADP
ap-610	52	8	nonnegative	nonnegative	ADJ
ap-610	52	9	values	value	NOUN
ap-610	52	10	and	and	CCONJ
ap-610	52	11	write	write	VERB
ap-610	52	12	the	the	DET
ap-610	52	13	solution	solution	NOUN
ap-610	52	14	of	of	ADP
ap-610	52	15	(	(	PUNCT
ap-610	52	16	3	3	NUM
ap-610	52	17	)	)	PUNCT
ap-610	52	18	as	as	ADP
ap-610	52	19	�	�	PROPN
ap-610	52	20	�	�	PROPN
ap-610	52	21	�	�	PROPN
ap-610	52	22	k	k	PROPN
ap-610	52	23	e	e	PROPN
ap-610	52	24	.	.	PUNCT
ap-610	53	1	(	(	PUNCT
ap-610	53	2	4	4	X
ap-610	53	3	)	)	PUNCT
ap-610	53	4	due	due	ADP
ap-610	53	5	to	to	ADP
ap-610	53	6	the	the	DET
ap-610	53	7	direct	direct	ADJ
ap-610	53	8	proportionality	proportionality	NOUN
ap-610	53	9	between	between	ADP
ap-610	53	10	�	�	PROPN
ap-610	53	11	and	and	CCONJ
ap-610	53	12	k	k	PROPN
ap-610	53	13	,	,	PUNCT
ap-610	53	14	the	the	DET
ap-610	53	15	velocity	velocity	NOUN
ap-610	53	16	of	of	ADP
ap-610	53	17	a	a	DET
ap-610	53	18	harmonic	harmonic	ADJ
ap-610	53	19	elastic	elastic	ADJ
ap-610	53	20	wave	wave	NOUN
ap-610	53	21	,	,	PUNCT
ap-610	53	22	c	c	PROPN
ap-610	53	23	k	k	PROPN
ap-610	53	24	e	e	PROPN
ap-610	53	25	�	�	PROPN
ap-610	53	26	�	�	PROPN
ap-610	53	27	�	�	PROPN
ap-610	53	28	�	�	PROPN
ap-610	53	29	,	,	PUNCT
ap-610	53	30	is	be	AUX
ap-610	53	31	constant	constant	ADJ
ap-610	53	32	,	,	PUNCT
ap-610	53	33	independent	independent	ADJ
ap-610	53	34	of	of	ADP
ap-610	53	35	the	the	DET
ap-610	53	36	wave	wave	NOUN
ap-610	53	37	number	number	NOUN
ap-610	53	38	k.	k.	PROPN
ap-610	54	1	since	since	SCONJ
ap-610	54	2	a	a	DET
ap-610	54	3	wave	wave	NOUN
ap-610	54	4	of	of	ADP
ap-610	54	5	a	a	DET
ap-610	54	6	general	general	ADJ
ap-610	54	7	shape	shape	NOUN
ap-610	54	8	can	can	AUX
ap-610	54	9	be	be	AUX
ap-610	54	10	represented	represent	VERB
ap-610	54	11	by	by	ADP
ap-610	54	12	a	a	DET
ap-610	54	13	linear	linear	ADJ
ap-610	54	14	combination	combination	NOUN
ap-610	54	15	of	of	ADP
ap-610	54	16	harmonic	harmonic	ADJ
ap-610	54	17	waves	wave	NOUN
ap-610	54	18	,	,	PUNCT
ap-610	54	19	even	even	ADV
ap-610	54	20	such	such	DET
ap-610	54	21	a	a	DET
ap-610	54	22	general	general	ADJ
ap-610	54	23	wave	wave	NOUN
ap-610	54	24	propagates	propagate	VERB
ap-610	54	25	at	at	ADP
ap-610	54	26	constant	constant	ADJ
ap-610	54	27	velocity	velocity	NOUN
ap-610	54	28	c	c	NOUN
ap-610	54	29	and	and	CCONJ
ap-610	54	30	its	its	PRON
ap-610	54	31	shape	shape	NOUN
ap-610	54	32	remains	remain	VERB
ap-610	54	33	invariant	invariant	ADJ
ap-610	54	34	.	.	PUNCT
ap-610	55	1	the	the	DET
ap-610	55	2	situation	situation	NOUN
ap-610	55	3	is	be	AUX
ap-610	55	4	different	different	ADJ
ap-610	55	5	in	in	ADP
ap-610	55	6	a	a	DET
ap-610	55	7	discrete	discrete	ADJ
ap-610	55	8	mechanical	mechanical	ADJ
ap-610	55	9	system	system	NOUN
ap-610	55	10	,	,	PUNCT
ap-610	55	11	which	which	PRON
ap-610	55	12	can	can	AUX
ap-610	55	13	be	be	AUX
ap-610	55	14	best	well	ADV
ap-610	55	15	exemplified	exemplify	VERB
ap-610	55	16	by	by	ADP
ap-610	55	17	a	a	DET
ap-610	55	18	regular	regular	ADJ
ap-610	55	19	infinite	infinite	ADJ
ap-610	55	20	one	one	NUM
ap-610	55	21	-	-	PUNCT
ap-610	55	22	dimensional	dimensional	ADJ
ap-610	55	23	array	array	NOUN
ap-610	55	24	of	of	ADP
ap-610	55	25	mass	mass	ADJ
ap-610	55	26	points	point	NOUN
ap-610	55	27	connected	connect	VERB
ap-610	55	28	by	by	ADP
ap-610	55	29	linear	linear	PROPN
ap-610	55	30	springs	spring	NOUN
ap-610	55	31	(	(	PUNCT
ap-610	55	32	fig	fig	NOUN
ap-610	55	33	.	.	PUNCT
ap-610	56	1	1a	1a	NOUN
ap-610	56	2	)	)	PUNCT
ap-610	56	3	.	.	PUNCT
ap-610	57	1	the	the	DET
ap-610	57	2	governing	govern	VERB
ap-610	57	3	equations	equation	NOUN
ap-610	57	4	of	of	ADP
ap-610	57	5	motion	motion	NOUN
ap-610	57	6	form	form	VERB
ap-610	57	7	a	a	DET
ap-610	57	8	system	system	NOUN
ap-610	57	9	of	of	ADP
ap-610	57	10	ordinary	ordinary	ADJ
ap-610	57	11	differential	differential	ADJ
ap-610	57	12	equations	equation	NOUN
ap-610	57	13	mu	mu	NOUN
ap-610	57	14	k	k	PROPN
ap-610	57	15	u	u	PROPN
ap-610	57	16	u	u	X
ap-610	57	17	k	k	PROPN
ap-610	57	18	u	u	X
ap-610	57	19	u	u	X
ap-610	57	20	j	j	PROPN
ap-610	57	21	zj	zj	PROPN
ap-610	57	22	j	j	PROPN
ap-610	57	23	j	j	PROPN
ap-610	57	24	j	j	PROPN
ap-610	57	25	j	j	PROPN
ap-610	57	26	�	�	PROPN
ap-610	57	27	�	�	PROPN
ap-610	57	28	(	(	PUNCT
ap-610	57	29	)	)	PUNCT
ap-610	57	30	(	(	PUNCT
ap-610	57	31	)	)	PUNCT
ap-610	57	32	,	,	PUNCT
ap-610	57	33	�	�	PROPN
ap-610	57	34	�	�	PROPN
ap-610	57	35	�	�	PROPN
ap-610	57	36	�	�	PROPN
ap-610	57	37	�	�	PROPN
ap-610	57	38	�	�	PROPN
ap-610	57	39	�	�	PROPN
ap-610	57	40	�	�	PROPN
ap-610	57	41	1	1	NUM
ap-610	57	42	1	1	NUM
ap-610	57	43	0	0	NUM
ap-610	57	44	,	,	PUNCT
ap-610	57	45	(	(	PUNCT
ap-610	57	46	5	5	NUM
ap-610	57	47	)	)	PUNCT
ap-610	57	48	where	where	SCONJ
ap-610	57	49	m	m	NOUN
ap-610	57	50	is	be	AUX
ap-610	57	51	the	the	DET
ap-610	57	52	mass	mass	NOUN
ap-610	57	53	of	of	ADP
ap-610	57	54	each	each	DET
ap-610	57	55	mass	mass	NOUN
ap-610	57	56	point	point	NOUN
ap-610	57	57	,	,	PUNCT
ap-610	57	58	k	k	PROPN
ap-610	57	59	is	be	AUX
ap-610	57	60	the	the	DET
ap-610	57	61	spring	spring	NOUN
ap-610	57	62	stiffness	stiffness	NOUN
ap-610	57	63	,	,	PUNCT
ap-610	57	64	uj	uj	PROPN
ap-610	57	65	is	be	AUX
ap-610	57	66	the	the	DET
ap-610	57	67	displacement	displacement	NOUN
ap-610	57	68	of	of	ADP
ap-610	57	69	mass	mass	ADJ
ap-610	57	70	point	point	NOUN
ap-610	57	71	number	number	NOUN
ap-610	57	72	j	j	PROPN
ap-610	57	73	initially	initially	ADV
ap-610	57	74	located	locate	VERB
ap-610	57	75	at	at	ADP
ap-610	57	76	xj	xj	PROPN
ap-610	57	77	,	,	PUNCT
ap-610	57	78	and	and	CCONJ
ap-610	57	79	z	z	NOUN
ap-610	57	80	is	be	AUX
ap-610	57	81	the	the	DET
ap-610	57	82	set	set	NOUN
ap-610	57	83	of	of	ADP
ap-610	57	84	all	all	DET
ap-610	57	85	integer	integer	NOUN
ap-610	57	86	numbers	number	NOUN
ap-610	57	87	.	.	PUNCT
ap-610	58	1	for	for	ADP
ap-610	58	2	an	an	DET
ap-610	58	3	assumed	assume	VERB
ap-610	58	4	harmonic	harmonic	ADJ
ap-610	58	5	wave	wave	NOUN
ap-610	58	6	of	of	ADP
ap-610	58	7	the	the	DET
ap-610	58	8	form	form	NOUN
ap-610	58	9	u	u	NOUN
ap-610	58	10	tj	tj	NOUN
ap-610	58	11	i	i	PRON
ap-610	58	12	kx	kx	PROPN
ap-610	58	13	tj	tj	PROPN
ap-610	58	14	(	(	PUNCT
ap-610	58	15	)	)	PUNCT
ap-610	58	16	(	(	PUNCT
ap-610	58	17	)	)	PUNCT
ap-610	58	18	�	�	PROPN
ap-610	58	19	�	�	PROPN
ap-610	58	20	e	e	PROPN
ap-610	58	21	�	�	PROPN
ap-610	58	22	(	(	PUNCT
ap-610	58	23	6	6	NUM
ap-610	58	24	)	)	PUNCT
ap-610	58	25	we	we	PRON
ap-610	58	26	obtain	obtain	VERB
ap-610	58	27	the	the	DET
ap-610	58	28	condition	condition	NOUN
ap-610	58	29	�	�	PROPN
ap-610	58	30	�	�	PROPN
ap-610	58	31	�	�	PROPN
ap-610	58	32	�	�	PROPN
ap-610	58	33	�	�	PROPN
ap-610	58	34	�	�	PROPN
ap-610	58	35	�	�	PROPN
ap-610	58	36	�	�	PROPN
ap-610	58	37	�	�	PROPN
ap-610	58	38	�	�	PROPN
ap-610	58	39	�	�	PROPN
ap-610	58	40	m	m	PROPN
ap-610	58	41	k	k	PROPN
ap-610	58	42	k	k	PROPN
ap-610	58	43	j	j	PROPN
ap-610	58	44	zik	zik	PROPN
ap-610	58	45	x	x	PROPN
ap-610	58	46	x	x	PROPN
ap-610	58	47	ik	ik	PROPN
ap-610	58	48	x	x	PROPN
ap-610	58	49	xj	xj	PROPN
ap-610	58	50	j	j	PROPN
ap-610	58	51	j	j	PROPN
ap-610	58	52	j	j	PROPN
ap-610	58	53	�	�	PROPN
ap-610	58	54	2	2	NUM
ap-610	58	55	1	1	NUM
ap-610	58	56	1	1	NUM
ap-610	58	57	01	01	NUM
ap-610	58	58	1	1	NUM
ap-610	58	59	(	(	PUNCT
ap-610	58	60	)	)	PUNCT
ap-610	58	61	(	(	PUNCT
ap-610	58	62	)	)	PUNCT
ap-610	58	63	,	,	PUNCT
ap-610	58	64	(	(	PUNCT
ap-610	58	65	)	)	PUNCT
ap-610	58	66	(	(	PUNCT
ap-610	58	67	)	)	PUNCT
ap-610	58	68	e	e	NOUN
ap-610	58	69	e	e	X
ap-610	58	70	.	.	PUNCT
ap-610	59	1	(	(	PUNCT
ap-610	59	2	7	7	X
ap-610	59	3	)	)	PUNCT
ap-610	59	4	the	the	DET
ap-610	59	5	spacing	spacing	NOUN
ap-610	59	6	of	of	ADP
ap-610	59	7	mass	mass	ADJ
ap-610	59	8	points	point	NOUN
ap-610	59	9	is	be	AUX
ap-610	59	10	assumed	assume	VERB
ap-610	59	11	to	to	PART
ap-610	59	12	be	be	AUX
ap-610	59	13	regular	regular	ADJ
ap-610	59	14	,	,	PUNCT
ap-610	59	15	i.e.	i.e.	X
ap-610	59	16	,	,	PUNCT
ap-610	59	17	x	x	PUNCT
ap-610	59	18	x	x	SYM
ap-610	59	19	x	x	PUNCT
ap-610	59	20	x	x	PROPN
ap-610	59	21	aj	aj	PROPN
ap-610	59	22	j	j	PROPN
ap-610	59	23	j	j	PROPN
ap-610	59	24	j	j	PROPN
ap-610	59	25	�	�	PROPN
ap-610	59	26	�	�	PROPN
ap-610	59	27	�	�	PROPN
ap-610	59	28	�	�	PROPN
ap-610	59	29	�	�	PROPN
ap-610	59	30	�	�	PROPN
ap-610	59	31	1	1	NUM
ap-610	59	32	1	1	NUM
ap-610	59	33	.	.	PUNCT
ap-610	60	1	the	the	DET
ap-610	60	2	circular	circular	ADJ
ap-610	60	3	frequency	frequency	NOUN
ap-610	60	4	corresponding	correspond	VERB
ap-610	60	5	to	to	PART
ap-610	60	6	wave	wave	VERB
ap-610	60	7	number	number	NOUN
ap-610	60	8	k	k	PROPN
ap-610	60	9	is	be	AUX
ap-610	60	10	thus	thus	ADV
ap-610	60	11	�	�	PROPN
ap-610	60	12	�	�	PROPN
ap-610	60	13	�	�	PROPN
ap-610	60	14	�	�	PROPN
ap-610	60	15	�	�	PROPN
ap-610	60	16	�	�	PROPN
ap-610	60	17	2	2	NUM
ap-610	60	18	1	1	NUM
ap-610	60	19	2	2	NUM
ap-610	60	20	1	1	NUM
ap-610	60	21	2	2	NUM
ap-610	60	22	2	2	NUM
ap-610	60	23	k	k	NOUN
ap-610	60	24	m	m	VERB
ap-610	60	25	ika	ika	NOUN
ap-610	60	26	k	k	NOUN
ap-610	60	27	m	m	PROPN
ap-610	60	28	ka	ka	PROPN
ap-610	61	1	k	k	PROPN
ap-610	61	2	m	m	VERB
ap-610	61	3	ka	ka	PROPN
ap-610	61	4	(	(	PUNCT
ap-610	61	5	cosh	cosh	PROPN
ap-610	61	6	)	)	PUNCT
ap-610	61	7	(	(	PUNCT
ap-610	61	8	cos	cos	X
ap-610	61	9	)	)	PUNCT
ap-610	61	10	sin	sin	NOUN
ap-610	61	11	.	.	PUNCT
ap-610	62	1	(	(	PUNCT
ap-610	62	2	8)	8)	NUM
ap-610	62	3	©	©	PROPN
ap-610	62	4	czech	czech	PROPN
ap-610	62	5	technical	technical	PROPN
ap-610	62	6	university	university	PROPN
ap-610	62	7	publishing	publishing	NOUN
ap-610	62	8	house	house	NOUN
ap-610	62	9	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	62	10	17	17	NUM
ap-610	62	11	acta	acta	PROPN
ap-610	62	12	polytechnica	polytechnica	PROPN
ap-610	62	13	vol	vol	NOUN
ap-610	62	14	.	.	PROPN
ap-610	63	1	44	44	NUM
ap-610	63	2	no	no	NOUN
ap-610	63	3	.	.	PUNCT
ap-610	64	1	5–6/2004	5–6/2004	NUM
ap-610	64	2	(	(	PUNCT
ap-610	64	3	a	a	NOUN
ap-610	64	4	)	)	PUNCT
ap-610	64	5	(	(	PUNCT
ap-610	64	6	b	b	X
ap-610	64	7	)	)	PUNCT
ap-610	64	8	fig	fig	NOUN
ap-610	64	9	.	.	PUNCT
ap-610	65	1	1	1	NUM
ap-610	65	2	:	:	PUNCT
ap-610	65	3	(	(	PUNCT
ap-610	65	4	a	a	X
ap-610	65	5	)	)	PUNCT
ap-610	65	6	discrete	discrete	ADJ
ap-610	65	7	mass	mass	ADJ
ap-610	65	8	-	-	PUNCT
ap-610	65	9	spring	spring	NOUN
ap-610	65	10	model	model	NOUN
ap-610	65	11	with	with	ADP
ap-610	65	12	nearest	near	ADJ
ap-610	65	13	-	-	PUNCT
ap-610	65	14	neighbor	neighbor	NOUN
ap-610	65	15	interaction	interaction	NOUN
ap-610	65	16	and	and	CCONJ
ap-610	65	17	(	(	PUNCT
ap-610	65	18	b	b	X
ap-610	65	19	)	)	PUNCT
ap-610	65	20	the	the	DET
ap-610	65	21	corresponding	correspond	VERB
ap-610	65	22	dispersion	dispersion	NOUN
ap-610	65	23	diagram	diagram	NOUN
ap-610	65	24	with	with	ADP
ap-610	65	25	the	the	DET
ap-610	65	26	normalized	normalize	VERB
ap-610	65	27	frequency	frequency	NOUN
ap-610	65	28	,	,	PUNCT
ap-610	65	29	�	�	PROPN
ap-610	65	30	m	m	VERB
ap-610	65	31	k	k	NOUN
ap-610	65	32	,	,	PUNCT
ap-610	65	33	plotted	plot	VERB
ap-610	65	34	as	as	ADP
ap-610	65	35	a	a	DET
ap-610	65	36	function	function	NOUN
ap-610	65	37	of	of	ADP
ap-610	65	38	the	the	DET
ap-610	65	39	normalized	normalize	VERB
ap-610	65	40	wave	wave	NOUN
ap-610	65	41	number	number	NOUN
ap-610	65	42	,	,	PUNCT
ap-610	65	43	ka	ka	PROPN
ap-610	65	44	�	�	PROPN
ap-610	65	45	for	for	ADP
ap-610	65	46	this	this	DET
ap-610	65	47	mass	mass	ADJ
ap-610	65	48	-	-	PUNCT
ap-610	65	49	spring	spring	NOUN
ap-610	65	50	system	system	NOUN
ap-610	65	51	,	,	PUNCT
ap-610	65	52	the	the	DET
ap-610	65	53	relationship	relationship	NOUN
ap-610	65	54	between	between	ADP
ap-610	65	55	�	�	PROPN
ap-610	65	56	and	and	CCONJ
ap-610	65	57	k	k	PROPN
ap-610	65	58	is	be	AUX
ap-610	65	59	nonlinear	nonlinear	ADJ
ap-610	65	60	and	and	CCONJ
ap-610	65	61	the	the	DET
ap-610	65	62	wave	wave	NOUN
ap-610	65	63	velocity	velocity	NOUN
ap-610	65	64	depends	depend	VERB
ap-610	65	65	on	on	ADP
ap-610	65	66	the	the	DET
ap-610	65	67	wave	wave	NOUN
ap-610	65	68	number	number	NOUN
ap-610	65	69	.	.	PUNCT
ap-610	66	1	in	in	ADP
ap-610	66	2	such	such	DET
ap-610	66	3	a	a	DET
ap-610	66	4	case	case	NOUN
ap-610	66	5	,	,	PUNCT
ap-610	66	6	one	one	PRON
ap-610	66	7	must	must	AUX
ap-610	66	8	distinguish	distinguish	VERB
ap-610	66	9	between	between	ADP
ap-610	66	10	the	the	DET
ap-610	66	11	phase	phase	NOUN
ap-610	66	12	velocity	velocity	NOUN
ap-610	66	13	,	,	PUNCT
ap-610	66	14	c	c	PROPN
ap-610	66	15	kp	kp	PROPN
ap-610	66	16	�	�	PROPN
ap-610	66	17	�	�	PROPN
ap-610	66	18	,	,	PUNCT
ap-610	66	19	and	and	CCONJ
ap-610	66	20	the	the	DET
ap-610	66	21	group	group	NOUN
ap-610	66	22	velocity	velocity	NOUN
ap-610	66	23	,	,	PUNCT
ap-610	66	24	c	c	NOUN
ap-610	66	25	kg	kg	NUM
ap-610	66	26	�	�	PROPN
ap-610	66	27	d	d	PROPN
ap-610	66	28	d	d	PROPN
ap-610	66	29	�	�	PROPN
ap-610	66	30	.	.	PUNCT
ap-610	67	1	in	in	ADP
ap-610	67	2	the	the	DET
ap-610	67	3	long	long	ADJ
ap-610	67	4	wave	wave	NOUN
ap-610	67	5	limit	limit	NOUN
ap-610	67	6	(	(	PUNCT
ap-610	67	7	i.e.	i.e.	X
ap-610	67	8	,	,	PUNCT
ap-610	67	9	for	for	ADP
ap-610	67	10	k	k	PROPN
ap-610	67	11	approaching	approach	VERB
ap-610	67	12	zero	zero	NUM
ap-610	67	13	)	)	PUNCT
ap-610	67	14	,	,	PUNCT
ap-610	67	15	both	both	CCONJ
ap-610	67	16	the	the	DET
ap-610	67	17	phase	phase	NOUN
ap-610	67	18	velocity	velocity	NOUN
ap-610	67	19	and	and	CCONJ
ap-610	67	20	the	the	DET
ap-610	67	21	group	group	NOUN
ap-610	67	22	velocity	velocity	NOUN
ap-610	67	23	tend	tend	VERB
ap-610	67	24	to	to	PART
ap-610	67	25	c	c	PROPN
ap-610	67	26	a	a	DET
ap-610	67	27	k	k	PROPN
ap-610	67	28	m0	m0	PROPN
ap-610	67	29	�	�	PROPN
ap-610	67	30	.	.	PUNCT
ap-610	68	1	as	as	SCONJ
ap-610	68	2	is	be	AUX
ap-610	68	3	clear	clear	ADJ
ap-610	68	4	from	from	ADP
ap-610	68	5	the	the	DET
ap-610	68	6	�	�	PROPN
ap-610	68	7	–	–	PUNCT
ap-610	68	8	k	k	PROPN
ap-610	68	9	diagram	diagram	NOUN
ap-610	68	10	in	in	ADP
ap-610	68	11	fig	fig	NOUN
ap-610	68	12	.	.	PUNCT
ap-610	69	1	1b	1b	NUM
ap-610	69	2	,	,	PUNCT
ap-610	69	3	c0	c0	PROPN
ap-610	69	4	is	be	AUX
ap-610	69	5	the	the	DET
ap-610	69	6	upper	upper	ADJ
ap-610	69	7	bound	bind	VERB
ap-610	69	8	on	on	ADP
ap-610	69	9	the	the	DET
ap-610	69	10	velocity	velocity	NOUN
ap-610	69	11	of	of	ADP
ap-610	69	12	waves	wave	NOUN
ap-610	69	13	at	at	ADP
ap-610	69	14	any	any	DET
ap-610	69	15	wave	wave	NOUN
ap-610	69	16	number	number	NOUN
ap-610	69	17	.	.	PUNCT
ap-610	70	1	as	as	SCONJ
ap-610	70	2	k	k	PROPN
ap-610	70	3	increases	increase	VERB
ap-610	70	4	from	from	ADP
ap-610	70	5	0	0	NUM
ap-610	70	6	to	to	PART
ap-610	70	7	2	2	NUM
ap-610	70	8	�	�	PROPN
ap-610	70	9	a	a	PRON
ap-610	70	10	,	,	PUNCT
ap-610	70	11	the	the	DET
ap-610	70	12	corresponding	corresponding	ADJ
ap-610	70	13	phase	phase	NOUN
ap-610	70	14	velocity	velocity	NOUN
ap-610	70	15	decreases	decrease	NOUN
ap-610	70	16	from	from	ADP
ap-610	70	17	c0	c0	NOUN
ap-610	70	18	to	to	ADP
ap-610	70	19	0	0	NUM
ap-610	70	20	.	.	PUNCT
ap-610	71	1	this	this	PRON
ap-610	71	2	means	mean	VERB
ap-610	71	3	that	that	SCONJ
ap-610	71	4	shorter	short	ADJ
ap-610	71	5	harmonic	harmonic	ADJ
ap-610	71	6	waves	wave	NOUN
ap-610	71	7	propagate	propagate	VERB
ap-610	71	8	at	at	ADP
ap-610	71	9	slower	slow	ADJ
ap-610	71	10	velocities	velocity	NOUN
ap-610	71	11	.	.	PUNCT
ap-610	72	1	for	for	ADP
ap-610	72	2	a	a	DET
ap-610	72	3	general	general	ADJ
ap-610	72	4	wave	wave	NOUN
ap-610	72	5	,	,	PUNCT
ap-610	72	6	propagation	propagation	NOUN
ap-610	72	7	of	of	ADP
ap-610	72	8	different	different	ADJ
ap-610	72	9	harmonic	harmonic	ADJ
ap-610	72	10	components	component	NOUN
ap-610	72	11	at	at	ADP
ap-610	72	12	different	different	ADJ
ap-610	72	13	velocities	velocity	NOUN
ap-610	72	14	leads	lead	VERB
ap-610	72	15	to	to	ADP
ap-610	72	16	changes	change	NOUN
ap-610	72	17	of	of	ADP
ap-610	72	18	the	the	DET
ap-610	72	19	wave	wave	NOUN
ap-610	72	20	shape	shape	NOUN
ap-610	72	21	.	.	PUNCT
ap-610	73	1	this	this	DET
ap-610	73	2	phenomenon	phenomenon	NOUN
ap-610	73	3	is	be	AUX
ap-610	73	4	known	know	VERB
ap-610	73	5	as	as	ADP
ap-610	73	6	dispersion	dispersion	NOUN
ap-610	73	7	,	,	PUNCT
ap-610	73	8	the	the	DET
ap-610	73	9	equation	equation	NOUN
ap-610	73	10	relating	relate	VERB
ap-610	73	11	�	�	PROPN
ap-610	73	12	and	and	CCONJ
ap-610	73	13	k	k	PROPN
ap-610	73	14	is	be	AUX
ap-610	73	15	called	call	VERB
ap-610	73	16	the	the	DET
ap-610	73	17	dispersion	dispersion	NOUN
ap-610	73	18	equation	equation	NOUN
ap-610	73	19	,	,	PUNCT
ap-610	73	20	the	the	DET
ap-610	73	21	resulting	result	VERB
ap-610	73	22	function	function	NOUN
ap-610	73	23	�	�	PROPN
ap-610	73	24	(	(	PUNCT
ap-610	73	25	)	)	PUNCT
ap-610	73	26	k	k	PROPN
ap-610	73	27	is	be	AUX
ap-610	73	28	the	the	DET
ap-610	73	29	dispersion	dispersion	NOUN
ap-610	73	30	law	law	NOUN
ap-610	73	31	,	,	PUNCT
ap-610	73	32	and	and	CCONJ
ap-610	73	33	its	its	PRON
ap-610	73	34	graph	graph	NOUN
ap-610	73	35	is	be	AUX
ap-610	73	36	the	the	DET
ap-610	73	37	dispersion	dispersion	NOUN
ap-610	73	38	curve	curve	NOUN
ap-610	73	39	.	.	PUNCT
ap-610	74	1	it	it	PRON
ap-610	74	2	is	be	AUX
ap-610	74	3	natural	natural	ADJ
ap-610	74	4	to	to	PART
ap-610	74	5	expect	expect	VERB
ap-610	74	6	that	that	SCONJ
ap-610	74	7	a	a	DET
ap-610	74	8	discrete	discrete	ADJ
ap-610	74	9	mechanical	mechanical	ADJ
ap-610	74	10	model	model	NOUN
ap-610	74	11	consisting	consist	VERB
ap-610	74	12	of	of	ADP
ap-610	74	13	mass	mass	ADJ
ap-610	74	14	points	point	NOUN
ap-610	74	15	m	m	AUX
ap-610	74	16	regularly	regularly	ADV
ap-610	74	17	spaced	space	VERB
ap-610	74	18	at	at	ADP
ap-610	74	19	distance	distance	NOUN
ap-610	74	20	a	a	PRON
ap-610	74	21	and	and	CCONJ
ap-610	74	22	connected	connect	VERB
ap-610	74	23	by	by	ADP
ap-610	74	24	springs	spring	NOUN
ap-610	74	25	of	of	ADP
ap-610	74	26	stiffness	stiffness	NOUN
ap-610	74	27	k	k	PROPN
ap-610	74	28	is	be	AUX
ap-610	74	29	in	in	ADP
ap-610	74	30	some	some	DET
ap-610	74	31	sense	sense	NOUN
ap-610	74	32	equivalent	equivalent	ADJ
ap-610	74	33	to	to	ADP
ap-610	74	34	a	a	DET
ap-610	74	35	continuum	continuum	ADJ
ap-610	74	36	characterized	characterize	VERB
ap-610	74	37	by	by	ADP
ap-610	74	38	mass	mass	ADJ
ap-610	74	39	density	density	NOUN
ap-610	74	40	�	�	PROPN
ap-610	74	41	�	�	PROPN
ap-610	74	42	m	m	PROPN
ap-610	74	43	a	a	PRON
ap-610	74	44	and	and	CCONJ
ap-610	74	45	elastic	elastic	ADJ
ap-610	74	46	modulus	modulus	NOUN
ap-610	74	47	e	e	X
ap-610	74	48	ka	ka	PROPN
ap-610	74	49	�	�	PROPN
ap-610	74	50	.	.	PUNCT
ap-610	75	1	however	however	ADV
ap-610	75	2	,	,	PUNCT
ap-610	75	3	this	this	DET
ap-610	75	4	“	"	PUNCT
ap-610	75	5	equivalence	equivalence	NOUN
ap-610	75	6	”	"	PUNCT
ap-610	75	7	has	have	VERB
ap-610	75	8	its	its	PRON
ap-610	75	9	limits	limit	NOUN
ap-610	75	10	.	.	PUNCT
ap-610	76	1	a	a	DET
ap-610	76	2	standard	standard	ADJ
ap-610	76	3	homogeneous	homogeneous	ADJ
ap-610	76	4	linear	linear	ADJ
ap-610	76	5	elastic	elastic	ADJ
ap-610	76	6	continuum	continuum	NOUN
ap-610	76	7	has	have	VERB
ap-610	76	8	a	a	DET
ap-610	76	9	linear	linear	ADJ
ap-610	76	10	dispersion	dispersion	NOUN
ap-610	76	11	curve	curve	NOUN
ap-610	76	12	with	with	ADP
ap-610	76	13	slope	slope	NOUN
ap-610	76	14	c	c	PROPN
ap-610	76	15	e	e	PROPN
ap-610	76	16	ka	ka	PROPN
ap-610	76	17	m	m	PROPN
ap-610	76	18	�	�	PROPN
ap-610	76	19	�	�	PROPN
ap-610	76	20	�	�	PROPN
ap-610	76	21	2	2	NUM
ap-610	76	22	,	,	PUNCT
ap-610	76	23	which	which	PRON
ap-610	76	24	coincides	coincide	VERB
ap-610	76	25	with	with	ADP
ap-610	76	26	the	the	DET
ap-610	76	27	initial	initial	ADJ
ap-610	76	28	slope	slope	NOUN
ap-610	77	1	c	c	PROPN
ap-610	77	2	a	a	DET
ap-610	77	3	k	k	PROPN
ap-610	77	4	m0	m0	PROPN
ap-610	77	5	�	�	PROPN
ap-610	77	6	of	of	ADP
ap-610	77	7	the	the	DET
ap-610	77	8	nonlinear	nonlinear	ADJ
ap-610	77	9	dispersion	dispersion	NOUN
ap-610	77	10	curve	curve	NOUN
ap-610	77	11	of	of	ADP
ap-610	77	12	the	the	DET
ap-610	77	13	discrete	discrete	ADJ
ap-610	77	14	model	model	NOUN
ap-610	77	15	.	.	PUNCT
ap-610	78	1	both	both	DET
ap-610	78	2	dispersion	dispersion	NOUN
ap-610	78	3	curves	curve	NOUN
ap-610	78	4	are	be	AUX
ap-610	78	5	almost	almost	ADV
ap-610	78	6	identical	identical	ADJ
ap-610	78	7	for	for	ADP
ap-610	78	8	long	long	ADJ
ap-610	78	9	waves	wave	NOUN
ap-610	78	10	,	,	PUNCT
ap-610	78	11	but	but	CCONJ
ap-610	78	12	for	for	ADP
ap-610	78	13	wave	wave	NOUN
ap-610	78	14	numbers	number	NOUN
ap-610	78	15	comparable	comparable	ADJ
ap-610	78	16	to	to	ADP
ap-610	78	17	�	�	PROPN
ap-610	78	18	a	a	PRON
ap-610	78	19	(	(	PUNCT
ap-610	78	20	i.e.	i.e.	X
ap-610	78	21	,	,	PUNCT
ap-610	78	22	for	for	ADP
ap-610	78	23	wavelengths	wavelength	NOUN
ap-610	78	24	comparable	comparable	ADJ
ap-610	78	25	to	to	ADP
ap-610	78	26	2a	2a	NUM
ap-610	78	27	)	)	PUNCT
ap-610	78	28	they	they	PRON
ap-610	78	29	differ	differ	VERB
ap-610	78	30	substantially	substantially	ADV
ap-610	78	31	.	.	PUNCT
ap-610	79	1	the	the	DET
ap-610	79	2	standard	standard	ADJ
ap-610	79	3	continuum	continuum	NOUN
ap-610	79	4	can	can	AUX
ap-610	79	5	be	be	AUX
ap-610	79	6	considered	consider	VERB
ap-610	79	7	as	as	ADP
ap-610	79	8	a	a	DET
ap-610	79	9	long	long	ADJ
ap-610	79	10	-	-	PUNCT
ap-610	79	11	wave	wave	NOUN
ap-610	79	12	approximation	approximation	NOUN
ap-610	79	13	of	of	ADP
ap-610	79	14	the	the	DET
ap-610	79	15	discrete	discrete	ADJ
ap-610	79	16	model	model	NOUN
ap-610	79	17	(	(	PUNCT
ap-610	79	18	or	or	CCONJ
ap-610	79	19	vice	vice	NOUN
ap-610	79	20	-	-	NOUN
ap-610	79	21	versa	versa	NOUN
ap-610	79	22	)	)	PUNCT
ap-610	79	23	.	.	PUNCT
ap-610	80	1	if	if	SCONJ
ap-610	80	2	the	the	DET
ap-610	80	3	actual	actual	ADJ
ap-610	80	4	physical	physical	ADJ
ap-610	80	5	system	system	NOUN
ap-610	80	6	is	be	AUX
ap-610	80	7	close	close	ADJ
ap-610	80	8	to	to	ADP
ap-610	80	9	the	the	DET
ap-610	80	10	mass	mass	ADJ
ap-610	80	11	-	-	PUNCT
ap-610	80	12	spring	spring	NOUN
ap-610	80	13	model	model	NOUN
ap-610	80	14	,	,	PUNCT
ap-610	80	15	the	the	DET
ap-610	80	16	“	"	PUNCT
ap-610	80	17	equivalent	equivalent	ADJ
ap-610	80	18	”	"	PUNCT
ap-610	80	19	continuum	continuum	ADJ
ap-610	80	20	model	model	NOUN
ap-610	80	21	does	do	AUX
ap-610	80	22	not	not	PART
ap-610	80	23	capture	capture	VERB
ap-610	80	24	the	the	DET
ap-610	80	25	phenomenon	phenomenon	NOUN
ap-610	80	26	of	of	ADP
ap-610	80	27	dispersion	dispersion	NOUN
ap-610	80	28	of	of	ADP
ap-610	80	29	short	short	ADJ
ap-610	80	30	elastic	elastic	ADJ
ap-610	80	31	waves	wave	NOUN
ap-610	80	32	.	.	PUNCT
ap-610	81	1	on	on	ADP
ap-610	81	2	the	the	DET
ap-610	81	3	other	other	ADJ
ap-610	81	4	hand	hand	NOUN
ap-610	81	5	,	,	PUNCT
ap-610	81	6	if	if	SCONJ
ap-610	81	7	a	a	DET
ap-610	81	8	homogeneous	homogeneous	ADJ
ap-610	81	9	elastic	elastic	ADJ
ap-610	81	10	continuum	continuum	NOUN
ap-610	81	11	is	be	AUX
ap-610	81	12	discretized	discretize	VERB
ap-610	81	13	in	in	ADP
ap-610	81	14	space	space	NOUN
ap-610	81	15	by	by	ADP
ap-610	81	16	finite	finite	ADJ
ap-610	81	17	differences	difference	NOUN
ap-610	81	18	(	(	PUNCT
ap-610	81	19	or	or	CCONJ
ap-610	81	20	by	by	ADP
ap-610	81	21	finite	finite	ADJ
ap-610	81	22	elements	element	NOUN
ap-610	81	23	with	with	ADP
ap-610	81	24	a	a	DET
ap-610	81	25	lumped	lump	VERB
ap-610	81	26	mass	mass	NOUN
ap-610	81	27	matrix	matrix	NOUN
ap-610	81	28	)	)	PUNCT
ap-610	81	29	,	,	PUNCT
ap-610	81	30	the	the	DET
ap-610	81	31	resulting	result	VERB
ap-610	81	32	set	set	NOUN
ap-610	81	33	of	of	ADP
ap-610	81	34	equations	equation	NOUN
ap-610	81	35	has	have	VERB
ap-610	81	36	the	the	DET
ap-610	81	37	form	form	NOUN
ap-610	81	38	(	(	PUNCT
ap-610	81	39	5	5	NUM
ap-610	81	40	)	)	PUNCT
ap-610	81	41	with	with	ADP
ap-610	81	42	m	m	PROPN
ap-610	81	43	a	a	DET
ap-610	81	44	�	�	PROPN
ap-610	81	45	�	�	PROPN
ap-610	81	46	and	and	CCONJ
ap-610	81	47	k	k	PROPN
ap-610	81	48	e	e	PROPN
ap-610	81	49	a	a	DET
ap-610	81	50	�	�	PROPN
ap-610	81	51	,	,	PUNCT
ap-610	81	52	where	where	SCONJ
ap-610	81	53	a	a	PRON
ap-610	81	54	is	be	AUX
ap-610	81	55	the	the	DET
ap-610	81	56	grid	grid	NOUN
ap-610	81	57	parameter	parameter	NOUN
ap-610	81	58	of	of	ADP
ap-610	81	59	the	the	DET
ap-610	81	60	numerical	numerical	ADJ
ap-610	81	61	method	method	NOUN
ap-610	81	62	(	(	PUNCT
ap-610	81	63	e.g.	e.g.	ADV
ap-610	81	64	,	,	PUNCT
ap-610	81	65	size	size	NOUN
ap-610	81	66	of	of	ADP
ap-610	81	67	finite	finite	ADJ
ap-610	81	68	elements	element	NOUN
ap-610	81	69	)	)	PUNCT
ap-610	81	70	.	.	PUNCT
ap-610	82	1	if	if	SCONJ
ap-610	82	2	these	these	DET
ap-610	82	3	ordinary	ordinary	ADJ
ap-610	82	4	differential	differential	ADJ
ap-610	82	5	equations	equation	NOUN
ap-610	82	6	are	be	AUX
ap-610	82	7	integrated	integrate	VERB
ap-610	82	8	exactly	exactly	ADV
ap-610	82	9	in	in	ADP
ap-610	82	10	time	time	NOUN
ap-610	82	11	,	,	PUNCT
ap-610	82	12	the	the	DET
ap-610	82	13	solution	solution	NOUN
ap-610	82	14	captures	capture	VERB
ap-610	82	15	correctly	correctly	ADV
ap-610	82	16	long	long	ADJ
ap-610	82	17	-	-	PUNCT
ap-610	82	18	wave	wave	NOUN
ap-610	82	19	phenomena	phenomenon	NOUN
ap-610	82	20	but	but	CCONJ
ap-610	82	21	introduces	introduce	VERB
ap-610	82	22	an	an	DET
ap-610	82	23	artificial	artificial	ADJ
ap-610	82	24	(	(	PUNCT
ap-610	82	25	numerical	numerical	ADJ
ap-610	82	26	)	)	PUNCT
ap-610	82	27	dispersion	dispersion	NOUN
ap-610	82	28	of	of	ADP
ap-610	82	29	short	short	ADJ
ap-610	82	30	waves	wave	NOUN
ap-610	82	31	with	with	ADP
ap-610	82	32	wavelengths	wavelength	NOUN
ap-610	82	33	comparable	comparable	ADJ
ap-610	82	34	to	to	ADP
ap-610	82	35	the	the	DET
ap-610	82	36	element	element	NOUN
ap-610	82	37	size	size	NOUN
ap-610	82	38	.	.	PUNCT
ap-610	83	1	note	note	VERB
ap-610	83	2	that	that	SCONJ
ap-610	83	3	the	the	DET
ap-610	83	4	numerical	numerical	ADJ
ap-610	83	5	dispersion	dispersion	NOUN
ap-610	83	6	disappears	disappear	VERB
ap-610	83	7	if	if	SCONJ
ap-610	83	8	equations	equation	NOUN
ap-610	83	9	(	(	PUNCT
ap-610	83	10	5	5	X
ap-610	83	11	)	)	PUNCT
ap-610	83	12	are	be	AUX
ap-610	83	13	integrated	integrate	VERB
ap-610	83	14	in	in	ADP
ap-610	83	15	time	time	NOUN
ap-610	83	16	using	use	VERB
ap-610	83	17	the	the	DET
ap-610	83	18	central	central	ADJ
ap-610	83	19	difference	difference	NOUN
ap-610	83	20	scheme	scheme	NOUN
ap-610	83	21	with	with	ADP
ap-610	83	22	time	time	NOUN
ap-610	83	23	step	step	NOUN
ap-610	83	24	�	�	PROPN
ap-610	83	25	t	t	PROPN
ap-610	83	26	a	a	DET
ap-610	83	27	c	c	PROPN
ap-610	83	28	�	�	PROPN
ap-610	83	29	,	,	PUNCT
ap-610	83	30	which	which	PRON
ap-610	83	31	is	be	AUX
ap-610	83	32	just	just	ADV
ap-610	83	33	at	at	ADP
ap-610	83	34	the	the	DET
ap-610	83	35	limit	limit	NOUN
ap-610	83	36	of	of	ADP
ap-610	83	37	numerical	numerical	ADJ
ap-610	83	38	stability	stability	NOUN
ap-610	83	39	.	.	PUNCT
ap-610	84	1	consequently	consequently	ADV
ap-610	84	2	,	,	PUNCT
ap-610	84	3	propagation	propagation	NOUN
ap-610	84	4	of	of	ADP
ap-610	84	5	shocks	shock	NOUN
ap-610	84	6	and	and	CCONJ
ap-610	84	7	other	other	ADJ
ap-610	84	8	wide	wide	ADJ
ap-610	84	9	-	-	PUNCT
ap-610	84	10	spectrum	spectrum	NOUN
ap-610	84	11	phenomena	phenomenon	NOUN
ap-610	84	12	are	be	AUX
ap-610	84	13	not	not	PART
ap-610	84	14	represented	represent	VERB
ap-610	84	15	accurately	accurately	ADV
ap-610	84	16	.	.	PUNCT
ap-610	85	1	discrete	discrete	ADJ
ap-610	85	2	mass	mass	ADJ
ap-610	85	3	-	-	PUNCT
ap-610	85	4	spring	spring	NOUN
ap-610	85	5	systems	system	NOUN
ap-610	85	6	are	be	AUX
ap-610	85	7	quite	quite	ADV
ap-610	85	8	realistic	realistic	ADJ
ap-610	85	9	models	model	NOUN
ap-610	85	10	for	for	ADP
ap-610	85	11	crystalline	crystalline	ADJ
ap-610	85	12	materials	material	NOUN
ap-610	85	13	on	on	ADP
ap-610	85	14	a	a	DET
ap-610	85	15	scale	scale	NOUN
ap-610	85	16	of	of	ADP
ap-610	85	17	observation	observation	NOUN
ap-610	85	18	close	close	ADV
ap-610	85	19	to	to	ADP
ap-610	85	20	the	the	DET
ap-610	85	21	atomic	atomic	ADJ
ap-610	85	22	spacing	spacing	NOUN
ap-610	85	23	.	.	PUNCT
ap-610	86	1	of	of	ADP
ap-610	86	2	course	course	ADV
ap-610	86	3	,	,	PUNCT
ap-610	86	4	real	real	ADJ
ap-610	86	5	crystal	crystal	NOUN
ap-610	86	6	lattices	lattice	NOUN
ap-610	86	7	are	be	AUX
ap-610	86	8	three	three	NUM
ap-610	86	9	-	-	PUNCT
ap-610	86	10	dimensional	dimensional	ADJ
ap-610	86	11	and	and	CCONJ
ap-610	86	12	interaction	interaction	NOUN
ap-610	86	13	forces	force	NOUN
ap-610	86	14	arise	arise	VERB
ap-610	86	15	not	not	PART
ap-610	86	16	only	only	ADV
ap-610	86	17	between	between	ADP
ap-610	86	18	immediate	immediate	ADJ
ap-610	86	19	neighbors	neighbor	NOUN
ap-610	86	20	but	but	CCONJ
ap-610	86	21	also	also	ADV
ap-610	86	22	at	at	ADP
ap-610	86	23	longer	long	ADJ
ap-610	86	24	distance	distance	NOUN
ap-610	86	25	.	.	PUNCT
ap-610	87	1	still	still	ADV
ap-610	87	2	,	,	PUNCT
ap-610	87	3	a	a	DET
ap-610	87	4	one	one	NUM
ap-610	87	5	-	-	PUNCT
ap-610	87	6	dimensional	dimensional	ADJ
ap-610	87	7	lattice	lattice	NOUN
ap-610	87	8	is	be	AUX
ap-610	87	9	an	an	DET
ap-610	87	10	acceptable	acceptable	ADJ
ap-610	87	11	model	model	NOUN
ap-610	87	12	for	for	ADP
ap-610	87	13	plane	plane	NOUN
ap-610	87	14	waves	wave	NOUN
ap-610	87	15	propagating	propagate	VERB
ap-610	87	16	perpendicular	perpendicular	NOUN
ap-610	87	17	to	to	ADP
ap-610	87	18	a	a	DET
ap-610	87	19	certain	certain	ADJ
ap-610	87	20	set	set	NOUN
ap-610	87	21	of	of	ADP
ap-610	87	22	crystallographic	crystallographic	ADJ
ap-610	87	23	planes	plane	NOUN
ap-610	87	24	.	.	PUNCT
ap-610	88	1	in	in	ADP
ap-610	88	2	this	this	DET
ap-610	88	3	case	case	NOUN
ap-610	88	4	,	,	PUNCT
ap-610	88	5	each	each	DET
ap-610	88	6	mass	mass	NOUN
ap-610	88	7	point	point	NOUN
ap-610	88	8	actually	actually	ADV
ap-610	88	9	represents	represent	VERB
ap-610	88	10	one	one	NUM
ap-610	88	11	plane	plane	NOUN
ap-610	88	12	of	of	ADP
ap-610	88	13	densely	densely	ADV
ap-610	88	14	packed	pack	VERB
ap-610	88	15	atoms	atom	NOUN
ap-610	88	16	instead	instead	ADV
ap-610	88	17	of	of	ADP
ap-610	88	18	one	one	NUM
ap-610	88	19	single	single	ADJ
ap-610	88	20	atom	atom	NOUN
ap-610	88	21	.	.	PUNCT
ap-610	89	1	interactions	interaction	NOUN
ap-610	89	2	at	at	ADP
ap-610	89	3	longer	long	ADJ
ap-610	89	4	distance	distance	NOUN
ap-610	89	5	can	can	AUX
ap-610	89	6	easily	easily	ADV
ap-610	89	7	be	be	AUX
ap-610	89	8	incorporated	incorporate	VERB
ap-610	89	9	by	by	ADP
ap-610	89	10	adding	add	VERB
ap-610	89	11	springs	spring	NOUN
ap-610	89	12	of	of	ADP
ap-610	89	13	stiffness	stiffness	ADJ
ap-610	89	14	k2	k2	NOUN
ap-610	89	15	,	,	PUNCT
ap-610	89	16	k3	k3	VERB
ap-610	89	17	,	,	PUNCT
ap-610	89	18	…	…	PUNCT
ap-610	89	19	,	,	PUNCT
ap-610	89	20	kn	kn	NOUN
ap-610	89	21	,	,	PUNCT
ap-610	89	22	connecting	connect	VERB
ap-610	89	23	pairs	pair	NOUN
ap-610	89	24	of	of	ADP
ap-610	89	25	mass	mass	ADJ
ap-610	89	26	points	point	NOUN
ap-610	89	27	spaced	space	VERB
ap-610	89	28	by	by	ADP
ap-610	89	29	2a	2a	NUM
ap-610	89	30	,	,	PUNCT
ap-610	89	31	3a	3a	NUM
ap-610	89	32	,	,	PUNCT
ap-610	89	33	…	…	PUNCT
ap-610	89	34	,	,	PUNCT
ap-610	89	35	na	na	NOUN
ap-610	89	36	.	.	PUNCT
ap-610	90	1	a	a	DET
ap-610	90	2	straightforward	straightforward	ADJ
ap-610	90	3	extension	extension	NOUN
ap-610	90	4	of	of	ADP
ap-610	90	5	the	the	DET
ap-610	90	6	foregoing	forego	VERB
ap-610	90	7	dispersion	dispersion	NOUN
ap-610	90	8	analysis	analysis	NOUN
ap-610	90	9	yields	yield	VERB
ap-610	90	10	the	the	DET
ap-610	90	11	dispersion	dispersion	NOUN
ap-610	90	12	relation	relation	NOUN
ap-610	90	13	�	�	PROPN
ap-610	90	14	�	�	PROPN
ap-610	90	15	�	�	PROPN
ap-610	90	16	�	�	PROPN
ap-610	90	17	�	�	PROPN
ap-610	90	18	�	�	PROPN
ap-610	90	19	�	�	PROPN
ap-610	90	20	�	�	PROPN
ap-610	90	21	�	�	PROPN
ap-610	90	22	�	�	PROPN
ap-610	90	23	�	�	PROPN
ap-610	90	24	�	�	PROPN
ap-610	90	25	m	m	PROPN
ap-610	90	26	k	k	ADJ
ap-610	90	27	kn	kn	PROPN
ap-610	90	28	ikna	ikna	PROPN
ap-610	90	29	n	n	CCONJ
ap-610	90	30	n	n	CCONJ
ap-610	90	31	n	n	PRON
ap-610	90	32	ikna	ikna	NOUN
ap-610	90	33	n	n	CCONJ
ap-610	90	34	n	n	PRON
ap-610	90	35	�	�	PROPN
ap-610	90	36	2	2	NUM
ap-610	90	37	1	1	NUM
ap-610	90	38	1	1	NUM
ap-610	90	39	1	1	NUM
ap-610	90	40	1	1	NUM
ap-610	90	41	0	0	NUM
ap-610	90	42	(	(	PUNCT
ap-610	90	43	)	)	PUNCT
ap-610	90	44	(	(	PUNCT
ap-610	90	45	)	)	PUNCT
ap-610	90	46	e	e	NOUN
ap-610	90	47	e	e	X
ap-610	90	48	(	(	PUNCT
ap-610	90	49	9	9	NUM
ap-610	90	50	)	)	PUNCT
ap-610	90	51	from	from	ADP
ap-610	90	52	which	which	PRON
ap-610	90	53	�	�	PROPN
ap-610	90	54	�	�	PROPN
ap-610	90	55	�	�	PROPN
ap-610	90	56	�	�	PROPN
ap-610	90	57	�	�	PROPN
ap-610	90	58	�	�	PROPN
ap-610	90	59	�	�	PROPN
ap-610	90	60	�	�	PROPN
ap-610	90	61	2	2	NUM
ap-610	90	62	1	1	NUM
ap-610	90	63	2	2	NUM
ap-610	90	64	2	2	NUM
ap-610	90	65	1	1	NUM
ap-610	90	66	2	2	NUM
ap-610	90	67	1	1	NUM
ap-610	90	68	m	m	NOUN
ap-610	90	69	k	k	PROPN
ap-610	91	1	kna	kna	PROPN
ap-610	91	2	m	m	PROPN
ap-610	91	3	k	k	PROPN
ap-610	91	4	kna	kna	PROPN
ap-610	91	5	n	n	CCONJ
ap-610	91	6	n	n	CCONJ
ap-610	91	7	n	n	CCONJ
ap-610	91	8	n	n	CCONJ
ap-610	91	9	n	n	CCONJ
ap-610	91	10	n	n	CCONJ
ap-610	91	11	(	(	PUNCT
ap-610	91	12	cos	cos	PROPN
ap-610	91	13	)	)	PUNCT
ap-610	91	14	sin	sin	NOUN
ap-610	91	15	.	.	PUNCT
ap-610	92	1	(	(	PUNCT
ap-610	92	2	10	10	NUM
ap-610	92	3	)	)	PUNCT
ap-610	92	4	18	18	NUM
ap-610	92	5	©	©	PROPN
ap-610	92	6	czech	czech	PROPN
ap-610	92	7	technical	technical	PROPN
ap-610	92	8	university	university	PROPN
ap-610	92	9	publishing	publishing	NOUN
ap-610	92	10	house	house	NOUN
ap-610	92	11	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	92	12	acta	acta	PROPN
ap-610	92	13	polytechnica	polytechnica	PROPN
ap-610	92	14	vol	vol	NOUN
ap-610	92	15	.	.	PROPN
ap-610	93	1	44	44	NUM
ap-610	93	2	no	no	NOUN
ap-610	93	3	.	.	PUNCT
ap-610	94	1	5–6/2004	5–6/2004	NUM
ap-610	94	2	(	(	PUNCT
ap-610	94	3	a	a	NOUN
ap-610	94	4	)	)	PUNCT
ap-610	94	5	(	(	PUNCT
ap-610	94	6	b	b	X
ap-610	94	7	)	)	PUNCT
ap-610	94	8	fig	fig	NOUN
ap-610	94	9	.	.	PUNCT
ap-610	95	1	2	2	NUM
ap-610	95	2	:	:	PUNCT
ap-610	95	3	(	(	PUNCT
ap-610	95	4	a	a	X
ap-610	95	5	)	)	PUNCT
ap-610	95	6	dispersion	dispersion	NOUN
ap-610	95	7	curve	curve	NOUN
ap-610	95	8	of	of	ADP
ap-610	95	9	a	a	DET
ap-610	95	10	mass	mass	ADJ
ap-610	95	11	-	-	PUNCT
ap-610	95	12	spring	spring	NOUN
ap-610	95	13	model	model	NOUN
ap-610	95	14	with	with	ADP
ap-610	95	15	interaction	interaction	NOUN
ap-610	95	16	up	up	ADP
ap-610	95	17	to	to	ADP
ap-610	95	18	distance	distance	NOUN
ap-610	95	19	,	,	PUNCT
ap-610	95	20	(	(	PUNCT
ap-610	95	21	b	b	X
ap-610	95	22	)	)	PUNCT
ap-610	95	23	dispersion	dispersion	NOUN
ap-610	95	24	curve	curve	NOUN
ap-610	95	25	of	of	ADP
ap-610	95	26	aluminum	aluminum	NOUN
ap-610	95	27	for	for	ADP
ap-610	95	28	longitudinal	longitudinal	ADJ
ap-610	95	29	waves	wave	NOUN
ap-610	95	30	in	in	ADP
ap-610	95	31	the	the	DET
ap-610	95	32	direction	direction	NOUN
ap-610	95	33	(	(	PUNCT
ap-610	95	34	after	after	ADP
ap-610	95	35	yarnel	yarnel	PROPN
ap-610	95	36	et	et	PROPN
ap-610	95	37	al	al	PROPN
ap-610	95	38	.	.	PROPN
ap-610	95	39	,	,	PUNCT
ap-610	95	40	1965	1965	NUM
ap-610	95	41	)	)	PUNCT
ap-610	95	42	in	in	ADP
ap-610	95	43	the	the	DET
ap-610	95	44	long	long	ADJ
ap-610	95	45	-	-	PUNCT
ap-610	95	46	wave	wave	NOUN
ap-610	95	47	limit	limit	NOUN
ap-610	95	48	(	(	PUNCT
ap-610	95	49	k	k	PROPN
ap-610	95	50	�	�	PROPN
ap-610	95	51	�	�	PROPN
ap-610	95	52	)	)	PUNCT
ap-610	95	53	,	,	PUNCT
ap-610	95	54	the	the	DET
ap-610	95	55	phase	phase	NOUN
ap-610	95	56	velocity	velocity	NOUN
ap-610	95	57	c	c	PROPN
ap-610	95	58	kp	kp	PROPN
ap-610	95	59	�	�	PROPN
ap-610	95	60	�	�	PROPN
ap-610	95	61	tends	tend	VERB
ap-610	95	62	to	to	ADP
ap-610	95	63	c	c	PROPN
ap-610	95	64	a	a	DET
ap-610	95	65	m	m	NOUN
ap-610	95	66	k	k	PROPN
ap-610	95	67	nn	nn	PROPN
ap-610	95	68	n	n	CCONJ
ap-610	95	69	n	n	ADV
ap-610	95	70	0	0	NUM
ap-610	95	71	2	2	NUM
ap-610	95	72	1	1	NUM
ap-610	95	73	�	�	PROPN
ap-610	95	74	�	�	PROPN
ap-610	95	75	�	�	PROPN
ap-610	95	76	.	.	PUNCT
ap-610	96	1	(	(	PUNCT
ap-610	96	2	11	11	NUM
ap-610	96	3	)	)	PUNCT
ap-610	96	4	an	an	DET
ap-610	96	5	example	example	NOUN
ap-610	96	6	of	of	ADP
ap-610	96	7	a	a	DET
ap-610	96	8	dispersion	dispersion	NOUN
ap-610	96	9	curve	curve	NOUN
ap-610	96	10	constructed	construct	VERB
ap-610	96	11	with	with	ADP
ap-610	96	12	n	n	X
ap-610	96	13	�	�	PROPN
ap-610	96	14	3	3	NUM
ap-610	96	15	and	and	CCONJ
ap-610	96	16	k1	k1	PROPN
ap-610	96	17	�	�	PROPN
ap-610	96	18	k2	k2	PROPN
ap-610	96	19	�	�	PROPN
ap-610	96	20	k3	k3	PROPN
ap-610	96	21	�	�	PROPN
ap-610	96	22	k	k	PROPN
ap-610	96	23	is	be	AUX
ap-610	96	24	shown	show	VERB
ap-610	96	25	in	in	ADP
ap-610	96	26	fig	fig	NOUN
ap-610	96	27	.	.	PUNCT
ap-610	97	1	2a	2a	NUM
ap-610	97	2	.	.	PUNCT
ap-610	98	1	this	this	DET
ap-610	98	2	curve	curve	NOUN
ap-610	98	3	has	have	VERB
ap-610	98	4	a	a	DET
ap-610	98	5	more	more	ADV
ap-610	98	6	general	general	ADJ
ap-610	98	7	shape	shape	NOUN
ap-610	98	8	than	than	ADP
ap-610	98	9	for	for	ADP
ap-610	98	10	the	the	DET
ap-610	98	11	nearest	near	ADJ
ap-610	98	12	-	-	PUNCT
ap-610	98	13	neighbor	neighbor	NOUN
ap-610	98	14	interaction	interaction	NOUN
ap-610	98	15	only	only	ADV
ap-610	98	16	(	(	PUNCT
ap-610	98	17	cf	cf	NOUN
ap-610	98	18	.	.	PUNCT
ap-610	99	1	fig	fig	NOUN
ap-610	99	2	.	.	PUNCT
ap-610	100	1	1b	1b	NUM
ap-610	100	2	)	)	PUNCT
ap-610	100	3	,	,	PUNCT
ap-610	100	4	but	but	CCONJ
ap-610	100	5	the	the	DET
ap-610	100	6	wave	wave	NOUN
ap-610	100	7	number	number	NOUN
ap-610	100	8	2	2	NUM
ap-610	100	9	�	�	PROPN
ap-610	100	10	a	a	PRON
ap-610	100	11	still	still	ADV
ap-610	100	12	corresponds	correspond	VERB
ap-610	100	13	to	to	ADP
ap-610	100	14	zero	zero	NUM
ap-610	100	15	frequency	frequency	NOUN
ap-610	100	16	.	.	PUNCT
ap-610	101	1	this	this	PRON
ap-610	101	2	is	be	AUX
ap-610	101	3	natural	natural	ADJ
ap-610	101	4	,	,	PUNCT
ap-610	101	5	because	because	SCONJ
ap-610	101	6	the	the	DET
ap-610	101	7	displacements	displacement	NOUN
ap-610	101	8	uj	uj	PROPN
ap-610	101	9	generated	generate	VERB
ap-610	101	10	by	by	ADP
ap-610	101	11	a	a	DET
ap-610	101	12	harmonic	harmonic	ADJ
ap-610	101	13	wave	wave	NOUN
ap-610	101	14	with	with	ADP
ap-610	101	15	wavelength	wavelength	NOUN
ap-610	101	16	a	a	PRON
ap-610	101	17	are	be	AUX
ap-610	101	18	the	the	DET
ap-610	101	19	same	same	ADJ
ap-610	101	20	at	at	ADP
ap-610	101	21	all	all	DET
ap-610	101	22	the	the	DET
ap-610	101	23	lattice	lattice	NOUN
ap-610	101	24	sites	site	NOUN
ap-610	101	25	.	.	PUNCT
ap-610	102	1	the	the	DET
ap-610	102	2	associated	associated	ADJ
ap-610	102	3	mode	mode	NOUN
ap-610	102	4	is	be	AUX
ap-610	102	5	a	a	DET
ap-610	102	6	uniform	uniform	ADJ
ap-610	102	7	translation	translation	NOUN
ap-610	102	8	of	of	ADP
ap-610	102	9	the	the	DET
ap-610	102	10	lattice	lattice	NOUN
ap-610	102	11	points	point	NOUN
ap-610	102	12	,	,	PUNCT
ap-610	102	13	which	which	PRON
ap-610	102	14	would	would	AUX
ap-610	102	15	not	not	PART
ap-610	102	16	lead	lead	VERB
ap-610	102	17	to	to	ADP
ap-610	102	18	any	any	DET
ap-610	102	19	vibrations	vibration	NOUN
ap-610	102	20	.	.	PUNCT
ap-610	103	1	a	a	DET
ap-610	103	2	striking	striking	ADJ
ap-610	103	3	property	property	NOUN
ap-610	103	4	of	of	ADP
ap-610	103	5	the	the	DET
ap-610	103	6	dispersion	dispersion	NOUN
ap-610	103	7	law	law	NOUN
ap-610	103	8	(	(	PUNCT
ap-610	103	9	10	10	NUM
ap-610	103	10	)	)	PUNCT
ap-610	103	11	is	be	AUX
ap-610	103	12	its	its	PRON
ap-610	103	13	periodicity	periodicity	NOUN
ap-610	103	14	.	.	PUNCT
ap-610	104	1	this	this	PRON
ap-610	104	2	is	be	AUX
ap-610	104	3	closely	closely	ADV
ap-610	104	4	related	relate	VERB
ap-610	104	5	to	to	ADP
ap-610	104	6	the	the	DET
ap-610	104	7	discrete	discrete	ADJ
ap-610	104	8	and	and	CCONJ
ap-610	104	9	periodic	periodic	ADJ
ap-610	104	10	nature	nature	NOUN
ap-610	104	11	of	of	ADP
ap-610	104	12	the	the	DET
ap-610	104	13	underlying	underlying	ADJ
ap-610	104	14	mechanical	mechanical	ADJ
ap-610	104	15	model	model	NOUN
ap-610	104	16	.	.	PUNCT
ap-610	105	1	in	in	ADP
ap-610	105	2	fact	fact	NOUN
ap-610	105	3	,	,	PUNCT
ap-610	105	4	wave	wave	NOUN
ap-610	105	5	numbers	number	NOUN
ap-610	105	6	that	that	PRON
ap-610	105	7	differ	differ	VERB
ap-610	105	8	by	by	ADP
ap-610	105	9	an	an	DET
ap-610	105	10	integer	integer	NOUN
ap-610	105	11	multiple	multiple	NOUN
ap-610	105	12	of	of	ADP
ap-610	105	13	�	�	PROPN
ap-610	105	14	a	a	DET
ap-610	105	15	correspond	correspond	NOUN
ap-610	105	16	to	to	ADP
ap-610	105	17	the	the	DET
ap-610	105	18	same	same	ADJ
ap-610	105	19	physical	physical	ADJ
ap-610	105	20	state	state	NOUN
ap-610	105	21	of	of	ADP
ap-610	105	22	the	the	DET
ap-610	105	23	mass	mass	ADJ
ap-610	105	24	-	-	PUNCT
ap-610	105	25	point	point	NOUN
ap-610	105	26	chain	chain	NOUN
ap-610	105	27	.	.	PUNCT
ap-610	106	1	consequently	consequently	ADV
ap-610	106	2	,	,	PUNCT
ap-610	106	3	the	the	DET
ap-610	106	4	dispersion	dispersion	NOUN
ap-610	106	5	curve	curve	NOUN
ap-610	106	6	of	of	ADP
ap-610	106	7	this	this	DET
ap-610	106	8	chain	chain	NOUN
ap-610	106	9	is	be	AUX
ap-610	106	10	uniquely	uniquely	ADV
ap-610	106	11	characterized	characterize	VERB
ap-610	106	12	by	by	ADP
ap-610	106	13	its	its	PRON
ap-610	106	14	initial	initial	ADJ
ap-610	106	15	part	part	NOUN
ap-610	106	16	for	for	ADP
ap-610	106	17	wave	wave	NOUN
ap-610	106	18	numbers	number	NOUN
ap-610	106	19	between	between	ADP
ap-610	106	20	0	0	NUM
ap-610	106	21	and	and	CCONJ
ap-610	106	22	�	�	PROPN
ap-610	106	23	a.	a.	NOUN
ap-610	106	24	this	this	DET
ap-610	106	25	range	range	NOUN
ap-610	106	26	of	of	ADP
ap-610	106	27	wave	wave	NOUN
ap-610	106	28	numbers	number	NOUN
ap-610	106	29	is	be	AUX
ap-610	106	30	in	in	ADP
ap-610	106	31	the	the	DET
ap-610	106	32	theory	theory	NOUN
ap-610	106	33	of	of	ADP
ap-610	106	34	crystal	crystal	NOUN
ap-610	106	35	vibrations	vibration	NOUN
ap-610	106	36	called	call	VERB
ap-610	106	37	the	the	DET
ap-610	106	38	first	first	ADJ
ap-610	106	39	brillouin	brillouin	NOUN
ap-610	106	40	zone	zone	NOUN
ap-610	106	41	.	.	PUNCT
ap-610	107	1	another	another	DET
ap-610	107	2	interesting	interesting	ADJ
ap-610	107	3	property	property	NOUN
ap-610	107	4	is	be	AUX
ap-610	107	5	that	that	SCONJ
ap-610	107	6	the	the	DET
ap-610	107	7	frequency	frequency	NOUN
ap-610	107	8	range	range	NOUN
ap-610	107	9	of	of	ADP
ap-610	107	10	harmonic	harmonic	ADJ
ap-610	107	11	waves	wave	NOUN
ap-610	107	12	is	be	AUX
ap-610	107	13	limited	limited	ADJ
ap-610	107	14	.	.	PUNCT
ap-610	108	1	the	the	DET
ap-610	108	2	dispersion	dispersion	NOUN
ap-610	108	3	law	law	NOUN
ap-610	108	4	maps	map	VERB
ap-610	108	5	the	the	DET
ap-610	108	6	first	first	ADJ
ap-610	108	7	brillouin	brillouin	NOUN
ap-610	108	8	zone	zone	NOUN
ap-610	108	9	onto	onto	ADP
ap-610	108	10	a	a	DET
ap-610	108	11	certain	certain	ADJ
ap-610	108	12	interval	interval	NOUN
ap-610	108	13	[	[	X
ap-610	108	14	0	0	NUM
ap-610	108	15	,	,	PUNCT
ap-610	108	16	�	�	PROPN
ap-610	108	17	max	max	PROPN
ap-610	108	18	]	]	PUNCT
ap-610	108	19	where	where	SCONJ
ap-610	108	20	�	�	PROPN
ap-610	108	21	max	max	PROPN
ap-610	108	22	is	be	AUX
ap-610	108	23	a	a	DET
ap-610	108	24	limiting	limit	VERB
ap-610	108	25	circular	circular	ADJ
ap-610	108	26	frequency	frequency	NOUN
ap-610	108	27	.	.	PUNCT
ap-610	109	1	if	if	SCONJ
ap-610	109	2	certain	certain	ADJ
ap-610	109	3	mass	mass	NOUN
ap-610	109	4	point	point	NOUN
ap-610	109	5	is	be	AUX
ap-610	109	6	externally	externally	ADV
ap-610	109	7	excited	excited	ADJ
ap-610	109	8	with	with	ADP
ap-610	109	9	a	a	DET
ap-610	109	10	circular	circular	ADJ
ap-610	109	11	frequency	frequency	NOUN
ap-610	109	12	larger	large	ADJ
ap-610	109	13	than	than	ADP
ap-610	109	14	�	�	PROPN
ap-610	109	15	max	max	PROPN
ap-610	109	16	,	,	PUNCT
ap-610	109	17	the	the	DET
ap-610	109	18	vibration	vibration	NOUN
ap-610	109	19	does	do	AUX
ap-610	109	20	not	not	PART
ap-610	109	21	propagate	propagate	VERB
ap-610	109	22	through	through	ADP
ap-610	109	23	the	the	DET
ap-610	109	24	entire	entire	ADJ
ap-610	109	25	chain	chain	NOUN
ap-610	109	26	and	and	CCONJ
ap-610	109	27	remains	remain	VERB
ap-610	109	28	localized	localize	VERB
ap-610	109	29	to	to	ADP
ap-610	109	30	the	the	DET
ap-610	109	31	neighborhood	neighborhood	NOUN
ap-610	109	32	of	of	ADP
ap-610	109	33	the	the	DET
ap-610	109	34	excited	excited	ADJ
ap-610	109	35	mass	mass	NOUN
ap-610	109	36	point	point	NOUN
ap-610	109	37	.	.	PUNCT
ap-610	110	1	the	the	DET
ap-610	110	2	discrete	discrete	ADJ
ap-610	110	3	chain	chain	NOUN
ap-610	110	4	therefore	therefore	ADV
ap-610	110	5	acts	act	VERB
ap-610	110	6	as	as	ADP
ap-610	110	7	a	a	DET
ap-610	110	8	low	low	ADJ
ap-610	110	9	-	-	PUNCT
ap-610	110	10	band	band	NOUN
ap-610	110	11	filter	filter	NOUN
ap-610	110	12	.	.	PUNCT
ap-610	111	1	dispersion	dispersion	NOUN
ap-610	111	2	of	of	ADP
ap-610	111	3	elastic	elastic	ADJ
ap-610	111	4	waves	wave	NOUN
ap-610	111	5	in	in	ADP
ap-610	111	6	crystals	crystal	NOUN
ap-610	111	7	is	be	AUX
ap-610	111	8	a	a	DET
ap-610	111	9	real	real	ADJ
ap-610	111	10	physical	physical	ADJ
ap-610	111	11	phenomenon	phenomenon	NOUN
ap-610	111	12	that	that	PRON
ap-610	111	13	can	can	AUX
ap-610	111	14	be	be	AUX
ap-610	111	15	observed	observe	VERB
ap-610	111	16	and	and	CCONJ
ap-610	111	17	studied	study	VERB
ap-610	111	18	experimentally	experimentally	ADV
ap-610	111	19	.	.	PUNCT
ap-610	112	1	fig	fig	NOUN
ap-610	112	2	.	.	PUNCT
ap-610	113	1	2b	2b	NUM
ap-610	113	2	shows	show	VERB
ap-610	113	3	an	an	DET
ap-610	113	4	example	example	NOUN
ap-610	113	5	of	of	ADP
ap-610	113	6	a	a	DET
ap-610	113	7	dispersion	dispersion	NOUN
ap-610	113	8	curve	curve	NOUN
ap-610	113	9	of	of	ADP
ap-610	113	10	aluminum	aluminum	NOUN
ap-610	113	11	,	,	PUNCT
ap-610	113	12	measured	measure	VERB
ap-610	113	13	by	by	ADP
ap-610	113	14	yarnel	yarnel	NOUN
ap-610	113	15	,	,	PUNCT
ap-610	113	16	warren	warren	PROPN
ap-610	113	17	and	and	CCONJ
ap-610	113	18	koenig	koenig	PROPN
ap-610	113	19	(	(	PUNCT
ap-610	113	20	1965	1965	NUM
ap-610	113	21	)	)	PUNCT
ap-610	113	22	.	.	PUNCT
ap-610	114	1	this	this	DET
ap-610	114	2	specific	specific	ADJ
ap-610	114	3	curve	curve	NOUN
ap-610	114	4	corresponds	correspond	VERB
ap-610	114	5	to	to	ADP
ap-610	114	6	waves	wave	NOUN
ap-610	114	7	propagating	propagate	VERB
ap-610	114	8	in	in	ADP
ap-610	114	9	the	the	DET
ap-610	114	10	crystallographic	crystallographic	ADJ
ap-610	114	11	direction	direction	NOUN
ap-610	114	12	(	(	PUNCT
ap-610	114	13	110	110	NUM
ap-610	114	14	)	)	PUNCT
ap-610	114	15	,	,	PUNCT
ap-610	114	16	and	and	CCONJ
ap-610	114	17	it	it	PRON
ap-610	114	18	can	can	AUX
ap-610	114	19	be	be	AUX
ap-610	114	20	well	well	ADV
ap-610	114	21	approximated	approximate	VERB
ap-610	114	22	by	by	ADP
ap-610	114	23	a	a	DET
ap-610	114	24	function	function	NOUN
ap-610	114	25	of	of	ADP
ap-610	114	26	the	the	DET
ap-610	114	27	form	form	NOUN
ap-610	114	28	(	(	PUNCT
ap-610	114	29	10	10	NUM
ap-610	114	30	)	)	PUNCT
ap-610	114	31	.	.	PUNCT
ap-610	115	1	2.2	2.2	NUM
ap-610	115	2	.	.	PUNCT
ap-610	115	3	strain	strain	NOUN
ap-610	115	4	-	-	PUNCT
ap-610	115	5	gradient	gradient	NOUN
ap-610	115	6	elasticity	elasticity	NOUN
ap-610	115	7	if	if	SCONJ
ap-610	115	8	dispersive	dispersive	ADJ
ap-610	115	9	phenomena	phenomenon	NOUN
ap-610	115	10	were	be	AUX
ap-610	115	11	limited	limit	VERB
ap-610	115	12	to	to	ADP
ap-610	115	13	the	the	DET
ap-610	115	14	atomistic	atomistic	ADJ
ap-610	115	15	scale	scale	NOUN
ap-610	115	16	,	,	PUNCT
ap-610	115	17	elastic	elastic	ADJ
ap-610	115	18	wave	wave	NOUN
ap-610	115	19	propagation	propagation	NOUN
ap-610	115	20	could	could	AUX
ap-610	115	21	be	be	AUX
ap-610	115	22	described	describe	VERB
ap-610	115	23	by	by	ADP
ap-610	115	24	discrete	discrete	ADJ
ap-610	115	25	atomistic	atomistic	ADJ
ap-610	115	26	models	model	NOUN
ap-610	115	27	on	on	ADP
ap-610	115	28	that	that	DET
ap-610	115	29	scale	scale	NOUN
ap-610	115	30	and	and	CCONJ
ap-610	115	31	by	by	ADP
ap-610	115	32	standard	standard	ADJ
ap-610	115	33	continuum	continuum	ADJ
ap-610	115	34	models	model	NOUN
ap-610	115	35	on	on	ADP
ap-610	115	36	any	any	DET
ap-610	115	37	coarser	coarse	ADJ
ap-610	115	38	scale	scale	NOUN
ap-610	115	39	.	.	PUNCT
ap-610	116	1	however	however	ADV
ap-610	116	2	,	,	PUNCT
ap-610	116	3	dispersion	dispersion	NOUN
ap-610	116	4	arises	arise	VERB
ap-610	116	5	not	not	PART
ap-610	116	6	only	only	ADV
ap-610	116	7	due	due	ADJ
ap-610	116	8	to	to	ADP
ap-610	116	9	the	the	DET
ap-610	116	10	discrete	discrete	ADJ
ap-610	116	11	character	character	NOUN
ap-610	116	12	of	of	ADP
ap-610	116	13	the	the	DET
ap-610	116	14	crystal	crystal	PROPN
ap-610	116	15	lattice	lattice	NOUN
ap-610	116	16	,	,	PUNCT
ap-610	116	17	but	but	CCONJ
ap-610	116	18	in	in	ADP
ap-610	116	19	general	general	ADJ
ap-610	116	20	due	due	ADP
ap-610	116	21	to	to	ADP
ap-610	116	22	any	any	DET
ap-610	116	23	type	type	NOUN
ap-610	116	24	of	of	ADP
ap-610	116	25	material	material	NOUN
ap-610	116	26	heterogeneity	heterogeneity	NOUN
ap-610	116	27	.	.	PUNCT
ap-610	117	1	leaving	leave	VERB
ap-610	117	2	aside	aside	ADP
ap-610	117	3	the	the	DET
ap-610	117	4	ideal	ideal	ADJ
ap-610	117	5	case	case	NOUN
ap-610	117	6	of	of	ADP
ap-610	117	7	a	a	DET
ap-610	117	8	perfect	perfect	ADJ
ap-610	117	9	monocrystal	monocrystal	ADJ
ap-610	117	10	,	,	PUNCT
ap-610	117	11	the	the	DET
ap-610	117	12	internal	internal	ADJ
ap-610	117	13	structure	structure	NOUN
ap-610	117	14	of	of	ADP
ap-610	117	15	all	all	DET
ap-610	117	16	materials	material	NOUN
ap-610	117	17	exhibits	exhibit	VERB
ap-610	117	18	heterogeneities	heterogeneity	NOUN
ap-610	117	19	on	on	ADP
ap-610	117	20	various	various	ADJ
ap-610	117	21	scales	scale	NOUN
ap-610	117	22	.	.	PUNCT
ap-610	118	1	some	some	DET
ap-610	118	2	defects	defect	NOUN
ap-610	118	3	in	in	ADP
ap-610	118	4	crystals	crystal	NOUN
ap-610	118	5	can	can	AUX
ap-610	118	6	still	still	ADV
ap-610	118	7	be	be	AUX
ap-610	118	8	treated	treat	VERB
ap-610	118	9	by	by	ADP
ap-610	118	10	atomistic	atomistic	ADJ
ap-610	118	11	models	model	NOUN
ap-610	118	12	,	,	PUNCT
ap-610	118	13	but	but	CCONJ
ap-610	118	14	in	in	ADP
ap-610	118	15	most	most	ADJ
ap-610	118	16	other	other	ADJ
ap-610	118	17	cases	case	NOUN
ap-610	118	18	the	the	DET
ap-610	118	19	material	material	NOUN
ap-610	118	20	needs	need	VERB
ap-610	118	21	to	to	PART
ap-610	118	22	be	be	AUX
ap-610	118	23	considered	consider	VERB
ap-610	118	24	as	as	ADP
ap-610	118	25	a	a	DET
ap-610	118	26	continuum	continuum	NOUN
ap-610	118	27	(	(	PUNCT
ap-610	118	28	because	because	SCONJ
ap-610	118	29	the	the	DET
ap-610	118	30	relevant	relevant	ADJ
ap-610	118	31	scale	scale	NOUN
ap-610	118	32	is	be	AUX
ap-610	118	33	already	already	ADV
ap-610	118	34	above	above	ADP
ap-610	118	35	the	the	DET
ap-610	118	36	atomistic	atomistic	ADJ
ap-610	118	37	one	one	NUM
ap-610	118	38	)	)	PUNCT
ap-610	118	39	with	with	ADP
ap-610	118	40	a	a	DET
ap-610	118	41	certain	certain	ADJ
ap-610	118	42	heterogeneous	heterogeneous	ADJ
ap-610	118	43	microstructure	microstructure	NOUN
ap-610	118	44	.	.	PUNCT
ap-610	119	1	for	for	ADP
ap-610	119	2	elastic	elastic	ADJ
ap-610	119	3	materials	material	NOUN
ap-610	119	4	,	,	PUNCT
ap-610	119	5	there	there	PRON
ap-610	119	6	exist	exist	VERB
ap-610	119	7	sophisticated	sophisticated	ADJ
ap-610	119	8	and	and	CCONJ
ap-610	119	9	mathematically	mathematically	ADV
ap-610	119	10	well	well	ADV
ap-610	119	11	-	-	PUNCT
ap-610	119	12	founded	found	VERB
ap-610	119	13	homogenization	homogenization	NOUN
ap-610	119	14	techniques	technique	NOUN
ap-610	119	15	providing	provide	VERB
ap-610	119	16	the	the	DET
ap-610	119	17	effective	effective	ADJ
ap-610	119	18	elastic	elastic	ADJ
ap-610	119	19	moduli	modulus	NOUN
ap-610	119	20	of	of	ADP
ap-610	119	21	a	a	DET
ap-610	119	22	homogeneous	homogeneous	ADJ
ap-610	119	23	material	material	NOUN
ap-610	119	24	that	that	PRON
ap-610	119	25	is	be	AUX
ap-610	119	26	in	in	ADP
ap-610	119	27	a	a	DET
ap-610	119	28	certain	certain	ADJ
ap-610	119	29	sense	sense	NOUN
ap-610	119	30	equivalent	equivalent	ADJ
ap-610	119	31	to	to	ADP
ap-610	119	32	the	the	DET
ap-610	119	33	heterogeneous	heterogeneous	ADJ
ap-610	119	34	one	one	NOUN
ap-610	119	35	and	and	CCONJ
ap-610	119	36	can	can	AUX
ap-610	119	37	replace	replace	VERB
ap-610	119	38	it	it	PRON
ap-610	119	39	in	in	ADP
ap-610	119	40	large	large	ADJ
ap-610	119	41	-	-	PUNCT
ap-610	119	42	scale	scale	NOUN
ap-610	119	43	simulations	simulation	NOUN
ap-610	119	44	.	.	PUNCT
ap-610	120	1	again	again	ADV
ap-610	120	2	,	,	PUNCT
ap-610	120	3	this	this	DET
ap-610	120	4	equivalence	equivalence	NOUN
ap-610	120	5	is	be	AUX
ap-610	120	6	limited	limit	VERB
ap-610	120	7	and	and	CCONJ
ap-610	120	8	holds	hold	VERB
ap-610	120	9	with	with	ADP
ap-610	120	10	reasonable	reasonable	ADJ
ap-610	120	11	accuracy	accuracy	NOUN
ap-610	120	12	for	for	ADP
ap-610	120	13	long	long	ADJ
ap-610	120	14	-	-	PUNCT
ap-610	120	15	wave	wave	NOUN
ap-610	120	16	phenomena	phenomenon	NOUN
ap-610	120	17	only	only	ADV
ap-610	120	18	.	.	PUNCT
ap-610	121	1	in	in	ADP
ap-610	121	2	the	the	DET
ap-610	121	3	present	present	ADJ
ap-610	121	4	context	context	NOUN
ap-610	121	5	,	,	PUNCT
ap-610	121	6	waves	wave	NOUN
ap-610	121	7	are	be	AUX
ap-610	121	8	considered	consider	VERB
ap-610	121	9	as	as	ADV
ap-610	121	10	long	long	ADV
ap-610	121	11	if	if	SCONJ
ap-610	121	12	the	the	DET
ap-610	121	13	wavelength	wavelength	NOUN
ap-610	121	14	is	be	AUX
ap-610	121	15	much	much	ADV
ap-610	121	16	larger	large	ADJ
ap-610	121	17	than	than	ADP
ap-610	121	18	the	the	DET
ap-610	121	19	characteristic	characteristic	ADJ
ap-610	121	20	size	size	NOUN
ap-610	121	21	of	of	ADP
ap-610	121	22	major	major	ADJ
ap-610	121	23	heterogeneous	heterogeneous	ADJ
ap-610	121	24	features	feature	NOUN
ap-610	121	25	in	in	ADP
ap-610	121	26	the	the	DET
ap-610	121	27	internal	internal	ADJ
ap-610	121	28	structure	structure	NOUN
ap-610	121	29	of	of	ADP
ap-610	121	30	the	the	DET
ap-610	121	31	material	material	NOUN
ap-610	121	32	.	.	PUNCT
ap-610	122	1	if	if	SCONJ
ap-610	122	2	there	there	PRON
ap-610	122	3	is	be	VERB
ap-610	122	4	a	a	DET
ap-610	122	5	need	need	NOUN
ap-610	122	6	to	to	PART
ap-610	122	7	describe	describe	VERB
ap-610	122	8	shorter	short	ADJ
ap-610	122	9	waves	wave	NOUN
ap-610	122	10	in	in	ADP
ap-610	122	11	a	a	DET
ap-610	122	12	realistic	realistic	ADJ
ap-610	122	13	manner	manner	NOUN
ap-610	122	14	,	,	PUNCT
ap-610	122	15	it	it	PRON
ap-610	122	16	is	be	AUX
ap-610	122	17	in	in	ADP
ap-610	122	18	principle	principle	NOUN
ap-610	122	19	possible	possible	ADJ
ap-610	122	20	to	to	PART
ap-610	122	21	explicitly	explicitly	ADV
ap-610	122	22	resolve	resolve	VERB
ap-610	122	23	the	the	DET
ap-610	122	24	details	detail	NOUN
ap-610	122	25	of	of	ADP
ap-610	122	26	the	the	DET
ap-610	122	27	heterogeneous	heterogeneous	ADJ
ap-610	122	28	internal	internal	ADJ
ap-610	122	29	structure	structure	NOUN
ap-610	122	30	,	,	PUNCT
ap-610	122	31	but	but	CCONJ
ap-610	122	32	this	this	DET
ap-610	122	33	approach	approach	NOUN
ap-610	122	34	often	often	ADV
ap-610	122	35	leads	lead	VERB
ap-610	122	36	to	to	ADP
ap-610	122	37	extreme	extreme	ADJ
ap-610	122	38	demands	demand	NOUN
ap-610	122	39	on	on	ADP
ap-610	122	40	the	the	DET
ap-610	122	41	computational	computational	ADJ
ap-610	122	42	resources	resource	NOUN
ap-610	122	43	.	.	PUNCT
ap-610	123	1	also	also	ADV
ap-610	123	2	,	,	PUNCT
ap-610	123	3	since	since	SCONJ
ap-610	123	4	the	the	DET
ap-610	123	5	particular	particular	ADJ
ap-610	123	6	microstructure	microstructure	NOUN
ap-610	123	7	is	be	AUX
ap-610	123	8	usually	usually	ADV
ap-610	123	9	not	not	PART
ap-610	123	10	known	know	VERB
ap-610	123	11	exactly	exactly	ADV
ap-610	123	12	but	but	CCONJ
ap-610	123	13	only	only	ADV
ap-610	123	14	in	in	ADP
ap-610	123	15	terms	term	NOUN
ap-610	123	16	of	of	ADP
ap-610	123	17	a	a	DET
ap-610	123	18	stochastic	stochastic	ADJ
ap-610	123	19	description	description	NOUN
ap-610	123	20	,	,	PUNCT
ap-610	123	21	the	the	DET
ap-610	123	22	method	method	NOUN
ap-610	123	23	of	of	ADP
ap-610	123	24	explicit	explicit	ADJ
ap-610	123	25	resolution	resolution	NOUN
ap-610	123	26	would	would	AUX
ap-610	123	27	need	need	VERB
ap-610	123	28	to	to	PART
ap-610	123	29	exploit	exploit	VERB
ap-610	123	30	a	a	DET
ap-610	123	31	monte	monte	NOUN
ap-610	123	32	-	-	PUNCT
ap-610	123	33	carlo	carlo	NOUN
ap-610	123	34	type	type	NOUN
ap-610	123	35	of	of	ADP
ap-610	123	36	technique	technique	NOUN
ap-610	123	37	or	or	CCONJ
ap-610	123	38	use	use	VERB
ap-610	123	39	stochastic	stochastic	ADJ
ap-610	123	40	differential	differential	ADJ
ap-610	123	41	equations	equation	NOUN
ap-610	123	42	,	,	PUNCT
ap-610	123	43	which	which	PRON
ap-610	123	44	again	again	ADV
ap-610	123	45	complicates	complicate	VERB
ap-610	123	46	the	the	DET
ap-610	123	47	procedure	procedure	NOUN
ap-610	123	48	and	and	CCONJ
ap-610	123	49	makes	make	VERB
ap-610	123	50	it	it	PRON
ap-610	123	51	computationally	computationally	ADV
ap-610	123	52	expensive	expensive	ADJ
ap-610	123	53	.	.	PUNCT
ap-610	124	1	as	as	ADP
ap-610	124	2	an	an	DET
ap-610	124	3	elegant	elegant	ADJ
ap-610	124	4	and	and	CCONJ
ap-610	124	5	efficient	efficient	ADJ
ap-610	124	6	alternative	alternative	NOUN
ap-610	124	7	,	,	PUNCT
ap-610	124	8	it	it	PRON
ap-610	124	9	is	be	AUX
ap-610	124	10	possible	possible	ADJ
ap-610	124	11	to	to	PART
ap-610	124	12	construct	construct	VERB
ap-610	124	13	enrichments	enrichment	NOUN
ap-610	124	14	of	of	ADP
ap-610	124	15	the	the	DET
ap-610	124	16	standard	standard	ADJ
ap-610	124	17	continuum	continuum	ADJ
ap-610	124	18	theory	theory	NOUN
ap-610	124	19	that	that	PRON
ap-610	124	20	reflect	reflect	VERB
ap-610	124	21	the	the	DET
ap-610	124	22	main	main	ADJ
ap-610	124	23	features	feature	NOUN
ap-610	124	24	of	of	ADP
ap-610	124	25	the	the	DET
ap-610	124	26	microstructure	microstructure	NOUN
ap-610	124	27	without	without	ADP
ap-610	124	28	using	use	VERB
ap-610	124	29	fast	fast	ADJ
ap-610	124	30	oscillating	oscillate	VERB
ap-610	124	31	material	material	NOUN
ap-610	124	32	properties	property	NOUN
ap-610	124	33	.	.	PUNCT
ap-610	125	1	in	in	ADP
ap-610	125	2	standard	standard	ADJ
ap-610	125	3	continuum	continuum	ADJ
ap-610	125	4	elasticity	elasticity	NOUN
ap-610	125	5	it	it	PRON
ap-610	125	6	is	be	AUX
ap-610	125	7	assumed	assume	VERB
ap-610	125	8	that	that	SCONJ
ap-610	125	9	the	the	DET
ap-610	125	10	density	density	NOUN
ap-610	125	11	of	of	ADP
ap-610	125	12	elastic	elastic	ADJ
ap-610	125	13	energy	energy	NOUN
ap-610	125	14	stored	store	VERB
ap-610	125	15	per	per	ADP
ap-610	125	16	unit	unit	NOUN
ap-610	125	17	volume	volume	NOUN
ap-610	125	18	,	,	PUNCT
ap-610	125	19	w	w	PROPN
ap-610	125	20	,	,	PUNCT
ap-610	125	21	depends	depend	VERB
ap-610	125	22	only	only	ADV
ap-610	125	23	on	on	ADP
ap-610	125	24	the	the	DET
ap-610	125	25	strain	strain	NOUN
ap-610	125	26	tensor	tensor	NOUN
ap-610	125	27	,	,	PUNCT
ap-610	125	28	which	which	PRON
ap-610	125	29	is	be	AUX
ap-610	125	30	directly	directly	ADV
ap-610	125	31	related	relate	VERB
ap-610	125	32	to	to	ADP
ap-610	125	33	the	the	DET
ap-610	125	34	deformation	deformation	NOUN
ap-610	125	35	gradient	gradient	NOUN
ap-610	125	36	,	,	PUNCT
ap-610	125	37	i.e.	i.e.	X
ap-610	125	38	,	,	PUNCT
ap-610	125	39	to	to	ADP
ap-610	125	40	the	the	DET
ap-610	125	41	first	first	ADJ
ap-610	125	42	gradient	gradient	NOUN
ap-610	125	43	of	of	ADP
ap-610	125	44	the	the	DET
ap-610	125	45	displacement	displacement	ADJ
ap-610	125	46	field	field	NOUN
ap-610	125	47	.	.	PUNCT
ap-610	126	1	the	the	DET
ap-610	126	2	elastic	elastic	ADJ
ap-610	126	3	energy	energy	NOUN
ap-610	126	4	stored	store	VERB
ap-610	126	5	by	by	ADP
ap-610	126	6	the	the	DET
ap-610	126	7	entire	entire	ADJ
ap-610	126	8	body	body	NOUN
ap-610	126	9	,	,	PUNCT
ap-610	126	10	w	w	PROPN
ap-610	126	11	,	,	PUNCT
ap-610	126	12	is	be	AUX
ap-610	126	13	then	then	ADV
ap-610	126	14	evaluated	evaluate	VERB
ap-610	126	15	as	as	ADP
ap-610	126	16	the	the	DET
ap-610	126	17	spatial	spatial	ADJ
ap-610	126	18	integral	integral	NOUN
ap-610	126	19	of	of	ADP
ap-610	126	20	the	the	DET
ap-610	126	21	elastic	elastic	ADJ
ap-610	126	22	energy	energy	NOUN
ap-610	126	23	density	density	NOUN
ap-610	126	24	.	.	PUNCT
ap-610	127	1	in	in	ADP
ap-610	127	2	the	the	DET
ap-610	127	3	one	one	NUM
ap-610	127	4	-	-	PUNCT
ap-610	127	5	dimensional	dimensional	ADJ
ap-610	127	6	setting	setting	NOUN
ap-610	127	7	,	,	PUNCT
ap-610	127	8	one	one	PRON
ap-610	127	9	can	can	AUX
ap-610	127	10	write	write	VERB
ap-610	127	11	w	w	PROPN
ap-610	127	12	w	w	PROPN
ap-610	127	13	u	u	PROPN
ap-610	127	14	x	x	SYM
ap-610	127	15	x	x	X
ap-610	127	16	l	l	X
ap-610	127	17	�	�	PROPN
ap-610	127	18	�	�	PROPN
ap-610	127	19	�	�	PROPN
ap-610	127	20	(	(	PUNCT
ap-610	127	21	(	(	PUNCT
ap-610	127	22	)	)	PUNCT
ap-610	127	23	)	)	PUNCT
ap-610	127	24	,	,	PUNCT
ap-610	128	1	d	d	X
ap-610	128	2	(	(	PUNCT
ap-610	128	3	12	12	NUM
ap-610	128	4	)	)	PUNCT
ap-610	128	5	where	where	SCONJ
ap-610	128	6	�	�	PROPN
ap-610	128	7	�	�	PROPN
ap-610	128	8	u	u	NOUN
ap-610	128	9	u	u	NOUN
ap-610	128	10	xd	xd	INTJ
ap-610	128	11	d	d	NOUN
ap-610	128	12	is	be	AUX
ap-610	128	13	the	the	DET
ap-610	128	14	strain	strain	NOUN
ap-610	128	15	,	,	PUNCT
ap-610	128	16	further	far	ADV
ap-610	128	17	denoted	denote	VERB
ap-610	128	18	as	as	ADP
ap-610	128	19	�	�	PROPN
ap-610	128	20	,	,	PUNCT
ap-610	128	21	and	and	CCONJ
ap-610	128	22	l	l	NOUN
ap-610	128	23	is	be	AUX
ap-610	128	24	the	the	DET
ap-610	128	25	interval	interval	NOUN
ap-610	128	26	representing	represent	VERB
ap-610	128	27	geometrically	geometrically	ADV
ap-610	128	28	the	the	DET
ap-610	128	29	one	one	NUM
ap-610	128	30	-	-	PUNCT
ap-610	128	31	dimensional	dimensional	ADJ
ap-610	128	32	body	body	NOUN
ap-610	128	33	.	.	PUNCT
ap-610	129	1	in	in	ADP
ap-610	129	2	linear	linear	PROPN
ap-610	129	3	elasticity	elasticity	NOUN
ap-610	129	4	,	,	PUNCT
ap-610	129	5	the	the	DET
ap-610	129	6	elastic	elastic	ADJ
ap-610	129	7	energy	energy	NOUN
ap-610	129	8	density	density	NOUN
ap-610	129	9	w	w	PROPN
ap-610	129	10	e	e	PROPN
ap-610	129	11	(	(	PUNCT
ap-610	129	12	)	)	PUNCT
ap-610	129	13	�	�	PROPN
ap-610	129	14	�	�	PROPN
ap-610	129	15	�	�	PROPN
ap-610	129	16	1	1	NUM
ap-610	129	17	2	2	NUM
ap-610	129	18	2	2	NUM
ap-610	129	19	(	(	PUNCT
ap-610	129	20	13	13	NUM
ap-610	129	21	)	)	PUNCT
ap-610	129	22	is	be	AUX
ap-610	129	23	a	a	DET
ap-610	129	24	quadratic	quadratic	ADJ
ap-610	129	25	function	function	NOUN
ap-610	129	26	of	of	ADP
ap-610	129	27	strain	strain	NOUN
ap-610	129	28	.	.	PUNCT
ap-610	130	1	one	one	NUM
ap-610	130	2	class	class	NOUN
ap-610	130	3	of	of	ADP
ap-610	130	4	enrichments	enrichment	NOUN
ap-610	130	5	is	be	AUX
ap-610	130	6	based	base	VERB
ap-610	130	7	on	on	ADP
ap-610	130	8	the	the	DET
ap-610	130	9	incorporation	incorporation	NOUN
ap-610	130	10	of	of	ADP
ap-610	130	11	higher	high	ADJ
ap-610	130	12	gradients	gradient	NOUN
ap-610	130	13	of	of	ADP
ap-610	130	14	the	the	DET
ap-610	130	15	displacement	displacement	ADJ
ap-610	130	16	field	field	NOUN
ap-610	130	17	(	(	PUNCT
ap-610	130	18	toupin	toupin	NOUN
ap-610	130	19	,	,	PUNCT
ap-610	130	20	1962;	1962;	PROPN
ap-610	130	21	mindlin	mindlin	PROPN
ap-610	130	22	1964	1964	NUM
ap-610	130	23	,	,	PUNCT
ap-610	130	24	1965	1965	NUM
ap-610	130	25	)	)	PUNCT
ap-610	130	26	.	.	PUNCT
ap-610	131	1	in	in	ADP
ap-610	131	2	general	general	ADJ
ap-610	131	3	,	,	PUNCT
ap-610	131	4	the	the	DET
ap-610	131	5	elastic	elastic	ADJ
ap-610	131	6	energy	energy	NOUN
ap-610	131	7	density	density	NOUN
ap-610	131	8	can	can	AUX
ap-610	131	9	be	be	AUX
ap-610	131	10	assumed	assume	VERB
ap-610	131	11	to	to	PART
ap-610	131	12	depend	depend	VERB
ap-610	131	13	on	on	ADP
ap-610	131	14	�	�	PROPN
ap-610	131	15	�	�	PROPN
ap-610	131	16	�	�	PROPN
ap-610	131	17	�	�	PROPN
ap-610	131	18	�	�	PROPN
ap-610	131	19	u	u	NOUN
ap-610	131	20	u	u	NOUN
ap-610	131	21	uiv	uiv	VERB
ap-610	131	22	,	,	PUNCT
ap-610	131	23	,	,	PUNCT
ap-610	131	24	,	,	PUNCT
ap-610	131	25	etc	etc	X
ap-610	131	26	.	.	X
ap-610	132	1	the	the	DET
ap-610	132	2	simplest	simple	ADJ
ap-610	132	3	strain	strain	NOUN
ap-610	132	4	-	-	PUNCT
ap-610	132	5	gradient	gradient	NOUN
ap-610	132	6	theory	theory	NOUN
ap-610	132	7	of	of	ADP
ap-610	132	8	elasticity	elasticity	NOUN
ap-610	132	9	uses	use	VERB
ap-610	132	10	enrichment	enrichment	NOUN
ap-610	132	11	by	by	ADP
ap-610	132	12	the	the	DET
ap-610	132	13	second	second	ADJ
ap-610	132	14	displacement	displacement	ADJ
ap-610	132	15	gradient	gradient	NOUN
ap-610	132	16	,	,	PUNCT
ap-610	132	17	�	�	PROPN
ap-610	132	18	�	�	NOUN
ap-610	132	19	u	u	PROPN
ap-610	132	20	,	,	PUNCT
ap-610	132	21	which	which	PRON
ap-610	132	22	is	be	AUX
ap-610	132	23	equal	equal	ADJ
ap-610	132	24	to	to	ADP
ap-610	132	25	the	the	DET
ap-610	132	26	strain	strain	NOUN
ap-610	132	27	gradient	gradient	NOUN
ap-610	132	28	,	,	PUNCT
ap-610	132	29	�	�	PROPN
ap-610	132	30	�	�	PROPN
ap-610	132	31	,	,	PUNCT
ap-610	132	32	further	far	ADV
ap-610	132	33	denoted	denote	VERB
ap-610	132	34	as	as	ADP
ap-610	132	35	�	�	PROPN
ap-610	132	36	.	.	PUNCT
ap-610	133	1	if	if	SCONJ
ap-610	133	2	we	we	PRON
ap-610	133	3	consider	consider	VERB
ap-610	133	4	one	one	NUM
ap-610	133	5	single	single	ADJ
ap-610	133	6	material	material	NOUN
ap-610	133	7	point	point	NOUN
ap-610	133	8	only	only	ADV
ap-610	133	9	,	,	PUNCT
ap-610	133	10	the	the	DET
ap-610	133	11	strain	strain	NOUN
ap-610	133	12	gradient	gradient	NOUN
ap-610	133	13	is	be	AUX
ap-610	133	14	locally	locally	ADV
ap-610	133	15	independent	independent	ADJ
ap-610	133	16	of	of	ADP
ap-610	133	17	the	the	DET
ap-610	133	18	strain	strain	NOUN
ap-610	133	19	value	value	NOUN
ap-610	133	20	.	.	PUNCT
ap-610	134	1	in	in	ADP
ap-610	134	2	the	the	DET
ap-610	134	3	linear	linear	ADJ
ap-610	134	4	case	case	NOUN
ap-610	134	5	,	,	PUNCT
ap-610	134	6	the	the	DET
ap-610	134	7	enriched	enrich	VERB
ap-610	134	8	elastic	elastic	ADJ
ap-610	134	9	energy	energy	NOUN
ap-610	134	10	density	density	NOUN
ap-610	134	11	potential	potential	NOUN
ap-610	134	12	is	be	AUX
ap-610	134	13	written	write	VERB
ap-610	134	14	as	as	ADP
ap-610	134	15	w	w	PROPN
ap-610	134	16	e	e	PROPN
ap-610	134	17	c	c	X
ap-610	134	18	(	(	PUNCT
ap-610	134	19	,	,	PUNCT
ap-610	134	20	)	)	PUNCT
ap-610	135	1	�	�	PROPN
ap-610	135	2	�	�	PROPN
ap-610	135	3	�	�	PROPN
ap-610	135	4	�	�	PROPN
ap-610	135	5	�	�	PROPN
ap-610	135	6	�	�	PROPN
ap-610	135	7	1	1	NUM
ap-610	135	8	2	2	NUM
ap-610	135	9	1	1	NUM
ap-610	135	10	2	2	NUM
ap-610	135	11	2	2	NUM
ap-610	135	12	2	2	NUM
ap-610	135	13	,	,	PUNCT
ap-610	135	14	(	(	PUNCT
ap-610	135	15	14	14	NUM
ap-610	135	16	)	)	PUNCT
ap-610	135	17	where	where	SCONJ
ap-610	135	18	c	c	NOUN
ap-610	135	19	is	be	AUX
ap-610	135	20	a	a	DET
ap-610	135	21	higher	high	ADJ
ap-610	135	22	-	-	PUNCT
ap-610	135	23	order	order	NOUN
ap-610	135	24	elastic	elastic	ADJ
ap-610	135	25	modulus	modulus	NOUN
ap-610	135	26	.	.	PUNCT
ap-610	136	1	the	the	DET
ap-610	136	2	variation	variation	NOUN
ap-610	136	3	of	of	ADP
ap-610	136	4	elastic	elastic	ADJ
ap-610	136	5	energy	energy	NOUN
ap-610	136	6	density	density	NOUN
ap-610	136	7	is	be	AUX
ap-610	136	8	given	give	VERB
ap-610	136	9	by	by	ADP
ap-610	136	10	�	�	PROPN
ap-610	136	11	�	�	PROPN
ap-610	136	12	�	�	PROPN
ap-610	136	13	�	�	PROPN
ap-610	136	14	�	�	PROPN
ap-610	136	15	�	�	PROPN
ap-610	136	16	�	�	PROPN
ap-610	136	17	�	�	PROPN
ap-610	136	18	�	�	PROPN
ap-610	136	19	�	�	PROPN
ap-610	136	20	�	�	PROPN
ap-610	136	21	�	�	PROPN
ap-610	136	22	w	w	PROPN
ap-610	136	23	w	w	PROPN
ap-610	136	24	w	w	PROPN
ap-610	136	25	�	�	PROPN
ap-610	136	26	�	�	PROPN
ap-610	136	27	�	�	PROPN
ap-610	136	28	�	�	PROPN
ap-610	136	29	,	,	PUNCT
ap-610	136	30	(	(	PUNCT
ap-610	136	31	15	15	NUM
ap-610	136	32	)	)	PUNCT
ap-610	136	33	where	where	SCONJ
ap-610	136	34	�	�	PROPN
ap-610	136	35	�	�	PROPN
ap-610	136	36	�	�	PROPN
ap-610	136	37	�	�	PROPN
ap-610	136	38	w	w	PROPN
ap-610	136	39	e	e	PROPN
ap-610	136	40	is	be	AUX
ap-610	136	41	the	the	DET
ap-610	136	42	(	(	PUNCT
ap-610	136	43	cauchy	cauchy	NOUN
ap-610	136	44	)	)	PUNCT
ap-610	136	45	stress	stress	NOUN
ap-610	136	46	and	and	CCONJ
ap-610	136	47	�	�	PROPN
ap-610	136	48	�	�	PROPN
ap-610	136	49	�	�	PROPN
ap-610	136	50	�	�	PROPN
ap-610	136	51	�	�	PROPN
ap-610	136	52	w	w	PROPN
ap-610	136	53	c	c	PROPN
ap-610	136	54	is	be	AUX
ap-610	136	55	the	the	DET
ap-610	136	56	so	so	ADV
ap-610	136	57	-	-	PUNCT
ap-610	136	58	called	call	VERB
ap-610	136	59	double	double	ADJ
ap-610	136	60	stress	stress	NOUN
ap-610	136	61	.	.	PUNCT
ap-610	137	1	based	base	VERB
ap-610	137	2	on	on	ADP
ap-610	137	3	the	the	DET
ap-610	137	4	extended	extended	ADJ
ap-610	137	5	form	form	NOUN
ap-610	137	6	of	of	ADP
ap-610	137	7	the	the	DET
ap-610	137	8	principle	principle	NOUN
ap-610	137	9	of	of	ADP
ap-610	137	10	virtual	virtual	ADJ
ap-610	137	11	work	work	NOUN
ap-610	137	12	,	,	PUNCT
ap-610	137	13	it	it	PRON
ap-610	137	14	is	be	AUX
ap-610	137	15	possible	possible	ADJ
ap-610	137	16	to	to	PART
ap-610	137	17	derive	derive	VERB
ap-610	137	18	the	the	DET
ap-610	137	19	static	static	ADJ
ap-610	137	20	equilibrium	equilibrium	NOUN
ap-610	137	21	equation	equation	NOUN
ap-610	137	22	(	(	PUNCT
ap-610	137	23	)	)	PUNCT
ap-610	137	24	�	�	PROPN
ap-610	137	25	�	�	PROPN
ap-610	137	26	�	�	PROPN
ap-610	137	27	�	�	PROPN
ap-610	137	28	�	�	PROPN
ap-610	137	29	�	�	PROPN
ap-610	137	30	b	b	PROPN
ap-610	137	31	0	0	NUM
ap-610	137	32	,	,	PUNCT
ap-610	137	33	(	(	PUNCT
ap-610	137	34	16	16	NUM
ap-610	137	35	)	)	PUNCT
ap-610	137	36	where	where	SCONJ
ap-610	137	37	b	b	NOUN
ap-610	137	38	is	be	AUX
ap-610	137	39	the	the	DET
ap-610	137	40	body	body	NOUN
ap-610	137	41	force	force	NOUN
ap-610	137	42	density	density	NOUN
ap-610	137	43	.	.	PUNCT
ap-610	138	1	in	in	ADP
ap-610	138	2	dynamics	dynamic	NOUN
ap-610	138	3	,	,	PUNCT
ap-610	138	4	b	b	PROPN
ap-610	138	5	is	be	AUX
ap-610	138	6	replaced	replace	VERB
ap-610	138	7	by	by	ADP
ap-610	138	8	the	the	DET
ap-610	138	9	inertial	inertial	ADJ
ap-610	138	10	force	force	NOUN
ap-610	138	11	density	density	NOUN
ap-610	138	12	,	,	PUNCT
ap-610	138	13	�	�	PROPN
ap-610	138	14	�	�	PROPN
ap-610	138	15	�	�	PROPN
ap-610	138	16	�	�	PROPN
ap-610	138	17	u.	u.	NOUN
ap-610	138	18	combining	combine	VERB
ap-610	138	19	this	this	PRON
ap-610	138	20	with	with	ADP
ap-610	138	21	the	the	DET
ap-610	138	22	constitutive	constitutive	ADJ
ap-610	138	23	equations	equation	NOUN
ap-610	138	24	�	�	PROPN
ap-610	138	25	�	�	PROPN
ap-610	138	26	e	e	PROPN
ap-610	138	27	and	and	CCONJ
ap-610	138	28	�	�	PROPN
ap-610	138	29	�	�	PROPN
ap-610	138	30	�	�	PROPN
ap-610	138	31	c	c	PROPN
ap-610	138	32	and	and	CCONJ
ap-610	138	33	with	with	ADP
ap-610	138	34	the	the	DET
ap-610	138	35	kinematic	kinematic	ADJ
ap-610	138	36	equations	equation	NOUN
ap-610	138	37	�	�	PROPN
ap-610	138	38	�	�	PROPN
ap-610	138	39	�	�	PROPN
ap-610	138	40	u	u	PROPN
ap-610	138	41	and	and	CCONJ
ap-610	138	42	�	�	PROPN
ap-610	138	43	�	�	PROPN
ap-610	138	44	�	�	PROPN
ap-610	138	45	�	�	PROPN
ap-610	138	46	u	u	NOUN
ap-610	138	47	,	,	PUNCT
ap-610	138	48	we	we	PRON
ap-610	138	49	obtain	obtain	VERB
ap-610	138	50	the	the	DET
ap-610	138	51	wave	wave	NOUN
ap-610	138	52	equation	equation	NOUN
ap-610	138	53	of	of	ADP
ap-610	138	54	strain	strain	NOUN
ap-610	138	55	-	-	PUNCT
ap-610	138	56	gradient	gradient	NOUN
ap-610	138	57	elasticity	elasticity	NOUN
ap-610	138	58	,	,	PUNCT
ap-610	138	59	©	©	PROPN
ap-610	138	60	czech	czech	PROPN
ap-610	138	61	technical	technical	PROPN
ap-610	138	62	university	university	PROPN
ap-610	138	63	publishing	publishing	NOUN
ap-610	138	64	house	house	NOUN
ap-610	138	65	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	138	66	19	19	NUM
ap-610	138	67	acta	acta	PROPN
ap-610	138	68	polytechnica	polytechnica	PROPN
ap-610	138	69	vol	vol	NOUN
ap-610	138	70	.	.	PROPN
ap-610	139	1	44	44	NUM
ap-610	140	1	no	no	NOUN
ap-610	140	2	.	.	PUNCT
ap-610	141	1	5–6/2004	5–6/2004	NUM
ap-610	141	2	�	�	PROPN
ap-610	141	3	�	�	PROPN
ap-610	141	4	�	�	PROPN
ap-610	141	5	u	u	ADJ
ap-610	141	6	eu	eu	PROPN
ap-610	141	7	cuiv	cuiv	PROPN
ap-610	141	8	�	�	PROPN
ap-610	141	9	�	�	PROPN
ap-610	141	10	�	�	PROPN
ap-610	141	11	�	�	PROPN
ap-610	141	12	�	�	PROPN
ap-610	141	13	0	0	NUM
ap-610	141	14	,	,	PUNCT
ap-610	141	15	(	(	PUNCT
ap-610	141	16	17	17	NUM
ap-610	141	17	)	)	PUNCT
ap-610	141	18	which	which	PRON
ap-610	141	19	differs	differ	VERB
ap-610	141	20	from	from	ADP
ap-610	141	21	the	the	DET
ap-610	141	22	standard	standard	ADJ
ap-610	141	23	wave	wave	NOUN
ap-610	141	24	equation	equation	NOUN
ap-610	141	25	(	(	PUNCT
ap-610	141	26	1	1	NUM
ap-610	141	27	)	)	PUNCT
ap-610	141	28	by	by	ADP
ap-610	141	29	the	the	DET
ap-610	141	30	presence	presence	NOUN
ap-610	141	31	of	of	ADP
ap-610	141	32	a	a	DET
ap-610	141	33	term	term	NOUN
ap-610	141	34	with	with	ADP
ap-610	141	35	the	the	DET
ap-610	141	36	fourth	fourth	ADJ
ap-610	141	37	spatial	spatial	ADJ
ap-610	141	38	derivative	derivative	NOUN
ap-610	141	39	of	of	ADP
ap-610	141	40	displacement	displacement	NOUN
ap-610	141	41	.	.	PUNCT
ap-610	142	1	substituting	substitute	VERB
ap-610	142	2	the	the	DET
ap-610	142	3	assumed	assume	VERB
ap-610	142	4	harmonic	harmonic	ADJ
ap-610	142	5	wave	wave	NOUN
ap-610	142	6	solution	solution	NOUN
ap-610	142	7	(	(	PUNCT
ap-610	142	8	2	2	NUM
ap-610	142	9	)	)	PUNCT
ap-610	142	10	into	into	ADP
ap-610	142	11	(	(	PUNCT
ap-610	142	12	17	17	NUM
ap-610	142	13	)	)	PUNCT
ap-610	142	14	,	,	PUNCT
ap-610	142	15	we	we	PRON
ap-610	142	16	obtain	obtain	VERB
ap-610	142	17	the	the	DET
ap-610	142	18	dispersion	dispersion	NOUN
ap-610	142	19	equation	equation	NOUN
ap-610	142	20	�	�	PROPN
ap-610	142	21	�	�	PROPN
ap-610	142	22	�	�	PROPN
ap-610	142	23	�	�	PROPN
ap-610	142	24	�	�	PROPN
ap-610	142	25	�	�	PROPN
ap-610	142	26	2	2	NUM
ap-610	142	27	2	2	NUM
ap-610	142	28	4	4	NUM
ap-610	142	29	0ek	0ek	NOUN
ap-610	142	30	ck	ck	INTJ
ap-610	142	31	(	(	PUNCT
ap-610	142	32	18	18	NUM
ap-610	142	33	)	)	PUNCT
ap-610	142	34	from	from	ADP
ap-610	142	35	which	which	PRON
ap-610	142	36	�	�	PROPN
ap-610	142	37	�	�	PROPN
ap-610	142	38	�	�	PROPN
ap-610	142	39	�	�	PROPN
ap-610	142	40	k	k	PROPN
ap-610	142	41	e	e	PROPN
ap-610	142	42	ck2	ck2	PROPN
ap-610	142	43	.	.	PUNCT
ap-610	143	1	(	(	PUNCT
ap-610	143	2	19	19	NUM
ap-610	143	3	)	)	PUNCT
ap-610	143	4	the	the	DET
ap-610	143	5	dispersion	dispersion	NOUN
ap-610	143	6	curve	curve	NOUN
ap-610	143	7	is	be	AUX
ap-610	143	8	plotted	plot	VERB
ap-610	143	9	in	in	ADP
ap-610	143	10	fig	fig	NOUN
ap-610	143	11	.	.	PUNCT
ap-610	144	1	3a	3a	NUM
ap-610	144	2	.	.	PUNCT
ap-610	145	1	the	the	DET
ap-610	145	2	phase	phase	NOUN
ap-610	145	3	velocity	velocity	NOUN
ap-610	145	4	c	c	NOUN
ap-610	146	1	k	k	PROPN
ap-610	146	2	e	e	PROPN
ap-610	146	3	ck	ck	PROPN
ap-610	146	4	p	p	PROPN
ap-610	146	5	�	�	PROPN
ap-610	146	6	�	�	PROPN
ap-610	146	7	�	�	PROPN
ap-610	146	8	�	�	PROPN
ap-610	146	9	�	�	PROPN
ap-610	146	10	2	2	NUM
ap-610	146	11	(	(	PUNCT
ap-610	146	12	20	20	NUM
ap-610	146	13	)	)	PUNCT
ap-610	146	14	is	be	AUX
ap-610	146	15	not	not	PART
ap-610	146	16	constant	constant	ADJ
ap-610	146	17	,	,	PUNCT
ap-610	146	18	except	except	SCONJ
ap-610	146	19	for	for	ADP
ap-610	146	20	the	the	DET
ap-610	146	21	case	case	NOUN
ap-610	146	22	when	when	SCONJ
ap-610	146	23	c	c	PROPN
ap-610	146	24	�	�	PROPN
ap-610	146	25	0	0	NUM
ap-610	146	26	and	and	CCONJ
ap-610	146	27	the	the	DET
ap-610	146	28	model	model	NOUN
ap-610	146	29	reduces	reduce	VERB
ap-610	146	30	to	to	ADP
ap-610	146	31	standard	standard	ADJ
ap-610	146	32	elasticity	elasticity	NOUN
ap-610	146	33	.	.	PUNCT
ap-610	147	1	in	in	ADP
ap-610	147	2	strain	strain	NOUN
ap-610	147	3	-	-	PUNCT
ap-610	147	4	gradient	gradient	NOUN
ap-610	147	5	elasticity	elasticity	NOUN
ap-610	147	6	it	it	PRON
ap-610	147	7	is	be	AUX
ap-610	147	8	usually	usually	ADV
ap-610	147	9	assumed	assume	VERB
ap-610	147	10	that	that	SCONJ
ap-610	147	11	the	the	DET
ap-610	147	12	higher	high	ADJ
ap-610	147	13	-	-	PUNCT
ap-610	147	14	order	order	NOUN
ap-610	147	15	modulus	modulus	NOUN
ap-610	147	16	c	c	NOUN
ap-610	147	17	is	be	AUX
ap-610	147	18	positive	positive	ADJ
ap-610	147	19	.	.	PUNCT
ap-610	148	1	this	this	DET
ap-610	148	2	assumption	assumption	NOUN
ap-610	148	3	leads	lead	VERB
ap-610	148	4	to	to	ADP
ap-610	148	5	a	a	DET
ap-610	148	6	convex	convex	ADJ
ap-610	148	7	energy	energy	NOUN
ap-610	148	8	potential	potential	NOUN
ap-610	148	9	and	and	CCONJ
ap-610	148	10	permits	permit	VERB
ap-610	148	11	to	to	PART
ap-610	148	12	generalize	generalize	VERB
ap-610	148	13	certain	certain	ADJ
ap-610	148	14	uniqueness	uniqueness	NOUN
ap-610	148	15	theorems	theorem	NOUN
ap-610	148	16	known	know	VERB
ap-610	148	17	from	from	ADP
ap-610	148	18	standard	standard	ADJ
ap-610	148	19	elasticity	elasticity	NOUN
ap-610	148	20	.	.	PUNCT
ap-610	149	1	however	however	ADV
ap-610	149	2	,	,	PUNCT
ap-610	149	3	for	for	ADP
ap-610	149	4	c	c	PROPN
ap-610	149	5	>	>	X
ap-610	149	6	0	0	PUNCT
ap-610	149	7	the	the	DET
ap-610	149	8	phase	phase	NOUN
ap-610	149	9	velocity	velocity	NOUN
ap-610	149	10	cp	cp	PROPN
ap-610	149	11	increases	increase	VERB
ap-610	149	12	with	with	ADP
ap-610	149	13	increasing	increase	VERB
ap-610	149	14	wave	wave	NOUN
ap-610	149	15	number	number	NOUN
ap-610	149	16	k.	k.	PROPN
ap-610	150	1	we	we	PRON
ap-610	150	2	have	have	AUX
ap-610	150	3	seen	see	VERB
ap-610	150	4	that	that	SCONJ
ap-610	150	5	the	the	DET
ap-610	150	6	discrete	discrete	ADJ
ap-610	150	7	mass	mass	ADJ
ap-610	150	8	-	-	PUNCT
ap-610	150	9	spring	spring	NOUN
ap-610	150	10	model	model	NOUN
ap-610	150	11	exhibits	exhibit	VERB
ap-610	150	12	the	the	DET
ap-610	150	13	opposite	opposite	ADJ
ap-610	150	14	trend	trend	NOUN
ap-610	150	15	,	,	PUNCT
ap-610	150	16	and	and	CCONJ
ap-610	150	17	this	this	PRON
ap-610	150	18	is	be	AUX
ap-610	150	19	also	also	ADV
ap-610	150	20	confirmed	confirm	VERB
ap-610	150	21	by	by	ADP
ap-610	150	22	measurements	measurement	NOUN
ap-610	150	23	of	of	ADP
ap-610	150	24	dispersion	dispersion	NOUN
ap-610	150	25	curves	curve	NOUN
ap-610	150	26	in	in	ADP
ap-610	150	27	real	real	ADJ
ap-610	150	28	crystals	crystal	NOUN
ap-610	150	29	.	.	PUNCT
ap-610	151	1	even	even	ADV
ap-610	151	2	for	for	ADP
ap-610	151	3	heterogeneous	heterogeneous	ADJ
ap-610	151	4	continua	continuum	NOUN
ap-610	151	5	,	,	PUNCT
ap-610	151	6	the	the	DET
ap-610	151	7	dispersion	dispersion	NOUN
ap-610	151	8	curves	curve	NOUN
ap-610	151	9	(	(	PUNCT
ap-610	151	10	determined	determine	VERB
ap-610	151	11	experimentally	experimentally	ADV
ap-610	151	12	or	or	CCONJ
ap-610	151	13	by	by	ADP
ap-610	151	14	analytical	analytical	ADJ
ap-610	151	15	solution	solution	NOUN
ap-610	151	16	of	of	ADP
ap-610	151	17	some	some	DET
ap-610	151	18	simple	simple	ADJ
ap-610	151	19	cases	case	NOUN
ap-610	151	20	)	)	PUNCT
ap-610	151	21	typically	typically	ADV
ap-610	151	22	have	have	VERB
ap-610	151	23	negative	negative	ADJ
ap-610	151	24	curvature	curvature	NOUN
ap-610	151	25	.	.	PUNCT
ap-610	152	1	so	so	ADV
ap-610	152	2	the	the	DET
ap-610	152	3	strain	strain	NOUN
ap-610	152	4	-	-	PUNCT
ap-610	152	5	gradient	gradient	NOUN
ap-610	152	6	theory	theory	NOUN
ap-610	152	7	gives	give	VERB
ap-610	152	8	a	a	DET
ap-610	152	9	reasonable	reasonable	ADJ
ap-610	152	10	approximation	approximation	NOUN
ap-610	152	11	of	of	ADP
ap-610	152	12	the	the	DET
ap-610	152	13	dispersion	dispersion	NOUN
ap-610	152	14	effect	effect	NOUN
ap-610	152	15	only	only	ADV
ap-610	152	16	if	if	SCONJ
ap-610	152	17	the	the	DET
ap-610	152	18	higher	high	ADJ
ap-610	152	19	-	-	PUNCT
ap-610	152	20	order	order	NOUN
ap-610	152	21	modulus	modulus	NOUN
ap-610	152	22	c	c	NOUN
ap-610	152	23	is	be	AUX
ap-610	152	24	negative	negative	ADJ
ap-610	152	25	.	.	PUNCT
ap-610	153	1	convexity	convexity	NOUN
ap-610	153	2	of	of	ADP
ap-610	153	3	the	the	DET
ap-610	153	4	elastic	elastic	ADJ
ap-610	153	5	potential	potential	NOUN
ap-610	153	6	is	be	AUX
ap-610	153	7	then	then	ADV
ap-610	153	8	lost	lose	VERB
ap-610	153	9	and	and	CCONJ
ap-610	153	10	uniqueness	uniqueness	NOUN
ap-610	153	11	can	can	AUX
ap-610	153	12	not	not	PART
ap-610	153	13	be	be	AUX
ap-610	153	14	guaranteed	guarantee	VERB
ap-610	153	15	.	.	PUNCT
ap-610	154	1	indeed	indeed	ADV
ap-610	154	2	,	,	PUNCT
ap-610	154	3	if	if	SCONJ
ap-610	154	4	c	c	PROPN
ap-610	154	5	el	el	PROPN
ap-610	154	6	�	�	PROPN
ap-610	154	7	�	�	PROPN
ap-610	154	8	2	2	NUM
ap-610	154	9	where	where	SCONJ
ap-610	154	10	l	l	NOUN
ap-610	154	11	is	be	AUX
ap-610	154	12	a	a	DET
ap-610	154	13	model	model	NOUN
ap-610	154	14	parameter	parameter	NOUN
ap-610	154	15	with	with	ADP
ap-610	154	16	the	the	DET
ap-610	154	17	dimension	dimension	NOUN
ap-610	154	18	of	of	ADP
ap-610	154	19	length	length	NOUN
ap-610	154	20	,	,	PUNCT
ap-610	154	21	the	the	DET
ap-610	154	22	phase	phase	NOUN
ap-610	154	23	velocity	velocity	NOUN
ap-610	154	24	of	of	ADP
ap-610	154	25	a	a	DET
ap-610	154	26	harmonic	harmonic	ADJ
ap-610	154	27	wave	wave	NOUN
ap-610	154	28	with	with	ADP
ap-610	154	29	wave	wave	NOUN
ap-610	154	30	number	number	NOUN
ap-610	154	31	k	k	PROPN
ap-610	154	32	lcrit	lcrit	PROPN
ap-610	154	33	�	�	PROPN
ap-610	154	34	1	1	NUM
ap-610	154	35	vanishes	vanish	VERB
ap-610	154	36	.	.	PUNCT
ap-610	155	1	this	this	PRON
ap-610	155	2	means	mean	VERB
ap-610	155	3	that	that	SCONJ
ap-610	155	4	the	the	DET
ap-610	155	5	equation	equation	NOUN
ap-610	155	6	of	of	ADP
ap-610	155	7	motion	motion	NOUN
ap-610	155	8	(	(	PUNCT
ap-610	155	9	17	17	NUM
ap-610	155	10	)	)	PUNCT
ap-610	155	11	is	be	AUX
ap-610	155	12	satisfied	satisfied	ADJ
ap-610	155	13	by	by	ADP
ap-610	155	14	a	a	DET
ap-610	155	15	stationary	stationary	ADJ
ap-610	155	16	wave	wave	NOUN
ap-610	155	17	of	of	ADP
ap-610	155	18	wavelength	wavelength	NOUN
ap-610	155	19	2	2	NUM
ap-610	155	20	2	2	NUM
ap-610	155	21	�	�	PROPN
ap-610	155	22	�	�	PROPN
ap-610	155	23	k	k	PROPN
ap-610	155	24	lcrit	lcrit	PROPN
ap-610	155	25	�	�	PROPN
ap-610	155	26	.	.	PUNCT
ap-610	156	1	a	a	DET
ap-610	156	2	similar	similar	ADJ
ap-610	156	3	result	result	NOUN
ap-610	156	4	was	be	AUX
ap-610	156	5	found	find	VERB
ap-610	156	6	for	for	ADP
ap-610	156	7	the	the	DET
ap-610	156	8	discrete	discrete	ADJ
ap-610	156	9	mass	mass	ADJ
ap-610	156	10	-	-	PUNCT
ap-610	156	11	spring	spring	NOUN
ap-610	156	12	model	model	NOUN
ap-610	156	13	,	,	PUNCT
ap-610	156	14	but	but	CCONJ
ap-610	156	15	in	in	ADP
ap-610	156	16	that	that	DET
ap-610	156	17	case	case	NOUN
ap-610	156	18	the	the	DET
ap-610	156	19	stationary	stationary	ADJ
ap-610	156	20	wave	wave	NOUN
ap-610	156	21	in	in	ADP
ap-610	156	22	reality	reality	NOUN
ap-610	156	23	represented	represent	VERB
ap-610	156	24	a	a	DET
ap-610	156	25	uniform	uniform	ADJ
ap-610	156	26	translation	translation	NOUN
ap-610	156	27	,	,	PUNCT
ap-610	156	28	because	because	SCONJ
ap-610	156	29	the	the	DET
ap-610	156	30	values	value	NOUN
ap-610	156	31	of	of	ADP
ap-610	156	32	the	the	DET
ap-610	156	33	displacements	displacement	NOUN
ap-610	156	34	had	have	VERB
ap-610	156	35	physical	physical	ADJ
ap-610	156	36	meaning	meaning	NOUN
ap-610	156	37	only	only	ADV
ap-610	156	38	at	at	ADP
ap-610	156	39	discrete	discrete	ADJ
ap-610	156	40	points	point	NOUN
ap-610	156	41	with	with	ADP
ap-610	156	42	spacing	space	VERB
ap-610	156	43	equal	equal	ADJ
ap-610	156	44	to	to	ADP
ap-610	156	45	the	the	DET
ap-610	156	46	critical	critical	ADJ
ap-610	156	47	wavelength	wavelength	NOUN
ap-610	156	48	.	.	PUNCT
ap-610	157	1	in	in	ADP
ap-610	157	2	contrast	contrast	NOUN
ap-610	157	3	to	to	ADP
ap-610	157	4	that	that	PRON
ap-610	157	5	,	,	PUNCT
ap-610	157	6	a	a	DET
ap-610	157	7	stationary	stationary	ADJ
ap-610	157	8	wave	wave	NOUN
ap-610	157	9	in	in	ADP
ap-610	157	10	a	a	DET
ap-610	157	11	continuous	continuous	ADJ
ap-610	157	12	elastic	elastic	ADJ
ap-610	157	13	medium	medium	NOUN
ap-610	157	14	is	be	AUX
ap-610	157	15	physically	physically	ADV
ap-610	157	16	inadmissible	inadmissible	ADJ
ap-610	157	17	.	.	PUNCT
ap-610	158	1	the	the	DET
ap-610	158	2	problem	problem	NOUN
ap-610	158	3	is	be	AUX
ap-610	158	4	aggravated	aggravate	VERB
ap-610	158	5	by	by	ADP
ap-610	158	6	the	the	DET
ap-610	158	7	fact	fact	NOUN
ap-610	158	8	that	that	SCONJ
ap-610	158	9	,	,	PUNCT
ap-610	158	10	for	for	ADP
ap-610	158	11	wave	wave	NOUN
ap-610	158	12	numbers	number	NOUN
ap-610	158	13	exceeding	exceed	VERB
ap-610	158	14	kcrit	kcrit	NOUN
ap-610	158	15	,	,	PUNCT
ap-610	158	16	the	the	DET
ap-610	158	17	circular	circular	ADJ
ap-610	158	18	frequency	frequency	NOUN
ap-610	158	19	�	�	PROPN
ap-610	158	20	solved	solve	VERB
ap-610	158	21	from	from	ADP
ap-610	158	22	the	the	DET
ap-610	158	23	dispersion	dispersion	NOUN
ap-610	158	24	equation	equation	NOUN
ap-610	158	25	(	(	PUNCT
ap-610	158	26	18	18	NUM
ap-610	158	27	)	)	PUNCT
ap-610	158	28	becomes	become	VERB
ap-610	158	29	imaginary	imaginary	ADJ
ap-610	158	30	.	.	PUNCT
ap-610	159	1	this	this	PRON
ap-610	159	2	means	mean	VERB
ap-610	159	3	that	that	SCONJ
ap-610	159	4	harmonic	harmonic	ADJ
ap-610	159	5	modes	mode	NOUN
ap-610	159	6	with	with	ADP
ap-610	159	7	wavelengths	wavelength	NOUN
ap-610	159	8	shorter	short	ADJ
ap-610	159	9	than	than	ADP
ap-610	159	10	2	2	NUM
ap-610	159	11	�	�	NOUN
ap-610	159	12	l	l	NOUN
ap-610	159	13	would	would	AUX
ap-610	159	14	spontaneously	spontaneously	ADV
ap-610	159	15	blow	blow	VERB
ap-610	159	16	up	up	ADP
ap-610	159	17	.	.	PUNCT
ap-610	160	1	the	the	DET
ap-610	160	2	source	source	NOUN
ap-610	160	3	of	of	ADP
ap-610	160	4	this	this	DET
ap-610	160	5	instability	instability	NOUN
ap-610	160	6	becomes	become	VERB
ap-610	160	7	apparent	apparent	ADJ
ap-610	160	8	if	if	SCONJ
ap-610	160	9	one	one	NOUN
ap-610	160	10	realizes	realize	VERB
ap-610	160	11	that	that	DET
ap-610	160	12	,	,	PUNCT
ap-610	160	13	for	for	ADP
ap-610	160	14	short	short	ADJ
ap-610	160	15	waves	wave	NOUN
ap-610	160	16	,	,	PUNCT
ap-610	160	17	the	the	DET
ap-610	160	18	negative	negative	ADJ
ap-610	160	19	higher	high	ADJ
ap-610	160	20	-	-	PUNCT
ap-610	160	21	order	order	NOUN
ap-610	160	22	part	part	NOUN
ap-610	160	23	the	the	DET
ap-610	160	24	elastic	elastic	ADJ
ap-610	160	25	energy	energy	NOUN
ap-610	160	26	,	,	PUNCT
ap-610	160	27	�	�	PROPN
ap-610	160	28	�	�	PROPN
ap-610	160	29	�	�	PROPN
ap-610	160	30	el	el	PROPN
ap-610	160	31	u2	u2	PROPN
ap-610	160	32	2	2	NUM
ap-610	160	33	(	(	PUNCT
ap-610	160	34	)	)	PUNCT
ap-610	160	35	,	,	PUNCT
ap-610	160	36	exceeds	exceed	NOUN
ap-610	160	37	in	in	ADP
ap-610	160	38	magnitude	magnitude	NOUN
ap-610	160	39	the	the	DET
ap-610	160	40	positive	positive	ADJ
ap-610	160	41	standard	standard	ADJ
ap-610	160	42	part	part	NOUN
ap-610	160	43	,	,	PUNCT
ap-610	160	44	e	e	X
ap-610	160	45	u	u	PROPN
ap-610	160	46	(	(	PUNCT
ap-610	160	47	)	)	PUNCT
ap-610	160	48	�	�	PROPN
ap-610	160	49	2	2	NUM
ap-610	160	50	,	,	PUNCT
ap-610	160	51	and	and	CCONJ
ap-610	160	52	so	so	ADV
ap-610	160	53	the	the	DET
ap-610	160	54	total	total	ADJ
ap-610	160	55	energy	energy	NOUN
ap-610	160	56	density	density	NOUN
ap-610	160	57	becomes	become	VERB
ap-610	160	58	negative	negative	ADJ
ap-610	160	59	.	.	PUNCT
ap-610	161	1	if	if	SCONJ
ap-610	161	2	the	the	DET
ap-610	161	3	amplitude	amplitude	NOUN
ap-610	161	4	of	of	ADP
ap-610	161	5	the	the	DET
ap-610	161	6	wave	wave	NOUN
ap-610	161	7	grows	grow	VERB
ap-610	161	8	,	,	PUNCT
ap-610	161	9	energy	energy	NOUN
ap-610	161	10	is	be	AUX
ap-610	161	11	released	release	VERB
ap-610	161	12	instead	instead	ADV
ap-610	161	13	of	of	ADP
ap-610	161	14	being	be	AUX
ap-610	161	15	consumed	consume	VERB
ap-610	161	16	.	.	PUNCT
ap-610	162	1	2.3	2.3	NUM
ap-610	162	2	models	model	NOUN
ap-610	162	3	with	with	ADP
ap-610	162	4	mixed	mixed	ADJ
ap-610	162	5	spatial	spatial	ADJ
ap-610	162	6	-	-	PUNCT
ap-610	162	7	temporal	temporal	ADJ
ap-610	162	8	derivatives	derivative	NOUN
ap-610	162	9	due	due	ADP
ap-610	162	10	to	to	ADP
ap-610	162	11	the	the	DET
ap-610	162	12	unstable	unstable	ADJ
ap-610	162	13	behavior	behavior	NOUN
ap-610	162	14	of	of	ADP
ap-610	162	15	short	short	ADJ
ap-610	162	16	waves	wave	NOUN
ap-610	162	17	,	,	PUNCT
ap-610	162	18	equation	equation	NOUN
ap-610	162	19	(	(	PUNCT
ap-610	162	20	17	17	NUM
ap-610	162	21	)	)	PUNCT
ap-610	162	22	is	be	AUX
ap-610	162	23	sometimes	sometimes	ADV
ap-610	162	24	called	call	VERB
ap-610	162	25	the	the	DET
ap-610	162	26	“	"	PUNCT
ap-610	162	27	bad	bad	ADJ
ap-610	162	28	boussinesq	boussinesq	NOUN
ap-610	162	29	problem	problem	NOUN
ap-610	162	30	”	"	PUNCT
ap-610	162	31	.	.	PUNCT
ap-610	163	1	this	this	DET
ap-610	163	2	equation	equation	NOUN
ap-610	163	3	can	can	AUX
ap-610	163	4	describe	describe	VERB
ap-610	163	5	dispersion	dispersion	NOUN
ap-610	163	6	of	of	ADP
ap-610	163	7	waves	wave	NOUN
ap-610	163	8	with	with	ADP
ap-610	163	9	“	"	PUNCT
ap-610	163	10	moderate	moderate	ADJ
ap-610	163	11	”	"	PUNCT
ap-610	163	12	wave	wave	NOUN
ap-610	163	13	numbers	number	NOUN
ap-610	163	14	but	but	CCONJ
ap-610	163	15	leads	lead	VERB
ap-610	163	16	to	to	ADP
ap-610	163	17	instabilities	instability	NOUN
ap-610	163	18	if	if	SCONJ
ap-610	163	19	waves	wave	NOUN
ap-610	163	20	shorter	short	ADJ
ap-610	163	21	than	than	ADP
ap-610	163	22	the	the	DET
ap-610	163	23	critical	critical	ADJ
ap-610	163	24	wavelength	wavelength	NOUN
ap-610	163	25	2	2	NUM
ap-610	163	26	�	�	NOUN
ap-610	163	27	l	l	NOUN
ap-610	163	28	are	be	AUX
ap-610	163	29	involved	involve	VERB
ap-610	163	30	.	.	PUNCT
ap-610	164	1	if	if	SCONJ
ap-610	164	2	the	the	DET
ap-610	164	3	body	body	NOUN
ap-610	164	4	of	of	ADP
ap-610	164	5	interest	interest	NOUN
ap-610	164	6	is	be	AUX
ap-610	164	7	discretized	discretize	VERB
ap-610	164	8	by	by	ADP
ap-610	164	9	finite	finite	ADJ
ap-610	164	10	elements	element	NOUN
ap-610	164	11	,	,	PUNCT
ap-610	164	12	the	the	DET
ap-610	164	13	minimum	minimum	ADJ
ap-610	164	14	wavelength	wavelength	NOUN
ap-610	164	15	that	that	PRON
ap-610	164	16	can	can	AUX
ap-610	164	17	be	be	AUX
ap-610	164	18	captured	capture	VERB
ap-610	164	19	by	by	ADP
ap-610	164	20	the	the	DET
ap-610	164	21	numerical	numerical	ADJ
ap-610	164	22	approximation	approximation	NOUN
ap-610	164	23	is	be	AUX
ap-610	164	24	proportional	proportional	ADJ
ap-610	164	25	to	to	ADP
ap-610	164	26	the	the	DET
ap-610	164	27	element	element	NOUN
ap-610	164	28	size	size	NOUN
ap-610	164	29	.	.	PUNCT
ap-610	165	1	therefore	therefore	ADV
ap-610	165	2	,	,	PUNCT
ap-610	165	3	for	for	ADP
ap-610	165	4	meshes	mesh	NOUN
ap-610	165	5	that	that	PRON
ap-610	165	6	are	be	AUX
ap-610	165	7	sufficiently	sufficiently	ADV
ap-610	165	8	coarse	coarse	ADJ
ap-610	165	9	with	with	ADP
ap-610	165	10	respect	respect	NOUN
ap-610	165	11	to	to	ADP
ap-610	165	12	the	the	DET
ap-610	165	13	material	material	NOUN
ap-610	165	14	length	length	NOUN
ap-610	165	15	parameter	parameter	PROPN
ap-610	165	16	l	l	PROPN
ap-610	165	17	,	,	PUNCT
ap-610	165	18	the	the	DET
ap-610	165	19	numerical	numerical	ADJ
ap-610	165	20	solution	solution	NOUN
ap-610	165	21	leads	lead	VERB
ap-610	165	22	to	to	ADP
ap-610	165	23	reasonable	reasonable	ADJ
ap-610	165	24	results	result	NOUN
ap-610	165	25	.	.	PUNCT
ap-610	166	1	however	however	ADV
ap-610	166	2	,	,	PUNCT
ap-610	166	3	upon	upon	SCONJ
ap-610	166	4	mesh	mesh	NOUN
ap-610	166	5	refinement	refinement	NOUN
ap-610	166	6	,	,	PUNCT
ap-610	166	7	the	the	DET
ap-610	166	8	solution	solution	NOUN
ap-610	166	9	becomes	becomes	AUX
ap-610	166	10	polluted	pollute	VERB
ap-610	166	11	by	by	ADP
ap-610	166	12	unstable	unstable	ADJ
ap-610	166	13	modes	mode	NOUN
ap-610	166	14	rapidly	rapidly	ADV
ap-610	166	15	oscillating	oscillate	VERB
ap-610	166	16	in	in	ADP
ap-610	166	17	space	space	NOUN
ap-610	166	18	.	.	PUNCT
ap-610	167	1	several	several	ADJ
ap-610	167	2	modifications	modification	NOUN
ap-610	167	3	of	of	ADP
ap-610	167	4	the	the	DET
ap-610	167	5	bad	bad	ADJ
ap-610	167	6	boussinesq	boussinesq	ADJ
ap-610	167	7	problem	problem	NOUN
ap-610	167	8	were	be	AUX
ap-610	167	9	proposed	propose	VERB
ap-610	167	10	in	in	ADP
ap-610	167	11	the	the	DET
ap-610	167	12	literature	literature	NOUN
ap-610	167	13	.	.	PUNCT
ap-610	168	1	fish	fish	NOUN
ap-610	168	2	,	,	PUNCT
ap-610	168	3	chen	chen	PROPN
ap-610	168	4	and	and	CCONJ
ap-610	168	5	nagai	nagai	PROPN
ap-610	168	6	(	(	PUNCT
ap-610	168	7	2002a	2002a	NUM
ap-610	168	8	)	)	PUNCT
ap-610	168	9	replaced	replace	VERB
ap-610	168	10	the	the	DET
ap-610	168	11	term	term	NOUN
ap-610	168	12	with	with	ADP
ap-610	168	13	the	the	DET
ap-610	168	14	fourth	fourth	ADJ
ap-610	168	15	spatial	spatial	ADJ
ap-610	168	16	derivative	derivative	NOUN
ap-610	168	17	,	,	PUNCT
ap-610	168	18	uiv	uiv	INTJ
ap-610	168	19	,	,	PUNCT
ap-610	168	20	by	by	ADP
ap-610	168	21	a	a	DET
ap-610	168	22	term	term	NOUN
ap-610	168	23	with	with	ADP
ap-610	168	24	a	a	DET
ap-610	168	25	mixed	mixed	ADJ
ap-610	168	26	derivative	derivative	ADJ
ap-610	168	27	,	,	PUNCT
ap-610	168	28	�	�	PROPN
ap-610	168	29	�	�	PROPN
ap-610	168	30	�	�	PROPN
ap-610	168	31	�	�	NOUN
ap-610	168	32	u	u	NOUN
ap-610	168	33	.	.	PUNCT
ap-610	169	1	their	their	PRON
ap-610	169	2	arguments	argument	NOUN
ap-610	169	3	can	can	AUX
ap-610	169	4	be	be	AUX
ap-610	169	5	rephrased	rephrase	VERB
ap-610	169	6	and	and	CCONJ
ap-610	169	7	expanded	expand	VERB
ap-610	169	8	as	as	SCONJ
ap-610	169	9	follows	follow	VERB
ap-610	169	10	:	:	PUNCT
ap-610	169	11	for	for	ADP
ap-610	169	12	small	small	ADJ
ap-610	169	13	wave	wave	NOUN
ap-610	169	14	numbers	number	NOUN
ap-610	169	15	,	,	PUNCT
ap-610	169	16	the	the	DET
ap-610	169	17	fourth	fourth	ADJ
ap-610	169	18	-	-	PUNCT
ap-610	169	19	order	order	NOUN
ap-610	169	20	term	term	NOUN
ap-610	169	21	in	in	ADP
ap-610	169	22	(	(	PUNCT
ap-610	169	23	17	17	NUM
ap-610	169	24	)	)	PUNCT
ap-610	169	25	is	be	AUX
ap-610	169	26	negligible	negligible	ADJ
ap-610	169	27	with	with	ADP
ap-610	169	28	respect	respect	NOUN
ap-610	169	29	to	to	ADP
ap-610	169	30	the	the	DET
ap-610	169	31	second	second	ADJ
ap-610	169	32	-	-	PUNCT
ap-610	169	33	order	order	NOUN
ap-610	169	34	terms	term	NOUN
ap-610	169	35	,	,	PUNCT
ap-610	169	36	so	so	SCONJ
ap-610	169	37	we	we	PRON
ap-610	169	38	can	can	AUX
ap-610	169	39	write	write	VERB
ap-610	169	40	eu	eu	PROPN
ap-610	169	41	u	u	PROPN
ap-610	169	42	�	�	PROPN
ap-610	169	43	�	�	PROPN
ap-610	169	44	�	�	PROPN
ap-610	169	45	�	�	PROPN
ap-610	169	46	�	�	PROPN
ap-610	169	47	.	.	PUNCT
ap-610	169	48	differentiating	differentiate	VERB
ap-610	169	49	this	this	PRON
ap-610	169	50	twice	twice	ADV
ap-610	169	51	with	with	ADP
ap-610	169	52	respect	respect	NOUN
ap-610	169	53	to	to	ADP
ap-610	169	54	x	x	SYM
ap-610	169	55	,	,	PUNCT
ap-610	169	56	we	we	PRON
ap-610	169	57	obtain	obtain	VERB
ap-610	169	58	eu	eu	PROPN
ap-610	169	59	uiv	uiv	PROPN
ap-610	169	60	�	�	PROPN
ap-610	169	61	�	�	PROPN
ap-610	169	62	�	�	PROPN
ap-610	169	63	�	�	PROPN
ap-610	169	64	�	�	PROPN
ap-610	169	65	.	.	PUNCT
ap-610	170	1	finally	finally	ADV
ap-610	170	2	,	,	PUNCT
ap-610	170	3	replacing	replace	VERB
ap-610	170	4	in	in	ADP
ap-610	170	5	(	(	PUNCT
ap-610	170	6	17	17	NUM
ap-610	170	7	)	)	PUNCT
ap-610	170	8	uiv	uiv	INTJ
ap-610	170	9	by	by	ADP
ap-610	170	10	(	(	PUNCT
ap-610	170	11	)	)	PUNCT
ap-610	170	12	�	�	PROPN
ap-610	170	13	�	�	PROPN
ap-610	170	14	�	�	PROPN
ap-610	170	15	e	e	PROPN
ap-610	170	16	u	u	NOUN
ap-610	170	17	�	�	PROPN
ap-610	170	18	�	�	PROPN
ap-610	170	19	and	and	CCONJ
ap-610	170	20	c	c	PROPN
ap-610	170	21	by	by	ADP
ap-610	170	22	�	�	PROPN
ap-610	170	23	el2	el2	PROPN
ap-610	170	24	yields	yield	VERB
ap-610	170	25	a	a	DET
ap-610	170	26	modified	modify	VERB
ap-610	170	27	wave	wave	NOUN
ap-610	170	28	equation	equation	NOUN
ap-610	170	29	�	�	PROPN
ap-610	170	30	�	�	PROPN
ap-610	170	31	�	�	PROPN
ap-610	170	32	�	�	PROPN
ap-610	170	33	�	�	PROPN
ap-610	170	34	�	�	PROPN
ap-610	170	35	u	u	NOUN
ap-610	170	36	eu	eu	PROPN
ap-610	170	37	l	l	PROPN
ap-610	170	38	u	u	PROPN
ap-610	170	39	�	�	PROPN
ap-610	170	40	�	�	PROPN
ap-610	170	41	�	�	PROPN
ap-610	170	42	�	�	PROPN
ap-610	170	43	�	�	PROPN
ap-610	170	44	�	�	PROPN
ap-610	170	45	�	�	PROPN
ap-610	170	46	2	2	NUM
ap-610	170	47	0	0	NUM
ap-610	170	48	(	(	PUNCT
ap-610	170	49	21	21	NUM
ap-610	170	50	)	)	PUNCT
ap-610	170	51	20	20	NUM
ap-610	170	52	©	©	PROPN
ap-610	170	53	czech	czech	PROPN
ap-610	170	54	technical	technical	PROPN
ap-610	170	55	university	university	PROPN
ap-610	170	56	publishing	publishing	NOUN
ap-610	170	57	house	house	NOUN
ap-610	170	58	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	170	59	acta	acta	PROPN
ap-610	170	60	polytechnica	polytechnica	PROPN
ap-610	170	61	vol	vol	NOUN
ap-610	170	62	.	.	PROPN
ap-610	171	1	44	44	NUM
ap-610	171	2	no	no	NOUN
ap-610	171	3	.	.	PUNCT
ap-610	172	1	5–6/2004	5–6/2004	NUM
ap-610	172	2	(	(	PUNCT
ap-610	172	3	a	a	NOUN
ap-610	172	4	)	)	PUNCT
ap-610	172	5	(	(	PUNCT
ap-610	172	6	b	b	X
ap-610	172	7	)	)	PUNCT
ap-610	172	8	fig	fig	NOUN
ap-610	172	9	.	.	PUNCT
ap-610	173	1	3	3	NUM
ap-610	173	2	:	:	PUNCT
ap-610	173	3	dispersion	dispersion	NOUN
ap-610	173	4	curves	curve	NOUN
ap-610	173	5	of	of	ADP
ap-610	173	6	(	(	PUNCT
ap-610	173	7	a	a	DET
ap-610	173	8	)	)	PUNCT
ap-610	173	9	strain	strain	NOUN
ap-610	173	10	-	-	PUNCT
ap-610	173	11	gradient	gradient	NOUN
ap-610	173	12	elasticity	elasticity	NOUN
ap-610	173	13	and	and	CCONJ
ap-610	173	14	gradient	gradient	NOUN
ap-610	173	15	models	model	NOUN
ap-610	173	16	with	with	ADP
ap-610	173	17	mixed	mixed	ADJ
ap-610	173	18	derivatives	derivative	NOUN
ap-610	173	19	,	,	PUNCT
ap-610	173	20	(	(	PUNCT
ap-610	173	21	b	b	X
ap-610	173	22	)	)	PUNCT
ap-610	173	23	nonlocal	nonlocal	ADJ
ap-610	173	24	elastic	elastic	ADJ
ap-610	173	25	models	model	NOUN
ap-610	173	26	with	with	ADP
ap-610	173	27	different	different	ADJ
ap-610	173	28	weight	weight	NOUN
ap-610	173	29	functions	function	NOUN
ap-610	173	30	;	;	PUNCT
ap-610	173	31	the	the	DET
ap-610	173	32	normalized	normalize	VERB
ap-610	173	33	circular	circular	ADJ
ap-610	173	34	frequency	frequency	NOUN
ap-610	173	35	is	be	AUX
ap-610	173	36	�	�	PROPN
ap-610	173	37	l	l	NOUN
ap-610	173	38	c0	c0	NOUN
ap-610	173	39	in	in	ADP
ap-610	173	40	case	case	NOUN
ap-610	173	41	(	(	PUNCT
ap-610	173	42	a	a	X
ap-610	173	43	)	)	PUNCT
ap-610	173	44	and	and	CCONJ
ap-610	173	45	�	�	PROPN
ap-610	173	46	a	a	DET
ap-610	173	47	c0	c0	NOUN
ap-610	173	48	in	in	ADP
ap-610	173	49	case	case	NOUN
ap-610	173	50	(	(	PUNCT
ap-610	173	51	b	b	NOUN
ap-610	173	52	)	)	PUNCT
ap-610	173	53	,	,	PUNCT
ap-610	173	54	and	and	CCONJ
ap-610	173	55	the	the	DET
ap-610	173	56	normalized	normalize	VERB
ap-610	173	57	wave	wave	NOUN
ap-610	173	58	number	number	NOUN
ap-610	173	59	is	be	AUX
ap-610	173	60	kl	kl	PROPN
ap-610	173	61	in	in	ADP
ap-610	173	62	case	case	NOUN
ap-610	173	63	(	(	PUNCT
ap-610	173	64	a	a	X
ap-610	173	65	)	)	PUNCT
ap-610	173	66	and	and	CCONJ
ap-610	173	67	ka	ka	PROPN
ap-610	173	68	�	�	PROPN
ap-610	173	69	in	in	ADP
ap-610	173	70	case	case	NOUN
ap-610	173	71	(	(	PUNCT
ap-610	173	72	b	b	NOUN
ap-610	173	73	)	)	PUNCT
ap-610	173	74	which	which	PRON
ap-610	173	75	was	be	AUX
ap-610	173	76	called	call	VERB
ap-610	173	77	by	by	ADP
ap-610	173	78	fish	fish	NOUN
ap-610	173	79	et	et	PROPN
ap-610	173	80	al	al	PROPN
ap-610	173	81	.	.	PROPN
ap-610	173	82	(	(	PUNCT
ap-610	173	83	2002a	2002a	NUM
ap-610	173	84	)	)	PUNCT
ap-610	173	85	the	the	DET
ap-610	173	86	“	"	PUNCT
ap-610	173	87	good	good	ADJ
ap-610	173	88	boussinesq	boussinesq	ADJ
ap-610	173	89	problem	problem	NOUN
ap-610	173	90	”	"	PUNCT
ap-610	173	91	.	.	PUNCT
ap-610	174	1	this	this	DET
ap-610	174	2	problem	problem	NOUN
ap-610	174	3	can	can	AUX
ap-610	174	4	be	be	AUX
ap-610	174	5	expected	expect	VERB
ap-610	174	6	to	to	PART
ap-610	174	7	have	have	VERB
ap-610	174	8	similar	similar	ADJ
ap-610	174	9	solutions	solution	NOUN
ap-610	174	10	to	to	ADP
ap-610	174	11	the	the	DET
ap-610	174	12	original	original	ADJ
ap-610	174	13	bad	bad	ADJ
ap-610	174	14	boussinesq	boussinesq	ADJ
ap-610	174	15	problem	problem	NOUN
ap-610	174	16	(	(	PUNCT
ap-610	174	17	17	17	NUM
ap-610	174	18	)	)	PUNCT
ap-610	174	19	at	at	ADP
ap-610	174	20	low	low	ADJ
ap-610	174	21	wave	wave	NOUN
ap-610	174	22	numbers	number	NOUN
ap-610	174	23	but	but	CCONJ
ap-610	174	24	a	a	DET
ap-610	174	25	different	different	ADJ
ap-610	174	26	asymptotic	asymptotic	ADJ
ap-610	174	27	behavior	behavior	NOUN
ap-610	174	28	for	for	ADP
ap-610	174	29	high	high	ADJ
ap-610	174	30	wave	wave	NOUN
ap-610	174	31	numbers	number	NOUN
ap-610	174	32	.	.	PUNCT
ap-610	175	1	indeed	indeed	ADV
ap-610	175	2	,	,	PUNCT
ap-610	175	3	the	the	DET
ap-610	175	4	usual	usual	ADJ
ap-610	175	5	procedure	procedure	NOUN
ap-610	175	6	leads	lead	VERB
ap-610	175	7	to	to	ADP
ap-610	175	8	the	the	DET
ap-610	175	9	dispersion	dispersion	NOUN
ap-610	175	10	equation	equation	NOUN
ap-610	175	11	�	�	PROPN
ap-610	175	12	�	�	PROPN
ap-610	175	13	�	�	PROPN
ap-610	175	14	�	�	PROPN
ap-610	175	15	�	�	PROPN
ap-610	175	16	�	�	PROPN
ap-610	175	17	�	�	PROPN
ap-610	175	18	�	�	PROPN
ap-610	175	19	2	2	NUM
ap-610	175	20	2	2	NUM
ap-610	175	21	2	2	NUM
ap-610	175	22	2	2	NUM
ap-610	175	23	2	2	NUM
ap-610	175	24	0ek	0ek	NOUN
ap-610	175	25	l	l	NOUN
ap-610	176	1	k	k	X
ap-610	177	1	(	(	PUNCT
ap-610	177	2	22	22	NUM
ap-610	177	3	)	)	PUNCT
ap-610	177	4	from	from	ADP
ap-610	177	5	which	which	PRON
ap-610	177	6	c	c	NOUN
ap-610	178	1	k	k	PROPN
ap-610	178	2	e	e	PROPN
ap-610	178	3	k	k	PROPN
ap-610	178	4	l	l	PROPN
ap-610	178	5	c	c	PROPN
ap-610	179	1	k	k	PROPN
ap-610	179	2	l	l	PROPN
ap-610	179	3	p	p	PROPN
ap-610	179	4	�	�	PROPN
ap-610	179	5	�	�	PROPN
ap-610	179	6	�	�	PROPN
ap-610	179	7	�	�	PROPN
ap-610	179	8	�	�	PROPN
ap-610	179	9	�	�	PROPN
ap-610	179	10	�	�	PROPN
ap-610	179	11	(	(	PUNCT
ap-610	179	12	)	)	PUNCT
ap-610	179	13	1	1	NUM
ap-610	179	14	1	1	NUM
ap-610	179	15	2	2	NUM
ap-610	179	16	2	2	NUM
ap-610	179	17	0	0	NUM
ap-610	179	18	2	2	NUM
ap-610	179	19	2	2	NUM
ap-610	179	20	.	.	PUNCT
ap-610	180	1	(	(	PUNCT
ap-610	180	2	23	23	NUM
ap-610	180	3	)	)	PUNCT
ap-610	180	4	for	for	ADP
ap-610	180	5	this	this	DET
ap-610	180	6	model	model	NOUN
ap-610	180	7	with	with	ADP
ap-610	180	8	enrichment	enrichment	NOUN
ap-610	180	9	by	by	ADP
ap-610	180	10	a	a	DET
ap-610	180	11	mixed	mixed	ADJ
ap-610	180	12	derivative	derivative	NOUN
ap-610	180	13	,	,	PUNCT
ap-610	180	14	the	the	DET
ap-610	180	15	phase	phase	NOUN
ap-610	180	16	velocity	velocity	NOUN
ap-610	180	17	remains	remain	VERB
ap-610	180	18	real	real	ADJ
ap-610	180	19	and	and	CCONJ
ap-610	180	20	positive	positive	ADJ
ap-610	180	21	for	for	ADP
ap-610	180	22	all	all	DET
ap-610	180	23	wave	wave	NOUN
ap-610	180	24	numbers	number	NOUN
ap-610	180	25	.	.	PUNCT
ap-610	181	1	the	the	DET
ap-610	181	2	dispersion	dispersion	NOUN
ap-610	181	3	curve	curve	NOUN
ap-610	181	4	,	,	PUNCT
ap-610	181	5	plotted	plot	VERB
ap-610	181	6	in	in	ADP
ap-610	181	7	fig	fig	NOUN
ap-610	181	8	.	.	PUNCT
ap-610	182	1	3a	3a	NUM
ap-610	182	2	,	,	PUNCT
ap-610	182	3	is	be	AUX
ap-610	182	4	monotonically	monotonically	ADV
ap-610	182	5	increasing	increase	VERB
ap-610	182	6	,	,	PUNCT
ap-610	182	7	has	have	VERB
ap-610	182	8	a	a	DET
ap-610	182	9	negative	negative	ADJ
ap-610	182	10	curvature	curvature	NOUN
ap-610	182	11	,	,	PUNCT
ap-610	182	12	and	and	CCONJ
ap-610	182	13	for	for	SCONJ
ap-610	182	14	k	k	PROPN
ap-610	182	15	�	�	PROPN
ap-610	182	16	�	�	PROPN
ap-610	182	17	approaches	approach	VERB
ap-610	182	18	a	a	DET
ap-610	182	19	horizontal	horizontal	ADJ
ap-610	182	20	asymptote	asymptote	NOUN
ap-610	182	21	at	at	ADP
ap-610	182	22	circular	circular	ADJ
ap-610	182	23	frequency	frequency	NOUN
ap-610	182	24	�	�	PROPN
ap-610	182	25	�	�	PROPN
ap-610	182	26	c	c	PROPN
ap-610	182	27	l0	l0	PROPN
ap-610	182	28	.	.	PUNCT
ap-610	183	1	the	the	DET
ap-610	183	2	model	model	NOUN
ap-610	183	3	can	can	AUX
ap-610	183	4	reasonably	reasonably	ADV
ap-610	183	5	reproduce	reproduce	VERB
ap-610	183	6	dispersion	dispersion	NOUN
ap-610	183	7	of	of	ADP
ap-610	183	8	waves	wave	NOUN
ap-610	183	9	at	at	ADP
ap-610	183	10	moderate	moderate	ADJ
ap-610	183	11	wavelengths	wavelength	NOUN
ap-610	183	12	and	and	CCONJ
ap-610	183	13	does	do	AUX
ap-610	183	14	not	not	PART
ap-610	183	15	give	give	VERB
ap-610	183	16	rise	rise	NOUN
ap-610	183	17	to	to	ADP
ap-610	183	18	instabilities	instability	NOUN
ap-610	183	19	for	for	ADP
ap-610	183	20	very	very	ADV
ap-610	183	21	short	short	ADJ
ap-610	183	22	waves	wave	NOUN
ap-610	183	23	.	.	PUNCT
ap-610	184	1	its	its	PRON
ap-610	184	2	extension	extension	NOUN
ap-610	184	3	to	to	ADP
ap-610	184	4	multiple	multiple	ADJ
ap-610	184	5	dimensions	dimension	NOUN
ap-610	184	6	is	be	AUX
ap-610	184	7	relatively	relatively	ADV
ap-610	184	8	complicated	complicated	ADJ
ap-610	184	9	(	(	PUNCT
ap-610	184	10	fish	fish	NOUN
ap-610	184	11	,	,	PUNCT
ap-610	184	12	chen	chen	PROPN
ap-610	184	13	and	and	CCONJ
ap-610	184	14	nagai	nagai	PROPN
ap-610	184	15	,	,	PUNCT
ap-610	184	16	2002b;	2002b;	NUM
ap-610	184	17	nagai	nagai	NOUN
ap-610	184	18	,	,	PUNCT
ap-610	184	19	fish	fish	NOUN
ap-610	184	20	and	and	CCONJ
ap-610	184	21	watanabe	watanabe	PROPN
ap-610	184	22	,	,	PUNCT
ap-610	184	23	2004	2004	NUM
ap-610	184	24	)	)	PUNCT
ap-610	184	25	.	.	PUNCT
ap-610	185	1	metrikine	metrikine	VERB
ap-610	185	2	and	and	CCONJ
ap-610	185	3	askes	ask	VERB
ap-610	185	4	(	(	PUNCT
ap-610	185	5	2002	2002	NUM
ap-610	185	6	)	)	PUNCT
ap-610	185	7	used	use	VERB
ap-610	185	8	a	a	DET
ap-610	185	9	different	different	ADJ
ap-610	185	10	line	line	NOUN
ap-610	185	11	of	of	ADP
ap-610	185	12	reasoning	reasoning	NOUN
ap-610	185	13	and	and	CCONJ
ap-610	185	14	arrived	arrive	VERB
ap-610	185	15	at	at	ADP
ap-610	185	16	an	an	DET
ap-610	185	17	equation	equation	NOUN
ap-610	185	18	of	of	ADP
ap-610	185	19	motion	motion	NOUN
ap-610	185	20	with	with	ADP
ap-610	185	21	two	two	NUM
ap-610	185	22	enrichments	enrichment	NOUN
ap-610	185	23	terms	term	NOUN
ap-610	185	24	,	,	PUNCT
ap-610	185	25	proportional	proportional	ADJ
ap-610	185	26	to	to	ADP
ap-610	185	27	�	�	PROPN
ap-610	185	28	�	�	PROPN
ap-610	185	29	�	�	PROPN
ap-610	185	30	�	�	NOUN
ap-610	185	31	u	u	NOUN
ap-610	185	32	and	and	CCONJ
ap-610	185	33	uiv	uiv	PROPN
ap-610	185	34	.	.	PUNCT
ap-610	186	1	in	in	ADP
ap-610	186	2	its	its	PRON
ap-610	186	3	most	most	ADV
ap-610	186	4	general	general	ADJ
ap-610	186	5	form	form	NOUN
ap-610	186	6	,	,	PUNCT
ap-610	186	7	this	this	DET
ap-610	186	8	equation	equation	NOUN
ap-610	186	9	can	can	AUX
ap-610	186	10	be	be	AUX
ap-610	186	11	written	write	VERB
ap-610	186	12	as	as	SCONJ
ap-610	186	13	�	�	PROPN
ap-610	186	14	�	�	PROPN
ap-610	186	15	�	�	PROPN
ap-610	186	16	�	�	PROPN
ap-610	186	17	�	�	PROPN
ap-610	186	18	(	(	PUNCT
ap-610	186	19	�	�	PROPN
ap-610	186	20	�	�	PROPN
ap-610	186	21	)	)	PUNCT
ap-610	186	22	u	u	PROPN
ap-610	186	23	eu	eu	PROPN
ap-610	186	24	l	l	PROPN
ap-610	186	25	u	u	PROPN
ap-610	186	26	eu	eu	PROPN
ap-610	186	27	�	�	PROPN
ap-610	186	28	�	�	PROPN
ap-610	186	29	�	�	PROPN
ap-610	186	30	�	�	PROPN
ap-610	186	31	�	�	PROPN
ap-610	186	32	�	�	PROPN
ap-610	186	33	�	�	PROPN
ap-610	186	34	�	�	PROPN
ap-610	186	35	�	�	PROPN
ap-610	186	36	�	�	PROPN
ap-610	186	37	2	2	NUM
ap-610	186	38	0	0	NUM
ap-610	186	39	,	,	PUNCT
ap-610	186	40	(	(	PUNCT
ap-610	186	41	24	24	NUM
ap-610	186	42	)	)	PUNCT
ap-610	186	43	where	where	SCONJ
ap-610	186	44	l	l	NOUN
ap-610	186	45	is	be	AUX
ap-610	186	46	an	an	DET
ap-610	186	47	internal	internal	ADJ
ap-610	186	48	length	length	NOUN
ap-610	186	49	and	and	CCONJ
ap-610	186	50	�	�	PROPN
ap-610	186	51	is	be	AUX
ap-610	186	52	an	an	DET
ap-610	186	53	additional	additional	ADJ
ap-610	186	54	model	model	NOUN
ap-610	186	55	parameter	parameter	NOUN
ap-610	186	56	.	.	PUNCT
ap-610	187	1	for	for	ADP
ap-610	187	2	l	l	PROPN
ap-610	187	3	�	�	PROPN
ap-610	187	4	0	0	NUM
ap-610	187	5	or	or	CCONJ
ap-610	187	6	for	for	ADP
ap-610	187	7	�	�	PROPN
ap-610	187	8	�	�	PROPN
ap-610	187	9	1	1	NUM
ap-610	187	10	,	,	PUNCT
ap-610	187	11	the	the	DET
ap-610	187	12	model	model	NOUN
ap-610	187	13	reduces	reduce	VERB
ap-610	187	14	to	to	ADP
ap-610	187	15	the	the	DET
ap-610	187	16	standard	standard	ADJ
ap-610	187	17	elastic	elastic	ADJ
ap-610	187	18	continuum	continuum	NOUN
ap-610	187	19	,	,	PUNCT
ap-610	187	20	while	while	SCONJ
ap-610	187	21	for	for	SCONJ
ap-610	187	22	�	�	PROPN
ap-610	187	23	�	�	PROPN
ap-610	187	24	0	0	NUM
ap-610	187	25	it	it	PRON
ap-610	187	26	reduces	reduce	VERB
ap-610	187	27	to	to	ADP
ap-610	187	28	the	the	DET
ap-610	187	29	good	good	ADJ
ap-610	187	30	boussinesq	boussinesq	ADJ
ap-610	187	31	problem	problem	NOUN
ap-610	187	32	of	of	ADP
ap-610	187	33	fish	fish	NOUN
ap-610	187	34	et	et	PROPN
ap-610	187	35	al	al	PROPN
ap-610	187	36	.	.	PROPN
ap-610	187	37	(	(	PUNCT
ap-610	187	38	2002a	2002a	NUM
ap-610	187	39	)	)	PUNCT
ap-610	187	40	.	.	PUNCT
ap-610	188	1	metrikine	metrikine	VERB
ap-610	188	2	and	and	CCONJ
ap-610	188	3	askes	ask	VERB
ap-610	188	4	(	(	PUNCT
ap-610	188	5	2002	2002	NUM
ap-610	188	6	)	)	PUNCT
ap-610	188	7	used	use	VERB
ap-610	188	8	certain	certain	ADJ
ap-610	188	9	heuristic	heuristic	ADJ
ap-610	188	10	arguments	argument	NOUN
ap-610	188	11	to	to	PART
ap-610	188	12	link	link	VERB
ap-610	188	13	l	l	NOUN
ap-610	188	14	and	and	CCONJ
ap-610	188	15	�	�	PROPN
ap-610	188	16	to	to	ADP
ap-610	188	17	the	the	DET
ap-610	188	18	microstructure	microstructure	NOUN
ap-610	188	19	and	and	CCONJ
ap-610	188	20	then	then	ADV
ap-610	188	21	proposed	propose	VERB
ap-610	188	22	a	a	DET
ap-610	188	23	parameter	parameter	NOUN
ap-610	188	24	identification	identification	NOUN
ap-610	188	25	procedure	procedure	NOUN
ap-610	188	26	based	base	VERB
ap-610	188	27	on	on	ADP
ap-610	188	28	a	a	DET
ap-610	188	29	reflection	reflection	NOUN
ap-610	188	30	-	-	PUNCT
ap-610	188	31	transmission	transmission	NOUN
ap-610	188	32	test	test	NOUN
ap-610	188	33	(	(	PUNCT
ap-610	188	34	askes	ask	VERB
ap-610	188	35	and	and	CCONJ
ap-610	188	36	metrikine	metrikine	NOUN
ap-610	188	37	,	,	PUNCT
ap-610	188	38	2002	2002	NUM
ap-610	188	39	)	)	PUNCT
ap-610	188	40	.	.	PUNCT
ap-610	189	1	of	of	ADP
ap-610	189	2	course	course	NOUN
ap-610	189	3	,	,	PUNCT
ap-610	189	4	one	one	PRON
ap-610	189	5	can	can	AUX
ap-610	189	6	also	also	ADV
ap-610	189	7	consider	consider	VERB
ap-610	189	8	l	l	NOUN
ap-610	189	9	and	and	CCONJ
ap-610	189	10	�	�	PROPN
ap-610	189	11	as	as	ADP
ap-610	189	12	free	free	ADJ
ap-610	189	13	model	model	NOUN
ap-610	189	14	parameters	parameter	NOUN
ap-610	189	15	and	and	CCONJ
ap-610	189	16	determine	determine	VERB
ap-610	189	17	them	they	PRON
ap-610	189	18	by	by	ADP
ap-610	189	19	optimal	optimal	ADJ
ap-610	189	20	fitting	fitting	NOUN
ap-610	189	21	of	of	ADP
ap-610	189	22	the	the	DET
ap-610	189	23	dispersion	dispersion	NOUN
ap-610	189	24	curve	curve	NOUN
ap-610	189	25	for	for	ADP
ap-610	189	26	a	a	DET
ap-610	189	27	given	give	VERB
ap-610	189	28	material	material	NOUN
ap-610	189	29	.	.	PUNCT
ap-610	190	1	the	the	DET
ap-610	190	2	dispersion	dispersion	NOUN
ap-610	190	3	equation	equation	NOUN
ap-610	190	4	corresponding	correspond	VERB
ap-610	190	5	to	to	ADP
ap-610	190	6	(	(	PUNCT
ap-610	190	7	24	24	NUM
ap-610	190	8	)	)	PUNCT
ap-610	190	9	,	,	PUNCT
ap-610	190	10	�	�	PROPN
ap-610	190	11	�	�	PROPN
ap-610	190	12	�	�	PROPN
ap-610	190	13	�	�	PROPN
ap-610	190	14	�	�	PROPN
ap-610	190	15	�	�	PROPN
ap-610	190	16	�	�	PROPN
ap-610	190	17	�	�	PROPN
ap-610	190	18	�	�	PROPN
ap-610	190	19	�	�	PROPN
ap-610	190	20	�	�	PROPN
ap-610	190	21	2	2	NUM
ap-610	190	22	2	2	NUM
ap-610	190	23	2	2	NUM
ap-610	190	24	2	2	NUM
ap-610	190	25	2	2	NUM
ap-610	190	26	2	2	NUM
ap-610	190	27	0ek	0ek	NOUN
ap-610	190	28	l	l	NOUN
ap-610	190	29	ek	ek	PROPN
ap-610	190	30	k	k	NOUN
ap-610	190	31	(	(	PUNCT
ap-610	190	32	)	)	PUNCT
ap-610	190	33	(	(	PUNCT
ap-610	190	34	25	25	NUM
ap-610	190	35	)	)	PUNCT
ap-610	190	36	yields	yield	VERB
ap-610	190	37	the	the	DET
ap-610	190	38	phase	phase	NOUN
ap-610	190	39	velocity	velocity	NOUN
ap-610	190	40	c	c	NOUN
ap-610	191	1	k	k	PROPN
ap-610	191	2	c	c	PROPN
ap-610	192	1	k	k	PROPN
ap-610	192	2	l	l	PROPN
ap-610	193	1	k	k	PROPN
ap-610	193	2	l	l	PUNCT
ap-610	193	3	p	p	PROPN
ap-610	193	4	�	�	PROPN
ap-610	193	5	�	�	PROPN
ap-610	193	6	�	�	PROPN
ap-610	193	7	�	�	PROPN
ap-610	193	8	�	�	PROPN
ap-610	193	9	�	�	PROPN
ap-610	193	10	0	0	NUM
ap-610	193	11	2	2	NUM
ap-610	193	12	2	2	NUM
ap-610	193	13	2	2	NUM
ap-610	193	14	2	2	NUM
ap-610	193	15	1	1	NUM
ap-610	193	16	1	1	NUM
ap-610	193	17	,	,	PUNCT
ap-610	193	18	(	(	PUNCT
ap-610	193	19	26	26	NUM
ap-610	193	20	)	)	PUNCT
ap-610	193	21	where	where	SCONJ
ap-610	193	22	c	c	PROPN
ap-610	193	23	e0	e0	PROPN
ap-610	193	24	�	�	PROPN
ap-610	193	25	�	�	PROPN
ap-610	193	26	,	,	PUNCT
ap-610	193	27	as	as	ADV
ap-610	193	28	usual	usual	ADJ
ap-610	193	29	.	.	PUNCT
ap-610	194	1	if	if	SCONJ
ap-610	194	2	parameter	parameter	PROPN
ap-610	194	3	�	�	PROPN
ap-610	194	4	is	be	AUX
ap-610	194	5	nonnegative	nonnegative	ADJ
ap-610	194	6	,	,	PUNCT
ap-610	194	7	the	the	DET
ap-610	194	8	phase	phase	NOUN
ap-610	194	9	velocity	velocity	NOUN
ap-610	194	10	remains	remain	VERB
ap-610	194	11	real	real	ADJ
ap-610	194	12	and	and	CCONJ
ap-610	194	13	positive	positive	ADJ
ap-610	194	14	for	for	ADP
ap-610	194	15	all	all	DET
ap-610	194	16	wave	wave	NOUN
ap-610	194	17	numbers	number	NOUN
ap-610	194	18	.	.	PUNCT
ap-610	195	1	for	for	ADP
ap-610	195	2	0	0	NUM
ap-610	195	3	<	<	X
ap-610	195	4	�	�	PROPN
ap-610	195	5	<	<	X
ap-610	195	6	1	1	NUM
ap-610	195	7	,	,	PUNCT
ap-610	195	8	the	the	DET
ap-610	195	9	dispersion	dispersion	NOUN
ap-610	195	10	curve	curve	NOUN
ap-610	195	11	has	have	AUX
ap-610	195	12	a	a	DET
ap-610	195	13	negative	negative	ADJ
ap-610	195	14	curvature;	curvature;	NOUN
ap-610	195	15	see	see	VERB
ap-610	195	16	fig	fig	NOUN
ap-610	195	17	.	.	PUNCT
ap-610	196	1	3a	3a	NUM
ap-610	196	2	.	.	PUNCT
ap-610	197	1	so	so	ADV
ap-610	197	2	,	,	PUNCT
ap-610	197	3	with	with	ADP
ap-610	197	4	a	a	DET
ap-610	197	5	proper	proper	ADJ
ap-610	197	6	choice	choice	NOUN
ap-610	197	7	of	of	ADP
ap-610	197	8	parameters	parameter	NOUN
ap-610	197	9	,	,	PUNCT
ap-610	197	10	the	the	DET
ap-610	197	11	model	model	NOUN
ap-610	197	12	can	can	AUX
ap-610	197	13	reasonably	reasonably	ADV
ap-610	197	14	approximate	approximate	ADJ
ap-610	197	15	dispersion	dispersion	NOUN
ap-610	197	16	and	and	CCONJ
ap-610	197	17	does	do	AUX
ap-610	197	18	not	not	PART
ap-610	197	19	suffer	suffer	VERB
ap-610	197	20	by	by	ADP
ap-610	197	21	unstable	unstable	ADJ
ap-610	197	22	behavior	behavior	NOUN
ap-610	197	23	of	of	ADP
ap-610	197	24	short	short	ADJ
ap-610	197	25	waves	wave	NOUN
ap-610	197	26	.	.	PUNCT
ap-610	198	1	its	its	PRON
ap-610	198	2	disadvantage	disadvantage	NOUN
ap-610	198	3	is	be	AUX
ap-610	198	4	that	that	SCONJ
ap-610	198	5	the	the	DET
ap-610	198	6	presence	presence	NOUN
ap-610	198	7	of	of	ADP
ap-610	198	8	the	the	DET
ap-610	198	9	fourth	fourth	ADJ
ap-610	198	10	derivative	derivative	ADJ
ap-610	198	11	uiv	uiv	NOUN
ap-610	198	12	requires	require	VERB
ap-610	198	13	either	either	CCONJ
ap-610	198	14	a	a	DET
ap-610	198	15	c1	c1	NOUN
ap-610	198	16	-	-	PUNCT
ap-610	198	17	continuous	continuous	ADJ
ap-610	198	18	finite	finite	ADJ
ap-610	198	19	element	element	NOUN
ap-610	198	20	approximation	approximation	NOUN
ap-610	198	21	(	(	PUNCT
ap-610	198	22	which	which	PRON
ap-610	198	23	is	be	AUX
ap-610	198	24	hard	hard	ADJ
ap-610	198	25	to	to	PART
ap-610	198	26	construct	construct	VERB
ap-610	198	27	on	on	ADP
ap-610	198	28	general	general	ADJ
ap-610	198	29	meshes	mesh	NOUN
ap-610	198	30	in	in	ADP
ap-610	198	31	multiple	multiple	ADJ
ap-610	198	32	dimensions	dimension	NOUN
ap-610	198	33	)	)	PUNCT
ap-610	198	34	or	or	CCONJ
ap-610	198	35	a	a	DET
ap-610	198	36	mixed	mixed	ADJ
ap-610	198	37	approach	approach	NOUN
ap-610	198	38	with	with	ADP
ap-610	198	39	independent	independent	ADJ
ap-610	198	40	approximations	approximation	NOUN
ap-610	198	41	of	of	ADP
ap-610	198	42	several	several	ADJ
ap-610	198	43	fields	field	NOUN
ap-610	198	44	(	(	PUNCT
ap-610	198	45	e.g.	e.g.	ADV
ap-610	198	46	,	,	PUNCT
ap-610	198	47	of	of	ADP
ap-610	198	48	the	the	DET
ap-610	198	49	displacement	displacement	ADJ
ap-610	198	50	field	field	NOUN
ap-610	198	51	and	and	CCONJ
ap-610	198	52	the	the	DET
ap-610	198	53	strain	strain	NOUN
ap-610	198	54	field	field	NOUN
ap-610	198	55	)	)	PUNCT
ap-610	198	56	.	.	PUNCT
ap-610	199	1	also	also	ADV
ap-610	199	2	,	,	PUNCT
ap-610	199	3	nonstandard	nonstandard	ADJ
ap-610	199	4	higher	high	ADJ
ap-610	199	5	-	-	PUNCT
ap-610	199	6	order	order	NOUN
ap-610	199	7	boundary	boundary	ADJ
ap-610	199	8	conditions	condition	NOUN
ap-610	199	9	are	be	AUX
ap-610	199	10	needed	need	VERB
ap-610	199	11	on	on	ADP
ap-610	199	12	the	the	DET
ap-610	199	13	physical	physical	ADJ
ap-610	199	14	boundary	boundary	NOUN
ap-610	199	15	of	of	ADP
ap-610	199	16	the	the	DET
ap-610	199	17	investigated	investigated	ADJ
ap-610	199	18	body	body	NOUN
ap-610	199	19	.	.	PUNCT
ap-610	200	1	2.4	2.4	NUM
ap-610	200	2	integral	integral	ADJ
ap-610	200	3	-	-	PUNCT
ap-610	200	4	type	type	NOUN
ap-610	200	5	nonlocal	nonlocal	ADJ
ap-610	200	6	elasticity	elasticity	NOUN
ap-610	200	7	another	another	DET
ap-610	200	8	class	class	NOUN
ap-610	200	9	of	of	ADP
ap-610	200	10	enrichments	enrichment	NOUN
ap-610	200	11	is	be	AUX
ap-610	200	12	based	base	VERB
ap-610	200	13	on	on	ADP
ap-610	200	14	weighted	weight	VERB
ap-610	200	15	spatial	spatial	ADJ
ap-610	200	16	averaging	averaging	NOUN
ap-610	200	17	.	.	PUNCT
ap-610	201	1	the	the	DET
ap-610	201	2	simplest	simple	ADJ
ap-610	201	3	model	model	NOUN
ap-610	201	4	of	of	ADP
ap-610	201	5	this	this	DET
ap-610	201	6	kind	kind	NOUN
ap-610	201	7	can	can	AUX
ap-610	201	8	be	be	AUX
ap-610	201	9	derived	derive	VERB
ap-610	201	10	from	from	ADP
ap-610	201	11	the	the	DET
ap-610	201	12	elastic	elastic	ADJ
ap-610	201	13	potential	potential	NOUN
ap-610	201	14	w	w	PROPN
ap-610	201	15	e	e	NOUN
ap-610	201	16	x	x	PUNCT
ap-610	201	17	x	x	SYM
ap-610	201	18	x	x	X
ap-610	201	19	ll	ll	PROPN
ap-610	201	20	�	�	PROPN
ap-610	201	21	�	�	PROPN
ap-610	201	22	�	�	PROPN
ap-610	201	23	1	1	NUM
ap-610	201	24	2	2	NUM
ap-610	201	25	(	(	PUNCT
ap-610	201	26	,	,	PUNCT
ap-610	201	27	)	)	PUNCT
ap-610	201	28	(	(	PUNCT
ap-610	201	29	)	)	PUNCT
ap-610	201	30	(	(	PUNCT
ap-610	201	31	)	)	PUNCT
ap-610	201	32	�	�	PROPN
ap-610	201	33	�	�	PROPN
ap-610	201	34	d	d	PROPN
ap-610	201	35	d	d	PROPN
ap-610	201	36	,	,	PUNCT
ap-610	201	37	(	(	PUNCT
ap-610	201	38	27	27	NUM
ap-610	201	39	)	)	PUNCT
ap-610	201	40	where	where	SCONJ
ap-610	201	41	e	e	X
ap-610	201	42	x	x	X
ap-610	201	43	(	(	PUNCT
ap-610	201	44	,	,	PUNCT
ap-610	201	45	)	)	PUNCT
ap-610	201	46	is	be	AUX
ap-610	201	47	a	a	DET
ap-610	201	48	function	function	NOUN
ap-610	201	49	describing	describe	VERB
ap-610	201	50	the	the	DET
ap-610	201	51	generalized	generalized	ADJ
ap-610	201	52	elastic	elastic	ADJ
ap-610	201	53	modulus	modulus	NOUN
ap-610	201	54	.	.	PUNCT
ap-610	202	1	the	the	DET
ap-610	202	2	variation	variation	NOUN
ap-610	202	3	of	of	ADP
ap-610	202	4	elastic	elastic	ADJ
ap-610	202	5	energy	energy	NOUN
ap-610	202	6	is	be	AUX
ap-610	202	7	evaluated	evaluate	VERB
ap-610	202	8	as	as	ADP
ap-610	202	9	�	�	PROPN
ap-610	202	10	�	�	PROPN
ap-610	202	11	�	�	PROPN
ap-610	202	12	�	�	PROPN
ap-610	202	13	�	�	PROPN
ap-610	202	14	�	�	PROPN
ap-610	202	15	�	�	PROPN
ap-610	202	16	w	w	PROPN
ap-610	202	17	e	e	NOUN
ap-610	202	18	x	x	PUNCT
ap-610	202	19	x	x	PUNCT
ap-610	202	20	x	x	PUNCT
ap-610	202	21	e	e	NOUN
ap-610	202	22	x	x	PUNCT
ap-610	202	23	x	x	SYM
ap-610	202	24	x	x	X
ap-610	202	25	ll	ll	VERB
ap-610	202	26	l	l	X
ap-610	202	27	�	�	PROPN
ap-610	202	28	�	�	PROPN
ap-610	202	29	�	�	PROPN
ap-610	202	30	�	�	PROPN
ap-610	202	31	�	�	PROPN
ap-610	202	32	1	1	NUM
ap-610	202	33	2	2	NUM
ap-610	202	34	1	1	NUM
ap-610	202	35	2	2	NUM
ap-610	202	36	(	(	PUNCT
ap-610	202	37	,	,	PUNCT
ap-610	202	38	)	)	PUNCT
ap-610	202	39	(	(	PUNCT
ap-610	202	40	)	)	PUNCT
ap-610	202	41	(	(	PUNCT
ap-610	202	42	)	)	PUNCT
ap-610	202	43	(	(	PUNCT
ap-610	202	44	,	,	PUNCT
ap-610	202	45	)	)	PUNCT
ap-610	202	46	(	(	PUNCT
ap-610	202	47	)	)	PUNCT
ap-610	202	48	(	(	PUNCT
ap-610	202	49	)	)	PUNCT
ap-610	203	1	d	d	X
ap-610	203	2	d	d	X
ap-610	203	3	d	d	PROPN
ap-610	203	4	�	�	PROPN
ap-610	203	5	�	�	PROPN
ap-610	203	6	�	�	PROPN
ap-610	203	7	�	�	PROPN
ap-610	203	8	�	�	PROPN
ap-610	203	9	�	�	PROPN
ap-610	203	10	�	�	PROPN
ap-610	203	11	d	d	PROPN
ap-610	203	12	d	d	PROPN
ap-610	203	13	d	d	X
ap-610	203	14	�	�	PROPN
ap-610	203	15	�	�	PROPN
ap-610	203	16	�	�	PROPN
ap-610	203	17	l	l	NOUN
ap-610	203	18	ll	ll	AUX
ap-610	203	19	e	e	VERB
ap-610	203	20	x	x	X
ap-610	203	21	e	e	NOUN
ap-610	203	22	x	x	SYM
ap-610	203	23	x	x	SYM
ap-610	203	24	x	x	SYM
ap-610	203	25	1	1	NUM
ap-610	203	26	2	2	NUM
ap-610	203	27	[	[	PUNCT
ap-610	203	28	(	(	PUNCT
ap-610	203	29	,	,	PUNCT
ap-610	203	30	)	)	PUNCT
ap-610	203	31	(	(	PUNCT
ap-610	203	32	,	,	PUNCT
ap-610	203	33	)	)	PUNCT
ap-610	203	34	]	]	PUNCT
ap-610	203	35	(	(	PUNCT
ap-610	203	36	)	)	PUNCT
ap-610	203	37	(	(	PUNCT
ap-610	203	38	)	)	PUNCT
ap-610	203	39	.	.	PUNCT
ap-610	204	1	(	(	PUNCT
ap-610	204	2	28	28	NUM
ap-610	204	3	)	)	PUNCT
ap-610	204	4	this	this	PRON
ap-610	204	5	can	can	AUX
ap-610	204	6	be	be	AUX
ap-610	204	7	written	write	VERB
ap-610	204	8	in	in	ADP
ap-610	204	9	the	the	DET
ap-610	204	10	usual	usual	ADJ
ap-610	204	11	form	form	NOUN
ap-610	204	12	�	�	PROPN
ap-610	204	13	�	�	PROPN
ap-610	204	14	�	�	PROPN
ap-610	204	15	w	w	NOUN
ap-610	204	16	x	x	NOUN
ap-610	204	17	x	x	SYM
ap-610	204	18	x	x	SYM
ap-610	204	19	l	l	X
ap-610	204	20	�	�	PROPN
ap-610	204	21	�	�	PROPN
ap-610	204	22	(	(	PUNCT
ap-610	204	23	)	)	PUNCT
ap-610	204	24	(	(	PUNCT
ap-610	204	25	)	)	PUNCT
ap-610	204	26	d	d	NOUN
ap-610	204	27	if	if	SCONJ
ap-610	204	28	the	the	DET
ap-610	204	29	stress	stress	NOUN
ap-610	204	30	is	be	AUX
ap-610	204	31	defined	define	VERB
ap-610	204	32	as	as	ADP
ap-610	204	33	�	�	PROPN
ap-610	204	34	(	(	PUNCT
ap-610	204	35	)	)	PUNCT
ap-610	204	36	(	(	PUNCT
ap-610	204	37	,	,	PUNCT
ap-610	204	38	)	)	PUNCT
ap-610	204	39	(	(	PUNCT
ap-610	204	40	)	)	PUNCT
ap-610	204	41	x	x	X
ap-610	204	42	e	e	NOUN
ap-610	204	43	xs	xs	PROPN
ap-610	204	44	l	l	PROPN
ap-610	204	45	�	�	PROPN
ap-610	204	46	�	�	PROPN
ap-610	204	47	d	d	PROPN
ap-610	204	48	,	,	PUNCT
ap-610	204	49	(	(	PUNCT
ap-610	204	50	29	29	NUM
ap-610	204	51	)	)	PUNCT
ap-610	204	52	where	where	SCONJ
ap-610	204	53	e	e	NOUN
ap-610	204	54	x	x	X
ap-610	204	55	e	e	NOUN
ap-610	204	56	x	x	PROPN
ap-610	204	57	e	e	PROPN
ap-610	204	58	xs	xs	PROPN
ap-610	204	59	(	(	PUNCT
ap-610	204	60	,	,	PUNCT
ap-610	204	61	)	)	PUNCT
ap-610	204	62	[	[	PUNCT
ap-610	204	63	(	(	PUNCT
ap-610	204	64	,	,	PUNCT
ap-610	204	65	)	)	PUNCT
ap-610	204	66	(	(	PUNCT
ap-610	204	67	,	,	PUNCT
ap-610	204	68	)	)	PUNCT
ap-610	204	69	]	]	PUNCT
ap-610	204	70	�	�	PROPN
ap-610	204	71	�	�	PROPN
ap-610	204	72	1	1	NUM
ap-610	204	73	2	2	NUM
ap-610	204	74	(	(	PUNCT
ap-610	204	75	30	30	NUM
ap-610	204	76	)	)	PUNCT
ap-610	204	77	is	be	AUX
ap-610	204	78	the	the	DET
ap-610	204	79	elastic	elastic	ADJ
ap-610	204	80	modulus	modulus	NOUN
ap-610	204	81	function	function	NOUN
ap-610	204	82	symmetrized	symmetrize	VERB
ap-610	204	83	with	with	ADP
ap-610	204	84	respect	respect	NOUN
ap-610	204	85	to	to	ADP
ap-610	204	86	its	its	PRON
ap-610	204	87	arguments	argument	NOUN
ap-610	204	88	.	.	PUNCT
ap-610	205	1	the	the	DET
ap-610	205	2	corresponding	correspond	VERB
ap-610	205	3	equilibrium	equilibrium	NOUN
ap-610	205	4	equations	equation	NOUN
ap-610	205	5	derived	derive	VERB
ap-610	205	6	from	from	ADP
ap-610	205	7	the	the	DET
ap-610	205	8	principle	principle	NOUN
ap-610	205	9	of	of	ADP
ap-610	205	10	virtual	virtual	ADJ
ap-610	205	11	work	work	NOUN
ap-610	205	12	then	then	ADV
ap-610	205	13	keep	keep	VERB
ap-610	205	14	their	their	PRON
ap-610	205	15	standard	standard	ADJ
ap-610	205	16	form	form	NOUN
ap-610	205	17	,	,	PUNCT
ap-610	205	18	�	�	PROPN
ap-610	205	19	�	�	PROPN
ap-610	205	20	�	�	PROPN
ap-610	205	21	b	b	PROPN
ap-610	205	22	0	0	NUM
ap-610	205	23	.	.	PUNCT
ap-610	206	1	consequently	consequently	ADV
ap-610	206	2	,	,	PUNCT
ap-610	206	3	the	the	DET
ap-610	206	4	wave	wave	NOUN
ap-610	206	5	equation	equation	NOUN
ap-610	206	6	for	for	ADP
ap-610	206	7	this	this	DET
ap-610	206	8	model	model	NOUN
ap-610	206	9	reads	read	VERB
ap-610	206	10	�	�	PROPN
ap-610	206	11	2	2	NUM
ap-610	206	12	2	2	NUM
ap-610	206	13	0	0	NUM
ap-610	206	14	u	u	NOUN
ap-610	206	15	x	x	PROPN
ap-610	206	16	t	t	NOUN
ap-610	206	17	t	t	NOUN
ap-610	206	18	x	x	PUNCT
ap-610	206	19	e	e	NOUN
ap-610	206	20	x	x	PUNCT
ap-610	206	21	u	u	NOUN
ap-610	206	22	t	t	PROPN
ap-610	206	23	s	s	PART
ap-610	206	24	l	l	NOUN
ap-610	206	25	(	(	PUNCT
ap-610	206	26	,	,	PUNCT
ap-610	206	27	)	)	PUNCT
ap-610	206	28	(	(	PUNCT
ap-610	206	29	,	,	PUNCT
ap-610	206	30	)	)	PUNCT
ap-610	206	31	(	(	PUNCT
ap-610	206	32	,	,	PUNCT
ap-610	206	33	)	)	PUNCT
ap-610	206	34	�	�	PROPN
ap-610	206	35	�	�	PROPN
ap-610	206	36	�	�	PROPN
ap-610	206	37	d	d	PROPN
ap-610	206	38	.	.	PUNCT
ap-610	207	1	(	(	PUNCT
ap-610	207	2	31	31	NUM
ap-610	207	3	)	)	PUNCT
ap-610	207	4	since	since	SCONJ
ap-610	207	5	function	function	NOUN
ap-610	207	6	e	e	PROPN
ap-610	207	7	xs	xs	PROPN
ap-610	207	8	(	(	PUNCT
ap-610	207	9	,	,	PUNCT
ap-610	207	10	)	)	PUNCT
ap-610	207	11	reflects	reflect	VERB
ap-610	207	12	the	the	DET
ap-610	207	13	strength	strength	NOUN
ap-610	207	14	of	of	ADP
ap-610	207	15	long	long	ADJ
ap-610	207	16	-	-	PUNCT
ap-610	207	17	distance	distance	NOUN
ap-610	207	18	interaction	interaction	NOUN
ap-610	207	19	between	between	ADP
ap-610	207	20	points	point	NOUN
ap-610	207	21	x	x	PUNCT
ap-610	207	22	and	and	CCONJ
ap-610	207	23	,	,	PUNCT
ap-610	207	24	its	its	PRON
ap-610	207	25	value	value	NOUN
ap-610	207	26	can	can	AUX
ap-610	207	27	be	be	AUX
ap-610	207	28	expected	expect	VERB
ap-610	207	29	to	to	PART
ap-610	207	30	be	be	AUX
ap-610	207	31	negligible	negligible	ADJ
ap-610	207	32	if	if	SCONJ
ap-610	207	33	the	the	DET
ap-610	207	34	distance	distance	NOUN
ap-610	207	35	between	between	ADP
ap-610	207	36	x	x	PUNCT
ap-610	207	37	and	and	CCONJ
ap-610	207	38	is	be	AUX
ap-610	207	39	large	large	ADJ
ap-610	207	40	compared	compare	VERB
ap-610	207	41	to	to	ADP
ap-610	207	42	the	the	DET
ap-610	207	43	internal	internal	ADJ
ap-610	207	44	length	length	NOUN
ap-610	207	45	of	of	ADP
ap-610	207	46	the	the	DET
ap-610	207	47	material	material	NOUN
ap-610	207	48	(	(	PUNCT
ap-610	207	49	which	which	PRON
ap-610	207	50	corresponds	correspond	VERB
ap-610	207	51	to	to	ADP
ap-610	207	52	the	the	DET
ap-610	207	53	characteristic	characteristic	ADJ
ap-610	207	54	size	size	NOUN
ap-610	207	55	and	and	CCONJ
ap-610	207	56	spacing	spacing	NOUN
ap-610	207	57	of	of	ADP
ap-610	207	58	major	major	ADJ
ap-610	207	59	heterogeneities	heterogeneity	NOUN
ap-610	207	60	)	)	PUNCT
ap-610	207	61	.	.	PUNCT
ap-610	208	1	for	for	ADP
ap-610	208	2	functions	function	NOUN
ap-610	208	3	es	es	X
ap-610	208	4	with	with	ADP
ap-610	208	5	a	a	DET
ap-610	208	6	sufficiently	sufficiently	ADV
ap-610	208	7	fast	fast	ADJ
ap-610	208	8	decay	decay	NOUN
ap-610	208	9	,	,	PUNCT
ap-610	208	10	the	the	DET
ap-610	208	11	integrals	integral	NOUN
ap-610	208	12	in	in	ADP
ap-610	208	13	(	(	PUNCT
ap-610	208	14	29	29	NUM
ap-610	208	15	)	)	PUNCT
ap-610	208	16	and	and	CCONJ
ap-610	208	17	(	(	PUNCT
ap-610	208	18	31	31	NUM
ap-610	208	19	)	)	PUNCT
ap-610	208	20	make	make	VERB
ap-610	208	21	sense	sense	NOUN
ap-610	208	22	even	even	ADV
ap-610	208	23	if	if	SCONJ
ap-610	208	24	the	the	DET
ap-610	208	25	integration	integration	NOUN
ap-610	208	26	domain	domain	NOUN
ap-610	208	27	l	l	NOUN
ap-610	208	28	is	be	AUX
ap-610	208	29	considered	consider	VERB
ap-610	208	30	as	as	ADP
ap-610	208	31	the	the	DET
ap-610	208	32	entire	entire	ADJ
ap-610	208	33	real	real	ADJ
ap-610	208	34	axis	axis	NOUN
ap-610	208	35	.	.	PUNCT
ap-610	209	1	if	if	SCONJ
ap-610	209	2	the	the	DET
ap-610	209	3	body	body	NOUN
ap-610	209	4	infinite	infinite	VERB
ap-610	209	5	and	and	CCONJ
ap-610	209	6	macroscopically	macroscopically	ADV
ap-610	209	7	homogeneous	homogeneous	ADJ
ap-610	209	8	,	,	PUNCT
ap-610	209	9	function	function	PROPN
ap-610	209	10	e	e	PROPN
ap-610	209	11	xs	xs	PROPN
ap-610	209	12	(	(	PUNCT
ap-610	209	13	,	,	PUNCT
ap-610	209	14	)	)	PUNCT
ap-610	209	15	should	should	AUX
ap-610	209	16	depend	depend	VERB
ap-610	209	17	only	only	ADV
ap-610	209	18	on	on	ADP
ap-610	209	19	the	the	DET
ap-610	209	20	distance	distance	NOUN
ap-610	209	21	between	between	ADP
ap-610	209	22	x	x	PUNCT
ap-610	209	23	and	and	CCONJ
ap-610	209	24	.	.	PUNCT
ap-610	210	1	bearing	bear	VERB
ap-610	210	2	in	in	ADP
ap-610	210	3	mind	mind	NOUN
ap-610	210	4	these	these	DET
ap-610	210	5	restrictive	restrictive	ADJ
ap-610	210	6	assumptions	assumption	NOUN
ap-610	210	7	,	,	PUNCT
ap-610	210	8	we	we	PRON
ap-610	210	9	present	present	VERB
ap-610	210	10	the	the	DET
ap-610	210	11	modulus	modulus	ADJ
ap-610	210	12	function	function	NOUN
ap-610	210	13	in	in	ADP
ap-610	210	14	the	the	DET
ap-610	210	15	form	form	NOUN
ap-610	210	16	e	e	NOUN
ap-610	210	17	x	x	X
ap-610	210	18	e	e	PROPN
ap-610	210	19	xs	xs	PROPN
ap-610	210	20	(	(	PUNCT
ap-610	210	21	,	,	PUNCT
ap-610	210	22	)	)	PUNCT
ap-610	210	23	(	(	PUNCT
ap-610	210	24	)	)	PUNCT
ap-610	210	25	�	�	PROPN
ap-610	210	26	�	�	PROPN
ap-610	210	27	�	�	PROPN
ap-610	210	28	0	0	NUM
ap-610	210	29	0	0	NUM
ap-610	210	30	,	,	PUNCT
ap-610	210	31	(	(	PUNCT
ap-610	210	32	32	32	NUM
ap-610	210	33	)	)	PUNCT
ap-610	210	34	where	where	SCONJ
ap-610	210	35	e0	e0	PROPN
ap-610	210	36	is	be	AUX
ap-610	210	37	a	a	DET
ap-610	210	38	reference	reference	NOUN
ap-610	210	39	value	value	NOUN
ap-610	210	40	of	of	ADP
ap-610	210	41	the	the	DET
ap-610	210	42	elastic	elastic	ADJ
ap-610	210	43	modulus	modulus	NOUN
ap-610	210	44	and	and	CCONJ
ap-610	210	45	�	�	PROPN
ap-610	210	46	0	0	NUM
ap-610	210	47	is	be	AUX
ap-610	210	48	a	a	DET
ap-610	210	49	dimensionless	dimensionless	NOUN
ap-610	210	50	even	even	ADV
ap-610	210	51	function	function	NOUN
ap-610	210	52	,	,	PUNCT
ap-610	210	53	further	far	ADV
ap-610	210	54	called	call	VERB
ap-610	210	55	the	the	DET
ap-610	210	56	nonlocal	nonlocal	ADJ
ap-610	210	57	weight	weight	NOUN
ap-610	210	58	function	function	NOUN
ap-610	210	59	.	.	PUNCT
ap-610	211	1	the	the	DET
ap-610	211	2	second	second	ADJ
ap-610	211	3	term	term	NOUN
ap-610	211	4	in	in	ADP
ap-610	211	5	the	the	DET
ap-610	211	6	wave	wave	NOUN
ap-610	211	7	equation	equation	NOUN
ap-610	211	8	(	(	PUNCT
ap-610	211	9	31	31	NUM
ap-610	211	10	)	)	PUNCT
ap-610	211	11	can	can	AUX
ap-610	211	12	then	then	ADV
ap-610	211	13	be	be	AUX
ap-610	211	14	transformed	transform	VERB
ap-610	211	15	as	as	SCONJ
ap-610	211	16	follows	follow	VERB
ap-610	211	17	:	:	PUNCT
ap-610	211	18	�	�	PROPN
ap-610	211	19	x	x	PUNCT
ap-610	211	20	e	e	NOUN
ap-610	211	21	x	x	PUNCT
ap-610	211	22	u	u	NOUN
ap-610	211	23	t	t	NOUN
ap-610	211	24	e	e	NOUN
ap-610	211	25	x	x	PUNCT
ap-610	211	26	x	x	PUNCT
ap-610	211	27	u	u	NOUN
ap-610	211	28	t	t	PROPN
ap-610	211	29	s	s	PROPN
ap-610	211	30	(	(	PUNCT
ap-610	211	31	,	,	PUNCT
ap-610	211	32	)	)	PUNCT
ap-610	211	33	(	(	PUNCT
ap-610	211	34	,	,	PUNCT
ap-610	211	35	)	)	PUNCT
ap-610	211	36	(	(	PUNCT
ap-610	211	37	)	)	PUNCT
ap-610	211	38	(	(	PUNCT
ap-610	211	39	,	,	PUNCT
ap-610	211	40	)	)	PUNCT
ap-610	212	1	d	d	X
ap-610	212	2	d	d	X
ap-610	212	3	�	�	PROPN
ap-610	212	4	�	�	PROPN
ap-610	212	5	�	�	PROPN
ap-610	212	6	�	�	PROPN
ap-610	212	7	�	�	PROPN
ap-610	212	8	0	0	NUM
ap-610	212	9	0	0	NUM
ap-610	212	10	�	�	PROPN
ap-610	212	11	�	�	PROPN
ap-610	212	12	�	�	PROPN
ap-610	212	13	�	�	PROPN
ap-610	212	14	�	�	PROPN
ap-610	212	15	�	�	PROPN
ap-610	212	16	�	�	PROPN
ap-610	212	17	�	�	PROPN
ap-610	212	18	�	�	PROPN
ap-610	212	19	e	e	NOUN
ap-610	212	20	x	x	NOUN
ap-610	212	21	x	x	PUNCT
ap-610	212	22	u	u	NOUN
ap-610	212	23	t	t	NOUN
ap-610	212	24	e	e	X
ap-610	212	25	x	x	PUNCT
ap-610	212	26	u	u	NOUN
ap-610	212	27	t	t	NOUN
ap-610	212	28	0	0	NUM
ap-610	212	29	0	0	NUM
ap-610	212	30	0	0	NUM
ap-610	212	31	0	0	NUM
ap-610	212	32	2	2	NUM
ap-610	212	33	�	�	PROPN
ap-610	212	34	�	�	PROPN
ap-610	212	35	(	(	PUNCT
ap-610	212	36	)	)	PUNCT
ap-610	212	37	(	(	PUNCT
ap-610	212	38	,	,	PUNCT
ap-610	212	39	)	)	PUNCT
ap-610	212	40	(	(	PUNCT
ap-610	212	41	)	)	PUNCT
ap-610	212	42	(	(	PUNCT
ap-610	212	43	,	,	PUNCT
ap-610	212	44	d	d	NOUN
ap-610	212	45	)	)	PUNCT
ap-610	212	46	.	.	PUNCT
ap-610	213	1	2	2	NUM
ap-610	213	2	d	d	PROPN
ap-610	213	3	�	�	PROPN
ap-610	213	4	�	�	PROPN
ap-610	213	5	(	(	PUNCT
ap-610	213	6	33	33	NUM
ap-610	213	7	)	)	PUNCT
ap-610	213	8	©	©	PROPN
ap-610	213	9	czech	czech	PROPN
ap-610	213	10	technical	technical	PROPN
ap-610	213	11	university	university	PROPN
ap-610	213	12	publishing	publishing	NOUN
ap-610	213	13	house	house	NOUN
ap-610	213	14	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	213	15	21	21	NUM
ap-610	213	16	acta	acta	PROPN
ap-610	213	17	polytechnica	polytechnica	PROPN
ap-610	213	18	vol	vol	NOUN
ap-610	213	19	.	.	PROPN
ap-610	213	20	44	44	NUM
ap-610	213	21	no	no	NOUN
ap-610	213	22	.	.	PUNCT
ap-610	214	1	5–6/2004	5–6/2004	NUM
ap-610	214	2	substituting	substitute	VERB
ap-610	214	3	the	the	DET
ap-610	214	4	assumed	assume	VERB
ap-610	214	5	harmonic	harmonic	ADJ
ap-610	214	6	form	form	NOUN
ap-610	214	7	of	of	ADP
ap-610	214	8	an	an	DET
ap-610	214	9	elastic	elastic	ADJ
ap-610	214	10	wave	wave	NOUN
ap-610	214	11	(	(	PUNCT
ap-610	214	12	2	2	NUM
ap-610	214	13	)	)	PUNCT
ap-610	214	14	into	into	ADP
ap-610	214	15	the	the	DET
ap-610	214	16	transformed	transform	VERB
ap-610	214	17	wave	wave	NOUN
ap-610	214	18	equation	equation	NOUN
ap-610	214	19	�	�	PROPN
ap-610	214	20	�	�	PROPN
ap-610	214	21	2	2	NUM
ap-610	214	22	2	2	NUM
ap-610	214	23	0	0	NUM
ap-610	214	24	0	0	NUM
ap-610	214	25	2	2	NUM
ap-610	214	26	2	2	NUM
ap-610	214	27	0	0	NUM
ap-610	214	28	u	u	NOUN
ap-610	214	29	x	x	PROPN
ap-610	214	30	t	t	NOUN
ap-610	214	31	t	t	X
ap-610	214	32	e	e	X
ap-610	214	33	x	x	PUNCT
ap-610	214	34	u	u	PROPN
ap-610	214	35	t	t	PROPN
ap-610	214	36	(	(	PUNCT
ap-610	214	37	,	,	PUNCT
ap-610	214	38	)	)	PUNCT
ap-610	214	39	(	(	PUNCT
ap-610	214	40	)	)	PUNCT
ap-610	214	41	(	(	PUNCT
ap-610	214	42	,	,	PUNCT
ap-610	214	43	)	)	PUNCT
ap-610	214	44	�	�	PROPN
ap-610	214	45	�	�	PROPN
ap-610	214	46	�	�	PROPN
ap-610	214	47	�	�	PROPN
ap-610	214	48	�	�	PROPN
ap-610	214	49	d	d	PROPN
ap-610	214	50	(	(	PUNCT
ap-610	214	51	34	34	NUM
ap-610	214	52	)	)	PUNCT
ap-610	214	53	we	we	PRON
ap-610	214	54	obtain	obtain	VERB
ap-610	214	55	the	the	DET
ap-610	214	56	dispersion	dispersion	NOUN
ap-610	214	57	equation	equation	NOUN
ap-610	214	58	�	�	PROPN
ap-610	214	59	�	�	PROPN
ap-610	214	60	�	�	PROPN
ap-610	214	61	�	�	PROPN
ap-610	214	62	�	�	PROPN
ap-610	214	63	�	�	PROPN
ap-610	214	64	2	2	NUM
ap-610	214	65	0	0	NUM
ap-610	214	66	2	2	NUM
ap-610	214	67	0	0	NUM
ap-610	214	68	0e	0e	NOUN
ap-610	214	69	k	k	X
ap-610	215	1	k	k	PUNCT
ap-610	215	2	*	*	PUNCT
ap-610	215	3	(	(	PUNCT
ap-610	215	4	)	)	PUNCT
ap-610	215	5	(	(	PUNCT
ap-610	215	6	35	35	NUM
ap-610	215	7	)	)	PUNCT
ap-610	215	8	in	in	ADP
ap-610	215	9	which	which	PRON
ap-610	215	10	�	�	PROPN
ap-610	215	11	�	�	PROPN
ap-610	215	12	0	0	NUM
ap-610	215	13	0	0	NUM
ap-610	215	14	*	*	PUNCT
ap-610	215	15	(	(	PUNCT
ap-610	215	16	)	)	PUNCT
ap-610	215	17	(	(	PUNCT
ap-610	215	18	)	)	PUNCT
ap-610	215	19	k	k	NOUN
ap-610	215	20	r	r	NOUN
ap-610	215	21	rikr	rikr	NOUN
ap-610	215	22	�	�	PROPN
ap-610	215	23	�	�	PROPN
ap-610	215	24	�	�	PROPN
ap-610	215	25	�	�	PROPN
ap-610	215	26	e	e	PROPN
ap-610	215	27	d	d	PROPN
ap-610	215	28	(	(	PUNCT
ap-610	215	29	36	36	NUM
ap-610	215	30	)	)	PUNCT
ap-610	215	31	is	be	AUX
ap-610	215	32	the	the	DET
ap-610	215	33	fourier	fourier	ADJ
ap-610	215	34	image	image	NOUN
ap-610	215	35	of	of	ADP
ap-610	215	36	the	the	DET
ap-610	215	37	nonlocal	nonlocal	ADJ
ap-610	215	38	weight	weight	NOUN
ap-610	215	39	function	function	NOUN
ap-610	215	40	�	�	PROPN
ap-610	215	41	0	0	NUM
ap-610	215	42	(	(	PUNCT
ap-610	215	43	)	)	PUNCT
ap-610	215	44	r	r	NOUN
ap-610	215	45	.	.	PUNCT
ap-610	216	1	finally	finally	ADV
ap-610	216	2	,	,	PUNCT
ap-610	216	3	the	the	DET
ap-610	216	4	phase	phase	NOUN
ap-610	216	5	velocity	velocity	NOUN
ap-610	216	6	is	be	AUX
ap-610	216	7	evaluated	evaluate	VERB
ap-610	216	8	as	as	ADP
ap-610	216	9	c	c	PROPN
ap-610	216	10	k	k	PROPN
ap-610	216	11	e	e	PROPN
ap-610	216	12	k	k	PROPN
ap-610	216	13	c	c	PROPN
ap-610	216	14	kp	kp	PROPN
ap-610	216	15	�	�	PROPN
ap-610	216	16	�	�	PROPN
ap-610	216	17	�	�	PROPN
ap-610	216	18	�	�	PROPN
ap-610	216	19	�	�	PROPN
ap-610	216	20	�	�	PROPN
ap-610	216	21	�	�	PROPN
ap-610	216	22	0	0	NUM
ap-610	216	23	0	0	NUM
ap-610	216	24	0	0	NUM
ap-610	216	25	0	0	NUM
ap-610	217	1	*	*	PUNCT
ap-610	217	2	*	*	PUNCT
ap-610	217	3	(	(	PUNCT
ap-610	217	4	)	)	PUNCT
ap-610	217	5	(	(	PUNCT
ap-610	217	6	)	)	PUNCT
ap-610	217	7	.	.	PUNCT
ap-610	218	1	(	(	PUNCT
ap-610	218	2	37	37	NUM
ap-610	218	3	)	)	PUNCT
ap-610	218	4	relation	relation	NOUN
ap-610	218	5	(	(	PUNCT
ap-610	218	6	35	35	NUM
ap-610	218	7	)	)	PUNCT
ap-610	218	8	shows	show	VERB
ap-610	218	9	that	that	SCONJ
ap-610	218	10	there	there	PRON
ap-610	218	11	is	be	VERB
ap-610	218	12	a	a	DET
ap-610	218	13	unique	unique	ADJ
ap-610	218	14	correspondence	correspondence	NOUN
ap-610	218	15	between	between	ADP
ap-610	218	16	the	the	DET
ap-610	218	17	dispersion	dispersion	NOUN
ap-610	218	18	law	law	NOUN
ap-610	218	19	and	and	CCONJ
ap-610	218	20	the	the	DET
ap-610	218	21	fourier	fourier	ADJ
ap-610	218	22	image	image	NOUN
ap-610	218	23	of	of	ADP
ap-610	218	24	the	the	DET
ap-610	218	25	nonlocal	nonlocal	ADJ
ap-610	218	26	weight	weight	NOUN
ap-610	218	27	function	function	NOUN
ap-610	218	28	.	.	PUNCT
ap-610	219	1	if	if	SCONJ
ap-610	219	2	the	the	DET
ap-610	219	3	dispersion	dispersion	NOUN
ap-610	219	4	law	law	NOUN
ap-610	219	5	of	of	ADP
ap-610	219	6	a	a	DET
ap-610	219	7	certain	certain	ADJ
ap-610	219	8	material	material	NOUN
ap-610	219	9	is	be	AUX
ap-610	219	10	given	give	VERB
ap-610	219	11	in	in	ADP
ap-610	219	12	the	the	DET
ap-610	219	13	form	form	NOUN
ap-610	219	14	�	�	PROPN
ap-610	219	15	(	(	PUNCT
ap-610	219	16	)	)	PUNCT
ap-610	219	17	(	(	PUNCT
ap-610	219	18	)	)	PUNCT
ap-610	219	19	k	k	PROPN
ap-610	219	20	kc	kc	PROPN
ap-610	219	21	kp	kp	PROPN
ap-610	219	22	�	�	PROPN
ap-610	219	23	where	where	SCONJ
ap-610	219	24	c	c	AUX
ap-610	219	25	kp	kp	X
ap-610	219	26	(	(	PUNCT
ap-610	219	27	)	)	PUNCT
ap-610	219	28	is	be	AUX
ap-610	219	29	a	a	DET
ap-610	219	30	known	know	VERB
ap-610	219	31	function	function	NOUN
ap-610	219	32	,	,	PUNCT
ap-610	219	33	it	it	PRON
ap-610	219	34	is	be	AUX
ap-610	219	35	possible	possible	ADJ
ap-610	219	36	to	to	PART
ap-610	219	37	construct	construct	VERB
ap-610	219	38	a	a	DET
ap-610	219	39	nonlocal	nonlocal	ADJ
ap-610	219	40	elasticity	elasticity	NOUN
ap-610	219	41	model	model	NOUN
ap-610	219	42	that	that	PRON
ap-610	219	43	exactly	exactly	ADV
ap-610	219	44	reproduces	reproduce	VERB
ap-610	219	45	the	the	DET
ap-610	219	46	dispersion	dispersion	NOUN
ap-610	219	47	properties	property	NOUN
ap-610	219	48	.	.	PUNCT
ap-610	220	1	for	for	ADP
ap-610	220	2	this	this	PRON
ap-610	220	3	,	,	PUNCT
ap-610	220	4	it	it	PRON
ap-610	220	5	suffices	suffice	VERB
ap-610	220	6	to	to	PART
ap-610	220	7	set	set	VERB
ap-610	220	8	e	e	PROPN
ap-610	220	9	c0	c0	X
ap-610	220	10	0	0	PROPN
ap-610	220	11	2	2	NUM
ap-610	220	12	�	�	PROPN
ap-610	220	13	�	�	PROPN
ap-610	220	14	where	where	SCONJ
ap-610	220	15	c	c	PROPN
ap-610	220	16	cp0	cp0	VERB
ap-610	220	17	0	0	NUM
ap-610	220	18	�	�	PROPN
ap-610	220	19	(	(	PUNCT
ap-610	220	20	)	)	PUNCT
ap-610	220	21	,	,	PUNCT
ap-610	220	22	and	and	CCONJ
ap-610	220	23	to	to	PART
ap-610	220	24	evaluate	evaluate	VERB
ap-610	220	25	the	the	DET
ap-610	220	26	weight	weight	NOUN
ap-610	220	27	function	function	NOUN
ap-610	220	28	by	by	ADP
ap-610	220	29	the	the	DET
ap-610	220	30	inverse	inverse	ADJ
ap-610	220	31	fourier	fourier	NOUN
ap-610	220	32	transform	transform	NOUN
ap-610	220	33	,	,	PUNCT
ap-610	220	34	taking	take	VERB
ap-610	220	35	into	into	ADP
ap-610	220	36	account	account	NOUN
ap-610	220	37	that	that	SCONJ
ap-610	220	38	the	the	DET
ap-610	220	39	phase	phase	NOUN
ap-610	220	40	velocity	velocity	NOUN
ap-610	220	41	does	do	AUX
ap-610	220	42	not	not	PART
ap-610	220	43	depend	depend	VERB
ap-610	220	44	on	on	ADP
ap-610	220	45	the	the	DET
ap-610	220	46	sign	sign	NOUN
ap-610	220	47	of	of	ADP
ap-610	220	48	the	the	DET
ap-610	220	49	wave	wave	NOUN
ap-610	220	50	number	number	NOUN
ap-610	220	51	:	:	PUNCT
ap-610	220	52	�	�	PROPN
ap-610	220	53	�	�	PROPN
ap-610	220	54	�	�	PROPN
ap-610	220	55	�	�	PROPN
ap-610	220	56	0	0	NUM
ap-610	220	57	0	0	NUM
ap-610	220	58	0	0	NUM
ap-610	220	59	2	2	NUM
ap-610	220	60	21	21	NUM
ap-610	220	61	2	2	NUM
ap-610	220	62	1	1	NUM
ap-610	220	63	(	(	PUNCT
ap-610	220	64	)	)	PUNCT
ap-610	220	65	lim	lim	PROPN
ap-610	220	66	(	(	PUNCT
ap-610	220	67	)	)	PUNCT
ap-610	220	68	(	(	PUNCT
ap-610	220	69	)	)	PUNCT
ap-610	221	1	cos*r	cos*r	INTJ
ap-610	221	2	k	k	X
ap-610	222	1	k	k	PROPN
ap-610	223	1	c	c	PROPN
ap-610	223	2	c	c	PROPN
ap-610	224	1	k	k	PROPN
ap-610	224	2	kr	kr	PROPN
ap-610	225	1	k	k	PROPN
ap-610	225	2	k	k	PROPN
ap-610	226	1	ikr	ikr	PROPN
ap-610	227	1	k	k	PROPN
ap-610	228	1	k	k	PROPN
ap-610	228	2	p	p	PROPN
ap-610	228	3	�	�	PROPN
ap-610	228	4	�	�	PROPN
ap-610	228	5	�	�	PROPN
ap-610	228	6	�	�	PROPN
ap-610	228	7	�	�	PROPN
ap-610	228	8	e	e	PROPN
ap-610	228	9	d	d	PROPN
ap-610	228	10	d	d	PROPN
ap-610	228	11	0	0	PROPN
ap-610	228	12	�	�	PROPN
ap-610	228	13	.	.	PUNCT
ap-610	229	1	(	(	PUNCT
ap-610	229	2	38	38	NUM
ap-610	229	3	)	)	PUNCT
ap-610	229	4	of	of	ADP
ap-610	229	5	course	course	NOUN
ap-610	229	6	,	,	PUNCT
ap-610	229	7	this	this	PRON
ap-610	229	8	is	be	AUX
ap-610	229	9	possible	possible	ADJ
ap-610	229	10	only	only	ADV
ap-610	229	11	if	if	SCONJ
ap-610	229	12	the	the	DET
ap-610	229	13	dispersion	dispersion	NOUN
ap-610	229	14	law	law	NOUN
ap-610	229	15	to	to	PART
ap-610	229	16	be	be	AUX
ap-610	229	17	reproduced	reproduce	VERB
ap-610	229	18	has	have	VERB
ap-610	229	19	reasonable	reasonable	ADJ
ap-610	229	20	properties	property	NOUN
ap-610	229	21	,	,	PUNCT
ap-610	229	22	such	such	ADJ
ap-610	229	23	that	that	SCONJ
ap-610	229	24	the	the	DET
ap-610	229	25	inverse	inverse	NOUN
ap-610	229	26	fourier	fourier	NOUN
ap-610	229	27	transform	transform	NOUN
ap-610	229	28	exists	exist	VERB
ap-610	229	29	.	.	PUNCT
ap-610	230	1	for	for	ADP
ap-610	230	2	instance	instance	NOUN
ap-610	230	3	,	,	PUNCT
ap-610	230	4	for	for	ADP
ap-610	230	5	the	the	DET
ap-610	230	6	dispersion	dispersion	NOUN
ap-610	230	7	law	law	NOUN
ap-610	230	8	corresponding	correspond	VERB
ap-610	230	9	to	to	ADP
ap-610	230	10	the	the	DET
ap-610	230	11	bad	bad	ADJ
ap-610	230	12	boussinesq	boussinesq	NOUN
ap-610	230	13	problem	problem	NOUN
ap-610	230	14	,	,	PUNCT
ap-610	230	15	c	c	PROPN
ap-610	230	16	kp	kp	X
ap-610	230	17	(	(	PUNCT
ap-610	230	18	)	)	PUNCT
ap-610	230	19	is	be	AUX
ap-610	230	20	given	give	VERB
ap-610	230	21	by	by	ADP
ap-610	230	22	(	(	PUNCT
ap-610	230	23	20	20	NUM
ap-610	230	24	)	)	PUNCT
ap-610	230	25	and	and	CCONJ
ap-610	230	26	the	the	DET
ap-610	230	27	integral	integral	ADJ
ap-610	230	28	in	in	ADP
ap-610	230	29	(	(	PUNCT
ap-610	230	30	38	38	NUM
ap-610	230	31	)	)	PUNCT
ap-610	230	32	does	do	AUX
ap-610	230	33	not	not	PART
ap-610	230	34	converge	converge	VERB
ap-610	230	35	(	(	PUNCT
ap-610	230	36	independently	independently	ADV
ap-610	230	37	of	of	ADP
ap-610	230	38	the	the	DET
ap-610	230	39	sign	sign	NOUN
ap-610	230	40	of	of	ADP
ap-610	230	41	c	c	NOUN
ap-610	230	42	)	)	PUNCT
ap-610	230	43	.	.	PUNCT
ap-610	231	1	on	on	ADP
ap-610	231	2	the	the	DET
ap-610	231	3	other	other	ADJ
ap-610	231	4	side	side	NOUN
ap-610	231	5	,	,	PUNCT
ap-610	231	6	for	for	ADP
ap-610	231	7	the	the	DET
ap-610	231	8	good	good	ADJ
ap-610	231	9	boussinesq	boussinesq	ADJ
ap-610	231	10	problem	problem	NOUN
ap-610	231	11	(	(	PUNCT
ap-610	231	12	21	21	NUM
ap-610	231	13	)	)	PUNCT
ap-610	231	14	we	we	PRON
ap-610	231	15	have	have	VERB
ap-610	231	16	c	c	PROPN
ap-610	231	17	k	k	PROPN
ap-610	231	18	c	c	PROPN
ap-610	231	19	k	k	PROPN
ap-610	231	20	lp	lp	PROPN
ap-610	231	21	(	(	PUNCT
ap-610	231	22	)	)	PUNCT
ap-610	231	23	�	�	PROPN
ap-610	231	24	�	�	PROPN
ap-610	231	25	0	0	NUM
ap-610	231	26	2	2	NUM
ap-610	231	27	21	21	NUM
ap-610	231	28	and	and	CCONJ
ap-610	231	29	the	the	DET
ap-610	231	30	inverse	inverse	ADJ
ap-610	231	31	fourier	fourier	NOUN
ap-610	231	32	transform	transform	NOUN
ap-610	231	33	(	(	PUNCT
ap-610	231	34	38	38	NUM
ap-610	231	35	)	)	PUNCT
ap-610	231	36	yields	yield	VERB
ap-610	231	37	�	�	PROPN
ap-610	231	38	�	�	PROPN
ap-610	231	39	0	0	NUM
ap-610	231	40	2	2	NUM
ap-610	231	41	2	2	NUM
ap-610	231	42	0	0	NUM
ap-610	231	43	1	1	NUM
ap-610	231	44	1	1	NUM
ap-610	231	45	1	1	NUM
ap-610	231	46	2	2	NUM
ap-610	231	47	(	(	PUNCT
ap-610	231	48	)	)	PUNCT
ap-610	232	1	cos	cos	ADP
ap-610	232	2	r	r	NOUN
ap-610	232	3	kr	kr	PROPN
ap-610	232	4	k	k	PROPN
ap-610	232	5	l	l	PROPN
ap-610	232	6	k	k	PROPN
ap-610	232	7	l	l	NOUN
ap-610	232	8	r	r	NOUN
ap-610	232	9	l	l	X
ap-610	232	10	�	�	PROPN
ap-610	232	11	�	�	PROPN
ap-610	232	12	�	�	PROPN
ap-610	232	13	�	�	PROPN
ap-610	232	14	�	�	PROPN
ap-610	232	15	d	d	PROPN
ap-610	232	16	e	e	PROPN
ap-610	232	17	.	.	PUNCT
ap-610	233	1	(	(	PUNCT
ap-610	233	2	39	39	NUM
ap-610	233	3	)	)	PUNCT
ap-610	233	4	a	a	DET
ap-610	233	5	nonlocal	nonlocal	ADJ
ap-610	233	6	elasticity	elasticity	NOUN
ap-610	233	7	model	model	NOUN
ap-610	233	8	with	with	ADP
ap-610	233	9	this	this	DET
ap-610	233	10	particular	particular	ADJ
ap-610	233	11	weight	weight	NOUN
ap-610	233	12	function	function	NOUN
ap-610	233	13	gives	give	VERB
ap-610	233	14	exactly	exactly	ADV
ap-610	233	15	the	the	DET
ap-610	233	16	same	same	ADJ
ap-610	233	17	dispersion	dispersion	NOUN
ap-610	233	18	law	law	NOUN
ap-610	233	19	as	as	ADP
ap-610	233	20	the	the	DET
ap-610	233	21	model	model	NOUN
ap-610	233	22	with	with	ADP
ap-610	233	23	enrichment	enrichment	NOUN
ap-610	233	24	by	by	ADP
ap-610	233	25	a	a	DET
ap-610	233	26	mixed	mixed	ADJ
ap-610	233	27	derivative	derivative	NOUN
ap-610	233	28	proposed	propose	VERB
ap-610	233	29	by	by	ADP
ap-610	233	30	fish	fish	NOUN
ap-610	233	31	et	et	PROPN
ap-610	233	32	al	al	PROPN
ap-610	233	33	.	.	PROPN
ap-610	233	34	(	(	PUNCT
ap-610	233	35	2002a	2002a	NUM
ap-610	233	36	)	)	PUNCT
ap-610	233	37	.	.	PUNCT
ap-610	234	1	on	on	ADP
ap-610	234	2	an	an	DET
ap-610	234	3	infinite	infinite	ADJ
ap-610	234	4	domain	domain	NOUN
ap-610	234	5	,	,	PUNCT
ap-610	234	6	both	both	DET
ap-610	234	7	models	model	NOUN
ap-610	234	8	are	be	AUX
ap-610	234	9	equivalent	equivalent	ADJ
ap-610	234	10	.	.	PUNCT
ap-610	235	1	the	the	DET
ap-610	235	2	transformation	transformation	NOUN
ap-610	235	3	of	of	ADP
ap-610	235	4	the	the	DET
ap-610	235	5	model	model	NOUN
ap-610	235	6	of	of	ADP
ap-610	235	7	fish	fish	NOUN
ap-610	235	8	et	et	PROPN
ap-610	235	9	al	al	PROPN
ap-610	235	10	.	.	PROPN
ap-610	235	11	(	(	PUNCT
ap-610	235	12	2002a	2002a	NUM
ap-610	235	13	)	)	PUNCT
ap-610	235	14	into	into	ADP
ap-610	235	15	a	a	DET
ap-610	235	16	integral	integral	ADJ
ap-610	235	17	-	-	PUNCT
ap-610	235	18	type	type	NOUN
ap-610	235	19	nonlocal	nonlocal	ADJ
ap-610	235	20	model	model	NOUN
ap-610	235	21	can	can	AUX
ap-610	235	22	also	also	ADV
ap-610	235	23	be	be	AUX
ap-610	235	24	performed	perform	VERB
ap-610	235	25	directly	directly	ADV
ap-610	235	26	.	.	PUNCT
ap-610	236	1	at	at	ADP
ap-610	236	2	a	a	DET
ap-610	236	3	fixed	fix	VERB
ap-610	236	4	time	time	NOUN
ap-610	236	5	instant	instant	NOUN
ap-610	236	6	,	,	PUNCT
ap-610	236	7	equation	equation	NOUN
ap-610	236	8	(	(	PUNCT
ap-610	236	9	21	21	NUM
ap-610	236	10	)	)	PUNCT
ap-610	236	11	can	can	AUX
ap-610	236	12	be	be	AUX
ap-610	236	13	written	write	VERB
ap-610	236	14	as	as	ADP
ap-610	236	15	�	�	PROPN
ap-610	236	16	�	�	PROPN
ap-610	236	17	�	�	PROPN
ap-610	236	18	�	�	PROPN
ap-610	236	19	u	u	PROPN
ap-610	236	20	l	l	NOUN
ap-610	236	21	u	u	X
ap-610	236	22	e	e	X
ap-610	236	23	u	u	ADJ
ap-610	236	24	�	�	PROPN
ap-610	236	25	�	�	PROPN
ap-610	236	26	�	�	PROPN
ap-610	236	27	�	�	PROPN
ap-610	236	28	�	�	PROPN
ap-610	236	29	�	�	PROPN
ap-610	236	30	2	2	NUM
ap-610	236	31	�	�	PROPN
ap-610	236	32	(	(	PUNCT
ap-610	236	33	40	40	NUM
ap-610	236	34	)	)	PUNCT
ap-610	236	35	and	and	CCONJ
ap-610	236	36	interpreted	interpret	VERB
ap-610	236	37	as	as	ADP
ap-610	236	38	an	an	DET
ap-610	236	39	ordinary	ordinary	ADJ
ap-610	236	40	differential	differential	ADJ
ap-610	236	41	equation	equation	NOUN
ap-610	236	42	for	for	ADP
ap-610	236	43	the	the	DET
ap-610	236	44	unknown	unknown	ADJ
ap-610	236	45	acceleration	acceleration	NOUN
ap-610	236	46	�	�	PROPN
ap-610	236	47	�	�	PROPN
ap-610	236	48	u	u	NOUN
ap-610	236	49	,	,	PUNCT
ap-610	236	50	with	with	ADP
ap-610	236	51	the	the	DET
ap-610	236	52	current	current	ADJ
ap-610	236	53	displacement	displacement	NOUN
ap-610	236	54	u	u	NOUN
ap-610	236	55	considered	consider	VERB
ap-610	236	56	as	as	SCONJ
ap-610	236	57	known	know	VERB
ap-610	236	58	.	.	PUNCT
ap-610	237	1	equation	equation	NOUN
ap-610	237	2	(	(	PUNCT
ap-610	237	3	40	40	NUM
ap-610	237	4	)	)	PUNCT
ap-610	237	5	has	have	VERB
ap-610	237	6	the	the	DET
ap-610	237	7	form	form	NOUN
ap-610	237	8	of	of	ADP
ap-610	237	9	the	the	DET
ap-610	237	10	so	so	ADV
ap-610	237	11	-	-	PUNCT
ap-610	237	12	called	call	VERB
ap-610	237	13	helmholtz	helmholtz	NOUN
ap-610	237	14	equation	equation	NOUN
ap-610	237	15	,	,	PUNCT
ap-610	237	16	and	and	CCONJ
ap-610	237	17	its	its	PRON
ap-610	237	18	solution	solution	NOUN
ap-610	237	19	satisfying	satisfy	VERB
ap-610	237	20	conditions	condition	NOUN
ap-610	237	21	of	of	ADP
ap-610	237	22	boundedness	boundedness	NOUN
ap-610	237	23	(	(	PUNCT
ap-610	237	24	which	which	PRON
ap-610	237	25	play	play	VERB
ap-610	237	26	the	the	DET
ap-610	237	27	role	role	NOUN
ap-610	237	28	of	of	ADP
ap-610	237	29	boundary	boundary	ADJ
ap-610	237	30	conditions	condition	NOUN
ap-610	237	31	at	at	ADP
ap-610	237	32	plus	plus	CCONJ
ap-610	237	33	and	and	CCONJ
ap-610	237	34	minus	minus	ADP
ap-610	237	35	infinity	infinity	NOUN
ap-610	237	36	)	)	PUNCT
ap-610	237	37	can	can	AUX
ap-610	237	38	be	be	AUX
ap-610	237	39	expressed	express	VERB
ap-610	237	40	as	as	ADP
ap-610	237	41	�	�	PROPN
ap-610	237	42	�	�	PROPN
ap-610	237	43	(	(	PUNCT
ap-610	237	44	,	,	PUNCT
ap-610	237	45	)	)	PUNCT
ap-610	237	46	(	(	PUNCT
ap-610	237	47	,	,	PUNCT
ap-610	237	48	)	)	PUNCT
ap-610	237	49	(	(	PUNCT
ap-610	237	50	,	,	PUNCT
ap-610	237	51	)	)	PUNCT
ap-610	237	52	u	u	NOUN
ap-610	237	53	x	x	NOUN
ap-610	237	54	t	t	NOUN
ap-610	237	55	e	e	X
ap-610	237	56	g	g	PROPN
ap-610	237	57	x	x	SYM
ap-610	237	58	u	u	PROPN
ap-610	237	59	t	t	PROPN
ap-610	237	60	�	�	PROPN
ap-610	237	61	�	�	PROPN
ap-610	237	62	�	�	PROPN
ap-610	237	63	�	�	PROPN
ap-610	237	64	�	�	PROPN
ap-610	237	65	�	�	PROPN
ap-610	237	66	d	d	PROPN
ap-610	237	67	,	,	PUNCT
ap-610	237	68	(	(	PUNCT
ap-610	237	69	41	41	NUM
ap-610	237	70	)	)	PUNCT
ap-610	237	71	where	where	SCONJ
ap-610	237	72	g	g	PROPN
ap-610	237	73	x	x	PROPN
ap-610	237	74	(	(	PUNCT
ap-610	237	75	,	,	PUNCT
ap-610	237	76	)	)	PUNCT
ap-610	237	77	is	be	AUX
ap-610	237	78	the	the	DET
ap-610	237	79	green	green	ADJ
ap-610	237	80	function	function	NOUN
ap-610	237	81	of	of	ADP
ap-610	237	82	the	the	DET
ap-610	237	83	helmholtz	helmholtz	NOUN
ap-610	237	84	equation	equation	NOUN
ap-610	237	85	,	,	PUNCT
ap-610	237	86	formally	formally	ADV
ap-610	237	87	obtained	obtain	VERB
ap-610	237	88	as	as	ADP
ap-610	237	89	the	the	DET
ap-610	237	90	solution	solution	NOUN
ap-610	237	91	of	of	ADP
ap-610	237	92	this	this	DET
ap-610	237	93	equation	equation	NOUN
ap-610	237	94	with	with	ADP
ap-610	237	95	the	the	DET
ap-610	237	96	dirac	dirac	NOUN
ap-610	237	97	distribution	distribution	NOUN
ap-610	237	98	�	�	PROPN
ap-610	237	99	(	(	PUNCT
ap-610	237	100	)	)	PUNCT
ap-610	237	101	on	on	ADP
ap-610	237	102	the	the	DET
ap-610	237	103	right	right	ADJ
ap-610	237	104	-	-	PUNCT
ap-610	237	105	hand	hand	NOUN
ap-610	237	106	side	side	NOUN
ap-610	237	107	.	.	PUNCT
ap-610	238	1	it	it	PRON
ap-610	238	2	turns	turn	VERB
ap-610	238	3	out	out	ADP
ap-610	238	4	that	that	SCONJ
ap-610	238	5	the	the	DET
ap-610	238	6	green	green	ADJ
ap-610	238	7	function	function	NOUN
ap-610	238	8	is	be	AUX
ap-610	238	9	in	in	ADP
ap-610	238	10	this	this	DET
ap-610	238	11	case	case	NOUN
ap-610	238	12	given	give	VERB
ap-610	238	13	by	by	ADP
ap-610	238	14	g	g	PROPN
ap-610	238	15	x	x	PROPN
ap-610	238	16	l	l	NOUN
ap-610	238	17	x	x	X
ap-610	238	18	l	l	NOUN
ap-610	238	19	(	(	PUNCT
ap-610	238	20	,	,	PUNCT
ap-610	238	21	)	)	PUNCT
ap-610	238	22	�	�	PROPN
ap-610	238	23	�	�	PROPN
ap-610	238	24	�	�	PROPN
ap-610	238	25	1	1	NUM
ap-610	238	26	2	2	NUM
ap-610	238	27	e	e	X
ap-610	238	28	(	(	PUNCT
ap-610	238	29	42	42	NUM
ap-610	238	30	)	)	PUNCT
ap-610	238	31	and	and	CCONJ
ap-610	238	32	so	so	ADV
ap-610	238	33	equation	equation	NOUN
ap-610	238	34	(	(	PUNCT
ap-610	238	35	41	41	NUM
ap-610	238	36	)	)	PUNCT
ap-610	238	37	is	be	AUX
ap-610	238	38	in	in	ADP
ap-610	238	39	fact	fact	NOUN
ap-610	238	40	equivalent	equivalent	ADJ
ap-610	238	41	with	with	ADP
ap-610	238	42	(	(	PUNCT
ap-610	238	43	34	34	NUM
ap-610	238	44	)	)	PUNCT
ap-610	238	45	if	if	SCONJ
ap-610	238	46	the	the	DET
ap-610	238	47	nonlocal	nonlocal	ADJ
ap-610	238	48	weight	weight	NOUN
ap-610	238	49	function	function	NOUN
ap-610	238	50	�	�	PROPN
ap-610	238	51	0	0	NUM
ap-610	238	52	is	be	AUX
ap-610	238	53	selected	select	VERB
ap-610	238	54	according	accord	VERB
ap-610	238	55	to	to	ADP
ap-610	238	56	formula	formula	NOUN
ap-610	238	57	(	(	PUNCT
ap-610	238	58	39	39	NUM
ap-610	238	59	)	)	PUNCT
ap-610	238	60	.	.	PUNCT
ap-610	239	1	2.5	2.5	NUM
ap-610	239	2	combination	combination	NOUN
ap-610	239	3	of	of	ADP
ap-610	239	4	nonlocal	nonlocal	ADJ
ap-610	239	5	averaging	averaging	NOUN
ap-610	239	6	and	and	CCONJ
ap-610	239	7	strain	strain	NOUN
ap-610	239	8	gradients	gradient	NOUN
ap-610	239	9	for	for	ADP
ap-610	239	10	the	the	DET
ap-610	239	11	dispersion	dispersion	NOUN
ap-610	239	12	law	law	NOUN
ap-610	239	13	corresponding	correspond	VERB
ap-610	239	14	to	to	ADP
ap-610	239	15	the	the	DET
ap-610	239	16	gradient	gradient	NOUN
ap-610	239	17	model	model	NOUN
ap-610	239	18	proposed	propose	VERB
ap-610	239	19	by	by	ADP
ap-610	239	20	metrikine	metrikine	NOUN
ap-610	239	21	and	and	CCONJ
ap-610	239	22	askes	ask	VERB
ap-610	239	23	(	(	PUNCT
ap-610	239	24	2002	2002	NUM
ap-610	239	25	)	)	PUNCT
ap-610	239	26	,	,	PUNCT
ap-610	239	27	the	the	DET
ap-610	239	28	integral	integral	ADJ
ap-610	239	29	in	in	ADP
ap-610	239	30	the	the	DET
ap-610	239	31	inverse	inverse	NOUN
ap-610	239	32	fourier	fourier	NOUN
ap-610	239	33	transform	transform	NOUN
ap-610	239	34	(	(	PUNCT
ap-610	239	35	38	38	NUM
ap-610	239	36	)	)	PUNCT
ap-610	239	37	does	do	AUX
ap-610	239	38	not	not	PART
ap-610	239	39	converge	converge	VERB
ap-610	239	40	.	.	PUNCT
ap-610	240	1	so	so	ADV
ap-610	240	2	this	this	DET
ap-610	240	3	model	model	NOUN
ap-610	240	4	is	be	AUX
ap-610	240	5	not	not	PART
ap-610	240	6	equivalent	equivalent	ADJ
ap-610	240	7	to	to	ADP
ap-610	240	8	any	any	DET
ap-610	240	9	integral	integral	ADJ
ap-610	240	10	-	-	PUNCT
ap-610	240	11	type	type	NOUN
ap-610	240	12	nonlocal	nonlocal	ADJ
ap-610	240	13	elastic	elastic	ADJ
ap-610	240	14	model	model	NOUN
ap-610	240	15	derived	derive	VERB
ap-610	240	16	from	from	ADP
ap-610	240	17	the	the	DET
ap-610	240	18	potential	potential	NOUN
ap-610	240	19	(	(	PUNCT
ap-610	240	20	27	27	NUM
ap-610	240	21	)	)	PUNCT
ap-610	240	22	.	.	PUNCT
ap-610	241	1	still	still	ADV
ap-610	241	2	,	,	PUNCT
ap-610	241	3	using	use	VERB
ap-610	241	4	the	the	DET
ap-610	241	5	alternative	alternative	ADJ
ap-610	241	6	procedure	procedure	NOUN
ap-610	241	7	based	base	VERB
ap-610	241	8	on	on	ADP
ap-610	241	9	the	the	DET
ap-610	241	10	green	green	ADJ
ap-610	241	11	function	function	NOUN
ap-610	241	12	,	,	PUNCT
ap-610	241	13	it	it	PRON
ap-610	241	14	is	be	AUX
ap-610	241	15	possible	possible	ADJ
ap-610	241	16	to	to	PART
ap-610	241	17	construct	construct	VERB
ap-610	241	18	a	a	DET
ap-610	241	19	more	more	ADV
ap-610	241	20	general	general	ADJ
ap-610	241	21	nonlocal	nonlocal	ADJ
ap-610	241	22	model	model	NOUN
ap-610	241	23	equivalent	equivalent	ADJ
ap-610	241	24	to	to	ADP
ap-610	241	25	the	the	DET
ap-610	241	26	original	original	ADJ
ap-610	241	27	enriched	enrich	VERB
ap-610	241	28	gradient	gradient	ADJ
ap-610	241	29	formulation	formulation	NOUN
ap-610	241	30	.	.	PUNCT
ap-610	242	1	indeed	indeed	ADV
ap-610	242	2	,	,	PUNCT
ap-610	242	3	rewriting	rewrite	VERB
ap-610	242	4	(	(	PUNCT
ap-610	242	5	24	24	NUM
ap-610	242	6	)	)	PUNCT
ap-610	242	7	as	as	ADP
ap-610	242	8	�	�	PROPN
ap-610	242	9	�	�	PROPN
ap-610	242	10	�	�	PROPN
ap-610	242	11	�	�	PROPN
ap-610	242	12	(	(	PUNCT
ap-610	242	13	)	)	PUNCT
ap-610	242	14	u	u	NOUN
ap-610	242	15	l	l	NOUN
ap-610	242	16	u	u	NOUN
ap-610	242	17	e	e	X
ap-610	242	18	u	u	PROPN
ap-610	242	19	l	l	NOUN
ap-610	242	20	uiv	uiv	PROPN
ap-610	242	21	�	�	PROPN
ap-610	242	22	�	�	PROPN
ap-610	242	23	�	�	PROPN
ap-610	242	24	�	�	PROPN
ap-610	242	25	�	�	PROPN
ap-610	242	26	�	�	PROPN
ap-610	242	27	�	�	PROPN
ap-610	242	28	2	2	NUM
ap-610	242	29	2	2	NUM
ap-610	242	30	�	�	PROPN
ap-610	242	31	�	�	PROPN
ap-610	242	32	(	(	PUNCT
ap-610	242	33	43	43	NUM
ap-610	242	34	)	)	PUNCT
ap-610	242	35	and	and	CCONJ
ap-610	242	36	“	"	PUNCT
ap-610	242	37	solving	solve	VERB
ap-610	242	38	”	"	PUNCT
ap-610	242	39	for	for	ADP
ap-610	242	40	the	the	DET
ap-610	242	41	acceleration	acceleration	NOUN
ap-610	242	42	,	,	PUNCT
ap-610	242	43	we	we	PRON
ap-610	242	44	obtain	obtain	VERB
ap-610	242	45	�	�	PROPN
ap-610	242	46	�	�	PROPN
ap-610	242	47	(	(	PUNCT
ap-610	242	48	,	,	PUNCT
ap-610	242	49	)	)	PUNCT
ap-610	242	50	(	(	PUNCT
ap-610	242	51	,	,	PUNCT
ap-610	242	52	)	)	PUNCT
ap-610	242	53	(	(	PUNCT
ap-610	242	54	,	,	PUNCT
ap-610	242	55	)	)	PUNCT
ap-610	242	56	(	(	PUNCT
ap-610	242	57	,	,	PUNCT
ap-610	242	58	)	)	PUNCT
ap-610	242	59	(	(	PUNCT
ap-610	242	60	,	,	PUNCT
ap-610	242	61	)	)	PUNCT
ap-610	242	62	u	u	NOUN
ap-610	242	63	x	x	NOUN
ap-610	242	64	t	t	NOUN
ap-610	242	65	e	e	X
ap-610	242	66	g	g	PROPN
ap-610	242	67	x	x	SYM
ap-610	242	68	u	u	NOUN
ap-610	242	69	t	t	NOUN
ap-610	242	70	l	l	NOUN
ap-610	242	71	g	g	NOUN
ap-610	242	72	x	x	X
ap-610	242	73	u	u	NOUN
ap-610	242	74	tiv	tiv	PROPN
ap-610	242	75	�	�	PROPN
ap-610	242	76	�	�	PROPN
ap-610	242	77	�	�	PROPN
ap-610	242	78	�	�	PROPN
ap-610	242	79	�	�	PROPN
ap-610	242	80	�	�	PROPN
ap-610	242	81	�	�	PROPN
ap-610	242	82	�	�	PROPN
ap-610	242	83	d	d	PROPN
ap-610	242	84	d2	d2	PROPN
ap-610	242	85	�	�	PROPN
ap-610	242	86	�	�	PROPN
ap-610	242	87	�	�	PROPN
ap-610	242	88	�	�	PROPN
ap-610	242	89	�	�	PROPN
ap-610	242	90	�	�	PROPN
ap-610	242	91	�	�	PROPN
ap-610	242	92	�	�	PROPN
ap-610	242	93	�	�	PROPN
ap-610	242	94	�	�	PROPN
ap-610	242	95	�	�	PROPN
ap-610	242	96	.	.	PUNCT
ap-610	243	1	(	(	PUNCT
ap-610	243	2	44	44	NUM
ap-610	243	3	)	)	PUNCT
ap-610	243	4	the	the	DET
ap-610	243	5	result	result	NOUN
ap-610	243	6	resembles	resemble	VERB
ap-610	243	7	the	the	DET
ap-610	243	8	wave	wave	NOUN
ap-610	243	9	equation	equation	NOUN
ap-610	243	10	of	of	ADP
ap-610	243	11	strain	strain	NOUN
ap-610	243	12	-	-	PUNCT
ap-610	243	13	gradient	gradient	NOUN
ap-610	243	14	elasticity	elasticity	NOUN
ap-610	243	15	(	(	PUNCT
ap-610	243	16	17	17	NUM
ap-610	243	17	)	)	PUNCT
ap-610	243	18	,	,	PUNCT
ap-610	243	19	but	but	CCONJ
ap-610	243	20	with	with	ADP
ap-610	243	21	the	the	DET
ap-610	243	22	derivatives	derivative	NOUN
ap-610	243	23	�	�	PROPN
ap-610	243	24	�	�	NOUN
ap-610	243	25	u	u	NOUN
ap-610	243	26	and	and	CCONJ
ap-610	243	27	uiv	uiv	PROPN
ap-610	243	28	replaced	replace	VERB
ap-610	243	29	by	by	ADP
ap-610	243	30	their	their	PRON
ap-610	243	31	weighted	weight	VERB
ap-610	243	32	spatial	spatial	ADJ
ap-610	243	33	averages	average	NOUN
ap-610	243	34	.	.	PUNCT
ap-610	244	1	this	this	DET
ap-610	244	2	observation	observation	NOUN
ap-610	244	3	motivates	motivate	VERB
ap-610	244	4	the	the	DET
ap-610	244	5	development	development	NOUN
ap-610	244	6	of	of	ADP
ap-610	244	7	a	a	DET
ap-610	244	8	nonlocal	nonlocal	ADJ
ap-610	244	9	strain	strain	NOUN
ap-610	244	10	-	-	PUNCT
ap-610	244	11	gradient	gradient	NOUN
ap-610	244	12	model	model	NOUN
ap-610	244	13	with	with	ADP
ap-610	244	14	the	the	DET
ap-610	244	15	elastic	elastic	ADJ
ap-610	244	16	energy	energy	NOUN
ap-610	244	17	potential	potential	NOUN
ap-610	244	18	given	give	VERB
ap-610	244	19	by	by	ADP
ap-610	244	20	w	w	PROPN
ap-610	244	21	e	e	NOUN
ap-610	244	22	x	x	PUNCT
ap-610	244	23	x	x	PUNCT
ap-610	244	24	x	x	X
ap-610	244	25	c	c	NOUN
ap-610	244	26	x	x	SYM
ap-610	244	27	x	x	PUNCT
ap-610	244	28	x	x	X
ap-610	245	1	ll	ll	AUX
ap-610	245	2	l	l	X
ap-610	245	3	�	�	PROPN
ap-610	245	4	�	�	PROPN
ap-610	245	5	�	�	PROPN
ap-610	245	6	�	�	PROPN
ap-610	245	7	�	�	PROPN
ap-610	245	8	�	�	PROPN
ap-610	245	9	1	1	NUM
ap-610	245	10	2	2	NUM
ap-610	245	11	1	1	NUM
ap-610	245	12	2	2	NUM
ap-610	245	13	(	(	PUNCT
ap-610	245	14	,	,	PUNCT
ap-610	245	15	)	)	PUNCT
ap-610	245	16	(	(	PUNCT
ap-610	245	17	)	)	PUNCT
ap-610	245	18	(	(	PUNCT
ap-610	245	19	)	)	PUNCT
ap-610	245	20	(	(	PUNCT
ap-610	245	21	,	,	PUNCT
ap-610	245	22	)	)	PUNCT
ap-610	245	23	(	(	PUNCT
ap-610	245	24	)	)	PUNCT
ap-610	245	25	(	(	PUNCT
ap-610	245	26	)	)	PUNCT
ap-610	245	27	�	�	PROPN
ap-610	245	28	�	�	PROPN
ap-610	245	29	�	�	PROPN
ap-610	245	30	�	�	PROPN
ap-610	246	1	d	d	PROPN
ap-610	246	2	d	d	PROPN
ap-610	246	3	d	d	X
ap-610	246	4	d	d	X
ap-610	246	5	l	l	X
ap-610	246	6	�	�	PROPN
ap-610	246	7	.	.	PUNCT
ap-610	247	1	(	(	PUNCT
ap-610	247	2	45	45	NUM
ap-610	247	3	)	)	PUNCT
ap-610	247	4	taking	take	VERB
ap-610	247	5	the	the	DET
ap-610	247	6	variation	variation	NOUN
ap-610	247	7	and	and	CCONJ
ap-610	247	8	using	use	VERB
ap-610	247	9	the	the	DET
ap-610	247	10	same	same	ADJ
ap-610	247	11	line	line	NOUN
ap-610	247	12	of	of	ADP
ap-610	247	13	reasoning	reasoning	NOUN
ap-610	247	14	as	as	ADP
ap-610	247	15	for	for	ADP
ap-610	247	16	the	the	DET
ap-610	247	17	basic	basic	ADJ
ap-610	247	18	version	version	NOUN
ap-610	247	19	of	of	ADP
ap-610	247	20	nonlocal	nonlocal	ADJ
ap-610	247	21	elasticity	elasticity	NOUN
ap-610	247	22	,	,	PUNCT
ap-610	247	23	we	we	PRON
ap-610	247	24	identify	identify	VERB
ap-610	247	25	the	the	DET
ap-610	247	26	constitutive	constitutive	ADJ
ap-610	247	27	equations	equation	NOUN
ap-610	247	28	�	�	PROPN
ap-610	247	29	(	(	PUNCT
ap-610	247	30	)	)	PUNCT
ap-610	247	31	(	(	PUNCT
ap-610	247	32	,	,	PUNCT
ap-610	247	33	)	)	PUNCT
ap-610	247	34	(	(	PUNCT
ap-610	247	35	)	)	PUNCT
ap-610	247	36	x	x	X
ap-610	247	37	e	e	NOUN
ap-610	247	38	xs	xs	PROPN
ap-610	247	39	l	l	PROPN
ap-610	247	40	�	�	PROPN
ap-610	247	41	�	�	PROPN
ap-610	247	42	d	d	PROPN
ap-610	247	43	(	(	PUNCT
ap-610	247	44	46	46	NUM
ap-610	247	45	)	)	PUNCT
ap-610	247	46	�	�	PROPN
ap-610	247	47	�	�	PROPN
ap-610	247	48	(	(	PUNCT
ap-610	247	49	)	)	PUNCT
ap-610	247	50	(	(	PUNCT
ap-610	247	51	,	,	PUNCT
ap-610	247	52	)	)	PUNCT
ap-610	247	53	(	(	PUNCT
ap-610	247	54	)	)	PUNCT
ap-610	247	55	x	x	SYM
ap-610	247	56	c	c	PROPN
ap-610	247	57	xs	xs	PROPN
ap-610	247	58	l	l	PROPN
ap-610	247	59	�	�	PROPN
ap-610	247	60	�	�	PROPN
ap-610	247	61	d	d	PROPN
ap-610	247	62	(	(	PUNCT
ap-610	247	63	47	47	NUM
ap-610	247	64	)	)	PUNCT
ap-610	247	65	in	in	ADP
ap-610	247	66	which	which	PRON
ap-610	247	67	c	c	NOUN
ap-610	247	68	x	x	X
ap-610	247	69	c	c	NOUN
ap-610	247	70	x	x	X
ap-610	247	71	c	c	PROPN
ap-610	247	72	xs	xs	PROPN
ap-610	247	73	(	(	PUNCT
ap-610	247	74	,	,	PUNCT
ap-610	247	75	)	)	PUNCT
ap-610	247	76	[	[	PUNCT
ap-610	247	77	(	(	PUNCT
ap-610	247	78	,	,	PUNCT
ap-610	247	79	)	)	PUNCT
ap-610	247	80	(	(	PUNCT
ap-610	247	81	,	,	PUNCT
ap-610	247	82	)	)	PUNCT
ap-610	247	83	]	]	PUNCT
ap-610	247	84	�	�	PROPN
ap-610	247	85	�	�	PROPN
ap-610	247	86	2	2	NUM
ap-610	247	87	is	be	AUX
ap-610	247	88	the	the	DET
ap-610	247	89	symmetrized	symmetrize	VERB
ap-610	247	90	higher	high	ADJ
ap-610	247	91	-	-	PUNCT
ap-610	247	92	order	order	NOUN
ap-610	247	93	modulus	modulus	NOUN
ap-610	247	94	.	.	PUNCT
ap-610	248	1	substituting	substitute	VERB
ap-610	248	2	this	this	PRON
ap-610	248	3	into	into	ADP
ap-610	248	4	the	the	DET
ap-610	248	5	equation	equation	NOUN
ap-610	248	6	of	of	ADP
ap-610	248	7	motion	motion	NOUN
ap-610	248	8	of	of	ADP
ap-610	248	9	the	the	DET
ap-610	248	10	strain	strain	NOUN
ap-610	248	11	-	-	PUNCT
ap-610	248	12	gradient	gradient	NOUN
ap-610	248	13	theory	theory	NOUN
ap-610	248	14	,	,	PUNCT
ap-610	248	15	�	�	PROPN
ap-610	248	16	�	�	PROPN
ap-610	248	17	�	�	PROPN
ap-610	248	18	�	�	PROPN
ap-610	248	19	(	(	PUNCT
ap-610	248	20	)	)	PUNCT
ap-610	248	21	u	u	PROPN
ap-610	248	22	�	�	PROPN
ap-610	248	23	�	�	PROPN
ap-610	248	24	�	�	PROPN
ap-610	248	25	�	�	PROPN
ap-610	248	26	�	�	PROPN
ap-610	248	27	0	0	NUM
ap-610	248	28	,	,	PUNCT
ap-610	248	29	and	and	CCONJ
ap-610	248	30	using	use	VERB
ap-610	248	31	the	the	DET
ap-610	248	32	kinematic	kinematic	ADJ
ap-610	248	33	relations	relation	NOUN
ap-610	248	34	�	�	PROPN
ap-610	248	35	�	�	PROPN
ap-610	248	36	�	�	PROPN
ap-610	248	37	u	u	PROPN
ap-610	248	38	and	and	CCONJ
ap-610	248	39	�	�	PROPN
ap-610	248	40	�	�	PROPN
ap-610	248	41	�	�	PROPN
ap-610	248	42	�	�	PROPN
ap-610	248	43	u	u	NOUN
ap-610	248	44	,	,	PUNCT
ap-610	248	45	we	we	PRON
ap-610	248	46	obtain	obtain	VERB
ap-610	248	47	the	the	DET
ap-610	248	48	wave	wave	NOUN
ap-610	248	49	equation	equation	NOUN
ap-610	248	50	�	�	NOUN
ap-610	248	51	2	2	NUM
ap-610	248	52	2	2	NUM
ap-610	248	53	2	2	NUM
ap-610	248	54	2	2	NUM
ap-610	248	55	u	u	NOUN
ap-610	248	56	x	x	PROPN
ap-610	248	57	t	t	NOUN
ap-610	248	58	t	t	NOUN
ap-610	248	59	x	x	PUNCT
ap-610	248	60	e	e	NOUN
ap-610	248	61	x	x	PUNCT
ap-610	248	62	u	u	NOUN
ap-610	248	63	t	t	NOUN
ap-610	248	64	x	x	X
ap-610	248	65	c	c	AUX
ap-610	248	66	x	x	SYM
ap-610	248	67	s	s	PROPN
ap-610	248	68	l	l	NOUN
ap-610	248	69	s	s	X
ap-610	248	70	(	(	PUNCT
ap-610	248	71	,	,	PUNCT
ap-610	248	72	)	)	PUNCT
ap-610	248	73	(	(	PUNCT
ap-610	248	74	,	,	PUNCT
ap-610	248	75	)	)	PUNCT
ap-610	248	76	(	(	PUNCT
ap-610	248	77	,	,	PUNCT
ap-610	248	78	)	)	PUNCT
ap-610	248	79	(	(	PUNCT
ap-610	248	80	,	,	PUNCT
ap-610	248	81	)	)	PUNCT
ap-610	248	82	�	�	PROPN
ap-610	248	83	�	�	PROPN
ap-610	248	84	�	�	PROPN
ap-610	248	85	�	�	PROPN
ap-610	248	86	d	d	NOUN
ap-610	248	87	2	2	NUM
ap-610	248	88	2	2	NUM
ap-610	248	89	0	0	NUM
ap-610	248	90	u	u	NOUN
ap-610	248	91	t	t	PROPN
ap-610	248	92	l	l	NOUN
ap-610	248	93	(	(	PUNCT
ap-610	248	94	,	,	PUNCT
ap-610	248	95	)	)	PUNCT
ap-610	248	96	d	d	X
ap-610	248	97	�	�	PROPN
ap-610	248	98	�	�	PROPN
ap-610	248	99	(	(	PUNCT
ap-610	248	100	48	48	NUM
ap-610	248	101	)	)	PUNCT
ap-610	248	102	22	22	NUM
ap-610	248	103	©	©	PROPN
ap-610	248	104	czech	czech	PROPN
ap-610	248	105	technical	technical	PROPN
ap-610	248	106	university	university	PROPN
ap-610	248	107	publishing	publishing	NOUN
ap-610	248	108	house	house	NOUN
ap-610	248	109	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	248	110	acta	acta	PROPN
ap-610	248	111	polytechnica	polytechnica	PROPN
ap-610	248	112	vol	vol	NOUN
ap-610	248	113	.	.	PROPN
ap-610	249	1	44	44	NUM
ap-610	249	2	no	no	NOUN
ap-610	249	3	.	.	PUNCT
ap-610	250	1	5–6/2004	5–6/2004	NUM
ap-610	250	2	that	that	PRON
ap-610	250	3	generalizes	generalize	VERB
ap-610	250	4	equation	equation	NOUN
ap-610	250	5	(	(	PUNCT
ap-610	250	6	31	31	NUM
ap-610	250	7	)	)	PUNCT
ap-610	250	8	.	.	PUNCT
ap-610	251	1	for	for	ADP
ap-610	251	2	the	the	DET
ap-610	251	3	moduli	moduli	NOUN
ap-610	251	4	functions	function	NOUN
ap-610	251	5	in	in	ADP
ap-610	251	6	the	the	DET
ap-610	251	7	special	special	ADJ
ap-610	251	8	form	form	NOUN
ap-610	251	9	e	e	X
ap-610	251	10	x	x	X
ap-610	251	11	e	e	PROPN
ap-610	251	12	xs	xs	PROPN
ap-610	251	13	(	(	PUNCT
ap-610	251	14	,	,	PUNCT
ap-610	251	15	)	)	PUNCT
ap-610	251	16	(	(	PUNCT
ap-610	251	17	)	)	PUNCT
ap-610	251	18	�	�	PROPN
ap-610	251	19	�	�	PROPN
ap-610	251	20	�	�	PROPN
ap-610	251	21	0	0	NUM
ap-610	251	22	0	0	NUM
ap-610	251	23	(	(	PUNCT
ap-610	251	24	49	49	NUM
ap-610	251	25	)	)	PUNCT
ap-610	251	26	c	c	NOUN
ap-610	251	27	x	x	PUNCT
ap-610	251	28	e	e	PROPN
ap-610	251	29	l	l	PROPN
ap-610	251	30	xs	xs	PROPN
ap-610	251	31	(	(	PUNCT
ap-610	251	32	,	,	PUNCT
ap-610	251	33	)	)	PUNCT
ap-610	251	34	(	(	PUNCT
ap-610	251	35	)	)	PUNCT
ap-610	251	36	�	�	PROPN
ap-610	251	37	�	�	PROPN
ap-610	251	38	�	�	PROPN
ap-610	251	39	0	0	NUM
ap-610	251	40	2	2	NUM
ap-610	251	41	1	1	NUM
ap-610	251	42	(	(	PUNCT
ap-610	251	43	50	50	NUM
ap-610	251	44	)	)	PUNCT
ap-610	251	45	dispersion	dispersion	NOUN
ap-610	251	46	analysis	analysis	NOUN
ap-610	251	47	provides	provide	VERB
ap-610	251	48	the	the	DET
ap-610	251	49	following	follow	VERB
ap-610	251	50	expression	expression	NOUN
ap-610	251	51	for	for	ADP
ap-610	251	52	the	the	DET
ap-610	251	53	phase	phase	NOUN
ap-610	251	54	velocity	velocity	NOUN
ap-610	251	55	:	:	PUNCT
ap-610	252	1	c	c	PROPN
ap-610	253	1	k	k	PROPN
ap-610	253	2	c	c	PROPN
ap-610	253	3	k	k	PROPN
ap-610	253	4	k	k	PROPN
ap-610	253	5	l	l	X
ap-610	253	6	kp	kp	X
ap-610	253	7	(	(	PUNCT
ap-610	253	8	)	)	PUNCT
ap-610	253	9	(	(	PUNCT
ap-610	253	10	)	)	PUNCT
ap-610	253	11	(	(	PUNCT
ap-610	253	12	)	)	PUNCT
ap-610	253	13	*	*	PUNCT
ap-610	253	14	*	*	PUNCT
ap-610	253	15	�	�	PROPN
ap-610	253	16	�	�	PROPN
ap-610	253	17	0	0	NUM
ap-610	253	18	0	0	NUM
ap-610	253	19	2	2	NUM
ap-610	253	20	2	2	NUM
ap-610	253	21	1	1	NUM
ap-610	253	22	�	�	PROPN
ap-610	253	23	�	�	PROPN
ap-610	253	24	.	.	PUNCT
ap-610	254	1	(	(	PUNCT
ap-610	254	2	51	51	NUM
ap-610	254	3	)	)	PUNCT
ap-610	254	4	here	here	ADV
ap-610	254	5	,	,	PUNCT
ap-610	254	6	�	�	PROPN
ap-610	254	7	1	1	NUM
ap-610	254	8	*	*	NOUN
ap-610	254	9	denotes	denote	NOUN
ap-610	254	10	the	the	DET
ap-610	254	11	fourier	fourier	ADJ
ap-610	254	12	image	image	NOUN
ap-610	254	13	of	of	ADP
ap-610	254	14	function	function	NOUN
ap-610	254	15	�	�	PROPN
ap-610	254	16	1	1	NUM
ap-610	254	17	.	.	PUNCT
ap-610	255	1	the	the	DET
ap-610	255	2	nonlocal	nonlocal	ADJ
ap-610	255	3	strain	strain	NOUN
ap-610	255	4	-	-	PUNCT
ap-610	255	5	gradient	gradient	NOUN
ap-610	255	6	model	model	NOUN
ap-610	255	7	just	just	ADV
ap-610	255	8	presented	present	VERB
ap-610	255	9	is	be	AUX
ap-610	255	10	quite	quite	ADV
ap-610	255	11	general	general	ADJ
ap-610	255	12	and	and	CCONJ
ap-610	255	13	covers	cover	VERB
ap-610	255	14	as	as	ADP
ap-610	255	15	special	special	ADJ
ap-610	255	16	cases	case	NOUN
ap-610	255	17	all	all	DET
ap-610	255	18	the	the	DET
ap-610	255	19	other	other	ADJ
ap-610	255	20	models	model	NOUN
ap-610	255	21	discussed	discuss	VERB
ap-610	255	22	so	so	ADV
ap-610	255	23	far	far	ADV
ap-610	255	24	.	.	PUNCT
ap-610	256	1	the	the	DET
ap-610	256	2	special	special	ADJ
ap-610	256	3	choices	choice	NOUN
ap-610	256	4	of	of	ADP
ap-610	256	5	weight	weight	NOUN
ap-610	256	6	functions	function	NOUN
ap-610	256	7	�	�	PROPN
ap-610	256	8	0	0	NUM
ap-610	256	9	and	and	CCONJ
ap-610	256	10	�	�	PROPN
ap-610	256	11	1	1	NUM
ap-610	256	12	are	be	AUX
ap-610	256	13	summarized	summarize	VERB
ap-610	256	14	in	in	ADP
ap-610	256	15	table	table	NOUN
ap-610	256	16	1	1	NUM
ap-610	256	17	.	.	PUNCT
ap-610	257	1	the	the	DET
ap-610	257	2	model	model	NOUN
ap-610	257	3	permits	permit	VERB
ap-610	257	4	to	to	PART
ap-610	257	5	reproduce	reproduce	VERB
ap-610	257	6	a	a	DET
ap-610	257	7	very	very	ADV
ap-610	257	8	wide	wide	ADJ
ap-610	257	9	class	class	NOUN
ap-610	257	10	of	of	ADP
ap-610	257	11	dispersion	dispersion	NOUN
ap-610	257	12	laws	law	NOUN
ap-610	257	13	.	.	PUNCT
ap-610	258	1	which	which	DET
ap-610	258	2	terms	term	NOUN
ap-610	258	3	need	need	VERB
ap-610	258	4	to	to	PART
ap-610	258	5	be	be	AUX
ap-610	258	6	activated	activate	VERB
ap-610	258	7	depends	depend	VERB
ap-610	258	8	on	on	ADP
ap-610	258	9	the	the	DET
ap-610	258	10	asymptotic	asymptotic	ADJ
ap-610	258	11	behavior	behavior	NOUN
ap-610	258	12	of	of	ADP
ap-610	258	13	the	the	DET
ap-610	258	14	dispersion	dispersion	NOUN
ap-610	258	15	curve	curve	NOUN
ap-610	258	16	at	at	ADP
ap-610	258	17	wave	wave	NOUN
ap-610	258	18	numbers	number	NOUN
ap-610	258	19	approaching	approach	VERB
ap-610	258	20	infinity	infinity	NOUN
ap-610	258	21	.	.	PUNCT
ap-610	259	1	if	if	SCONJ
ap-610	259	2	the	the	DET
ap-610	259	3	dispersion	dispersion	NOUN
ap-610	259	4	law	law	NOUN
ap-610	259	5	�	�	PROPN
ap-610	259	6	(	(	PUNCT
ap-610	259	7	k	k	NOUN
ap-610	259	8	)	)	PUNCT
ap-610	259	9	is	be	AUX
ap-610	259	10	bounded	bound	VERB
ap-610	259	11	,	,	PUNCT
ap-610	259	12	it	it	PRON
ap-610	259	13	is	be	AUX
ap-610	259	14	sufficient	sufficient	ADJ
ap-610	259	15	to	to	PART
ap-610	259	16	use	use	VERB
ap-610	259	17	a	a	DET
ap-610	259	18	regular	regular	ADJ
ap-610	259	19	weight	weight	NOUN
ap-610	259	20	function	function	NOUN
ap-610	259	21	�	�	PROPN
ap-610	259	22	0	0	NUM
ap-610	259	23	obtained	obtain	VERB
ap-610	259	24	by	by	ADP
ap-610	259	25	the	the	DET
ap-610	259	26	inverse	inverse	NOUN
ap-610	259	27	fourier	fourier	NOUN
ap-610	259	28	transform	transform	NOUN
ap-610	259	29	of	of	ADP
ap-610	259	30	(	(	PUNCT
ap-610	259	31	)	)	PUNCT
ap-610	259	32	�	�	PROPN
ap-610	259	33	c	c	PROPN
ap-610	259	34	k0	k0	PROPN
ap-610	259	35	2	2	NUM
ap-610	259	36	.	.	PUNCT
ap-610	260	1	if	if	SCONJ
ap-610	260	2	�	�	PROPN
ap-610	260	3	(	(	PUNCT
ap-610	260	4	k	k	NOUN
ap-610	260	5	)	)	PUNCT
ap-610	260	6	tends	tend	VERB
ap-610	260	7	to	to	PART
ap-610	260	8	infinity	infinity	VERB
ap-610	260	9	but	but	CCONJ
ap-610	260	10	remains	remain	VERB
ap-610	260	11	of	of	ADP
ap-610	260	12	order	order	NOUN
ap-610	260	13	o(k	o(k	NOUN
ap-610	260	14	)	)	PUNCT
ap-610	260	15	,	,	PUNCT
ap-610	260	16	it	it	PRON
ap-610	260	17	is	be	AUX
ap-610	260	18	possible	possible	ADJ
ap-610	260	19	to	to	PART
ap-610	260	20	use	use	VERB
ap-610	260	21	either	either	CCONJ
ap-610	260	22	a	a	DET
ap-610	260	23	weight	weight	NOUN
ap-610	260	24	function	function	NOUN
ap-610	260	25	�	�	NOUN
ap-610	260	26	0	0	NUM
ap-610	260	27	with	with	ADP
ap-610	260	28	a	a	DET
ap-610	260	29	singular	singular	ADJ
ap-610	260	30	part	part	NOUN
ap-610	260	31	of	of	ADP
ap-610	260	32	the	the	DET
ap-610	260	33	dirac	dirac	NOUN
ap-610	260	34	type	type	NOUN
ap-610	260	35	,	,	PUNCT
ap-610	260	36	or	or	CCONJ
ap-610	260	37	regular	regular	ADJ
ap-610	260	38	functions	function	NOUN
ap-610	260	39	�	�	NOUN
ap-610	260	40	0	0	NUM
ap-610	260	41	and	and	CCONJ
ap-610	260	42	�	�	PROPN
ap-610	260	43	1	1	NUM
ap-610	260	44	.	.	PUNCT
ap-610	261	1	finally	finally	ADV
ap-610	261	2	,	,	PUNCT
ap-610	261	3	if	if	SCONJ
ap-610	261	4	�	�	PROPN
ap-610	261	5	(	(	PUNCT
ap-610	261	6	k	k	NOUN
ap-610	261	7	)	)	PUNCT
ap-610	261	8	grows	grow	VERB
ap-610	261	9	superlinearly	superlinearly	ADV
ap-610	261	10	but	but	CCONJ
ap-610	261	11	remains	remain	VERB
ap-610	261	12	of	of	ADP
ap-610	261	13	order	order	NOUN
ap-610	261	14	o(k2	o(k2	NOUN
ap-610	261	15	)	)	PUNCT
ap-610	261	16	,	,	PUNCT
ap-610	261	17	function	function	NOUN
ap-610	261	18	�	�	PROPN
ap-610	261	19	1	1	NUM
ap-610	261	20	must	must	AUX
ap-610	261	21	have	have	VERB
ap-610	261	22	a	a	DET
ap-610	261	23	singular	singular	ADJ
ap-610	261	24	dirac	dirac	NOUN
ap-610	261	25	-	-	PUNCT
ap-610	261	26	type	type	NOUN
ap-610	261	27	part	part	NOUN
ap-610	261	28	.	.	PUNCT
ap-610	262	1	still	still	ADV
ap-610	262	2	faster	fast	ADJ
ap-610	262	3	growth	growth	NOUN
ap-610	262	4	could	could	AUX
ap-610	262	5	be	be	AUX
ap-610	262	6	reproduced	reproduce	VERB
ap-610	262	7	by	by	ADP
ap-610	262	8	models	model	NOUN
ap-610	262	9	with	with	ADP
ap-610	262	10	second	second	ADJ
ap-610	262	11	(	(	PUNCT
ap-610	262	12	mindlin	mindlin	NOUN
ap-610	262	13	,	,	PUNCT
ap-610	262	14	1965	1965	NUM
ap-610	262	15	)	)	PUNCT
ap-610	262	16	or	or	CCONJ
ap-610	262	17	still	still	ADV
ap-610	262	18	higher	high	ADJ
ap-610	262	19	(	(	PUNCT
ap-610	262	20	green	green	ADJ
ap-610	262	21	and	and	CCONJ
ap-610	262	22	rivlin	rivlin	PROPN
ap-610	262	23	,	,	PUNCT
ap-610	262	24	1964	1964	NUM
ap-610	262	25	)	)	PUNCT
ap-610	262	26	strain	strain	NOUN
ap-610	262	27	gradients	gradient	NOUN
ap-610	262	28	,	,	PUNCT
ap-610	262	29	but	but	CCONJ
ap-610	262	30	it	it	PRON
ap-610	262	31	seems	seem	VERB
ap-610	262	32	that	that	SCONJ
ap-610	262	33	dispersion	dispersion	NOUN
ap-610	262	34	laws	law	NOUN
ap-610	262	35	of	of	ADP
ap-610	262	36	real	real	ADJ
ap-610	262	37	materials	material	NOUN
ap-610	262	38	do	do	AUX
ap-610	262	39	not	not	PART
ap-610	262	40	exhibit	exhibit	VERB
ap-610	262	41	such	such	ADJ
ap-610	262	42	behavior	behavior	NOUN
ap-610	262	43	,	,	PUNCT
ap-610	262	44	so	so	SCONJ
ap-610	262	45	this	this	DET
ap-610	262	46	question	question	NOUN
ap-610	262	47	is	be	AUX
ap-610	262	48	purely	purely	ADV
ap-610	262	49	academic	academic	ADJ
ap-610	262	50	.	.	PUNCT
ap-610	263	1	in	in	ADP
ap-610	263	2	fact	fact	NOUN
ap-610	263	3	,	,	PUNCT
ap-610	263	4	all	all	DET
ap-610	263	5	dispersion	dispersion	NOUN
ap-610	263	6	laws	law	NOUN
ap-610	263	7	with	with	ADP
ap-610	263	8	superlinear	superlinear	ADJ
ap-610	263	9	growth	growth	NOUN
ap-610	263	10	at	at	ADP
ap-610	263	11	k	k	PROPN
ap-610	263	12	�	�	PROPN
ap-610	263	13	�	�	PROPN
ap-610	263	14	are	be	AUX
ap-610	263	15	suspicious	suspicious	ADJ
ap-610	263	16	because	because	SCONJ
ap-610	263	17	the	the	DET
ap-610	263	18	phase	phase	NOUN
ap-610	263	19	velocity	velocity	NOUN
ap-610	263	20	becomes	become	VERB
ap-610	263	21	unbounded	unbounded	ADJ
ap-610	263	22	and	and	CCONJ
ap-610	263	23	disturbances	disturbance	NOUN
ap-610	263	24	can	can	AUX
ap-610	263	25	propagate	propagate	VERB
ap-610	263	26	at	at	ADP
ap-610	263	27	an	an	DET
ap-610	263	28	arbitrary	arbitrary	ADJ
ap-610	263	29	velocity	velocity	NOUN
ap-610	263	30	if	if	SCONJ
ap-610	263	31	the	the	DET
ap-610	263	32	wavelength	wavelength	NOUN
ap-610	263	33	is	be	AUX
ap-610	263	34	selected	select	VERB
ap-610	263	35	as	as	ADP
ap-610	263	36	sufficiently	sufficiently	ADV
ap-610	263	37	short	short	ADJ
ap-610	263	38	.	.	PUNCT
ap-610	264	1	2.6	2.6	NUM
ap-610	264	2	nonlocal	nonlocal	ADJ
ap-610	264	3	model	model	NOUN
ap-610	264	4	reproducing	reproduce	VERB
ap-610	264	5	dispersion	dispersion	NOUN
ap-610	264	6	of	of	ADP
ap-610	264	7	discrete	discrete	ADJ
ap-610	264	8	lattice	lattice	NOUN
ap-610	264	9	it	it	PRON
ap-610	264	10	is	be	AUX
ap-610	264	11	interesting	interesting	ADJ
ap-610	264	12	that	that	SCONJ
ap-610	264	13	the	the	DET
ap-610	264	14	nonlocal	nonlocal	ADJ
ap-610	264	15	elastic	elastic	ADJ
ap-610	264	16	model	model	NOUN
ap-610	264	17	with	with	ADP
ap-610	264	18	a	a	DET
ap-610	264	19	weight	weight	NOUN
ap-610	264	20	function	function	NOUN
ap-610	264	21	�	�	PROPN
ap-610	264	22	0	0	NUM
ap-610	264	23	that	that	PRON
ap-610	264	24	linearly	linearly	ADV
ap-610	264	25	decreases	decrease	VERB
ap-610	264	26	from	from	ADP
ap-610	264	27	its	its	PRON
ap-610	264	28	maximum	maximum	ADJ
ap-610	264	29	value	value	NOUN
ap-610	264	30	at	at	ADP
ap-610	264	31	r	r	PROPN
ap-610	264	32	�	�	PROPN
ap-610	264	33	0	0	NUM
ap-610	264	34	to	to	ADP
ap-610	264	35	zero	zero	NUM
ap-610	264	36	at	at	ADP
ap-610	264	37	r	r	PROPN
ap-610	264	38	�	�	PROPN
ap-610	264	39	a	a	PRON
ap-610	264	40	and	and	CCONJ
ap-610	264	41	vanishes	vanish	VERB
ap-610	264	42	for	for	ADP
ap-610	264	43	r	r	NOUN
ap-610	264	44	>	>	X
ap-610	264	45	a	a	DET
ap-610	264	46	leads	lead	NOUN
ap-610	264	47	to	to	ADP
ap-610	264	48	exactly	exactly	ADV
ap-610	264	49	the	the	DET
ap-610	264	50	same	same	ADJ
ap-610	264	51	dispersion	dispersion	NOUN
ap-610	264	52	law	law	NOUN
ap-610	264	53	as	as	ADP
ap-610	264	54	the	the	DET
ap-610	264	55	simplest	simple	ADJ
ap-610	264	56	mass	mass	ADJ
ap-610	264	57	-	-	PUNCT
ap-610	264	58	spring	spring	NOUN
ap-610	264	59	model	model	NOUN
ap-610	264	60	with	with	ADP
ap-610	264	61	nearest	near	ADJ
ap-610	264	62	-	-	PUNCT
ap-610	264	63	neighbor	neighbor	NOUN
ap-610	264	64	interactions	interaction	NOUN
ap-610	264	65	and	and	CCONJ
ap-610	264	66	with	with	ADP
ap-610	264	67	spacing	space	VERB
ap-610	264	68	a	a	PRON
ap-610	264	69	between	between	ADP
ap-610	264	70	neighboring	neighboring	NOUN
ap-610	264	71	mass	mass	NOUN
ap-610	264	72	points	point	NOUN
ap-610	264	73	.	.	PUNCT
ap-610	265	1	table	table	NOUN
ap-610	265	2	2	2	NUM
ap-610	265	3	shows	show	VERB
ap-610	265	4	several	several	ADJ
ap-610	265	5	other	other	ADJ
ap-610	265	6	nonlocal	nonlocal	ADJ
ap-610	265	7	weight	weight	NOUN
ap-610	265	8	functions	function	NOUN
ap-610	265	9	and	and	CCONJ
ap-610	265	10	their	their	PRON
ap-610	265	11	fourier	fourier	NOUN
ap-610	265	12	images	image	NOUN
ap-610	265	13	that	that	PRON
ap-610	265	14	can	can	AUX
ap-610	265	15	be	be	AUX
ap-610	265	16	used	use	VERB
ap-610	265	17	to	to	PART
ap-610	265	18	construct	construct	VERB
ap-610	265	19	the	the	DET
ap-610	265	20	corresponding	corresponding	ADJ
ap-610	265	21	dispersion	dispersion	NOUN
ap-610	265	22	curves	curve	NOUN
ap-610	265	23	,	,	PUNCT
ap-610	265	24	©	©	PROPN
ap-610	265	25	czech	czech	PROPN
ap-610	265	26	technical	technical	PROPN
ap-610	265	27	university	university	PROPN
ap-610	265	28	publishing	publishing	NOUN
ap-610	265	29	house	house	NOUN
ap-610	265	30	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	265	31	23	23	NUM
ap-610	265	32	acta	acta	PROPN
ap-610	265	33	polytechnica	polytechnica	PROPN
ap-610	265	34	vol	vol	NOUN
ap-610	265	35	.	.	PROPN
ap-610	266	1	44	44	NUM
ap-610	266	2	no	no	NOUN
ap-610	266	3	.	.	PUNCT
ap-610	267	1	5–6/2004	5–6/2004	NUM
ap-610	267	2	model	model	NOUN
ap-610	267	3	�	�	PROPN
ap-610	267	4	0	0	NUM
ap-610	267	5	(	(	PUNCT
ap-610	267	6	)	)	PUNCT
ap-610	267	7	r	r	NOUN
ap-610	267	8	�	�	PROPN
ap-610	267	9	1	1	NUM
ap-610	267	10	(	(	PUNCT
ap-610	267	11	)	)	PUNCT
ap-610	267	12	r	r	NOUN
ap-610	267	13	standard	standard	ADJ
ap-610	267	14	elasticity	elasticity	NOUN
ap-610	267	15	�	�	PROPN
ap-610	267	16	(	(	PUNCT
ap-610	267	17	)	)	PUNCT
ap-610	267	18	r	r	NOUN
ap-610	267	19	0	0	NUM
ap-610	267	20	strain	strain	NOUN
ap-610	267	21	-	-	PUNCT
ap-610	267	22	gradient	gradient	NOUN
ap-610	267	23	elasticity	elasticity	NOUN
ap-610	267	24	�	�	PROPN
ap-610	267	25	(	(	PUNCT
ap-610	267	26	)	)	PUNCT
ap-610	267	27	r	r	NOUN
ap-610	267	28	�	�	PROPN
ap-610	267	29	(	(	PUNCT
ap-610	267	30	)	)	PUNCT
ap-610	267	31	r	r	NOUN
ap-610	267	32	fish	fish	NOUN
ap-610	267	33	et	et	PROPN
ap-610	267	34	al	al	PROPN
ap-610	267	35	.	.	PROPN
ap-610	267	36	1	1	NUM
ap-610	267	37	2l	2l	NOUN
ap-610	267	38	r	r	NOUN
ap-610	267	39	le	le	X
ap-610	267	40	�	�	PROPN
ap-610	267	41	0	0	NUM
ap-610	267	42	metrikine	metrikine	NOUN
ap-610	267	43	and	and	CCONJ
ap-610	267	44	askes	ask	VERB
ap-610	267	45	1	1	NUM
ap-610	267	46	2l	2l	NOUN
ap-610	267	47	r	r	NOUN
ap-610	267	48	le	le	X
ap-610	267	49	�	�	PROPN
ap-610	267	50	�	�	PROPN
ap-610	267	51	2l	2l	PROPN
ap-610	267	52	r	r	NOUN
ap-610	267	53	le	le	X
ap-610	267	54	�	�	PROPN
ap-610	267	55	mass	mass	ADJ
ap-610	267	56	-	-	PUNCT
ap-610	267	57	spring	spring	NOUN
ap-610	267	58	chain	chain	NOUN
ap-610	267	59	a	a	DET
ap-610	267	60	r	r	NOUN
ap-610	267	61	a	a	DET
ap-610	267	62	�	�	PROPN
ap-610	267	63	2	2	NUM
ap-610	267	64	0	0	NUM
ap-610	267	65	the	the	DET
ap-610	267	66	brackets	bracket	NOUN
ap-610	267	67	�	�	PROPN
ap-610	267	68	denote	denote	VERB
ap-610	267	69	the	the	DET
ap-610	267	70	positive	positive	ADJ
ap-610	267	71	part	part	NOUN
ap-610	267	72	operator	operator	NOUN
ap-610	267	73	,	,	PUNCT
ap-610	267	74	defined	define	VERB
ap-610	267	75	by	by	ADP
ap-610	267	76	x	x	X
ap-610	267	77	x	x	SYM
ap-610	267	78	x	x	SYM
ap-610	267	79	�	�	PROPN
ap-610	267	80	�	�	PROPN
ap-610	267	81	(	(	PUNCT
ap-610	267	82	)	)	PUNCT
ap-610	267	83	2	2	NUM
ap-610	267	84	.	.	PUNCT
ap-610	267	85	table	table	NOUN
ap-610	267	86	1	1	NUM
ap-610	267	87	:	:	PUNCT
ap-610	267	88	special	special	ADJ
ap-610	267	89	cases	case	NOUN
ap-610	267	90	of	of	ADP
ap-610	267	91	nonlocal	nonlocal	ADJ
ap-610	267	92	strain	strain	NOUN
ap-610	267	93	-	-	PUNCT
ap-610	267	94	gradient	gradient	NOUN
ap-610	267	95	elasticity	elasticity	NOUN
ap-610	267	96	model	model	NOUN
ap-610	267	97	�	�	PROPN
ap-610	267	98	0	0	PROPN
ap-610	267	99	(	(	PUNCT
ap-610	267	100	)	)	PUNCT
ap-610	267	101	r	r	NOUN
ap-610	267	102	�	�	PROPN
ap-610	267	103	0	0	NUM
ap-610	267	104	*	*	PUNCT
ap-610	267	105	(	(	PUNCT
ap-610	267	106	)	)	PUNCT
ap-610	267	107	k	k	PROPN
ap-610	267	108	standard	standard	PROPN
ap-610	267	109	elasticity	elasticity	PROPN
ap-610	267	110	�	�	PROPN
ap-610	267	111	(	(	PUNCT
ap-610	267	112	r	r	NOUN
ap-610	267	113	)	)	PUNCT
ap-610	267	114	1	1	NUM
ap-610	267	115	mass	mass	NOUN
ap-610	267	116	-	-	PUNCT
ap-610	267	117	spring	spring	NOUN
ap-610	267	118	(	(	PUNCT
ap-610	267	119	neighbors	neighbor	NOUN
ap-610	267	120	)	)	PUNCT
ap-610	267	121	a	a	DET
ap-610	267	122	r	r	NOUN
ap-610	267	123	a	a	DET
ap-610	267	124	�	�	PROPN
ap-610	267	125	2	2	NUM
ap-610	267	126	2	2	NUM
ap-610	267	127	1	1	NUM
ap-610	267	128	2	2	NUM
ap-610	267	129	2	2	NUM
ap-610	267	130	(	(	PUNCT
ap-610	267	131	cos	cos	PROPN
ap-610	267	132	)	)	PUNCT
ap-610	267	133	�	�	PROPN
ap-610	267	134	ka	ka	PROPN
ap-610	268	1	k	k	PROPN
ap-610	269	1	a	a	DET
ap-610	269	2	mass	mass	NOUN
ap-610	269	3	-	-	PUNCT
ap-610	269	4	spring	spring	NOUN
ap-610	269	5	(	(	PUNCT
ap-610	269	6	long	long	ADJ
ap-610	269	7	interaction	interaction	NOUN
ap-610	269	8	)	)	PUNCT
ap-610	270	1	k	k	NOUN
ap-610	271	1	na	na	NOUN
ap-610	271	2	r	r	NOUN
ap-610	271	3	a	a	DET
ap-610	271	4	n	n	NOUN
ap-610	271	5	k	k	PROPN
ap-610	271	6	n	n	CCONJ
ap-610	271	7	n	n	PROPN
ap-610	271	8	�	�	PROPN
ap-610	271	9	�	�	PROPN
ap-610	271	10	�	�	PROPN
ap-610	271	11	2	2	NUM
ap-610	271	12	2	2	NUM
ap-610	271	13	2	2	NUM
ap-610	271	14	1	1	NUM
ap-610	271	15	2	2	NUM
ap-610	271	16	2	2	NUM
ap-610	271	17	2	2	NUM
ap-610	271	18	k	k	NOUN
ap-610	271	19	kna	kna	PROPN
ap-610	271	20	k	k	PROPN
ap-610	272	1	a	a	PROPN
ap-610	272	2	n	n	X
ap-610	272	3	k	k	PROPN
ap-610	272	4	n	n	CCONJ
ap-610	272	5	n	n	PROPN
ap-610	272	6	(	(	PUNCT
ap-610	272	7	cos	cos	PROPN
ap-610	272	8	)	)	PUNCT
ap-610	272	9	�	�	PROPN
ap-610	272	10	�	�	PROPN
ap-610	272	11	�	�	PROPN
ap-610	272	12	eringen	eringen	PROPN
ap-610	272	13	see	see	VERB
ap-610	272	14	eq	eq	ADP
ap-610	272	15	.	.	PUNCT
ap-610	273	1	(	(	PUNCT
ap-610	273	2	54	54	NUM
ap-610	273	3	)	)	SYM
ap-610	273	4	2	2	NUM
ap-610	273	5	1	1	NUM
ap-610	273	6	2	2	NUM
ap-610	273	7	2	2	NUM
ap-610	273	8	(	(	PUNCT
ap-610	273	9	cos	cos	PROPN
ap-610	273	10	)	)	PUNCT
ap-610	273	11	�	�	PROPN
ap-610	273	12	ka	ka	PROPN
ap-610	274	1	k	k	PROPN
ap-610	274	2	a	a	DET
ap-610	274	3	if	if	SCONJ
ap-610	274	4	k	k	PROPN
ap-610	274	5	a	a	DET
ap-610	274	6	�	�	PROPN
ap-610	274	7	�	�	PROPN
ap-610	274	8	uniform	uniform	NOUN
ap-610	274	9	averaging	average	VERB
ap-610	274	10	1	1	NUM
ap-610	274	11	2a	2a	NUM
ap-610	274	12	for	for	ADP
ap-610	274	13	r	r	PROPN
ap-610	274	14	a	a	DET
ap-610	274	15	�	�	PROPN
ap-610	274	16	sin	sin	PROPN
ap-610	274	17	ka	ka	PROPN
ap-610	274	18	ka	ka	PROPN
ap-610	274	19	fish	fish	PROPN
ap-610	274	20	et	et	PROPN
ap-610	274	21	al	al	PROPN
ap-610	274	22	.	.	PROPN
ap-610	274	23	1	1	NUM
ap-610	274	24	2a	2a	NUM
ap-610	274	25	r	r	NOUN
ap-610	274	26	ae	ae	PROPN
ap-610	274	27	�	�	PROPN
ap-610	274	28	1	1	NUM
ap-610	274	29	1	1	NUM
ap-610	274	30	2	2	NUM
ap-610	274	31	2	2	NUM
ap-610	274	32	�	�	PROPN
ap-610	274	33	k	k	PROPN
ap-610	274	34	a	a	DET
ap-610	274	35	gauss	gauss	ADJ
ap-610	274	36	weight	weight	NOUN
ap-610	274	37	function	function	NOUN
ap-610	274	38	1	1	NUM
ap-610	274	39	2	2	NUM
ap-610	274	40	2	2	NUM
ap-610	274	41	a	a	DET
ap-610	274	42	r	r	NOUN
ap-610	274	43	a	a	DET
ap-610	274	44	�	�	PROPN
ap-610	274	45	e	e	NOUN
ap-610	274	46	�	�	PROPN
ap-610	274	47	e	e	PROPN
ap-610	274	48	4	4	NUM
ap-610	274	49	�	�	PROPN
ap-610	274	50	k	k	PROPN
ap-610	274	51	a2	a2	PROPN
ap-610	274	52	2	2	NUM
ap-610	274	53	quartic	quartic	ADJ
ap-610	274	54	weight	weight	NOUN
ap-610	274	55	function	function	NOUN
ap-610	274	56	15	15	NUM
ap-610	274	57	16	16	NUM
ap-610	274	58	1	1	NUM
ap-610	274	59	2	2	NUM
ap-610	274	60	2	2	NUM
ap-610	274	61	2	2	NUM
ap-610	274	62	a	a	DET
ap-610	274	63	r	r	NOUN
ap-610	274	64	a	a	DET
ap-610	274	65	�	�	PROPN
ap-610	274	66	15	15	NUM
ap-610	274	67	3	3	NUM
ap-610	274	68	35	35	NUM
ap-610	274	69	5	5	NUM
ap-610	274	70	2	2	NUM
ap-610	274	71	2	2	NUM
ap-610	274	72	k	k	NOUN
ap-610	274	73	a	a	PROPN
ap-610	274	74	k	k	X
ap-610	274	75	a	a	PROPN
ap-610	274	76	ka	ka	PROPN
ap-610	274	77	ka	ka	PROPN
ap-610	274	78	ka	ka	PROPN
ap-610	275	1	[	[	X
ap-610	275	2	(	(	PUNCT
ap-610	275	3	)	)	PUNCT
ap-610	275	4	sin	sin	NOUN
ap-610	275	5	cos	cos	PROPN
ap-610	275	6	]	]	PUNCT
ap-610	275	7	�	�	PROPN
ap-610	275	8	�	�	PROPN
ap-610	275	9	table	table	NOUN
ap-610	275	10	2	2	NUM
ap-610	275	11	:	:	PUNCT
ap-610	275	12	nonlocal	nonlocal	ADJ
ap-610	275	13	weight	weight	NOUN
ap-610	275	14	functions	function	NOUN
ap-610	275	15	and	and	CCONJ
ap-610	275	16	their	their	PRON
ap-610	275	17	fourier	fourier	NOUN
ap-610	275	18	images	image	NOUN
ap-610	275	19	which	which	PRON
ap-610	275	20	are	be	AUX
ap-610	275	21	plotted	plot	VERB
ap-610	275	22	in	in	ADP
ap-610	275	23	fig	fig	NOUN
ap-610	275	24	.	.	PUNCT
ap-610	276	1	3b	3b	NUM
ap-610	276	2	.	.	PUNCT
ap-610	277	1	the	the	DET
ap-610	277	2	dispersion	dispersion	NOUN
ap-610	277	3	law	law	NOUN
ap-610	277	4	of	of	ADP
ap-610	277	5	a	a	DET
ap-610	277	6	mass	mass	ADJ
ap-610	277	7	-	-	PUNCT
ap-610	277	8	spring	spring	NOUN
ap-610	277	9	model	model	NOUN
ap-610	277	10	with	with	ADP
ap-610	277	11	long	long	ADJ
ap-610	277	12	-	-	PUNCT
ap-610	277	13	distance	distance	NOUN
ap-610	277	14	interactions	interaction	NOUN
ap-610	277	15	can	can	AUX
ap-610	277	16	be	be	AUX
ap-610	277	17	reproduced	reproduce	VERB
ap-610	277	18	by	by	ADP
ap-610	277	19	a	a	DET
ap-610	277	20	nonlocal	nonlocal	ADJ
ap-610	277	21	model	model	NOUN
ap-610	277	22	with	with	ADP
ap-610	277	23	a	a	DET
ap-610	277	24	piecewise	piecewise	NOUN
ap-610	277	25	linear	linear	NOUN
ap-610	277	26	weight	weight	NOUN
ap-610	277	27	function	function	NOUN
ap-610	277	28	whose	whose	DET
ap-610	277	29	characteristics	characteristic	NOUN
ap-610	277	30	uniquely	uniquely	ADV
ap-610	277	31	depend	depend	VERB
ap-610	277	32	on	on	ADP
ap-610	277	33	the	the	DET
ap-610	277	34	spring	spring	NOUN
ap-610	277	35	stiffnesses	stiffness	NOUN
ap-610	277	36	.	.	PUNCT
ap-610	278	1	if	if	SCONJ
ap-610	278	2	all	all	DET
ap-610	278	3	stiffnesses	stiffness	NOUN
ap-610	278	4	used	use	VERB
ap-610	278	5	by	by	ADP
ap-610	278	6	the	the	DET
ap-610	278	7	discrete	discrete	ADJ
ap-610	278	8	model	model	NOUN
ap-610	278	9	are	be	AUX
ap-610	278	10	positive	positive	ADJ
ap-610	278	11	,	,	PUNCT
ap-610	278	12	the	the	DET
ap-610	278	13	weight	weight	NOUN
ap-610	278	14	function	function	NOUN
ap-610	278	15	is	be	AUX
ap-610	278	16	concave	concave	VERB
ap-610	278	17	(	(	PUNCT
ap-610	278	18	for	for	ADP
ap-610	278	19	nonzero	nonzero	NOUN
ap-610	278	20	r	r	NOUN
ap-610	278	21	)	)	PUNCT
ap-610	278	22	.	.	PUNCT
ap-610	279	1	the	the	DET
ap-610	279	2	dispersion	dispersion	NOUN
ap-610	279	3	law	law	NOUN
ap-610	279	4	gives	give	VERB
ap-610	279	5	real	real	ADJ
ap-610	279	6	frequencies	frequency	NOUN
ap-610	279	7	for	for	ADP
ap-610	279	8	all	all	DET
ap-610	279	9	wave	wave	NOUN
ap-610	279	10	numbers	number	NOUN
ap-610	279	11	,	,	PUNCT
ap-610	279	12	but	but	CCONJ
ap-610	279	13	for	for	ADP
ap-610	279	14	wave	wave	NOUN
ap-610	279	15	numbers	number	NOUN
ap-610	279	16	that	that	PRON
ap-610	279	17	are	be	AUX
ap-610	279	18	integer	integer	NOUN
ap-610	279	19	multiples	multiple	NOUN
ap-610	279	20	of	of	ADP
ap-610	279	21	2	2	NUM
ap-610	279	22	�	�	PROPN
ap-610	279	23	a	a	DET
ap-610	279	24	the	the	DET
ap-610	279	25	frequency	frequency	NOUN
ap-610	279	26	vanishes	vanish	VERB
ap-610	279	27	,	,	PUNCT
ap-610	279	28	i.e.	i.e.	X
ap-610	279	29	,	,	PUNCT
ap-610	279	30	the	the	DET
ap-610	279	31	model	model	NOUN
ap-610	279	32	admits	admit	VERB
ap-610	279	33	stationary	stationary	ADJ
ap-610	279	34	waves	wave	NOUN
ap-610	279	35	of	of	ADP
ap-610	279	36	wavelength	wavelength	NOUN
ap-610	279	37	a	a	PRON
ap-610	279	38	,	,	PUNCT
ap-610	279	39	a	a	DET
ap-610	279	40	2	2	NUM
ap-610	279	41	,	,	PUNCT
ap-610	279	42	a	a	DET
ap-610	279	43	3	3	NUM
ap-610	279	44	,	,	PUNCT
ap-610	279	45	etc	etc	X
ap-610	279	46	.	.	X
ap-610	280	1	this	this	PRON
ap-610	280	2	is	be	AUX
ap-610	280	3	natural	natural	ADJ
ap-610	280	4	for	for	ADP
ap-610	280	5	the	the	DET
ap-610	280	6	discrete	discrete	ADJ
ap-610	280	7	model	model	NOUN
ap-610	280	8	,	,	PUNCT
ap-610	280	9	as	as	SCONJ
ap-610	280	10	already	already	ADV
ap-610	280	11	explained	explain	VERB
ap-610	280	12	,	,	PUNCT
ap-610	280	13	but	but	CCONJ
ap-610	280	14	the	the	DET
ap-610	280	15	same	same	ADJ
ap-610	280	16	property	property	NOUN
ap-610	280	17	is	be	AUX
ap-610	280	18	shared	share	VERB
ap-610	280	19	by	by	ADP
ap-610	280	20	the	the	DET
ap-610	280	21	nonlocal	nonlocal	ADJ
ap-610	280	22	continuum	continuum	ADJ
ap-610	280	23	model	model	NOUN
ap-610	280	24	.	.	PUNCT
ap-610	281	1	for	for	ADP
ap-610	281	2	the	the	DET
ap-610	281	3	simplest	simple	ADJ
ap-610	281	4	weight	weight	NOUN
ap-610	281	5	function	function	NOUN
ap-610	281	6	,	,	PUNCT
ap-610	281	7	constant	constant	ADJ
ap-610	281	8	for	for	ADP
ap-610	281	9	r	r	NOUN
ap-610	281	10	between	between	ADP
ap-610	281	11	0	0	NUM
ap-610	281	12	and	and	CCONJ
ap-610	281	13	a	a	PRON
ap-610	281	14	and	and	CCONJ
ap-610	281	15	vanishing	vanish	VERB
ap-610	281	16	for	for	ADP
ap-610	281	17	r	r	NOUN
ap-610	281	18	>	>	X
ap-610	281	19	a	a	PRON
ap-610	281	20	,	,	PUNCT
ap-610	281	21	the	the	DET
ap-610	281	22	dispersion	dispersion	NOUN
ap-610	281	23	law	law	NOUN
ap-610	281	24	gives	give	VERB
ap-610	281	25	real	real	ADJ
ap-610	281	26	frequencies	frequency	NOUN
ap-610	281	27	only	only	ADV
ap-610	281	28	for	for	ADP
ap-610	281	29	wave	wave	NOUN
ap-610	281	30	numbers	number	NOUN
ap-610	281	31	in	in	ADP
ap-610	281	32	intervals	interval	NOUN
ap-610	281	33	[	[	X
ap-610	281	34	0	0	NUM
ap-610	281	35	,	,	PUNCT
ap-610	281	36	�	�	PROPN
ap-610	281	37	/a	/a	PROPN
ap-610	281	38	]	]	X
ap-610	281	39	,	,	PUNCT
ap-610	281	40	[	[	X
ap-610	281	41	2	2	NUM
ap-610	281	42	�	�	NOUN
ap-610	281	43	/a	/a	NOUN
ap-610	281	44	,	,	PUNCT
ap-610	281	45	3	3	NUM
ap-610	281	46	�	�	PROPN
ap-610	281	47	/a	/a	NOUN
ap-610	281	48	]	]	X
ap-610	281	49	,	,	PUNCT
ap-610	281	50	[	[	X
ap-610	281	51	4	4	NUM
ap-610	281	52	�	�	NOUN
ap-610	281	53	/a	/a	NOUN
ap-610	281	54	,	,	PUNCT
ap-610	281	55	5	5	NUM
ap-610	281	56	�	�	NOUN
ap-610	281	57	/a	/a	NOUN
ap-610	281	58	]	]	X
ap-610	281	59	,	,	PUNCT
ap-610	281	60	etc	etc	X
ap-610	281	61	.	.	X
ap-610	281	62	between	between	ADP
ap-610	281	63	these	these	DET
ap-610	281	64	bands	band	NOUN
ap-610	281	65	,	,	PUNCT
ap-610	281	66	the	the	DET
ap-610	281	67	frequency	frequency	NOUN
ap-610	281	68	becomes	become	VERB
ap-610	281	69	imaginary	imaginary	ADJ
ap-610	281	70	,	,	PUNCT
ap-610	281	71	which	which	PRON
ap-610	281	72	indicates	indicate	VERB
ap-610	281	73	an	an	DET
ap-610	281	74	instability	instability	NOUN
ap-610	281	75	.	.	PUNCT
ap-610	282	1	the	the	DET
ap-610	282	2	potential	potential	ADJ
ap-610	282	3	appearance	appearance	NOUN
ap-610	282	4	of	of	ADP
ap-610	282	5	periodic	periodic	ADJ
ap-610	282	6	modes	mode	NOUN
ap-610	282	7	that	that	PRON
ap-610	282	8	carry	carry	VERB
ap-610	282	9	no	no	DET
ap-610	282	10	energy	energy	NOUN
ap-610	282	11	for	for	ADP
ap-610	282	12	the	the	DET
ap-610	282	13	nonlocal	nonlocal	ADJ
ap-610	282	14	model	model	NOUN
ap-610	282	15	with	with	ADP
ap-610	282	16	uniform	uniform	ADJ
ap-610	282	17	strain	strain	NOUN
ap-610	282	18	averaging	average	VERB
ap-610	282	19	over	over	ADP
ap-610	282	20	a	a	DET
ap-610	282	21	finite	finite	ADJ
ap-610	282	22	neighborhood	neighborhood	NOUN
ap-610	282	23	was	be	AUX
ap-610	282	24	mentioned	mention	VERB
ap-610	282	25	by	by	ADP
ap-610	282	26	bažant	bažant	NOUN
ap-610	282	27	and	and	CCONJ
ap-610	282	28	chang	chang	PROPN
ap-610	282	29	(	(	PUNCT
ap-610	282	30	1984	1984	NUM
ap-610	282	31	)	)	PUNCT
ap-610	282	32	.	.	PUNCT
ap-610	283	1	it	it	PRON
ap-610	283	2	is	be	AUX
ap-610	283	3	clear	clear	ADJ
ap-610	283	4	that	that	SCONJ
ap-610	283	5	every	every	DET
ap-610	283	6	periodic	periodic	ADJ
ap-610	283	7	function	function	NOUN
ap-610	283	8	with	with	ADP
ap-610	283	9	period	period	NOUN
ap-610	283	10	2a	2a	NUM
ap-610	283	11	is	be	AUX
ap-610	283	12	mapped	map	VERB
ap-610	283	13	by	by	ADP
ap-610	283	14	the	the	DET
ap-610	283	15	nonlocal	nonlocal	ADJ
ap-610	283	16	operator	operator	NOUN
ap-610	283	17	onto	onto	ADP
ap-610	283	18	a	a	DET
ap-610	283	19	zero	zero	NUM
ap-610	283	20	function	function	NOUN
ap-610	283	21	,	,	PUNCT
ap-610	283	22	and	and	CCONJ
ap-610	283	23	therefore	therefore	ADV
ap-610	283	24	has	have	VERB
ap-610	283	25	no	no	DET
ap-610	283	26	influence	influence	NOUN
ap-610	283	27	on	on	ADP
ap-610	283	28	the	the	DET
ap-610	283	29	nonlocal	nonlocal	ADJ
ap-610	283	30	average	average	NOUN
ap-610	283	31	.	.	PUNCT
ap-610	284	1	each	each	DET
ap-610	284	2	such	such	ADJ
ap-610	284	3	function	function	NOUN
ap-610	284	4	can	can	AUX
ap-610	284	5	be	be	AUX
ap-610	284	6	decomposed	decompose	VERB
ap-610	284	7	into	into	ADP
ap-610	284	8	a	a	DET
ap-610	284	9	sum	sum	NOUN
ap-610	284	10	of	of	ADP
ap-610	284	11	harmonic	harmonic	ADJ
ap-610	284	12	functions	function	NOUN
ap-610	284	13	of	of	ADP
ap-610	284	14	wavelengths	wavelength	NOUN
ap-610	284	15	2a	2a	NUM
ap-610	284	16	,	,	PUNCT
ap-610	284	17	2	2	NUM
ap-610	284	18	2a	2a	NUM
ap-610	284	19	,	,	PUNCT
ap-610	284	20	2	2	NUM
ap-610	284	21	3a	3a	NUM
ap-610	284	22	,	,	PUNCT
ap-610	284	23	etc	etc	X
ap-610	284	24	.	.	X
ap-610	284	25	,	,	PUNCT
ap-610	284	26	which	which	PRON
ap-610	284	27	correspond	correspond	VERB
ap-610	284	28	to	to	ADP
ap-610	284	29	zero	zero	NUM
ap-610	284	30	frequencies	frequency	NOUN
ap-610	284	31	.	.	PUNCT
ap-610	285	1	thus	thus	ADV
ap-610	285	2	the	the	DET
ap-610	285	3	static	static	ADJ
ap-610	285	4	solution	solution	NOUN
ap-610	285	5	can	can	AUX
ap-610	285	6	be	be	AUX
ap-610	285	7	modified	modify	VERB
ap-610	285	8	by	by	ADP
ap-610	285	9	a	a	DET
ap-610	285	10	periodic	periodic	ADJ
ap-610	285	11	function	function	NOUN
ap-610	285	12	with	with	ADP
ap-610	285	13	period	period	NOUN
ap-610	285	14	2a	2a	NUM
ap-610	285	15	without	without	ADP
ap-610	285	16	disturbing	disturb	VERB
ap-610	285	17	equilibrium	equilibrium	NOUN
ap-610	285	18	.	.	PUNCT
ap-610	286	1	the	the	DET
ap-610	286	2	dispersion	dispersion	NOUN
ap-610	286	3	analysis	analysis	NOUN
ap-610	286	4	indicates	indicate	VERB
ap-610	286	5	that	that	SCONJ
ap-610	286	6	in	in	ADP
ap-610	286	7	dynamics	dynamic	NOUN
ap-610	286	8	the	the	DET
ap-610	286	9	situation	situation	NOUN
ap-610	286	10	is	be	AUX
ap-610	286	11	even	even	ADV
ap-610	286	12	worse	bad	ADJ
ap-610	286	13	,	,	PUNCT
ap-610	286	14	because	because	SCONJ
ap-610	286	15	harmonic	harmonic	ADJ
ap-610	286	16	modes	mode	NOUN
ap-610	286	17	with	with	ADP
ap-610	286	18	wave	wave	NOUN
ap-610	286	19	numbers	number	NOUN
ap-610	286	20	in	in	ADP
ap-610	286	21	the	the	DET
ap-610	286	22	intervals	interval	NOUN
ap-610	286	23	(	(	PUNCT
ap-610	286	24	�	�	PROPN
ap-610	286	25	/a	/a	NOUN
ap-610	286	26	,	,	PUNCT
ap-610	286	27	2	2	NUM
ap-610	286	28	�	�	PROPN
ap-610	286	29	/a	/a	NOUN
ap-610	286	30	)	)	PUNCT
ap-610	286	31	,	,	PUNCT
ap-610	286	32	(	(	PUNCT
ap-610	286	33	3	3	NUM
ap-610	286	34	�	�	NOUN
ap-610	286	35	/a	/a	NOUN
ap-610	286	36	,	,	PUNCT
ap-610	286	37	4	4	NUM
ap-610	286	38	�	�	NOUN
ap-610	286	39	/a	/a	NOUN
ap-610	286	40	)	)	PUNCT
ap-610	286	41	,	,	PUNCT
ap-610	286	42	etc	etc	X
ap-610	286	43	.	.	X
ap-610	286	44	,	,	PUNCT
ap-610	286	45	are	be	AUX
ap-610	286	46	associated	associate	VERB
ap-610	286	47	with	with	ADP
ap-610	286	48	imaginary	imaginary	ADJ
ap-610	286	49	frequencies	frequency	NOUN
ap-610	286	50	and	and	CCONJ
ap-610	286	51	would	would	AUX
ap-610	286	52	blow	blow	VERB
ap-610	286	53	up	up	ADP
ap-610	286	54	.	.	PUNCT
ap-610	287	1	to	to	PART
ap-610	287	2	avoid	avoid	VERB
ap-610	287	3	the	the	DET
ap-610	287	4	potential	potential	ADJ
ap-610	287	5	appearance	appearance	NOUN
ap-610	287	6	of	of	ADP
ap-610	287	7	unstable	unstable	ADJ
ap-610	287	8	modes	mode	NOUN
ap-610	287	9	,	,	PUNCT
ap-610	287	10	it	it	PRON
ap-610	287	11	is	be	AUX
ap-610	287	12	sufficient	sufficient	ADJ
ap-610	287	13	to	to	PART
ap-610	287	14	use	use	VERB
ap-610	287	15	weight	weight	NOUN
ap-610	287	16	functions	function	NOUN
ap-610	287	17	with	with	ADP
ap-610	287	18	positive	positive	ADJ
ap-610	287	19	values	value	NOUN
ap-610	287	20	of	of	ADP
ap-610	287	21	their	their	PRON
ap-610	287	22	fourier	fourier	NOUN
ap-610	287	23	images	image	NOUN
ap-610	287	24	for	for	ADP
ap-610	287	25	any	any	DET
ap-610	287	26	positive	positive	ADJ
ap-610	287	27	wave	wave	NOUN
ap-610	287	28	number	number	NOUN
ap-610	287	29	k.	k.	PROPN
ap-610	288	1	this	this	PRON
ap-610	288	2	is	be	AUX
ap-610	288	3	the	the	DET
ap-610	288	4	case	case	NOUN
ap-610	288	5	for	for	ADP
ap-610	288	6	instance	instance	NOUN
ap-610	288	7	for	for	ADP
ap-610	288	8	the	the	DET
ap-610	288	9	green	green	ADJ
ap-610	288	10	function	function	NOUN
ap-610	288	11	of	of	ADP
ap-610	288	12	the	the	DET
ap-610	288	13	helmholtz	helmholtz	NOUN
ap-610	288	14	equation	equation	NOUN
ap-610	288	15	,	,	PUNCT
ap-610	288	16	and	and	CCONJ
ap-610	288	17	also	also	ADV
ap-610	288	18	for	for	ADP
ap-610	288	19	the	the	DET
ap-610	288	20	gauss	gauss	ADJ
ap-610	288	21	-	-	PUNCT
ap-610	288	22	type	type	NOUN
ap-610	288	23	weight	weight	NOUN
ap-610	288	24	function	function	NOUN
ap-610	288	25	�	�	PROPN
ap-610	288	26	�	�	PROPN
ap-610	288	27	0	0	NUM
ap-610	288	28	1	1	NUM
ap-610	288	29	2	2	NUM
ap-610	288	30	2	2	NUM
ap-610	288	31	(	(	PUNCT
ap-610	288	32	)	)	PUNCT
ap-610	288	33	r	r	NOUN
ap-610	288	34	a	a	DET
ap-610	288	35	r	r	NOUN
ap-610	288	36	a	a	DET
ap-610	288	37	�	�	PROPN
ap-610	288	38	�	�	PROPN
ap-610	288	39	e	e	X
ap-610	288	40	(	(	PUNCT
ap-610	288	41	52	52	NUM
ap-610	288	42	)	)	PUNCT
ap-610	288	43	that	that	PRON
ap-610	288	44	is	be	AUX
ap-610	288	45	often	often	ADV
ap-610	288	46	used	use	VERB
ap-610	288	47	by	by	ADP
ap-610	288	48	nonlocal	nonlocal	ADJ
ap-610	288	49	models	model	NOUN
ap-610	288	50	.	.	PUNCT
ap-610	289	1	on	on	ADP
ap-610	289	2	the	the	DET
ap-610	289	3	other	other	ADJ
ap-610	289	4	hand	hand	NOUN
ap-610	289	5	,	,	PUNCT
ap-610	289	6	the	the	DET
ap-610	289	7	fourier	fourier	ADJ
ap-610	289	8	image	image	NOUN
ap-610	289	9	of	of	ADP
ap-610	289	10	the	the	DET
ap-610	289	11	truncated	truncated	ADJ
ap-610	289	12	quartic	quartic	ADJ
ap-610	289	13	polynomial	polynomial	ADJ
ap-610	289	14	function	function	NOUN
ap-610	289	15	�	�	PROPN
ap-610	289	16	0	0	NUM
ap-610	289	17	2	2	NUM
ap-610	289	18	2	2	NUM
ap-610	289	19	2	2	NUM
ap-610	289	20	15	15	NUM
ap-610	289	21	16	16	NUM
ap-610	289	22	1	1	NUM
ap-610	289	23	(	(	PUNCT
ap-610	289	24	)	)	PUNCT
ap-610	289	25	r	r	NOUN
ap-610	289	26	a	a	DET
ap-610	289	27	r	r	NOUN
ap-610	289	28	a	a	DET
ap-610	289	29	�	�	PROPN
ap-610	289	30	�	�	PROPN
ap-610	289	31	(	(	PUNCT
ap-610	289	32	53	53	NUM
ap-610	289	33	)	)	PUNCT
ap-610	289	34	is	be	AUX
ap-610	289	35	positive	positive	ADJ
ap-610	289	36	only	only	ADV
ap-610	289	37	for	for	ADP
ap-610	289	38	wave	wave	NOUN
ap-610	289	39	numbers	number	NOUN
ap-610	289	40	smaller	small	ADJ
ap-610	289	41	than	than	ADP
ap-610	289	42	5.763	5.763	NUM
ap-610	289	43	/	/	SYM
ap-610	289	44	a.	a.	NOUN
ap-610	289	45	consequently	consequently	ADV
ap-610	289	46	,	,	PUNCT
ap-610	289	47	instabilities	instability	NOUN
ap-610	289	48	could	could	AUX
ap-610	289	49	develop	develop	VERB
ap-610	289	50	for	for	ADP
ap-610	289	51	fine	fine	ADJ
ap-610	289	52	meshes	mesh	NOUN
ap-610	289	53	with	with	ADP
ap-610	289	54	element	element	ADJ
ap-610	289	55	size	size	NOUN
ap-610	289	56	in	in	ADP
ap-610	289	57	the	the	DET
ap-610	289	58	order	order	NOUN
ap-610	289	59	of	of	ADP
ap-610	289	60	a.	a.	NOUN
ap-610	289	61	the	the	DET
ap-610	289	62	relationship	relationship	NOUN
ap-610	289	63	between	between	ADP
ap-610	289	64	atomic	atomic	ADJ
ap-610	289	65	lattices	lattice	NOUN
ap-610	289	66	and	and	CCONJ
ap-610	289	67	the	the	DET
ap-610	289	68	nonlocal	nonlocal	ADJ
ap-610	289	69	integral	integral	ADJ
ap-610	289	70	models	model	NOUN
ap-610	289	71	was	be	AUX
ap-610	289	72	studied	study	VERB
ap-610	289	73	by	by	ADP
ap-610	289	74	eringen	eringen	PROPN
ap-610	289	75	(	(	PUNCT
ap-610	289	76	1972	1972	NUM
ap-610	289	77	)	)	PUNCT
ap-610	289	78	,	,	PUNCT
ap-610	289	79	who	who	PRON
ap-610	289	80	proposed	propose	VERB
ap-610	289	81	a	a	DET
ap-610	289	82	weight	weight	NOUN
ap-610	289	83	function	function	NOUN
ap-610	289	84	that	that	PRON
ap-610	289	85	should	should	AUX
ap-610	289	86	correspond	correspond	VERB
ap-610	289	87	to	to	ADP
ap-610	289	88	the	the	DET
ap-610	289	89	mass	mass	ADJ
ap-610	289	90	-	-	PUNCT
ap-610	289	91	spring	spring	NOUN
ap-610	289	92	model	model	NOUN
ap-610	289	93	.	.	PUNCT
ap-610	290	1	however	however	ADV
ap-610	290	2	,	,	PUNCT
ap-610	290	3	eringen	eringen	PROPN
ap-610	290	4	did	do	AUX
ap-610	290	5	not	not	PART
ap-610	290	6	use	use	VERB
ap-610	290	7	the	the	DET
ap-610	290	8	complete	complete	ADJ
ap-610	290	9	inverse	inverse	NOUN
ap-610	290	10	fourier	fourier	NOUN
ap-610	290	11	transform	transform	NOUN
ap-610	290	12	but	but	CCONJ
ap-610	290	13	integrated	integrate	VERB
ap-610	290	14	(	(	PUNCT
ap-610	290	15	38	38	NUM
ap-610	290	16	)	)	PUNCT
ap-610	290	17	only	only	ADV
ap-610	290	18	in	in	ADP
ap-610	290	19	the	the	DET
ap-610	290	20	limits	limit	NOUN
ap-610	290	21	�	�	PROPN
ap-610	290	22	�	�	PROPN
ap-610	290	23	�	�	PROPN
ap-610	290	24	�	�	PROPN
ap-610	290	25	�	�	PROPN
ap-610	290	26	a	a	DET
ap-610	290	27	k	k	PROPN
ap-610	290	28	a.	a.	NOUN
ap-610	290	29	consequently	consequently	ADV
ap-610	290	30	,	,	PUNCT
ap-610	290	31	his	his	PRON
ap-610	290	32	nonlocal	nonlocal	ADJ
ap-610	290	33	model	model	NOUN
ap-610	290	34	would	would	AUX
ap-610	290	35	reproduce	reproduce	VERB
ap-610	290	36	the	the	DET
ap-610	290	37	dispersion	dispersion	NOUN
ap-610	290	38	law	law	NOUN
ap-610	290	39	of	of	ADP
ap-610	290	40	the	the	DET
ap-610	290	41	mass	mass	ADJ
ap-610	290	42	-	-	PUNCT
ap-610	290	43	spring	spring	NOUN
ap-610	290	44	model	model	NOUN
ap-610	290	45	only	only	ADV
ap-610	290	46	for	for	ADP
ap-610	290	47	wavelengths	wavelength	NOUN
ap-610	290	48	larger	large	ADJ
ap-610	290	49	than	than	ADP
ap-610	290	50	2a	2a	NUM
ap-610	290	51	.	.	PUNCT
ap-610	291	1	all	all	DET
ap-610	291	2	smaller	small	ADJ
ap-610	291	3	wavelengths	wavelength	NOUN
ap-610	291	4	would	would	AUX
ap-610	291	5	be	be	AUX
ap-610	291	6	associated	associate	VERB
ap-610	291	7	with	with	ADP
ap-610	291	8	a	a	DET
ap-610	291	9	zero	zero	NUM
ap-610	291	10	frequency	frequency	NOUN
ap-610	291	11	,	,	PUNCT
ap-610	291	12	i.e.	i.e.	X
ap-610	291	13	,	,	PUNCT
ap-610	291	14	stationary	stationary	ADJ
ap-610	291	15	waves	wave	NOUN
ap-610	291	16	could	could	AUX
ap-610	291	17	easily	easily	ADV
ap-610	291	18	appear	appear	VERB
ap-610	291	19	.	.	PUNCT
ap-610	292	1	eringen	eringen	PROPN
ap-610	292	2	’s	’s	PART
ap-610	292	3	weight	weight	NOUN
ap-610	292	4	function	function	NOUN
ap-610	292	5	�	�	PROPN
ap-610	292	6	�	�	PROPN
ap-610	292	7	�	�	PROPN
ap-610	292	8	�	�	PROPN
ap-610	292	9	�	�	PROPN
ap-610	292	10	�	�	PROPN
ap-610	292	11	�	�	PROPN
ap-610	292	12	�	�	PROPN
ap-610	292	13	�	�	PROPN
ap-610	292	14	0	0	NUM
ap-610	292	15	2	2	NUM
ap-610	292	16	3	3	NUM
ap-610	292	17	2	2	NUM
ap-610	292	18	4	4	NUM
ap-610	292	19	2	2	NUM
ap-610	292	20	2	2	NUM
ap-610	292	21	1	1	NUM
ap-610	292	22	1	1	NUM
ap-610	292	23	2	2	NUM
ap-610	292	24	1	1	NUM
ap-610	292	25	2	2	NUM
ap-610	292	26	2	2	NUM
ap-610	292	27	(	(	PUNCT
ap-610	292	28	)	)	PUNCT
ap-610	292	29	cos	cos	ADP
ap-610	292	30	x	x	PUNCT
ap-610	292	31	a	a	X
ap-610	292	32	x	x	X
ap-610	292	33	a	a	DET
ap-610	292	34	a	a	DET
ap-610	292	35	�	�	PROPN
ap-610	292	36	�	�	PROPN
ap-610	292	37	�	�	PROPN
ap-610	292	38	�	�	PROPN
ap-610	292	39	�	�	PROPN
ap-610	292	40	�	�	PROPN
ap-610	292	41	�	�	PROPN
ap-610	292	42	�	�	PROPN
ap-610	292	43	�	�	PROPN
ap-610	292	44	�	�	PROPN
ap-610	292	45	�	�	PROPN
ap-610	292	46	�	�	PROPN
ap-610	292	47	�	�	PROPN
ap-610	292	48	�	�	PROPN
ap-610	292	49	si	si	PROPN
ap-610	292	50	si	si	PROPN
ap-610	292	51	2	2	NUM
ap-610	292	52	2	2	NUM
ap-610	292	53	2	2	NUM
ap-610	292	54	4	4	NUM
ap-610	292	55	2	2	NUM
ap-610	292	56	1	1	NUM
ap-610	292	57	4	4	NUM
ap-610	292	58	2	2	NUM
ap-610	292	59	2	2	NUM
ap-610	292	60	x	x	SYM
ap-610	292	61	x	x	X
ap-610	292	62	a	a	PRON
ap-610	292	63	x	x	SYM
ap-610	292	64	a	a	DET
ap-610	292	65	x	x	SYM
ap-610	292	66	a	a	DET
ap-610	292	67	x	x	SYM
ap-610	292	68	a	a	PRON
ap-610	292	69	x	x	SYM
ap-610	292	70	a	a	DET
ap-610	292	71	�	�	PROPN
ap-610	292	72	�	�	PROPN
ap-610	292	73	�	�	PROPN
ap-610	292	74	�	�	PROPN
ap-610	292	75	�	�	PROPN
ap-610	292	76	�	�	PROPN
ap-610	292	77	�	�	PROPN
ap-610	292	78	�	�	PROPN
ap-610	292	79	�	�	PROPN
ap-610	292	80	�	�	PROPN
ap-610	292	81	�	�	PROPN
ap-610	292	82	�	�	PROPN
ap-610	292	83	�	�	PROPN
ap-610	292	84	�	�	PROPN
ap-610	292	85	�	�	PROPN
ap-610	292	86	�	�	PROPN
ap-610	292	87	�	�	PROPN
ap-610	292	88	�	�	PROPN
ap-610	292	89	�	�	PROPN
ap-610	292	90	�	�	PROPN
ap-610	292	91	sin	sin	VERB
ap-610	293	1	si	si	PROPN
ap-610	293	2	si	si	PROPN
ap-610	293	3	�	�	PROPN
ap-610	293	4	�	�	PROPN
ap-610	293	5	1	1	NUM
ap-610	293	6	4	4	NUM
ap-610	293	7	2	2	NUM
ap-610	293	8	2	2	NUM
ap-610	293	9	�	�	PROPN
ap-610	293	10	�	�	PROPN
ap-610	293	11	�	�	PROPN
ap-610	293	12	�	�	PROPN
ap-610	293	13	�	�	PROPN
ap-610	293	14	�	�	PROPN
ap-610	293	15	�	�	PROPN
ap-610	293	16	�	�	PROPN
ap-610	293	17	�	�	PROPN
ap-610	293	18	�	�	PROPN
ap-610	293	19	�	�	PROPN
ap-610	293	20	�	�	PROPN
ap-610	293	21	�	�	PROPN
ap-610	293	22	�	�	PROPN
ap-610	293	23	�	�	PROPN
ap-610	293	24	�	�	PROPN
ap-610	293	25	�	�	PROPN
ap-610	293	26	�	�	PROPN
ap-610	293	27	�	�	PROPN
ap-610	293	28	x	x	PUNCT
ap-610	293	29	a	a	PRON
ap-610	293	30	x	x	X
ap-610	293	31	a	a	DET
ap-610	293	32	si	si	X
ap-610	293	33	(	(	PUNCT
ap-610	293	34	54	54	NUM
ap-610	293	35	)	)	PUNCT
ap-610	293	36	(	(	PUNCT
ap-610	293	37	where	where	SCONJ
ap-610	293	38	si	si	PROPN
ap-610	293	39	dx	dx	PROPN
ap-610	293	40	x	x	PROPN
ap-610	293	41	�	�	PROPN
ap-610	293	42	�	�	PROPN
ap-610	293	43	�	�	PROPN
ap-610	293	44	�	�	PROPN
ap-610	293	45	�	�	PROPN
ap-610	293	46	�	�	PROPN
ap-610	293	47	1	1	NUM
ap-610	293	48	0	0	NUM
ap-610	293	49	sin	sin	NOUN
ap-610	293	50	)	)	PUNCT
ap-610	293	51	is	be	AUX
ap-610	293	52	also	also	ADV
ap-610	293	53	much	much	ADV
ap-610	293	54	more	more	ADV
ap-610	293	55	complicated	complicated	ADJ
ap-610	293	56	than	than	ADP
ap-610	293	57	the	the	DET
ap-610	293	58	piecewise	piecewise	NOUN
ap-610	293	59	linear	linear	NOUN
ap-610	293	60	function	function	NOUN
ap-610	293	61	reproducing	reproduce	VERB
ap-610	293	62	the	the	DET
ap-610	293	63	dispersion	dispersion	NOUN
ap-610	293	64	of	of	ADP
ap-610	293	65	the	the	DET
ap-610	293	66	discrete	discrete	ADJ
ap-610	293	67	model	model	NOUN
ap-610	293	68	exactly	exactly	ADV
ap-610	293	69	for	for	ADP
ap-610	293	70	arbitrary	arbitrary	ADJ
ap-610	293	71	wave	wave	NOUN
ap-610	293	72	numbers	number	NOUN
ap-610	293	73	,	,	PUNCT
ap-610	293	74	and	and	CCONJ
ap-610	293	75	does	do	AUX
ap-610	293	76	not	not	PART
ap-610	293	77	seem	seem	VERB
ap-610	293	78	to	to	PART
ap-610	293	79	be	be	AUX
ap-610	293	80	very	very	ADV
ap-610	293	81	practical	practical	ADJ
ap-610	293	82	.	.	PUNCT
ap-610	294	1	3	3	NUM
ap-610	294	2	size	size	NOUN
ap-610	294	3	effects	effect	NOUN
ap-610	294	4	in	in	ADP
ap-610	294	5	microscale	microscale	ADJ
ap-610	294	6	plasticity	plasticity	NOUN
ap-610	294	7	3.1	3.1	NUM
ap-610	294	8	experimental	experimental	ADJ
ap-610	294	9	observations	observation	NOUN
ap-610	294	10	among	among	ADP
ap-610	294	11	phenomena	phenomenon	NOUN
ap-610	294	12	that	that	PRON
ap-610	294	13	are	be	AUX
ap-610	294	14	hard	hard	ADJ
ap-610	294	15	to	to	PART
ap-610	294	16	model	model	VERB
ap-610	294	17	and	and	CCONJ
ap-610	294	18	predict	predict	VERB
ap-610	294	19	by	by	ADP
ap-610	294	20	standard	standard	ADJ
ap-610	294	21	continuum	continuum	ADJ
ap-610	294	22	theories	theory	NOUN
ap-610	294	23	,	,	PUNCT
ap-610	294	24	one	one	PRON
ap-610	294	25	finds	find	VERB
ap-610	294	26	also	also	ADV
ap-610	294	27	various	various	ADJ
ap-610	294	28	forms	form	NOUN
ap-610	294	29	of	of	ADP
ap-610	294	30	size	size	NOUN
ap-610	294	31	effects	effect	NOUN
ap-610	294	32	on	on	ADP
ap-610	294	33	the	the	DET
ap-610	294	34	apparent	apparent	ADJ
ap-610	294	35	“	"	PUNCT
ap-610	294	36	material	material	ADJ
ap-610	294	37	”	"	PUNCT
ap-610	294	38	properties	property	NOUN
ap-610	294	39	.	.	PUNCT
ap-610	295	1	such	such	ADJ
ap-610	295	2	effects	effect	NOUN
ap-610	295	3	can	can	AUX
ap-610	295	4	be	be	AUX
ap-610	295	5	observed	observe	VERB
ap-610	295	6	already	already	ADV
ap-610	295	7	in	in	ADP
ap-610	295	8	the	the	DET
ap-610	295	9	elastic	elastic	ADJ
ap-610	295	10	range	range	NOUN
ap-610	295	11	.	.	PUNCT
ap-610	296	1	for	for	ADP
ap-610	296	2	instance	instance	NOUN
ap-610	296	3	,	,	PUNCT
ap-610	296	4	according	accord	VERB
ap-610	296	5	to	to	ADP
ap-610	296	6	standard	standard	ADJ
ap-610	296	7	elasticity	elasticity	NOUN
ap-610	296	8	,	,	PUNCT
ap-610	296	9	the	the	DET
ap-610	296	10	torsional	torsional	ADJ
ap-610	296	11	stiffness	stiffness	NOUN
ap-610	296	12	of	of	ADP
ap-610	296	13	a	a	DET
ap-610	296	14	prismatic	prismatic	ADJ
ap-610	296	15	beam	beam	NOUN
ap-610	296	16	with	with	ADP
ap-610	296	17	a	a	DET
ap-610	296	18	circular	circular	ADJ
ap-610	296	19	cross	cross	NOUN
ap-610	296	20	section	section	NOUN
ap-610	296	21	should	should	AUX
ap-610	296	22	be	be	AUX
ap-610	296	23	proportional	proportional	ADJ
ap-610	296	24	to	to	ADP
ap-610	296	25	the	the	DET
ap-610	296	26	shear	shear	NOUN
ap-610	296	27	modulus	modulus	NOUN
ap-610	296	28	of	of	ADP
ap-610	296	29	elasticity	elasticity	NOUN
ap-610	296	30	,	,	PUNCT
ap-610	296	31	g	g	NOUN
ap-610	296	32	,	,	PUNCT
ap-610	296	33	and	and	CCONJ
ap-610	296	34	to	to	ADP
ap-610	296	35	the	the	DET
ap-610	296	36	third	third	ADJ
ap-610	296	37	power	power	NOUN
ap-610	296	38	of	of	ADP
ap-610	296	39	the	the	DET
ap-610	296	40	sectional	sectional	ADJ
ap-610	296	41	diameter	diameter	NOUN
ap-610	296	42	,	,	PUNCT
ap-610	296	43	d.	d.	PROPN
ap-610	296	44	however	however	ADV
ap-610	296	45	,	,	PUNCT
ap-610	296	46	if	if	SCONJ
ap-610	296	47	the	the	DET
ap-610	296	48	torsional	torsional	ADJ
ap-610	296	49	stiffness	stiffness	NOUN
ap-610	296	50	is	be	AUX
ap-610	296	51	evaluated	evaluate	VERB
ap-610	296	52	experimentally	experimentally	ADV
ap-610	296	53	as	as	ADP
ap-610	296	54	the	the	DET
ap-610	296	55	ratio	ratio	NOUN
ap-610	296	56	between	between	ADP
ap-610	296	57	the	the	DET
ap-610	296	58	torque	torque	NOUN
ap-610	296	59	and	and	CCONJ
ap-610	296	60	the	the	DET
ap-610	296	61	relative	relative	ADJ
ap-610	296	62	twist	twist	NOUN
ap-610	296	63	angle	angle	NOUN
ap-610	296	64	,	,	PUNCT
ap-610	296	65	it	it	PRON
ap-610	296	66	turns	turn	VERB
ap-610	296	67	out	out	ADP
ap-610	296	68	that	that	SCONJ
ap-610	296	69	the	the	DET
ap-610	296	70	expected	expect	VERB
ap-610	296	71	proportionality	proportionality	NOUN
ap-610	296	72	to	to	PART
ap-610	296	73	d3	d3	VERB
ap-610	296	74	holds	hold	NOUN
ap-610	296	75	with	with	ADP
ap-610	296	76	sufficient	sufficient	ADJ
ap-610	296	77	accuracy	accuracy	NOUN
ap-610	296	78	only	only	ADV
ap-610	296	79	for	for	ADP
ap-610	296	80	diameters	diameter	NOUN
ap-610	296	81	larger	large	ADJ
ap-610	296	82	than	than	ADP
ap-610	296	83	a	a	DET
ap-610	296	84	certain	certain	ADJ
ap-610	296	85	threshold	threshold	NOUN
ap-610	296	86	value	value	NOUN
ap-610	296	87	(	(	PUNCT
ap-610	296	88	morrison	morrison	PROPN
ap-610	296	89	,	,	PUNCT
ap-610	296	90	1939;	1939;	PROPN
ap-610	296	91	lakes	lakes	PROPN
ap-610	296	92	,	,	PUNCT
ap-610	296	93	1986;	1986;	PROPN
ap-610	296	94	fleck	fleck	NOUN
ap-610	296	95	,	,	PUNCT
ap-610	296	96	muller	muller	NOUN
ap-610	296	97	,	,	PUNCT
ap-610	296	98	ashby	ashby	PROPN
ap-610	296	99	and	and	CCONJ
ap-610	296	100	hutchinson	hutchinson	PROPN
ap-610	296	101	,	,	PUNCT
ap-610	296	102	1994	1994	NUM
ap-610	296	103	)	)	PUNCT
ap-610	296	104	.	.	PUNCT
ap-610	297	1	if	if	SCONJ
ap-610	297	2	the	the	DET
ap-610	297	3	results	result	NOUN
ap-610	297	4	obtained	obtain	VERB
ap-610	297	5	for	for	ADP
ap-610	297	6	thick	thick	ADJ
ap-610	297	7	wires	wire	NOUN
ap-610	297	8	are	be	AUX
ap-610	297	9	extrapolated	extrapolate	VERB
ap-610	297	10	to	to	ADP
ap-610	297	11	thin	thin	ADJ
ap-610	297	12	wires	wire	NOUN
ap-610	297	13	,	,	PUNCT
ap-610	297	14	the	the	DET
ap-610	297	15	actual	actual	ADJ
ap-610	297	16	stiffness	stiffness	NOUN
ap-610	297	17	is	be	AUX
ap-610	297	18	underestimated	underestimate	VERB
ap-610	297	19	.	.	PUNCT
ap-610	298	1	in	in	ADP
ap-610	298	2	the	the	DET
ap-610	298	3	context	context	NOUN
ap-610	298	4	of	of	ADP
ap-610	298	5	the	the	DET
ap-610	298	6	standard	standard	ADJ
ap-610	298	7	theory	theory	NOUN
ap-610	298	8	,	,	PUNCT
ap-610	298	9	this	this	PRON
ap-610	298	10	can	can	AUX
ap-610	298	11	be	be	AUX
ap-610	298	12	interpreted	interpret	VERB
ap-610	298	13	as	as	ADP
ap-610	298	14	a	a	DET
ap-610	298	15	dependence	dependence	NOUN
ap-610	298	16	of	of	ADP
ap-610	298	17	the	the	DET
ap-610	298	18	elastic	elastic	ADJ
ap-610	298	19	modulus	modulus	NOUN
ap-610	298	20	on	on	ADP
ap-610	298	21	the	the	DET
ap-610	298	22	size	size	NOUN
ap-610	298	23	of	of	ADP
ap-610	298	24	the	the	DET
ap-610	298	25	sample	sample	NOUN
ap-610	298	26	.	.	PUNCT
ap-610	299	1	however	however	ADV
ap-610	299	2	,	,	PUNCT
ap-610	299	3	such	such	DET
ap-610	299	4	an	an	DET
ap-610	299	5	explanation	explanation	NOUN
ap-610	299	6	is	be	AUX
ap-610	299	7	not	not	PART
ap-610	299	8	satisfactory	satisfactory	ADJ
ap-610	299	9	from	from	ADP
ap-610	299	10	the	the	DET
ap-610	299	11	theoretical	theoretical	ADJ
ap-610	299	12	point	point	NOUN
ap-610	299	13	of	of	ADP
ap-610	299	14	view	view	NOUN
ap-610	299	15	.	.	PUNCT
ap-610	300	1	in	in	ADP
ap-610	300	2	a	a	DET
ap-610	300	3	more	more	ADV
ap-610	300	4	fundamental	fundamental	ADJ
ap-610	300	5	approach	approach	NOUN
ap-610	300	6	,	,	PUNCT
ap-610	300	7	it	it	PRON
ap-610	300	8	is	be	AUX
ap-610	300	9	admitted	admit	VERB
ap-610	300	10	that	that	SCONJ
ap-610	300	11	the	the	DET
ap-610	300	12	standard	standard	ADJ
ap-610	300	13	continuum	continuum	ADJ
ap-610	300	14	elasticity	elasticity	NOUN
ap-610	300	15	theory	theory	NOUN
ap-610	300	16	provides	provide	VERB
ap-610	300	17	only	only	ADV
ap-610	300	18	a	a	DET
ap-610	300	19	large	large	ADJ
ap-610	300	20	-	-	PUNCT
ap-610	300	21	size	size	NOUN
ap-610	300	22	approximation	approximation	NOUN
ap-610	300	23	to	to	ADP
ap-610	300	24	the	the	DET
ap-610	300	25	static	static	ADJ
ap-610	300	26	torsion	torsion	NOUN
ap-610	300	27	problem	problem	NOUN
ap-610	300	28	,	,	PUNCT
ap-610	300	29	just	just	ADV
ap-610	300	30	as	as	SCONJ
ap-610	300	31	it	it	PRON
ap-610	300	32	provides	provide	VERB
ap-610	300	33	only	only	ADV
ap-610	300	34	a	a	DET
ap-610	300	35	long	long	ADJ
ap-610	300	36	-	-	PUNCT
ap-610	300	37	wave	wave	NOUN
ap-610	300	38	approximation	approximation	NOUN
ap-610	300	39	to	to	ADP
ap-610	300	40	the	the	DET
ap-610	300	41	dynamic	dynamic	ADJ
ap-610	300	42	wave	wave	NOUN
ap-610	300	43	dispersion	dispersion	NOUN
ap-610	300	44	problem	problem	NOUN
ap-610	300	45	.	.	PUNCT
ap-610	301	1	if	if	SCONJ
ap-610	301	2	the	the	DET
ap-610	301	3	size	size	NOUN
ap-610	301	4	of	of	ADP
ap-610	301	5	the	the	DET
ap-610	301	6	structure	structure	NOUN
ap-610	301	7	is	be	AUX
ap-610	301	8	comparable	comparable	ADJ
ap-610	301	9	to	to	ADP
ap-610	301	10	a	a	DET
ap-610	301	11	certain	certain	ADJ
ap-610	301	12	internal	internal	ADJ
ap-610	301	13	length	length	NOUN
ap-610	301	14	scale	scale	NOUN
ap-610	301	15	of	of	ADP
ap-610	301	16	the	the	DET
ap-610	301	17	material	material	NOUN
ap-610	301	18	,	,	PUNCT
ap-610	301	19	higher	high	ADJ
ap-610	301	20	-	-	PUNCT
ap-610	301	21	order	order	NOUN
ap-610	301	22	effects	effect	NOUN
ap-610	301	23	appear	appear	VERB
ap-610	301	24	and	and	CCONJ
ap-610	301	25	the	the	DET
ap-610	301	26	classical	classical	ADJ
ap-610	301	27	concept	concept	NOUN
ap-610	301	28	of	of	ADP
ap-610	301	29	a	a	DET
ap-610	301	30	homogeneous	homogeneous	ADJ
ap-610	301	31	local	local	ADJ
ap-610	301	32	continuum	continuum	NOUN
ap-610	301	33	needs	need	VERB
ap-610	301	34	an	an	DET
ap-610	301	35	adjustment	adjustment	NOUN
ap-610	301	36	.	.	PUNCT
ap-610	302	1	in	in	ADP
ap-610	302	2	elasticity	elasticity	NOUN
ap-610	302	3	,	,	PUNCT
ap-610	302	4	such	such	DET
ap-610	302	5	an	an	DET
ap-610	302	6	adjustment	adjustment	NOUN
ap-610	302	7	that	that	PRON
ap-610	302	8	accounts	account	VERB
ap-610	302	9	for	for	ADP
ap-610	302	10	the	the	DET
ap-610	302	11	principal	principal	ADJ
ap-610	302	12	features	feature	NOUN
ap-610	302	13	of	of	ADP
ap-610	302	14	the	the	DET
ap-610	302	15	microstructure	microstructure	NOUN
ap-610	302	16	is	be	AUX
ap-610	302	17	provided	provide	VERB
ap-610	302	18	by	by	ADP
ap-610	302	19	various	various	ADJ
ap-610	302	20	theories	theory	NOUN
ap-610	302	21	enriched	enrich	VERB
ap-610	302	22	by	by	ADP
ap-610	302	23	higher	high	ADJ
ap-610	302	24	-	-	PUNCT
ap-610	302	25	order	order	NOUN
ap-610	302	26	gradients	gradient	NOUN
ap-610	302	27	or	or	CCONJ
ap-610	302	28	integral	integral	ADJ
ap-610	302	29	-	-	PUNCT
ap-610	302	30	type	type	NOUN
ap-610	302	31	nonlocal	nonlocal	ADJ
ap-610	302	32	terms	term	NOUN
ap-610	302	33	,	,	PUNCT
ap-610	302	34	already	already	ADV
ap-610	302	35	exposed	expose	VERB
ap-610	302	36	in	in	ADP
ap-610	302	37	section	section	NOUN
ap-610	302	38	2	2	NUM
ap-610	302	39	.	.	PUNCT
ap-610	303	1	in	in	ADP
ap-610	303	2	general	general	ADJ
ap-610	303	3	,	,	PUNCT
ap-610	303	4	by	by	ADP
ap-610	303	5	size	size	NOUN
ap-610	303	6	effect	effect	NOUN
ap-610	303	7	we	we	PRON
ap-610	303	8	mean	mean	VERB
ap-610	303	9	a	a	DET
ap-610	303	10	situation	situation	NOUN
ap-610	303	11	when	when	SCONJ
ap-610	303	12	a	a	DET
ap-610	303	13	certain	certain	ADJ
ap-610	303	14	parameter	parameter	NOUN
ap-610	303	15	normally	normally	ADV
ap-610	303	16	considered	consider	VERB
ap-610	303	17	as	as	ADP
ap-610	303	18	a	a	DET
ap-610	303	19	material	material	NOUN
ap-610	303	20	property	property	NOUN
ap-610	303	21	appears	appear	VERB
ap-610	303	22	to	to	PART
ap-610	303	23	be	be	AUX
ap-610	303	24	dependent	dependent	ADJ
ap-610	303	25	on	on	ADP
ap-610	303	26	the	the	DET
ap-610	303	27	size	size	NOUN
ap-610	303	28	of	of	ADP
ap-610	303	29	the	the	DET
ap-610	303	30	sample	sample	NOUN
ap-610	303	31	or	or	CCONJ
ap-610	303	32	specimen	speciman	NOUN
ap-610	303	33	for	for	ADP
ap-610	303	34	which	which	PRON
ap-610	303	35	it	it	PRON
ap-610	303	36	is	be	AUX
ap-610	303	37	evaluated	evaluate	VERB
ap-610	303	38	.	.	PUNCT
ap-610	304	1	the	the	DET
ap-610	304	2	reason	reason	NOUN
ap-610	304	3	for	for	ADP
ap-610	304	4	this	this	DET
ap-610	304	5	unexpected	unexpected	ADJ
ap-610	304	6	behavior	behavior	NOUN
ap-610	304	7	is	be	AUX
ap-610	304	8	usually	usually	ADV
ap-610	304	9	that	that	SCONJ
ap-610	304	10	the	the	DET
ap-610	304	11	specimens	specimen	NOUN
ap-610	304	12	are	be	AUX
ap-610	304	13	either	either	CCONJ
ap-610	304	14	too	too	ADV
ap-610	304	15	small	small	ADJ
ap-610	304	16	or	or	CCONJ
ap-610	304	17	too	too	ADV
ap-610	304	18	big	big	ADJ
ap-610	304	19	and	and	CCONJ
ap-610	304	20	the	the	DET
ap-610	304	21	underlying	underlying	ADJ
ap-610	304	22	theory	theory	NOUN
ap-610	304	23	is	be	AUX
ap-610	304	24	not	not	PART
ap-610	304	25	adequate	adequate	ADJ
ap-610	304	26	on	on	ADP
ap-610	304	27	the	the	DET
ap-610	304	28	extreme	extreme	ADJ
ap-610	304	29	scale	scale	NOUN
ap-610	304	30	.	.	PUNCT
ap-610	305	1	important	important	ADJ
ap-610	305	2	size	size	NOUN
ap-610	305	3	effects	effect	NOUN
ap-610	305	4	in	in	ADP
ap-610	305	5	microscale	microscale	ADJ
ap-610	305	6	plasticity	plasticity	NOUN
ap-610	305	7	have	have	AUX
ap-610	305	8	been	be	AUX
ap-610	305	9	detected	detect	VERB
ap-610	305	10	in	in	ADP
ap-610	305	11	indentation	indentation	NOUN
ap-610	305	12	tests	test	NOUN
ap-610	305	13	(	(	PUNCT
ap-610	305	14	nix	nix	PROPN
ap-610	305	15	,	,	PUNCT
ap-610	305	16	1989;	1989;	PROPN
ap-610	305	17	ma	ma	PROPN
ap-610	305	18	and	and	CCONJ
ap-610	305	19	clarke	clarke	PROPN
ap-610	305	20	,	,	PUNCT
ap-610	305	21	1995;	1995;	PROPN
ap-610	305	22	poole	poole	NOUN
ap-610	305	23	,	,	PUNCT
ap-610	305	24	ashby	ashby	NOUN
ap-610	305	25	and	and	CCONJ
ap-610	305	26	fleck	fleck	NOUN
ap-610	305	27	,	,	PUNCT
ap-610	305	28	1996	1996	NUM
ap-610	305	29	)	)	PUNCT
ap-610	305	30	,	,	PUNCT
ap-610	305	31	bending	bend	VERB
ap-610	305	32	of	of	ADP
ap-610	305	33	thin	thin	ADJ
ap-610	305	34	sheets	sheet	NOUN
ap-610	305	35	(	(	PUNCT
ap-610	305	36	stolken	stolken	VERB
ap-610	305	37	and	and	CCONJ
ap-610	305	38	evans	evan	NOUN
ap-610	305	39	,	,	PUNCT
ap-610	305	40	1998	1998	NUM
ap-610	305	41	)	)	PUNCT
ap-610	305	42	,	,	PUNCT
ap-610	305	43	plastic	plastic	NOUN
ap-610	305	44	torsion	torsion	NOUN
ap-610	305	45	(	(	PUNCT
ap-610	305	46	fleck	fleck	NOUN
ap-610	305	47	et	et	PROPN
ap-610	305	48	al	al	PROPN
ap-610	305	49	.	.	PROPN
ap-610	305	50	,	,	PUNCT
ap-610	305	51	24	24	NUM
ap-610	305	52	©	©	PROPN
ap-610	305	53	czech	czech	PROPN
ap-610	305	54	technical	technical	PROPN
ap-610	305	55	university	university	PROPN
ap-610	305	56	publishing	publishing	NOUN
ap-610	305	57	house	house	NOUN
ap-610	305	58	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	305	59	acta	acta	PROPN
ap-610	305	60	polytechnica	polytechnica	PROPN
ap-610	305	61	vol	vol	NOUN
ap-610	305	62	.	.	PROPN
ap-610	306	1	44	44	NUM
ap-610	307	1	no	no	NOUN
ap-610	307	2	.	.	PUNCT
ap-610	308	1	5–6/2004	5–6/2004	NUM
ap-610	308	2	1996	1996	NUM
ap-610	308	3	)	)	PUNCT
ap-610	308	4	,	,	PUNCT
ap-610	308	5	and	and	CCONJ
ap-610	308	6	void	void	VERB
ap-610	308	7	growth	growth	NOUN
ap-610	308	8	.	.	PUNCT
ap-610	309	1	from	from	ADP
ap-610	309	2	the	the	DET
ap-610	309	3	practical	practical	ADJ
ap-610	309	4	point	point	NOUN
ap-610	309	5	of	of	ADP
ap-610	309	6	view	view	NOUN
ap-610	309	7	,	,	PUNCT
ap-610	309	8	proper	proper	ADJ
ap-610	309	9	understanding	understanding	NOUN
ap-610	309	10	and	and	CCONJ
ap-610	309	11	modeling	modeling	NOUN
ap-610	309	12	of	of	ADP
ap-610	309	13	size	size	NOUN
ap-610	309	14	effects	effect	NOUN
ap-610	309	15	on	on	ADP
ap-610	309	16	the	the	DET
ap-610	309	17	small	small	ADJ
ap-610	309	18	scale	scale	NOUN
ap-610	309	19	is	be	AUX
ap-610	309	20	essential	essential	ADJ
ap-610	309	21	for	for	ADP
ap-610	309	22	applications	application	NOUN
ap-610	309	23	of	of	ADP
ap-610	309	24	simulation	simulation	NOUN
ap-610	309	25	methods	method	NOUN
ap-610	309	26	in	in	ADP
ap-610	309	27	the	the	DET
ap-610	309	28	analysis	analysis	NOUN
ap-610	309	29	and	and	CCONJ
ap-610	309	30	design	design	NOUN
ap-610	309	31	of	of	ADP
ap-610	309	32	microand	microand	NOUN
ap-610	309	33	nano	nano	NOUN
ap-610	309	34	-	-	PUNCT
ap-610	309	35	devices	device	NOUN
ap-610	309	36	used	use	VERB
ap-610	309	37	in	in	ADP
ap-610	309	38	modern	modern	ADJ
ap-610	309	39	technology	technology	NOUN
ap-610	309	40	.	.	PUNCT
ap-610	310	1	3.2	3.2	NUM
ap-610	310	2	illustrative	illustrative	ADJ
ap-610	310	3	example	example	NOUN
ap-610	310	4	:	:	PUNCT
ap-610	310	5	shear	shear	ADJ
ap-610	310	6	layer	layer	NOUN
ap-610	310	7	to	to	PART
ap-610	310	8	illustrate	illustrate	VERB
ap-610	310	9	the	the	DET
ap-610	310	10	power	power	NOUN
ap-610	310	11	of	of	ADP
ap-610	310	12	plasticity	plasticity	NOUN
ap-610	310	13	theories	theory	NOUN
ap-610	310	14	extended	extend	VERB
ap-610	310	15	by	by	ADP
ap-610	310	16	gradient	gradient	NOUN
ap-610	310	17	or	or	CCONJ
ap-610	310	18	integral	integral	ADJ
ap-610	310	19	-	-	PUNCT
ap-610	310	20	type	type	NOUN
ap-610	310	21	nonlocal	nonlocal	ADJ
ap-610	310	22	terms	term	NOUN
ap-610	310	23	,	,	PUNCT
ap-610	310	24	we	we	PRON
ap-610	310	25	will	will	AUX
ap-610	310	26	analyze	analyze	VERB
ap-610	310	27	a	a	DET
ap-610	310	28	rather	rather	ADV
ap-610	310	29	academic	academic	ADJ
ap-610	310	30	but	but	CCONJ
ap-610	310	31	instructive	instructive	ADJ
ap-610	310	32	problem	problem	NOUN
ap-610	310	33	of	of	ADP
ap-610	310	34	a	a	DET
ap-610	310	35	material	material	NOUN
ap-610	310	36	layer	layer	NOUN
ap-610	310	37	of	of	ADP
ap-610	310	38	thickness	thickness	NOUN
ap-610	310	39	l	l	NOUN
ap-610	310	40	,	,	PUNCT
ap-610	310	41	placed	place	VERB
ap-610	310	42	between	between	ADP
ap-610	310	43	stiff	stiff	ADJ
ap-610	310	44	loading	loading	NOUN
ap-610	310	45	plates	plate	NOUN
ap-610	310	46	and	and	CCONJ
ap-610	310	47	loaded	load	VERB
ap-610	310	48	statically	statically	ADV
ap-610	310	49	by	by	ADP
ap-610	310	50	shear	shear	NOUN
ap-610	310	51	.	.	PUNCT
ap-610	311	1	this	this	DET
ap-610	311	2	problem	problem	NOUN
ap-610	311	3	can	can	AUX
ap-610	311	4	be	be	AUX
ap-610	311	5	modeled	model	VERB
ap-610	311	6	in	in	ADP
ap-610	311	7	one	one	NUM
ap-610	311	8	spatial	spatial	ADJ
ap-610	311	9	dimension	dimension	NOUN
ap-610	311	10	,	,	PUNCT
ap-610	311	11	which	which	PRON
ap-610	311	12	facilitates	facilitate	VERB
ap-610	311	13	its	its	PRON
ap-610	311	14	analytical	analytical	ADJ
ap-610	311	15	solution	solution	NOUN
ap-610	311	16	.	.	PUNCT
ap-610	312	1	the	the	DET
ap-610	312	2	choice	choice	NOUN
ap-610	312	3	of	of	ADP
ap-610	312	4	the	the	DET
ap-610	312	5	coordinate	coordinate	NOUN
ap-610	312	6	system	system	NOUN
ap-610	312	7	and	and	CCONJ
ap-610	312	8	the	the	DET
ap-610	312	9	type	type	NOUN
ap-610	312	10	of	of	ADP
ap-610	312	11	loading	loading	NOUN
ap-610	312	12	are	be	AUX
ap-610	312	13	shown	show	VERB
ap-610	312	14	in	in	ADP
ap-610	312	15	fig	fig	NOUN
ap-610	312	16	.	.	PUNCT
ap-610	313	1	4	4	X
ap-610	313	2	.	.	X
ap-610	314	1	it	it	PRON
ap-610	314	2	is	be	AUX
ap-610	314	3	assumed	assume	VERB
ap-610	314	4	that	that	SCONJ
ap-610	314	5	the	the	DET
ap-610	314	6	elastic	elastic	ADJ
ap-610	314	7	properties	property	NOUN
ap-610	314	8	of	of	ADP
ap-610	314	9	the	the	DET
ap-610	314	10	material	material	NOUN
ap-610	314	11	are	be	AUX
ap-610	314	12	isotropic	isotropic	ADJ
ap-610	314	13	and	and	CCONJ
ap-610	314	14	plastic	plastic	ADJ
ap-610	314	15	flow	flow	NOUN
ap-610	314	16	is	be	AUX
ap-610	314	17	isochoric	isochoric	ADJ
ap-610	314	18	(	(	PUNCT
ap-610	314	19	preserves	preserve	NOUN
ap-610	314	20	volume	volume	NOUN
ap-610	314	21	)	)	PUNCT
ap-610	314	22	,	,	PUNCT
ap-610	314	23	so	so	SCONJ
ap-610	314	24	that	that	SCONJ
ap-610	314	25	volumetric	volumetric	NOUN
ap-610	314	26	and	and	CCONJ
ap-610	314	27	deviatoric	deviatoric	ADJ
ap-610	314	28	effects	effect	NOUN
ap-610	314	29	can	can	AUX
ap-610	314	30	be	be	AUX
ap-610	314	31	decoupled	decouple	VERB
ap-610	314	32	.	.	PUNCT
ap-610	315	1	if	if	SCONJ
ap-610	315	2	this	this	PRON
ap-610	315	3	is	be	AUX
ap-610	315	4	the	the	DET
ap-610	315	5	case	case	NOUN
ap-610	315	6	,	,	PUNCT
ap-610	315	7	the	the	DET
ap-610	315	8	relevant	relevant	ADJ
ap-610	315	9	components	component	NOUN
ap-610	315	10	of	of	ADP
ap-610	315	11	stress	stress	NOUN
ap-610	315	12	and	and	CCONJ
ap-610	315	13	strain	strain	NOUN
ap-610	315	14	are	be	AUX
ap-610	315	15	the	the	DET
ap-610	315	16	shear	shear	NOUN
ap-610	315	17	stress	stress	PROPN
ap-610	315	18	�	�	PROPN
ap-610	315	19	xy	xy	PROPN
ap-610	315	20	�	�	PROPN
ap-610	315	21	and	and	CCONJ
ap-610	315	22	the	the	DET
ap-610	315	23	engineering	engineering	NOUN
ap-610	315	24	shear	shear	NOUN
ap-610	315	25	strain	strain	VERB
ap-610	315	26	2	2	NUM
ap-610	315	27	�	�	PROPN
ap-610	315	28	�	�	PROPN
ap-610	315	29	xy	xy	PROPN
ap-610	315	30	�	�	PROPN
ap-610	315	31	.	.	PUNCT
ap-610	316	1	both	both	PRON
ap-610	316	2	of	of	ADP
ap-610	316	3	them	they	PRON
ap-610	316	4	are	be	AUX
ap-610	316	5	considered	consider	VERB
ap-610	316	6	as	as	ADP
ap-610	316	7	independent	independent	ADJ
ap-610	316	8	of	of	ADP
ap-610	316	9	spatial	spatial	ADJ
ap-610	316	10	coordinates	coordinate	NOUN
ap-610	316	11	y	y	PROPN
ap-610	316	12	and	and	CCONJ
ap-610	316	13	z.	z.	PROPN
ap-610	316	14	from	from	ADP
ap-610	316	15	the	the	DET
ap-610	316	16	equilibrium	equilibrium	NOUN
ap-610	316	17	equation	equation	NOUN
ap-610	316	18	with	with	ADP
ap-610	316	19	vanishing	vanish	VERB
ap-610	316	20	body	body	NOUN
ap-610	316	21	forces	force	NOUN
ap-610	316	22	,	,	PUNCT
ap-610	316	23	it	it	PRON
ap-610	316	24	follows	follow	VERB
ap-610	316	25	that	that	SCONJ
ap-610	316	26	�	�	PROPN
ap-610	316	27	is	be	AUX
ap-610	316	28	also	also	ADV
ap-610	316	29	independent	independent	ADJ
ap-610	316	30	of	of	ADP
ap-610	316	31	x	x	PRON
ap-610	316	32	,	,	PUNCT
ap-610	316	33	i.e.	i.e.	X
ap-610	316	34	,	,	PUNCT
ap-610	316	35	it	it	PRON
ap-610	316	36	is	be	AUX
ap-610	316	37	uniformly	uniformly	ADV
ap-610	316	38	distributed	distribute	VERB
ap-610	316	39	in	in	ADP
ap-610	316	40	space	space	NOUN
ap-610	316	41	and	and	CCONJ
ap-610	316	42	varies	vary	VERB
ap-610	316	43	only	only	ADV
ap-610	316	44	as	as	ADP
ap-610	316	45	a	a	DET
ap-610	316	46	function	function	NOUN
ap-610	316	47	of	of	ADP
ap-610	316	48	the	the	DET
ap-610	316	49	pseudo	pseudo	NOUN
ap-610	316	50	-	-	NOUN
ap-610	316	51	time	time	NOUN
ap-610	316	52	parameterizing	parameterize	VERB
ap-610	316	53	the	the	DET
ap-610	316	54	loading	loading	NOUN
ap-610	316	55	process	process	NOUN
ap-610	316	56	.	.	PUNCT
ap-610	317	1	classical	classical	ADJ
ap-610	317	2	plasticity	plasticity	NOUN
ap-610	317	3	with	with	ADP
ap-610	317	4	linear	linear	ADJ
ap-610	317	5	isotropic	isotropic	NOUN
ap-610	317	6	hardening	hardening	NOUN
ap-610	317	7	is	be	AUX
ap-610	317	8	described	describe	VERB
ap-610	317	9	by	by	ADP
ap-610	317	10	the	the	DET
ap-610	317	11	basic	basic	ADJ
ap-610	317	12	equations	equation	NOUN
ap-610	317	13	�	�	PROPN
ap-610	317	14	�	�	PROPN
ap-610	317	15	�	�	PROPN
ap-610	317	16	�	�	PROPN
ap-610	317	17	�	�	PROPN
ap-610	317	18	g	g	PROPN
ap-610	317	19	p	p	X
ap-610	317	20	(	(	PUNCT
ap-610	317	21	)	)	PUNCT
ap-610	317	22	(	(	PUNCT
ap-610	317	23	55	55	NUM
ap-610	317	24	)	)	PUNCT
ap-610	317	25	�	�	PROPN
ap-610	317	26	�	�	PROPN
ap-610	317	27	sgn	sgn	PROPN
ap-610	317	28	(	(	PUNCT
ap-610	317	29	)	)	PUNCT
ap-610	317	30	�	�	PROPN
ap-610	317	31	�	�	PROPN
ap-610	317	32	�	�	PROPN
ap-610	317	33	p	p	PROPN
ap-610	317	34	�	�	PROPN
ap-610	317	35	(	(	PUNCT
ap-610	317	36	56	56	NUM
ap-610	317	37	)	)	PUNCT
ap-610	317	38	�	�	PROPN
ap-610	317	39	,	,	PUNCT
ap-610	317	40	(	(	PUNCT
ap-610	317	41	,	,	PUNCT
ap-610	317	42	)	)	PUNCT
ap-610	317	43	,	,	PUNCT
ap-610	317	44	�	�	PROPN
ap-610	317	45	(	(	PUNCT
ap-610	317	46	,	,	PUNCT
ap-610	317	47	)	)	PUNCT
ap-610	317	48	�	�	PROPN
ap-610	317	49	�	�	PROPN
ap-610	317	50	�	�	PROPN
ap-610	317	51	�	�	PROPN
ap-610	317	52	�	�	PROPN
ap-610	317	53	�	�	PROPN
ap-610	317	54	�	�	PROPN
ap-610	317	55	�	�	PROPN
ap-610	317	56	�	�	PROPN
ap-610	317	57	0	0	NUM
ap-610	317	58	0	0	NUM
ap-610	317	59	0f	0f	NOUN
ap-610	317	60	f	f	X
ap-610	317	61	(	(	PUNCT
ap-610	317	62	57	57	NUM
ap-610	317	63	)	)	PUNCT
ap-610	317	64	where	where	SCONJ
ap-610	317	65	�	�	PROPN
ap-610	317	66	p	p	PROPN
ap-610	317	67	is	be	AUX
ap-610	317	68	the	the	DET
ap-610	317	69	plastic	plastic	ADJ
ap-610	317	70	strain	strain	NOUN
ap-610	317	71	and	and	CCONJ
ap-610	317	72	�	�	PROPN
ap-610	317	73	is	be	AUX
ap-610	317	74	the	the	DET
ap-610	317	75	cumulative	cumulative	ADJ
ap-610	317	76	plastic	plastic	NOUN
ap-610	317	77	strain	strain	NOUN
ap-610	317	78	.	.	PUNCT
ap-610	318	1	the	the	DET
ap-610	318	2	yield	yield	NOUN
ap-610	318	3	function	function	NOUN
ap-610	318	4	f	f	PROPN
ap-610	318	5	is	be	AUX
ap-610	318	6	given	give	VERB
ap-610	318	7	by	by	ADP
ap-610	318	8	f	f	PROPN
ap-610	318	9	y	y	PROPN
ap-610	318	10	(	(	PUNCT
ap-610	318	11	,	,	PUNCT
ap-610	318	12	)	)	PUNCT
ap-610	318	13	(	(	PUNCT
ap-610	318	14	)	)	PUNCT
ap-610	318	15	�	�	PROPN
ap-610	318	16	�	�	PROPN
ap-610	318	17	�	�	PROPN
ap-610	318	18	�	�	PROPN
ap-610	318	19	�	�	PROPN
ap-610	318	20	�	�	PROPN
ap-610	318	21	�	�	PROPN
ap-610	318	22	(	(	PUNCT
ap-610	318	23	58	58	NUM
ap-610	318	24	)	)	PUNCT
ap-610	318	25	where	where	SCONJ
ap-610	318	26	�	�	PROPN
ap-610	318	27	y	y	PROPN
ap-610	318	28	is	be	AUX
ap-610	318	29	the	the	DET
ap-610	318	30	current	current	ADJ
ap-610	318	31	yield	yield	NOUN
ap-610	318	32	stress	stress	NOUN
ap-610	318	33	in	in	ADP
ap-610	318	34	shear	shear	NOUN
ap-610	318	35	,	,	PUNCT
ap-610	318	36	evaluated	evaluate	VERB
ap-610	318	37	from	from	ADP
ap-610	318	38	the	the	DET
ap-610	318	39	hardening	harden	VERB
ap-610	318	40	law	law	NOUN
ap-610	318	41	�	�	PROPN
ap-610	318	42	�	�	PROPN
ap-610	318	43	�	�	PROPN
ap-610	318	44	�	�	PROPN
ap-610	318	45	y	y	PROPN
ap-610	318	46	h	h	PROPN
ap-610	318	47	(	(	PUNCT
ap-610	318	48	)	)	PUNCT
ap-610	318	49	�	�	PROPN
ap-610	318	50	�	�	PROPN
ap-610	318	51	0	0	PROPN
ap-610	318	52	(	(	PUNCT
ap-610	318	53	59	59	NUM
ap-610	318	54	)	)	PUNCT
ap-610	318	55	with	with	ADP
ap-610	318	56	�	�	PROPN
ap-610	318	57	0	0	NUM
ap-610	318	58	�	�	PROPN
ap-610	318	59	initial	initial	ADJ
ap-610	318	60	yield	yield	NOUN
ap-610	318	61	stress	stress	NOUN
ap-610	318	62	in	in	ADP
ap-610	318	63	shear	shear	NOUN
ap-610	318	64	and	and	CCONJ
ap-610	318	65	h	h	PROPN
ap-610	318	66	�	�	PROPN
ap-610	318	67	hardening	harden	VERB
ap-610	318	68	modulus	modulus	NOUN
ap-610	318	69	(	(	PUNCT
ap-610	318	70	in	in	ADP
ap-610	318	71	shear	shear	NOUN
ap-610	318	72	)	)	PUNCT
ap-610	318	73	.	.	PUNCT
ap-610	319	1	during	during	ADP
ap-610	319	2	monotonic	monotonic	ADJ
ap-610	319	3	loading	loading	NOUN
ap-610	319	4	with	with	ADP
ap-610	319	5	positive	positive	ADJ
ap-610	319	6	value	value	NOUN
ap-610	319	7	of	of	ADP
ap-610	319	8	shear	shear	NOUN
ap-610	319	9	stress	stress	PROPN
ap-610	319	10	�	�	PROPN
ap-610	319	11	,	,	PUNCT
ap-610	319	12	there	there	PRON
ap-610	319	13	is	be	VERB
ap-610	319	14	no	no	DET
ap-610	319	15	difference	difference	NOUN
ap-610	319	16	between	between	ADP
ap-610	319	17	the	the	DET
ap-610	319	18	plastic	plastic	ADJ
ap-610	319	19	shear	shear	NOUN
ap-610	319	20	strain	strain	VERB
ap-610	319	21	�	�	PROPN
ap-610	319	22	p	p	NOUN
ap-610	319	23	and	and	CCONJ
ap-610	319	24	the	the	DET
ap-610	319	25	cumulative	cumulative	ADJ
ap-610	319	26	plastic	plastic	NOUN
ap-610	319	27	strain	strain	NOUN
ap-610	319	28	�	�	NOUN
ap-610	319	29	.	.	PUNCT
ap-610	320	1	we	we	PRON
ap-610	320	2	will	will	AUX
ap-610	320	3	therefore	therefore	ADV
ap-610	320	4	replace	replace	VERB
ap-610	320	5	�	�	PROPN
ap-610	320	6	p	p	NOUN
ap-610	320	7	by	by	ADP
ap-610	320	8	�	�	PROPN
ap-610	320	9	and	and	CCONJ
ap-610	320	10	call	call	VERB
ap-610	320	11	it	it	PRON
ap-610	320	12	simply	simply	ADV
ap-610	320	13	the	the	DET
ap-610	320	14	plastic	plastic	ADJ
ap-610	320	15	strain	strain	NOUN
ap-610	320	16	.	.	PUNCT
ap-610	321	1	if	if	SCONJ
ap-610	321	2	the	the	DET
ap-610	321	3	hardening	harden	VERB
ap-610	321	4	modulus	modulus	NOUN
ap-610	321	5	is	be	AUX
ap-610	321	6	positive	positive	ADJ
ap-610	321	7	and	and	CCONJ
ap-610	321	8	the	the	DET
ap-610	321	9	loading	loading	NOUN
ap-610	321	10	is	be	AUX
ap-610	321	11	monotonic	monotonic	ADJ
ap-610	321	12	,	,	PUNCT
ap-610	321	13	the	the	DET
ap-610	321	14	stress	stress	NOUN
ap-610	321	15	�	�	PROPN
ap-610	321	16	uniquely	uniquely	ADV
ap-610	321	17	determines	determine	VERB
ap-610	321	18	the	the	DET
ap-610	321	19	corresponding	correspond	VERB
ap-610	321	20	strain	strain	PROPN
ap-610	321	21	�	�	PROPN
ap-610	321	22	.	.	PUNCT
ap-610	322	1	since	since	SCONJ
ap-610	322	2	the	the	DET
ap-610	322	3	stress	stress	NOUN
ap-610	322	4	is	be	AUX
ap-610	322	5	uniform	uniform	ADJ
ap-610	322	6	,	,	PUNCT
ap-610	322	7	the	the	DET
ap-610	322	8	strain	strain	NOUN
ap-610	322	9	must	must	AUX
ap-610	322	10	be	be	AUX
ap-610	322	11	uniform	uniform	ADJ
ap-610	322	12	as	as	ADV
ap-610	322	13	well	well	ADV
ap-610	322	14	.	.	PUNCT
ap-610	323	1	therefore	therefore	ADV
ap-610	323	2	,	,	PUNCT
ap-610	323	3	the	the	DET
ap-610	323	4	strain	strain	NOUN
ap-610	323	5	at	at	ADP
ap-610	323	6	any	any	DET
ap-610	323	7	point	point	NOUN
ap-610	323	8	is	be	AUX
ap-610	323	9	equal	equal	ADJ
ap-610	323	10	to	to	ADP
ap-610	323	11	the	the	DET
ap-610	323	12	average	average	ADJ
ap-610	323	13	strain	strain	NOUN
ap-610	323	14	determined	determine	VERB
ap-610	323	15	as	as	ADP
ap-610	323	16	the	the	DET
ap-610	323	17	ratio	ratio	NOUN
ap-610	323	18	between	between	ADP
ap-610	323	19	the	the	DET
ap-610	323	20	relative	relative	ADJ
ap-610	323	21	displacement	displacement	NOUN
ap-610	323	22	of	of	ADP
ap-610	323	23	the	the	DET
ap-610	323	24	loading	loading	NOUN
ap-610	323	25	plates	plate	NOUN
ap-610	323	26	,	,	PUNCT
ap-610	323	27	�	�	PROPN
ap-610	323	28	v	v	NOUN
ap-610	323	29	v	v	ADP
ap-610	323	30	l	l	NOUN
ap-610	323	31	v	v	PROPN
ap-610	323	32	l	l	X
ap-610	323	33	�	�	PROPN
ap-610	323	34	�	�	PROPN
ap-610	323	35	�	�	PROPN
ap-610	323	36	(	(	PUNCT
ap-610	323	37	)	)	PUNCT
ap-610	323	38	(	(	PUNCT
ap-610	323	39	)	)	PUNCT
ap-610	323	40	2	2	NUM
ap-610	323	41	2	2	NUM
ap-610	323	42	,	,	PUNCT
ap-610	323	43	and	and	CCONJ
ap-610	323	44	the	the	DET
ap-610	323	45	layer	layer	NOUN
ap-610	323	46	thickness	thickness	NOUN
ap-610	323	47	,	,	PUNCT
ap-610	323	48	l.	l.	NOUN
ap-610	323	49	the	the	DET
ap-610	323	50	stress	stress	NOUN
ap-610	323	51	-	-	PUNCT
ap-610	323	52	strain	strain	NOUN
ap-610	323	53	curve	curve	NOUN
ap-610	323	54	can	can	AUX
ap-610	323	55	be	be	AUX
ap-610	323	56	directly	directly	ADV
ap-610	323	57	determined	determine	VERB
ap-610	323	58	from	from	ADP
ap-610	323	59	the	the	DET
ap-610	323	60	measured	measured	ADJ
ap-610	323	61	dependence	dependence	NOUN
ap-610	323	62	between	between	ADP
ap-610	323	63	v	v	NOUN
ap-610	323	64	and	and	CCONJ
ap-610	323	65	the	the	DET
ap-610	323	66	tangential	tangential	ADJ
ap-610	323	67	traction	traction	NOUN
ap-610	323	68	on	on	ADP
ap-610	323	69	the	the	DET
ap-610	323	70	boundary	boundary	NOUN
ap-610	323	71	,	,	PUNCT
ap-610	323	72	t	t	PROPN
ap-610	323	73	,	,	PUNCT
ap-610	323	74	and	and	CCONJ
ap-610	323	75	it	it	PRON
ap-610	323	76	should	should	AUX
ap-610	323	77	be	be	AUX
ap-610	323	78	independent	independent	ADJ
ap-610	323	79	of	of	ADP
ap-610	323	80	the	the	DET
ap-610	323	81	layer	layer	NOUN
ap-610	323	82	thickness	thickness	NOUN
ap-610	323	83	.	.	PUNCT
ap-610	324	1	therefore	therefore	ADV
ap-610	324	2	,	,	PUNCT
ap-610	324	3	the	the	DET
ap-610	324	4	standard	standard	ADJ
ap-610	324	5	plasticity	plasticity	NOUN
ap-610	324	6	model	model	NOUN
ap-610	324	7	does	do	AUX
ap-610	324	8	not	not	PART
ap-610	324	9	indicate	indicate	VERB
ap-610	324	10	any	any	DET
ap-610	324	11	size	size	NOUN
ap-610	324	12	effect	effect	NOUN
ap-610	324	13	.	.	PUNCT
ap-610	325	1	3.3	3.3	NUM
ap-610	325	2	explicit	explicit	ADJ
ap-610	325	3	gradient	gradient	NOUN
ap-610	325	4	plasticity	plasticity	NOUN
ap-610	325	5	if	if	SCONJ
ap-610	325	6	the	the	DET
ap-610	325	7	layer	layer	NOUN
ap-610	325	8	thickness	thickness	NOUN
ap-610	325	9	is	be	AUX
ap-610	325	10	comparable	comparable	ADJ
ap-610	325	11	to	to	ADP
ap-610	325	12	the	the	DET
ap-610	325	13	characteristic	characteristic	ADJ
ap-610	325	14	length	length	NOUN
ap-610	325	15	of	of	ADP
ap-610	325	16	the	the	DET
ap-610	325	17	material	material	NOUN
ap-610	325	18	microstructure	microstructure	NOUN
ap-610	325	19	,	,	PUNCT
ap-610	325	20	the	the	DET
ap-610	325	21	assumption	assumption	NOUN
ap-610	325	22	of	of	ADP
ap-610	325	23	the	the	DET
ap-610	325	24	local	local	ADJ
ap-610	325	25	dependence	dependence	NOUN
ap-610	325	26	of	of	ADP
ap-610	325	27	stress	stress	NOUN
ap-610	325	28	on	on	ADP
ap-610	325	29	the	the	DET
ap-610	325	30	history	history	NOUN
ap-610	325	31	of	of	ADP
ap-610	325	32	strain	strain	NOUN
ap-610	325	33	at	at	ADP
ap-610	325	34	the	the	DET
ap-610	325	35	same	same	ADJ
ap-610	325	36	material	material	NOUN
ap-610	325	37	point	point	NOUN
ap-610	325	38	becomes	become	VERB
ap-610	325	39	questionable	questionable	ADJ
ap-610	325	40	.	.	PUNCT
ap-610	326	1	the	the	DET
ap-610	326	2	reason	reason	NOUN
ap-610	326	3	is	be	AUX
ap-610	326	4	that	that	SCONJ
ap-610	326	5	the	the	DET
ap-610	326	6	hardening	harden	VERB
ap-610	326	7	process	process	NOUN
ap-610	326	8	does	do	AUX
ap-610	326	9	not	not	PART
ap-610	326	10	take	take	VERB
ap-610	326	11	place	place	NOUN
ap-610	326	12	at	at	ADP
ap-610	326	13	each	each	DET
ap-610	326	14	infinitely	infinitely	ADV
ap-610	326	15	small	small	ADJ
ap-610	326	16	material	material	NOUN
ap-610	326	17	point	point	NOUN
ap-610	326	18	separately	separately	ADV
ap-610	326	19	and	and	CCONJ
ap-610	326	20	independently	independently	ADV
ap-610	326	21	of	of	ADP
ap-610	326	22	the	the	DET
ap-610	326	23	surrounding	surround	VERB
ap-610	326	24	points	point	NOUN
ap-610	326	25	.	.	PUNCT
ap-610	327	1	this	this	PRON
ap-610	327	2	can	can	AUX
ap-610	327	3	be	be	AUX
ap-610	327	4	taken	take	VERB
ap-610	327	5	into	into	ADP
ap-610	327	6	account	account	NOUN
ap-610	327	7	by	by	ADP
ap-610	327	8	sophisticated	sophisticated	ADJ
ap-610	327	9	models	model	NOUN
ap-610	327	10	that	that	PRON
ap-610	327	11	consider	consider	VERB
ap-610	327	12	the	the	DET
ap-610	327	13	details	detail	NOUN
ap-610	327	14	of	of	ADP
ap-610	327	15	the	the	DET
ap-610	327	16	hardening	harden	VERB
ap-610	327	17	mechanisms	mechanism	NOUN
ap-610	327	18	,	,	PUNCT
ap-610	327	19	e.g.	e.g.	ADV
ap-610	327	20	,	,	PUNCT
ap-610	327	21	by	by	ADP
ap-610	327	22	discrete	discrete	ADJ
ap-610	327	23	dislocation	dislocation	NOUN
ap-610	327	24	models	model	NOUN
ap-610	327	25	.	.	PUNCT
ap-610	328	1	as	as	ADP
ap-610	328	2	a	a	DET
ap-610	328	3	simpler	simple	ADJ
ap-610	328	4	alternative	alternative	NOUN
ap-610	328	5	,	,	PUNCT
ap-610	328	6	one	one	PRON
ap-610	328	7	can	can	AUX
ap-610	328	8	use	use	VERB
ap-610	328	9	enriched	enriched	ADJ
ap-610	328	10	continuum	continuum	ADJ
ap-610	328	11	models	model	NOUN
ap-610	328	12	that	that	PRON
ap-610	328	13	take	take	VERB
ap-610	328	14	into	into	ADP
ap-610	328	15	account	account	NOUN
ap-610	328	16	the	the	DET
ap-610	328	17	micromechanical	micromechanical	ADJ
ap-610	328	18	processes	process	NOUN
ap-610	328	19	only	only	ADV
ap-610	328	20	”	"	PUNCT
ap-610	328	21	on	on	ADP
ap-610	328	22	the	the	DET
ap-610	328	23	average	average	NOUN
ap-610	328	24	”	"	PUNCT
ap-610	328	25	,	,	PUNCT
ap-610	328	26	but	but	CCONJ
ap-610	328	27	by	by	ADP
ap-610	328	28	terms	term	NOUN
ap-610	328	29	of	of	ADP
ap-610	328	30	a	a	DET
ap-610	328	31	higher	high	ADJ
ap-610	328	32	order	order	NOUN
ap-610	328	33	than	than	ADP
ap-610	328	34	in	in	ADP
ap-610	328	35	the	the	DET
ap-610	328	36	standard	standard	ADJ
ap-610	328	37	continuum	continuum	ADJ
ap-610	328	38	theory	theory	NOUN
ap-610	328	39	.	.	PUNCT
ap-610	329	1	motivated	motivate	VERB
ap-610	329	2	by	by	ADP
ap-610	329	3	certain	certain	ADJ
ap-610	329	4	micromechanical	micromechanical	ADJ
ap-610	329	5	considerations	consideration	NOUN
ap-610	329	6	,	,	PUNCT
ap-610	329	7	aifantis	aifantis	PROPN
ap-610	329	8	(	(	PUNCT
ap-610	329	9	1984	1984	NUM
ap-610	329	10	)	)	PUNCT
ap-610	329	11	proposed	proposed	AUX
ap-610	329	12	a	a	DET
ap-610	329	13	family	family	NOUN
ap-610	329	14	of	of	ADP
ap-610	329	15	models	model	NOUN
ap-610	329	16	with	with	ADP
ap-610	329	17	the	the	DET
ap-610	329	18	yield	yield	NOUN
ap-610	329	19	stress	stress	NOUN
ap-610	329	20	dependent	dependent	ADJ
ap-610	329	21	not	not	PART
ap-610	329	22	only	only	ADV
ap-610	329	23	on	on	ADP
ap-610	329	24	the	the	DET
ap-610	329	25	value	value	NOUN
ap-610	329	26	of	of	ADP
ap-610	329	27	the	the	DET
ap-610	329	28	cumulative	cumulative	ADJ
ap-610	329	29	plastic	plastic	NOUN
ap-610	329	30	strain	strain	NOUN
ap-610	329	31	(	(	PUNCT
ap-610	329	32	internal	internal	ADJ
ap-610	329	33	variable	variable	NOUN
ap-610	329	34	driving	drive	VERB
ap-610	329	35	the	the	DET
ap-610	329	36	hardening	harden	VERB
ap-610	329	37	process	process	NOUN
ap-610	329	38	)	)	PUNCT
ap-610	329	39	but	but	CCONJ
ap-610	329	40	also	also	ADV
ap-610	329	41	on	on	ADP
ap-610	329	42	its	its	PRON
ap-610	329	43	first	first	ADJ
ap-610	329	44	and	and	CCONJ
ap-610	329	45	second	second	ADJ
ap-610	329	46	gradients	gradient	NOUN
ap-610	329	47	.	.	PUNCT
ap-610	330	1	in	in	ADP
ap-610	330	2	the	the	DET
ap-610	330	3	one	one	NUM
ap-610	330	4	-	-	PUNCT
ap-610	330	5	dimensional	dimensional	ADJ
ap-610	330	6	setting	setting	NOUN
ap-610	330	7	and	and	CCONJ
ap-610	330	8	for	for	ADP
ap-610	330	9	linear	linear	ADJ
ap-610	330	10	hardening	hardening	NOUN
ap-610	330	11	,	,	PUNCT
ap-610	330	12	the	the	DET
ap-610	330	13	simplest	simple	ADJ
ap-610	330	14	version	version	NOUN
ap-610	330	15	of	of	ADP
ap-610	330	16	the	the	DET
ap-610	330	17	aifantis	aifantis	PROPN
ap-610	330	18	gradient	gradient	NOUN
ap-610	330	19	plasticity	plasticity	NOUN
ap-610	330	20	model	model	NOUN
ap-610	330	21	replaces	replace	VERB
ap-610	330	22	the	the	DET
ap-610	330	23	hardening	harden	VERB
ap-610	330	24	law	law	NOUN
ap-610	330	25	(	(	PUNCT
ap-610	330	26	59	59	NUM
ap-610	330	27	)	)	PUNCT
ap-610	330	28	by	by	ADP
ap-610	330	29	�	�	PROPN
ap-610	330	30	�	�	PROPN
ap-610	330	31	�	�	PROPN
ap-610	330	32	�	�	PROPN
ap-610	330	33	�	�	PROPN
ap-610	330	34	�	�	PROPN
ap-610	330	35	y	y	PROPN
ap-610	330	36	,	,	PUNCT
ap-610	330	37	h	h	NOUN
ap-610	330	38	hl	hl	PROPN
ap-610	330	39	(	(	PUNCT
ap-610	330	40	)	)	PUNCT
ap-610	330	41	�	�	PROPN
ap-610	330	42	�	�	PROPN
ap-610	330	43	�	�	PROPN
ap-610	330	44	�	�	PROPN
ap-610	330	45	�	�	PROPN
ap-610	330	46	�	�	PROPN
ap-610	330	47	�	�	PROPN
ap-610	330	48	0	0	NUM
ap-610	330	49	2	2	NUM
ap-610	330	50	(	(	PUNCT
ap-610	330	51	60	60	NUM
ap-610	330	52	)	)	PUNCT
ap-610	330	53	where	where	SCONJ
ap-610	330	54	l	l	NOUN
ap-610	330	55	is	be	AUX
ap-610	330	56	a	a	DET
ap-610	330	57	parameter	parameter	NOUN
ap-610	330	58	with	with	ADP
ap-610	330	59	the	the	DET
ap-610	330	60	dimension	dimension	NOUN
ap-610	330	61	of	of	ADP
ap-610	330	62	length	length	NOUN
ap-610	330	63	.	.	PUNCT
ap-610	331	1	the	the	DET
ap-610	331	2	elastic	elastic	ADJ
ap-610	331	3	part	part	NOUN
ap-610	331	4	of	of	ADP
ap-610	331	5	the	the	DET
ap-610	331	6	model	model	NOUN
ap-610	331	7	remains	remain	VERB
ap-610	331	8	unchanged	unchanged	ADJ
ap-610	331	9	,	,	PUNCT
ap-610	331	10	and	and	CCONJ
ap-610	331	11	so	so	ADV
ap-610	331	12	the	the	DET
ap-610	331	13	strain	strain	NOUN
ap-610	331	14	is	be	AUX
ap-610	331	15	uniform	uniform	ADJ
ap-610	331	16	in	in	ADP
ap-610	331	17	the	the	DET
ap-610	331	18	elastic	elastic	ADJ
ap-610	331	19	range	range	NOUN
ap-610	331	20	.	.	PUNCT
ap-610	332	1	after	after	ADP
ap-610	332	2	the	the	DET
ap-610	332	3	onset	onset	NOUN
ap-610	332	4	of	of	ADP
ap-610	332	5	yielding	yield	VERB
ap-610	332	6	,	,	PUNCT
ap-610	332	7	the	the	DET
ap-610	332	8	yield	yield	NOUN
ap-610	332	9	condition	condition	NOUN
ap-610	332	10	must	must	AUX
ap-610	332	11	be	be	AUX
ap-610	332	12	satisfied	satisfied	ADJ
ap-610	332	13	in	in	ADP
ap-610	332	14	the	the	DET
ap-610	332	15	plastic	plastic	NOUN
ap-610	332	16	zone	zone	NOUN
ap-610	332	17	.	.	PUNCT
ap-610	333	1	it	it	PRON
ap-610	333	2	is	be	AUX
ap-610	333	3	easy	easy	ADJ
ap-610	333	4	to	to	PART
ap-610	333	5	show	show	VERB
ap-610	333	6	that	that	SCONJ
ap-610	333	7	in	in	ADP
ap-610	333	8	the	the	DET
ap-610	333	9	present	present	ADJ
ap-610	333	10	case	case	NOUN
ap-610	333	11	the	the	DET
ap-610	333	12	plastic	plastic	NOUN
ap-610	333	13	zone	zone	NOUN
ap-610	333	14	must	must	AUX
ap-610	333	15	extend	extend	VERB
ap-610	333	16	over	over	ADP
ap-610	333	17	the	the	DET
ap-610	333	18	entire	entire	ADJ
ap-610	333	19	layer	layer	NOUN
ap-610	333	20	.	.	PUNCT
ap-610	334	1	the	the	DET
ap-610	334	2	yield	yield	NOUN
ap-610	334	3	condition	condition	NOUN
ap-610	334	4	f	f	PROPN
ap-610	334	5	�	�	PROPN
ap-610	334	6	0	0	NUM
ap-610	334	7	combined	combine	VERB
ap-610	334	8	with	with	ADP
ap-610	334	9	the	the	DET
ap-610	334	10	hardening	harden	VERB
ap-610	334	11	law	law	NOUN
ap-610	334	12	(	(	PUNCT
ap-610	334	13	60	60	NUM
ap-610	334	14	)	)	PUNCT
ap-610	334	15	then	then	ADV
ap-610	334	16	provides	provide	VERB
ap-610	334	17	the	the	DET
ap-610	334	18	ordinary	ordinary	ADJ
ap-610	334	19	differential	differential	ADJ
ap-610	334	20	equation	equation	NOUN
ap-610	334	21	�	�	PROPN
ap-610	334	22	�	�	PROPN
ap-610	334	23	�	�	PROPN
ap-610	334	24	�	�	PROPN
ap-610	334	25	�	�	PROPN
ap-610	334	26	�	�	PROPN
ap-610	334	27	�	�	PROPN
ap-610	334	28	�	�	PROPN
ap-610	334	29	�	�	PROPN
ap-610	334	30	l	l	NOUN
ap-610	334	31	h	h	NOUN
ap-610	334	32	2	2	NUM
ap-610	334	33	0	0	NUM
ap-610	334	34	(	(	PUNCT
ap-610	334	35	61	61	NUM
ap-610	334	36	)	)	PUNCT
ap-610	334	37	for	for	ADP
ap-610	334	38	the	the	DET
ap-610	334	39	unknown	unknown	ADJ
ap-610	334	40	function	function	NOUN
ap-610	334	41	�	�	PROPN
ap-610	334	42	.	.	PUNCT
ap-610	335	1	this	this	DET
ap-610	335	2	equation	equation	NOUN
ap-610	335	3	should	should	AUX
ap-610	335	4	be	be	AUX
ap-610	335	5	supplemented	supplement	VERB
ap-610	335	6	by	by	ADP
ap-610	335	7	boundary	boundary	ADJ
ap-610	335	8	conditions	condition	NOUN
ap-610	335	9	at	at	ADP
ap-610	335	10	the	the	DET
ap-610	335	11	layer	layer	NOUN
ap-610	335	12	boundaries	boundary	NOUN
ap-610	335	13	.	.	PUNCT
ap-610	336	1	the	the	DET
ap-610	336	2	choice	choice	NOUN
ap-610	336	3	of	of	ADP
ap-610	336	4	the	the	DET
ap-610	336	5	specific	specific	ADJ
ap-610	336	6	form	form	NOUN
ap-610	336	7	of	of	ADP
ap-610	336	8	boundary	boundary	ADJ
ap-610	336	9	conditions	condition	NOUN
ap-610	336	10	has	have	VERB
ap-610	336	11	a	a	DET
ap-610	336	12	major	major	ADJ
ap-610	336	13	influence	influence	NOUN
ap-610	336	14	on	on	ADP
ap-610	336	15	the	the	DET
ap-610	336	16	solution	solution	NOUN
ap-610	336	17	and	and	CCONJ
ap-610	336	18	on	on	ADP
ap-610	336	19	the	the	DET
ap-610	336	20	resulting	result	VERB
ap-610	336	21	size	size	NOUN
ap-610	336	22	effect	effect	NOUN
ap-610	336	23	.	.	PUNCT
ap-610	337	1	for	for	ADP
ap-610	337	2	homogeneous	homogeneous	ADJ
ap-610	337	3	neumann	neumann	PROPN
ap-610	337	4	boundary	boundary	ADJ
ap-610	337	5	conditions	condition	NOUN
ap-610	337	6	,	,	PUNCT
ap-610	337	7	enforcing	enforce	VERB
ap-610	337	8	a	a	DET
ap-610	337	9	vanishing	vanish	VERB
ap-610	337	10	normal	normal	ADJ
ap-610	337	11	derivative	derivative	NOUN
ap-610	337	12	of	of	ADP
ap-610	337	13	�	�	PROPN
ap-610	337	14	at	at	ADP
ap-610	337	15	the	the	DET
ap-610	337	16	boundary	boundary	NOUN
ap-610	337	17	,	,	PUNCT
ap-610	337	18	the	the	DET
ap-610	337	19	uniform	uniform	ADJ
ap-610	337	20	solution	solution	NOUN
ap-610	337	21	obtained	obtain	VERB
ap-610	337	22	with	with	ADP
ap-610	337	23	the	the	DET
ap-610	337	24	classical	classical	ADJ
ap-610	337	25	model	model	NOUN
ap-610	337	26	would	would	AUX
ap-610	337	27	remain	remain	VERB
ap-610	337	28	valid	valid	ADJ
ap-610	337	29	even	even	ADV
ap-610	337	30	for	for	ADP
ap-610	337	31	the	the	DET
ap-610	337	32	gradient	gradient	NOUN
ap-610	337	33	model	model	NOUN
ap-610	337	34	.	.	PUNCT
ap-610	338	1	however	however	ADV
ap-610	338	2	,	,	PUNCT
ap-610	338	3	if	if	SCONJ
ap-610	338	4	the	the	DET
ap-610	338	5	shear	shear	NOUN
ap-610	338	6	layer	layer	NOUN
ap-610	338	7	is	be	AUX
ap-610	338	8	fixed	fix	VERB
ap-610	338	9	to	to	ADP
ap-610	338	10	rigid	rigid	ADJ
ap-610	338	11	or	or	CCONJ
ap-610	338	12	very	very	ADV
ap-610	338	13	stiff	stiff	ADJ
ap-610	338	14	loading	loading	NOUN
ap-610	338	15	plates	plate	NOUN
ap-610	338	16	and	and	CCONJ
ap-610	338	17	the	the	DET
ap-610	338	18	bond	bond	NOUN
ap-610	338	19	between	between	ADP
ap-610	338	20	the	the	DET
ap-610	338	21	two	two	NUM
ap-610	338	22	materials	material	NOUN
ap-610	338	23	is	be	AUX
ap-610	338	24	perfect	perfect	ADJ
ap-610	338	25	,	,	PUNCT
ap-610	338	26	the	the	DET
ap-610	338	27	boundary	boundary	ADJ
ap-610	338	28	(	(	PUNCT
ap-610	338	29	or	or	CCONJ
ap-610	338	30	rather	rather	ADV
ap-610	338	31	the	the	DET
ap-610	338	32	material	material	NOUN
ap-610	338	33	interface	interface	NOUN
ap-610	338	34	)	)	PUNCT
ap-610	338	35	acts	act	VERB
ap-610	338	36	as	as	ADP
ap-610	338	37	an	an	DET
ap-610	338	38	obstacle	obstacle	NOUN
ap-610	338	39	for	for	ADP
ap-610	338	40	dislocation	dislocation	NOUN
ap-610	338	41	motion	motion	NOUN
ap-610	338	42	,	,	PUNCT
ap-610	338	43	which	which	PRON
ap-610	338	44	is	be	AUX
ap-610	338	45	the	the	DET
ap-610	338	46	main	main	ADJ
ap-610	338	47	mechanism	mechanism	NOUN
ap-610	338	48	of	of	ADP
ap-610	338	49	plastic	plastic	ADJ
ap-610	338	50	flow	flow	NOUN
ap-610	338	51	in	in	ADP
ap-610	338	52	crystalline	crystalline	ADJ
ap-610	338	53	materials	material	NOUN
ap-610	338	54	.	.	PUNCT
ap-610	339	1	this	this	PRON
ap-610	339	2	has	have	AUX
ap-610	339	3	been	be	AUX
ap-610	339	4	confirmed	confirm	VERB
ap-610	339	5	by	by	ADP
ap-610	339	6	simulations	simulation	NOUN
ap-610	339	7	based	base	VERB
ap-610	339	8	on	on	ADP
ap-610	339	9	discrete	discrete	ADJ
ap-610	339	10	dislocation	dislocation	NOUN
ap-610	339	11	models	model	NOUN
ap-610	339	12	(	(	PUNCT
ap-610	339	13	shu	shu	NOUN
ap-610	339	14	,	,	PUNCT
ap-610	339	15	fleck	fleck	PROPN
ap-610	339	16	,	,	PUNCT
ap-610	339	17	van	van	PROPN
ap-610	339	18	der	der	NOUN
ap-610	339	19	giessen	giessen	VERB
ap-610	339	20	and	and	CCONJ
ap-610	339	21	needleman	needleman	PROPN
ap-610	339	22	,	,	PUNCT
ap-610	339	23	2001	2001	NUM
ap-610	339	24	)	)	PUNCT
ap-610	339	25	.	.	PUNCT
ap-610	340	1	in	in	ADP
ap-610	340	2	the	the	DET
ap-610	340	3	extreme	extreme	ADJ
ap-610	340	4	case	case	NOUN
ap-610	340	5	,	,	PUNCT
ap-610	340	6	plastic	plastic	ADJ
ap-610	340	7	flow	flow	NOUN
ap-610	340	8	is	be	AUX
ap-610	340	9	completely	completely	ADV
ap-610	340	10	prevented	prevent	VERB
ap-610	340	11	and	and	CCONJ
ap-610	340	12	the	the	DET
ap-610	340	13	cumulative	cumulative	ADJ
ap-610	340	14	plastic	plastic	NOUN
ap-610	340	15	strain	strain	NOUN
ap-610	340	16	©	©	PROPN
ap-610	340	17	czech	czech	PROPN
ap-610	340	18	technical	technical	PROPN
ap-610	340	19	university	university	PROPN
ap-610	340	20	publishing	publishing	NOUN
ap-610	340	21	house	house	NOUN
ap-610	340	22	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	340	23	25	25	NUM
ap-610	340	24	acta	acta	PROPN
ap-610	340	25	polytechnica	polytechnica	PROPN
ap-610	340	26	vol	vol	NOUN
ap-610	340	27	.	.	PROPN
ap-610	341	1	44	44	NUM
ap-610	341	2	no	no	NOUN
ap-610	341	3	.	.	PUNCT
ap-610	342	1	5–6/2004	5–6/2004	NUM
ap-610	342	2	fig	fig	NOUN
ap-610	342	3	.	.	PUNCT
ap-610	343	1	4	4	NUM
ap-610	343	2	:	:	PUNCT
ap-610	343	3	material	material	NOUN
ap-610	343	4	layer	layer	NOUN
ap-610	343	5	between	between	ADP
ap-610	343	6	stiff	stiff	ADJ
ap-610	343	7	plates	plate	NOUN
ap-610	343	8	loaded	load	VERB
ap-610	343	9	by	by	ADP
ap-610	343	10	shear	shear	PROPN
ap-610	343	11	�	�	PROPN
ap-610	343	12	must	must	AUX
ap-610	343	13	vanish	vanish	VERB
ap-610	343	14	at	at	ADP
ap-610	343	15	the	the	DET
ap-610	343	16	boundary	boundary	NOUN
ap-610	343	17	.	.	PUNCT
ap-610	344	1	for	for	ADP
ap-610	344	2	homogeneous	homogeneous	ADJ
ap-610	344	3	dirichlet	dirichlet	PROPN
ap-610	344	4	boundary	boundary	PROPN
ap-610	344	5	conditions	condition	NOUN
ap-610	344	6	,	,	PUNCT
ap-610	344	7	�	�	PROPN
ap-610	344	8	(	(	PUNCT
ap-610	344	9	)	)	PUNCT
ap-610	344	10	�	�	PROPN
ap-610	344	11	�	�	PROPN
ap-610	344	12	l	l	NOUN
ap-610	344	13	2	2	NUM
ap-610	344	14	0	0	NUM
ap-610	344	15	,	,	PUNCT
ap-610	344	16	the	the	DET
ap-610	344	17	solution	solution	NOUN
ap-610	344	18	of	of	ADP
ap-610	344	19	(	(	PUNCT
ap-610	344	20	61	61	NUM
ap-610	344	21	)	)	PUNCT
ap-610	344	22	is	be	AUX
ap-610	344	23	�	�	PROPN
ap-610	344	24	�	�	PROPN
ap-610	344	25	�	�	PROPN
ap-610	344	26	(	(	PUNCT
ap-610	344	27	)	)	PUNCT
ap-610	345	1	cosh	cosh	PROPN
ap-610	345	2	cosh	cosh	NOUN
ap-610	345	3	x	x	PUNCT
ap-610	345	4	h	h	NOUN
ap-610	345	5	x	x	X
ap-610	345	6	l	l	NOUN
ap-610	345	7	l	l	X
ap-610	345	8	l	l	X
ap-610	345	9	�	�	PROPN
ap-610	345	10	�	�	PROPN
ap-610	345	11	�	�	PROPN
ap-610	345	12	�	�	PROPN
ap-610	345	13	�	�	PROPN
ap-610	345	14	�	�	PROPN
ap-610	345	15	�	�	PROPN
ap-610	345	16	�	�	PROPN
ap-610	345	17	�	�	PROPN
ap-610	345	18	�	�	PROPN
ap-610	345	19	�	�	PROPN
ap-610	345	20	0	0	NUM
ap-610	345	21	1	1	NUM
ap-610	345	22	2	2	NUM
ap-610	345	23	.	.	PUNCT
ap-610	346	1	(	(	PUNCT
ap-610	346	2	62	62	NUM
ap-610	346	3	)	)	PUNCT
ap-610	346	4	the	the	DET
ap-610	346	5	distribution	distribution	NOUN
ap-610	346	6	of	of	ADP
ap-610	346	7	plastic	plastic	ADJ
ap-610	346	8	strain	strain	NOUN
ap-610	346	9	(	(	PUNCT
ap-610	346	10	normalized	normalize	VERB
ap-610	346	11	by	by	ADP
ap-610	346	12	the	the	DET
ap-610	346	13	factor	factor	NOUN
ap-610	346	14	(	(	PUNCT
ap-610	346	15	)	)	PUNCT
ap-610	346	16	�	�	PROPN
ap-610	346	17	�	�	PROPN
ap-610	346	18	�	�	PROPN
ap-610	346	19	0	0	NUM
ap-610	346	20	h	h	NOUN
ap-610	346	21	that	that	PRON
ap-610	346	22	would	would	AUX
ap-610	346	23	correspond	correspond	VERB
ap-610	346	24	to	to	ADP
ap-610	346	25	the	the	DET
ap-610	346	26	value	value	NOUN
ap-610	346	27	of	of	ADP
ap-610	346	28	uniform	uniform	ADJ
ap-610	346	29	plastic	plastic	NOUN
ap-610	346	30	strain	strain	NOUN
ap-610	346	31	in	in	ADP
ap-610	346	32	the	the	DET
ap-610	346	33	standard	standard	ADJ
ap-610	346	34	theory	theory	NOUN
ap-610	346	35	)	)	PUNCT
ap-610	346	36	across	across	ADP
ap-610	346	37	the	the	DET
ap-610	346	38	layer	layer	NOUN
ap-610	346	39	thickness	thickness	NOUN
ap-610	346	40	is	be	AUX
ap-610	346	41	plotted	plot	VERB
ap-610	346	42	in	in	ADP
ap-610	346	43	fig	fig	NOUN
ap-610	346	44	.	.	PUNCT
ap-610	347	1	5b	5b	NOUN
ap-610	347	2	for	for	ADP
ap-610	347	3	different	different	ADJ
ap-610	347	4	relative	relative	ADJ
ap-610	347	5	sizes	size	NOUN
ap-610	347	6	,	,	PUNCT
ap-610	347	7	l	l	PROPN
ap-610	347	8	l.	l.	NOUN
ap-610	347	9	if	if	SCONJ
ap-610	347	10	the	the	DET
ap-610	347	11	layer	layer	NOUN
ap-610	347	12	thickness	thickness	NOUN
ap-610	347	13	is	be	AUX
ap-610	347	14	substantially	substantially	ADV
ap-610	347	15	larger	large	ADJ
ap-610	347	16	than	than	ADP
ap-610	347	17	the	the	DET
ap-610	347	18	material	material	NOUN
ap-610	347	19	length	length	NOUN
ap-610	347	20	,	,	PUNCT
ap-610	347	21	the	the	DET
ap-610	347	22	plastic	plastic	ADJ
ap-610	347	23	strain	strain	NOUN
ap-610	347	24	is	be	AUX
ap-610	347	25	almost	almost	ADV
ap-610	347	26	uniform	uniform	ADJ
ap-610	347	27	,	,	PUNCT
ap-610	347	28	except	except	SCONJ
ap-610	347	29	for	for	ADP
ap-610	347	30	narrow	narrow	ADJ
ap-610	347	31	boundary	boundary	ADJ
ap-610	347	32	layers	layer	NOUN
ap-610	347	33	.	.	PUNCT
ap-610	348	1	with	with	ADP
ap-610	348	2	decreasing	decrease	VERB
ap-610	348	3	structural	structural	ADJ
ap-610	348	4	size	size	NOUN
ap-610	348	5	l	l	PROPN
ap-610	348	6	,	,	PUNCT
ap-610	348	7	the	the	DET
ap-610	348	8	relative	relative	ADJ
ap-610	348	9	importance	importance	NOUN
ap-610	348	10	of	of	ADP
ap-610	348	11	these	these	DET
ap-610	348	12	boundary	boundary	ADJ
ap-610	348	13	layers	layer	NOUN
ap-610	348	14	with	with	ADP
ap-610	348	15	reduced	reduced	ADJ
ap-610	348	16	plastic	plastic	ADJ
ap-610	348	17	strain	strain	NOUN
ap-610	348	18	levels	level	NOUN
ap-610	348	19	increases	increase	NOUN
ap-610	348	20	,	,	PUNCT
ap-610	348	21	which	which	PRON
ap-610	348	22	makes	make	VERB
ap-610	348	23	the	the	DET
ap-610	348	24	overall	overall	ADJ
ap-610	348	25	response	response	NOUN
ap-610	348	26	stiffer	stiff	ADJ
ap-610	348	27	.	.	PUNCT
ap-610	349	1	to	to	PART
ap-610	349	2	characterize	characterize	VERB
ap-610	349	3	the	the	DET
ap-610	349	4	overall	overall	ADJ
ap-610	349	5	response	response	NOUN
ap-610	349	6	of	of	ADP
ap-610	349	7	the	the	DET
ap-610	349	8	layer	layer	NOUN
ap-610	349	9	,	,	PUNCT
ap-610	349	10	the	the	DET
ap-610	349	11	relative	relative	ADJ
ap-610	349	12	tangential	tangential	ADJ
ap-610	349	13	displacement	displacement	NOUN
ap-610	349	14	of	of	ADP
ap-610	349	15	one	one	NUM
ap-610	349	16	loading	loading	NOUN
ap-610	349	17	plate	plate	NOUN
ap-610	349	18	with	with	ADP
ap-610	349	19	respect	respect	NOUN
ap-610	349	20	to	to	ADP
ap-610	349	21	the	the	DET
ap-610	349	22	other	other	ADJ
ap-610	349	23	can	can	AUX
ap-610	349	24	be	be	AUX
ap-610	349	25	evaluated	evaluate	VERB
ap-610	349	26	as	as	ADP
ap-610	349	27	�	�	NOUN
ap-610	349	28	v	v	NOUN
ap-610	349	29	x	x	NOUN
ap-610	349	30	x	x	X
ap-610	349	31	g	g	NOUN
ap-610	349	32	x	x	SYM
ap-610	349	33	x	x	PUNCT
ap-610	349	34	l	l	NOUN
ap-610	350	1	g	g	NOUN
ap-610	350	2	h	h	NOUN
ap-610	350	3	l	l	NOUN
ap-610	350	4	l	l	NOUN
ap-610	350	5	l	l	X
ap-610	350	6	l	l	X
ap-610	350	7	�	�	PROPN
ap-610	350	8	�	�	PROPN
ap-610	350	9	�	�	PROPN
ap-610	350	10	�	�	PROPN
ap-610	350	11	�	�	PROPN
ap-610	350	12	�	�	PROPN
ap-610	350	13	�	�	PROPN
ap-610	350	14	�	�	PROPN
ap-610	350	15	�	�	PROPN
ap-610	350	16	�	�	PROPN
ap-610	350	17	�	�	PROPN
ap-610	350	18	�	�	PROPN
ap-610	350	19	�	�	PROPN
ap-610	350	20	�	�	PROPN
ap-610	350	21	�	�	PROPN
ap-610	350	22	�	�	PROPN
ap-610	350	23	�	�	PROPN
ap-610	350	24	�	�	PROPN
ap-610	350	25	�	�	PROPN
ap-610	350	26	�	�	PROPN
ap-610	350	27	�	�	PROPN
ap-610	350	28	�	�	PROPN
ap-610	350	29	�	�	PROPN
ap-610	350	30	�	�	PROPN
ap-610	350	31	(	(	PUNCT
ap-610	350	32	)	)	PUNCT
ap-610	350	33	(	(	PUNCT
ap-610	350	34	)	)	PUNCT
ap-610	350	35	d	d	SYM
ap-610	350	36	d	d	SYM
ap-610	350	37	2	2	NUM
ap-610	350	38	2	2	NUM
ap-610	350	39	2	2	NUM
ap-610	350	40	2	2	NUM
ap-610	350	41	0	0	NUM
ap-610	350	42	l	l	NOUN
ap-610	350	43	l	l	NOUN
ap-610	350	44	l	l	X
ap-610	350	45	l	l	X
ap-610	350	46	�	�	PROPN
ap-610	350	47	�	�	PROPN
ap-610	350	48	�	�	PROPN
ap-610	350	49	�	�	PROPN
ap-610	350	50	�	�	PROPN
ap-610	350	51	�	�	PROPN
ap-610	350	52	�	�	PROPN
ap-610	350	53	2	2	NUM
ap-610	350	54	2	2	NUM
ap-610	350	55	tanh	tanh	NOUN
ap-610	350	56	.	.	PUNCT
ap-610	351	1	(	(	PUNCT
ap-610	351	2	63	63	NUM
ap-610	351	3	)	)	PUNCT
ap-610	351	4	defining	define	VERB
ap-610	351	5	the	the	DET
ap-610	351	6	average	average	ADJ
ap-610	351	7	shear	shear	NOUN
ap-610	351	8	strain	strain	NOUN
ap-610	351	9	~	~	SYM
ap-610	351	10	�	�	PROPN
ap-610	351	11	�	�	PROPN
ap-610	351	12	�	�	PROPN
ap-610	351	13	v	v	NOUN
ap-610	351	14	l	l	NOUN
ap-610	351	15	,	,	PUNCT
ap-610	351	16	we	we	PRON
ap-610	351	17	can	can	AUX
ap-610	351	18	transform	transform	VERB
ap-610	351	19	(	(	PUNCT
ap-610	351	20	63	63	NUM
ap-610	351	21	)	)	PUNCT
ap-610	351	22	into	into	ADP
ap-610	351	23	the	the	DET
ap-610	351	24	average	average	ADJ
ap-610	351	25	stress	stress	NOUN
ap-610	351	26	-	-	PUNCT
ap-610	351	27	strain	strain	NOUN
ap-610	351	28	law	law	NOUN
ap-610	351	29	�	�	PROPN
ap-610	351	30	�	�	PROPN
ap-610	351	31	�	�	PROPN
ap-610	351	32	�	�	PROPN
ap-610	351	33	�	�	PROPN
ap-610	351	34	�	�	PROPN
ap-610	351	35	�	�	PROPN
ap-610	351	36	0	0	NUM
ap-610	351	37	0	0	NUM
ap-610	351	38	~	~	PUNCT
ap-610	351	39	(	(	PUNCT
ap-610	351	40	~	~	PUNCT
ap-610	351	41	)	)	PUNCT
ap-610	351	42	gep	gep	NOUN
ap-610	351	43	,	,	PUNCT
ap-610	351	44	(	(	PUNCT
ap-610	351	45	64	64	NUM
ap-610	351	46	)	)	PUNCT
ap-610	351	47	where	where	SCONJ
ap-610	351	48	�	�	PROPN
ap-610	351	49	�	�	PROPN
ap-610	351	50	0	0	NUM
ap-610	351	51	0	0	NUM
ap-610	351	52	�	�	PROPN
ap-610	351	53	g	g	PROPN
ap-610	351	54	is	be	AUX
ap-610	351	55	the	the	DET
ap-610	351	56	limit	limit	NOUN
ap-610	351	57	elastic	elastic	ADJ
ap-610	351	58	shear	shear	NOUN
ap-610	351	59	strain	strain	NOUN
ap-610	351	60	and	and	CCONJ
ap-610	351	61	~	~	PUNCT
ap-610	351	62	tanhg	tanhg	NOUN
ap-610	351	63	g	g	NOUN
ap-610	351	64	h	h	NOUN
ap-610	352	1	l	l	NOUN
ap-610	352	2	l	l	NOUN
ap-610	352	3	l	l	X
ap-610	352	4	lep	lep	PROPN
ap-610	352	5	�	�	PROPN
ap-610	352	6	�	�	PROPN
ap-610	352	7	�	�	PROPN
ap-610	352	8	�	�	PROPN
ap-610	352	9	�	�	PROPN
ap-610	352	10	�	�	PROPN
ap-610	352	11	�	�	PROPN
ap-610	352	12	�	�	PROPN
ap-610	352	13	�	�	PROPN
ap-610	352	14	�	�	PROPN
ap-610	352	15	�	�	PROPN
ap-610	352	16	�	�	PROPN
ap-610	352	17	�	�	PROPN
ap-610	352	18	�	�	PROPN
ap-610	352	19	�	�	PROPN
ap-610	352	20	1	1	NUM
ap-610	352	21	1	1	NUM
ap-610	352	22	1	1	NUM
ap-610	352	23	2	2	NUM
ap-610	352	24	2	2	NUM
ap-610	352	25	1	1	NUM
ap-610	352	26	(	(	PUNCT
ap-610	352	27	65	65	NUM
ap-610	352	28	)	)	PUNCT
ap-610	352	29	is	be	AUX
ap-610	352	30	the	the	DET
ap-610	352	31	elastoplastic	elastoplastic	ADJ
ap-610	352	32	(	(	PUNCT
ap-610	352	33	tangent	tangent	ADJ
ap-610	352	34	)	)	PUNCT
ap-610	352	35	shear	shear	NOUN
ap-610	352	36	modulus	modulus	NOUN
ap-610	352	37	.	.	PUNCT
ap-610	353	1	according	accord	VERB
ap-610	353	2	to	to	ADP
ap-610	353	3	(	(	PUNCT
ap-610	353	4	64)–(65	64)–(65	NUM
ap-610	353	5	)	)	PUNCT
ap-610	353	6	,	,	PUNCT
ap-610	353	7	the	the	DET
ap-610	353	8	overall	overall	ADJ
ap-610	353	9	response	response	NOUN
ap-610	353	10	of	of	ADP
ap-610	353	11	the	the	DET
ap-610	353	12	specimen	speciman	NOUN
ap-610	353	13	after	after	ADP
ap-610	353	14	the	the	DET
ap-610	353	15	onset	onset	NOUN
ap-610	353	16	of	of	ADP
ap-610	353	17	yielding	yield	VERB
ap-610	353	18	is	be	AUX
ap-610	353	19	linear	linear	ADJ
ap-610	353	20	and	and	CCONJ
ap-610	353	21	is	be	AUX
ap-610	353	22	equivalent	equivalent	ADJ
ap-610	353	23	to	to	ADP
ap-610	353	24	the	the	DET
ap-610	353	25	response	response	NOUN
ap-610	353	26	of	of	ADP
ap-610	353	27	the	the	DET
ap-610	353	28	same	same	ADJ
ap-610	353	29	specimen	speciman	NOUN
ap-610	353	30	made	make	VERB
ap-610	353	31	of	of	ADP
ap-610	353	32	the	the	DET
ap-610	353	33	standard	standard	ADJ
ap-610	353	34	elastoplastic	elastoplastic	ADJ
ap-610	353	35	material	material	NOUN
ap-610	353	36	with	with	ADP
ap-610	353	37	hardening	harden	VERB
ap-610	353	38	modulus	modulus	NOUN
ap-610	353	39	~	~	PUNCT
ap-610	353	40	tanh	tanh	PROPN
ap-610	353	41	h	h	PROPN
ap-610	353	42	h	h	PROPN
ap-610	354	1	l	l	NOUN
ap-610	354	2	l	l	NOUN
ap-610	354	3	l	l	X
ap-610	354	4	l	l	X
ap-610	354	5	�	�	PROPN
ap-610	354	6	�	�	PROPN
ap-610	354	7	1	1	NUM
ap-610	354	8	2	2	NUM
ap-610	354	9	2	2	NUM
ap-610	354	10	.	.	PUNCT
ap-610	355	1	(	(	PUNCT
ap-610	355	2	66	66	NUM
ap-610	355	3	)	)	PUNCT
ap-610	355	4	this	this	DET
ap-610	355	5	“	"	PUNCT
ap-610	355	6	apparent	apparent	ADJ
ap-610	355	7	”	"	PUNCT
ap-610	355	8	hardening	harden	VERB
ap-610	355	9	modulus	modulus	NOUN
ap-610	355	10	depends	depend	VERB
ap-610	355	11	not	not	PART
ap-610	355	12	only	only	ADV
ap-610	355	13	on	on	ADP
ap-610	355	14	the	the	DET
ap-610	355	15	material	material	NOUN
ap-610	355	16	parameters	parameter	NOUN
ap-610	355	17	h	h	NOUN
ap-610	355	18	and	and	CCONJ
ap-610	355	19	l	l	NOUN
ap-610	355	20	but	but	CCONJ
ap-610	355	21	also	also	ADV
ap-610	355	22	on	on	ADP
ap-610	355	23	the	the	DET
ap-610	355	24	layer	layer	NOUN
ap-610	355	25	thickness	thickness	NOUN
ap-610	355	26	l	l	NOUN
ap-610	355	27	,	,	PUNCT
ap-610	355	28	i.e.	i.e.	X
ap-610	355	29	,	,	PUNCT
ap-610	355	30	on	on	ADP
ap-610	355	31	the	the	DET
ap-610	355	32	size	size	NOUN
ap-610	355	33	of	of	ADP
ap-610	355	34	the	the	DET
ap-610	355	35	specimen	speciman	NOUN
ap-610	355	36	for	for	ADP
ap-610	355	37	which	which	PRON
ap-610	355	38	it	it	PRON
ap-610	355	39	is	be	AUX
ap-610	355	40	evaluated;	evaluated;	PROPN
ap-610	355	41	see	see	VERB
ap-610	355	42	fig	fig	NOUN
ap-610	355	43	.	.	PUNCT
ap-610	356	1	5a	5a	NUM
ap-610	356	2	.	.	PUNCT
ap-610	357	1	therefore	therefore	ADV
ap-610	357	2	,	,	PUNCT
ap-610	357	3	it	it	PRON
ap-610	357	4	can	can	AUX
ap-610	357	5	not	not	PART
ap-610	357	6	be	be	AUX
ap-610	357	7	considered	consider	VERB
ap-610	357	8	as	as	ADP
ap-610	357	9	an	an	DET
ap-610	357	10	intrinsic	intrinsic	ADJ
ap-610	357	11	material	material	NOUN
ap-610	357	12	parameter	parameter	NOUN
ap-610	357	13	.	.	PUNCT
ap-610	358	1	if	if	SCONJ
ap-610	358	2	the	the	DET
ap-610	358	3	actual	actual	ADJ
ap-610	358	4	behavior	behavior	NOUN
ap-610	358	5	of	of	ADP
ap-610	358	6	the	the	DET
ap-610	358	7	material	material	NOUN
ap-610	358	8	is	be	AUX
ap-610	358	9	close	close	ADJ
ap-610	358	10	to	to	ADP
ap-610	358	11	the	the	DET
ap-610	358	12	gradient	gradient	NOUN
ap-610	358	13	model	model	NOUN
ap-610	358	14	but	but	CCONJ
ap-610	358	15	the	the	DET
ap-610	358	16	experimental	experimental	ADJ
ap-610	358	17	results	result	NOUN
ap-610	358	18	are	be	AUX
ap-610	358	19	interpreted	interpret	VERB
ap-610	358	20	using	use	VERB
ap-610	358	21	the	the	DET
ap-610	358	22	standard	standard	ADJ
ap-610	358	23	elastoplastic	elastoplastic	ADJ
ap-610	358	24	model	model	NOUN
ap-610	358	25	,	,	PUNCT
ap-610	358	26	the	the	DET
ap-610	358	27	value	value	NOUN
ap-610	358	28	of	of	ADP
ap-610	358	29	the	the	DET
ap-610	358	30	hardening	harden	VERB
ap-610	358	31	modulus	modulus	NOUN
ap-610	358	32	will	will	AUX
ap-610	358	33	appear	appear	VERB
ap-610	358	34	to	to	PART
ap-610	358	35	be	be	AUX
ap-610	358	36	size	size	NOUN
ap-610	358	37	-	-	PUNCT
ap-610	358	38	dependent	dependent	ADJ
ap-610	358	39	.	.	PUNCT
ap-610	359	1	the	the	DET
ap-610	359	2	reason	reason	NOUN
ap-610	359	3	is	be	AUX
ap-610	359	4	that	that	SCONJ
ap-610	359	5	the	the	DET
ap-610	359	6	model	model	NOUN
ap-610	359	7	is	be	AUX
ap-610	359	8	oversimplified	oversimplify	VERB
ap-610	359	9	and	and	CCONJ
ap-610	359	10	the	the	DET
ap-610	359	11	comparison	comparison	NOUN
ap-610	359	12	between	between	ADP
ap-610	359	13	theory	theory	NOUN
ap-610	359	14	and	and	CCONJ
ap-610	359	15	experiments	experiment	NOUN
ap-610	359	16	uses	use	VERB
ap-610	359	17	only	only	ADV
ap-610	359	18	global	global	ADJ
ap-610	359	19	characteristics	characteristic	NOUN
ap-610	359	20	such	such	ADJ
ap-610	359	21	as	as	ADP
ap-610	359	22	the	the	DET
ap-610	359	23	measured	measured	ADJ
ap-610	359	24	relation	relation	NOUN
ap-610	359	25	between	between	ADP
ap-610	359	26	the	the	DET
ap-610	359	27	loading	loading	NOUN
ap-610	359	28	force	force	NOUN
ap-610	359	29	and	and	CCONJ
ap-610	359	30	the	the	DET
ap-610	359	31	relative	relative	ADJ
ap-610	359	32	displacement	displacement	NOUN
ap-610	359	33	of	of	ADP
ap-610	359	34	one	one	NUM
ap-610	359	35	loading	loading	NOUN
ap-610	359	36	plate	plate	NOUN
ap-610	359	37	with	with	ADP
ap-610	359	38	respect	respect	NOUN
ap-610	359	39	to	to	ADP
ap-610	359	40	the	the	DET
ap-610	359	41	other	other	ADJ
ap-610	359	42	.	.	PUNCT
ap-610	360	1	if	if	SCONJ
ap-610	360	2	detailed	detailed	ADJ
ap-610	360	3	measurements	measurement	NOUN
ap-610	360	4	of	of	ADP
ap-610	360	5	the	the	DET
ap-610	360	6	strain	strain	NOUN
ap-610	360	7	field	field	NOUN
ap-610	360	8	inside	inside	ADP
ap-610	360	9	the	the	DET
ap-610	360	10	specimen	speciman	NOUN
ap-610	360	11	were	be	AUX
ap-610	360	12	available	available	ADJ
ap-610	360	13	,	,	PUNCT
ap-610	360	14	they	they	PRON
ap-610	360	15	would	would	AUX
ap-610	360	16	reveal	reveal	VERB
ap-610	360	17	a	a	DET
ap-610	360	18	discrepancy	discrepancy	NOUN
ap-610	360	19	between	between	ADP
ap-610	360	20	the	the	DET
ap-610	360	21	actual	actual	ADJ
ap-610	360	22	strain	strain	NOUN
ap-610	360	23	distribution	distribution	NOUN
ap-610	360	24	and	and	CCONJ
ap-610	360	25	the	the	DET
ap-610	360	26	theoretical	theoretical	ADJ
ap-610	360	27	solution	solution	NOUN
ap-610	360	28	based	base	VERB
ap-610	360	29	on	on	ADP
ap-610	360	30	the	the	DET
ap-610	360	31	oversimplified	oversimplified	ADJ
ap-610	360	32	assumptions	assumption	NOUN
ap-610	360	33	.	.	PUNCT
ap-610	361	1	this	this	PRON
ap-610	361	2	would	would	AUX
ap-610	361	3	give	give	VERB
ap-610	361	4	a	a	DET
ap-610	361	5	hint	hint	NOUN
ap-610	361	6	regarding	regard	VERB
ap-610	361	7	the	the	DET
ap-610	361	8	necessary	necessary	ADJ
ap-610	361	9	refinement	refinement	NOUN
ap-610	361	10	of	of	ADP
ap-610	361	11	the	the	DET
ap-610	361	12	theoretical	theoretical	ADJ
ap-610	361	13	model	model	NOUN
ap-610	361	14	by	by	ADP
ap-610	361	15	inclusion	inclusion	NOUN
ap-610	361	16	of	of	ADP
ap-610	361	17	higher	high	ADJ
ap-610	361	18	-	-	PUNCT
ap-610	361	19	order	order	NOUN
ap-610	361	20	terms	term	NOUN
ap-610	361	21	.	.	PUNCT
ap-610	362	1	but	but	CCONJ
ap-610	362	2	even	even	ADV
ap-610	362	3	if	if	SCONJ
ap-610	362	4	such	such	ADJ
ap-610	362	5	detailed	detailed	ADJ
ap-610	362	6	measurements	measurement	NOUN
ap-610	362	7	are	be	AUX
ap-610	362	8	not	not	PART
ap-610	362	9	possible	possible	ADJ
ap-610	362	10	or	or	CCONJ
ap-610	362	11	not	not	PART
ap-610	362	12	available	available	ADJ
ap-610	362	13	,	,	PUNCT
ap-610	362	14	the	the	DET
ap-610	362	15	development	development	NOUN
ap-610	362	16	of	of	ADP
ap-610	362	17	an	an	DET
ap-610	362	18	appropriate	appropriate	ADJ
ap-610	362	19	enriched	enriched	ADJ
ap-610	362	20	continuum	continuum	ADJ
ap-610	362	21	theory	theory	NOUN
ap-610	362	22	can	can	AUX
ap-610	362	23	be	be	AUX
ap-610	362	24	guided	guide	VERB
ap-610	362	25	by	by	ADP
ap-610	362	26	the	the	DET
ap-610	362	27	experimentally	experimentally	ADV
ap-610	362	28	detected	detect	VERB
ap-610	362	29	size	size	NOUN
ap-610	362	30	effect	effect	NOUN
ap-610	362	31	.	.	PUNCT
ap-610	363	1	it	it	PRON
ap-610	363	2	turns	turn	VERB
ap-610	363	3	out	out	ADP
ap-610	363	4	that	that	SCONJ
ap-610	363	5	the	the	DET
ap-610	363	6	size	size	NOUN
ap-610	363	7	effect	effect	NOUN
ap-610	363	8	for	for	ADP
ap-610	363	9	one	one	NUM
ap-610	363	10	specific	specific	ADJ
ap-610	363	11	type	type	NOUN
ap-610	363	12	of	of	ADP
ap-610	363	13	test	test	NOUN
ap-610	363	14	performed	perform	VERB
ap-610	363	15	on	on	ADP
ap-610	363	16	a	a	DET
ap-610	363	17	series	series	NOUN
ap-610	363	18	of	of	ADP
ap-610	363	19	geometrically	geometrically	ADV
ap-610	363	20	similar	similar	ADJ
ap-610	363	21	specimens	specimen	NOUN
ap-610	363	22	can	can	AUX
ap-610	363	23	often	often	ADV
ap-610	363	24	be	be	AUX
ap-610	363	25	well	well	ADV
ap-610	363	26	reproduced	reproduce	VERB
ap-610	363	27	by	by	ADP
ap-610	363	28	several	several	ADJ
ap-610	363	29	different	different	ADJ
ap-610	363	30	types	type	NOUN
ap-610	363	31	of	of	ADP
ap-610	363	32	enriched	enrich	VERB
ap-610	363	33	models	model	NOUN
ap-610	363	34	that	that	PRON
ap-610	363	35	are	be	AUX
ap-610	363	36	not	not	PART
ap-610	363	37	necessarily	necessarily	ADV
ap-610	363	38	equivalent	equivalent	ADJ
ap-610	363	39	in	in	ADP
ap-610	363	40	a	a	DET
ap-610	363	41	general	general	ADJ
ap-610	363	42	case	case	NOUN
ap-610	363	43	.	.	PUNCT
ap-610	364	1	ideally	ideally	ADV
ap-610	364	2	,	,	PUNCT
ap-610	364	3	the	the	DET
ap-610	364	4	enriched	enrich	VERB
ap-610	364	5	theory	theory	NOUN
ap-610	364	6	should	should	AUX
ap-610	364	7	be	be	AUX
ap-610	364	8	verified	verify	VERB
ap-610	364	9	by	by	ADP
ap-610	364	10	several	several	ADJ
ap-610	364	11	tests	test	NOUN
ap-610	364	12	leading	lead	VERB
ap-610	364	13	to	to	ADP
ap-610	364	14	different	different	ADJ
ap-610	364	15	types	type	NOUN
ap-610	364	16	of	of	ADP
ap-610	364	17	stress	stress	NOUN
ap-610	364	18	and	and	CCONJ
ap-610	364	19	strain	strain	NOUN
ap-610	364	20	distributions	distribution	NOUN
ap-610	364	21	,	,	PUNCT
ap-610	364	22	and	and	CCONJ
ap-610	364	23	also	also	ADV
ap-610	364	24	supported	support	VERB
ap-610	364	25	by	by	ADP
ap-610	364	26	micromechanical	micromechanical	ADJ
ap-610	364	27	arguments	argument	NOUN
ap-610	364	28	and	and	CCONJ
ap-610	364	29	confirmed	confirm	VERB
ap-610	364	30	by	by	ADP
ap-610	364	31	observations	observation	NOUN
ap-610	364	32	of	of	ADP
ap-610	364	33	the	the	DET
ap-610	364	34	actual	actual	ADJ
ap-610	364	35	processes	process	NOUN
ap-610	364	36	in	in	ADP
ap-610	364	37	the	the	DET
ap-610	364	38	microstructure	microstructure	NOUN
ap-610	364	39	.	.	PUNCT
ap-610	365	1	only	only	ADV
ap-610	365	2	then	then	ADV
ap-610	365	3	can	can	AUX
ap-610	365	4	the	the	DET
ap-610	365	5	model	model	NOUN
ap-610	365	6	be	be	AUX
ap-610	365	7	assumed	assume	VERB
ap-610	365	8	to	to	PART
ap-610	365	9	reasonably	reasonably	ADV
ap-610	365	10	reproduce	reproduce	VERB
ap-610	365	11	the	the	DET
ap-610	365	12	actual	actual	ADJ
ap-610	365	13	material	material	NOUN
ap-610	365	14	behavior	behavior	NOUN
ap-610	365	15	and	and	CCONJ
ap-610	365	16	to	to	PART
ap-610	365	17	have	have	VERB
ap-610	365	18	some	some	DET
ap-610	365	19	predictive	predictive	ADJ
ap-610	365	20	power	power	NOUN
ap-610	365	21	.	.	PUNCT
ap-610	366	1	if	if	SCONJ
ap-610	366	2	only	only	ADV
ap-610	366	3	one	one	NUM
ap-610	366	4	series	series	NOUN
ap-610	366	5	of	of	ADP
ap-610	366	6	experiments	experiment	NOUN
ap-610	366	7	is	be	AUX
ap-610	366	8	fitted	fit	VERB
ap-610	366	9	,	,	PUNCT
ap-610	366	10	the	the	DET
ap-610	366	11	model	model	NOUN
ap-610	366	12	can	can	AUX
ap-610	366	13	usually	usually	ADV
ap-610	366	14	serve	serve	VERB
ap-610	366	15	for	for	ADP
ap-610	366	16	reliable	reliable	ADJ
ap-610	366	17	interpolation	interpolation	NOUN
ap-610	366	18	in	in	ADP
ap-610	366	19	the	the	DET
ap-610	366	20	limits	limit	NOUN
ap-610	366	21	that	that	PRON
ap-610	366	22	have	have	AUX
ap-610	366	23	been	be	AUX
ap-610	366	24	covered	cover	VERB
ap-610	366	25	by	by	ADP
ap-610	366	26	the	the	DET
ap-610	366	27	experiments	experiment	NOUN
ap-610	366	28	,	,	PUNCT
ap-610	366	29	but	but	CCONJ
ap-610	366	30	extrapolation	extrapolation	NOUN
ap-610	366	31	to	to	ADP
ap-610	366	32	smaller	small	ADJ
ap-610	366	33	or	or	CCONJ
ap-610	366	34	larger	large	ADJ
ap-610	366	35	sizes	size	NOUN
ap-610	366	36	can	can	AUX
ap-610	366	37	be	be	AUX
ap-610	366	38	dangerous	dangerous	ADJ
ap-610	366	39	.	.	PUNCT
ap-610	367	1	the	the	DET
ap-610	367	2	diagram	diagram	NOUN
ap-610	367	3	linking	link	VERB
ap-610	367	4	the	the	DET
ap-610	367	5	shear	shear	NOUN
ap-610	367	6	stress	stress	NOUN
ap-610	367	7	to	to	ADP
ap-610	367	8	the	the	DET
ap-610	367	9	average	average	ADJ
ap-610	367	10	shear	shear	NOUN
ap-610	367	11	strain	strain	NOUN
ap-610	367	12	for	for	ADP
ap-610	367	13	different	different	ADJ
ap-610	367	14	thicknesses	thickness	NOUN
ap-610	367	15	l	l	NOUN
ap-610	367	16	of	of	ADP
ap-610	367	17	the	the	DET
ap-610	367	18	shear	shear	NOUN
ap-610	367	19	layer	layer	NOUN
ap-610	367	20	is	be	AUX
ap-610	367	21	plotted	plot	VERB
ap-610	367	22	in	in	ADP
ap-610	367	23	fig	fig	NOUN
ap-610	367	24	.	.	PUNCT
ap-610	368	1	6a	6a	NOUN
ap-610	368	2	,	,	PUNCT
ap-610	368	3	and	and	CCONJ
ap-610	368	4	the	the	DET
ap-610	368	5	dependence	dependence	NOUN
ap-610	368	6	of	of	ADP
ap-610	368	7	the	the	DET
ap-610	368	8	apparent	apparent	ADJ
ap-610	368	9	hardening	harden	VERB
ap-610	368	10	modulus	modulus	NOUN
ap-610	368	11	~h	~h	PROPN
ap-610	368	12	on	on	ADP
ap-610	368	13	the	the	DET
ap-610	368	14	specimen	speciman	NOUN
ap-610	368	15	size	size	NOUN
ap-610	368	16	(	(	PUNCT
ap-610	368	17	layer	layer	NOUN
ap-610	368	18	thickness	thickness	NOUN
ap-610	368	19	)	)	PUNCT
ap-610	368	20	is	be	AUX
ap-610	368	21	shown	show	VERB
ap-610	368	22	in	in	ADP
ap-610	368	23	fig	fig	NOUN
ap-610	368	24	.	.	PUNCT
ap-610	369	1	5a	5a	NUM
ap-610	369	2	.	.	PUNCT
ap-610	370	1	if	if	SCONJ
ap-610	370	2	the	the	DET
ap-610	370	3	layer	layer	NOUN
ap-610	370	4	thickness	thickness	NOUN
ap-610	370	5	is	be	AUX
ap-610	370	6	much	much	ADV
ap-610	370	7	larger	large	ADJ
ap-610	370	8	than	than	ADP
ap-610	370	9	the	the	DET
ap-610	370	10	material	material	NOUN
ap-610	370	11	length	length	NOUN
ap-610	370	12	l	l	PROPN
ap-610	370	13	,	,	PUNCT
ap-610	370	14	the	the	DET
ap-610	370	15	stress	stress	NOUN
ap-610	370	16	-	-	PUNCT
ap-610	370	17	strain	strain	NOUN
ap-610	370	18	curve	curve	NOUN
ap-610	370	19	is	be	AUX
ap-610	370	20	practically	practically	ADV
ap-610	370	21	size	size	NOUN
ap-610	370	22	-	-	PUNCT
ap-610	370	23	independent	independent	NOUN
ap-610	370	24	and	and	CCONJ
ap-610	370	25	the	the	DET
ap-610	370	26	apparent	apparent	ADJ
ap-610	370	27	hardening	harden	VERB
ap-610	370	28	modulus	modulus	NOUN
ap-610	370	29	~h	~h	NUM
ap-610	370	30	evaluated	evaluate	VERB
ap-610	370	31	from	from	ADP
ap-610	370	32	the	the	DET
ap-610	370	33	26	26	NUM
ap-610	370	34	©	©	PROPN
ap-610	370	35	czech	czech	PROPN
ap-610	370	36	technical	technical	PROPN
ap-610	370	37	university	university	PROPN
ap-610	370	38	publishing	publishing	NOUN
ap-610	370	39	house	house	NOUN
ap-610	370	40	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	370	41	acta	acta	PROPN
ap-610	370	42	polytechnica	polytechnica	PROPN
ap-610	370	43	vol	vol	NOUN
ap-610	370	44	.	.	PROPN
ap-610	371	1	44	44	NUM
ap-610	371	2	no	no	NOUN
ap-610	371	3	.	.	PUNCT
ap-610	372	1	5–6/2004	5–6/2004	NUM
ap-610	372	2	(	(	PUNCT
ap-610	372	3	a	a	NOUN
ap-610	372	4	)	)	PUNCT
ap-610	372	5	(	(	PUNCT
ap-610	372	6	b	b	X
ap-610	372	7	)	)	PUNCT
ap-610	372	8	fig	fig	NOUN
ap-610	372	9	.	.	PUNCT
ap-610	373	1	5	5	NUM
ap-610	373	2	:	:	PUNCT
ap-610	373	3	explicit	explicit	ADJ
ap-610	373	4	gradient	gradient	ADJ
ap-610	373	5	plasticity	plasticity	NOUN
ap-610	373	6	:	:	PUNCT
ap-610	373	7	(	(	PUNCT
ap-610	373	8	a	a	X
ap-610	373	9	)	)	PUNCT
ap-610	373	10	dependence	dependence	NOUN
ap-610	373	11	of	of	ADP
ap-610	373	12	the	the	DET
ap-610	373	13	apparent	apparent	ADJ
ap-610	373	14	hardening	harden	VERB
ap-610	373	15	modulus	modulus	NOUN
ap-610	373	16	on	on	ADP
ap-610	373	17	the	the	DET
ap-610	373	18	size	size	NOUN
ap-610	373	19	of	of	ADP
ap-610	373	20	the	the	DET
ap-610	373	21	specimen	speciman	NOUN
ap-610	373	22	(	(	PUNCT
ap-610	373	23	layer	layer	NOUN
ap-610	373	24	thickness	thickness	NOUN
ap-610	373	25	)	)	PUNCT
ap-610	373	26	,	,	PUNCT
ap-610	373	27	(	(	PUNCT
ap-610	373	28	b	b	X
ap-610	373	29	)	)	PUNCT
ap-610	373	30	distribution	distribution	NOUN
ap-610	373	31	of	of	ADP
ap-610	373	32	plastic	plastic	ADJ
ap-610	373	33	strain	strain	NOUN
ap-610	373	34	across	across	ADP
ap-610	373	35	the	the	DET
ap-610	373	36	layer	layer	NOUN
ap-610	373	37	test	test	NOUN
ap-610	373	38	is	be	AUX
ap-610	373	39	very	very	ADV
ap-610	373	40	close	close	ADJ
ap-610	373	41	to	to	ADP
ap-610	373	42	the	the	DET
ap-610	373	43	model	model	NOUN
ap-610	373	44	parameter	parameter	PROPN
ap-610	373	45	h	h	PROPN
ap-610	373	46	,	,	PUNCT
ap-610	373	47	considered	consider	VERB
ap-610	373	48	here	here	ADV
ap-610	373	49	as	as	ADP
ap-610	373	50	an	an	DET
ap-610	373	51	intrinsic	intrinsic	ADJ
ap-610	373	52	material	material	NOUN
ap-610	373	53	property	property	NOUN
ap-610	373	54	.	.	PUNCT
ap-610	374	1	so	so	ADV
ap-610	374	2	the	the	DET
ap-610	374	3	standard	standard	ADJ
ap-610	374	4	theory	theory	NOUN
ap-610	374	5	can	can	AUX
ap-610	374	6	be	be	AUX
ap-610	374	7	used	use	VERB
ap-610	374	8	as	as	ADP
ap-610	374	9	a	a	DET
ap-610	374	10	good	good	ADJ
ap-610	374	11	approximation	approximation	NOUN
ap-610	374	12	if	if	SCONJ
ap-610	374	13	the	the	DET
ap-610	374	14	specimen	speciman	NOUN
ap-610	374	15	is	be	AUX
ap-610	374	16	large	large	ADJ
ap-610	374	17	.	.	PUNCT
ap-610	375	1	for	for	ADP
ap-610	375	2	layer	layer	NOUN
ap-610	375	3	thicknesses	thickness	NOUN
ap-610	375	4	smaller	small	ADJ
ap-610	375	5	than	than	ADP
ap-610	375	6	about	about	ADP
ap-610	375	7	20l	20l	NOUN
ap-610	375	8	,	,	PUNCT
ap-610	375	9	the	the	DET
ap-610	375	10	stress	stress	NOUN
ap-610	375	11	-	-	PUNCT
ap-610	375	12	strain	strain	NOUN
ap-610	375	13	curve	curve	NOUN
ap-610	375	14	becomes	become	VERB
ap-610	375	15	size	size	NOUN
ap-610	375	16	-	-	PUNCT
ap-610	375	17	dependent	dependent	ADJ
ap-610	375	18	and	and	CCONJ
ap-610	375	19	it	it	PRON
ap-610	375	20	rises	rise	VERB
ap-610	375	21	above	above	ADP
ap-610	375	22	the	the	DET
ap-610	375	23	basic	basic	ADJ
ap-610	375	24	stress	stress	NOUN
ap-610	375	25	-	-	PUNCT
ap-610	375	26	strain	strain	NOUN
ap-610	375	27	curve	curve	NOUN
ap-610	375	28	valid	valid	NOUN
ap-610	375	29	in	in	ADP
ap-610	375	30	the	the	DET
ap-610	375	31	large	large	ADJ
ap-610	375	32	-	-	PUNCT
ap-610	375	33	size	size	NOUN
ap-610	375	34	limit	limit	NOUN
ap-610	375	35	.	.	PUNCT
ap-610	376	1	the	the	DET
ap-610	376	2	apparent	apparent	ADJ
ap-610	376	3	hardening	harden	VERB
ap-610	376	4	modulus	modulus	NOUN
ap-610	376	5	increases	increase	NOUN
ap-610	376	6	with	with	ADP
ap-610	376	7	decreasing	decrease	VERB
ap-610	376	8	size	size	NOUN
ap-610	376	9	.	.	PUNCT
ap-610	377	1	even	even	ADV
ap-610	377	2	though	though	SCONJ
ap-610	377	3	the	the	DET
ap-610	377	4	shear	shear	NOUN
ap-610	377	5	test	test	NOUN
ap-610	377	6	of	of	ADP
ap-610	377	7	a	a	DET
ap-610	377	8	layer	layer	NOUN
ap-610	377	9	is	be	AUX
ap-610	377	10	difficult	difficult	ADJ
ap-610	377	11	to	to	PART
ap-610	377	12	perform	perform	VERB
ap-610	377	13	,	,	PUNCT
ap-610	377	14	this	this	DET
ap-610	377	15	trend	trend	NOUN
ap-610	377	16	can	can	AUX
ap-610	377	17	be	be	AUX
ap-610	377	18	considered	consider	VERB
ap-610	377	19	as	as	ADP
ap-610	377	20	realistic	realistic	ADJ
ap-610	377	21	because	because	SCONJ
ap-610	377	22	stronger	strong	ADJ
ap-610	377	23	hardening	hardening	NOUN
ap-610	377	24	for	for	ADP
ap-610	377	25	smaller	small	ADJ
ap-610	377	26	specimens	specimen	NOUN
ap-610	377	27	is	be	AUX
ap-610	377	28	indeed	indeed	ADV
ap-610	377	29	observed	observe	VERB
ap-610	377	30	in	in	ADP
ap-610	377	31	experiments	experiment	NOUN
ap-610	377	32	with	with	ADP
ap-610	377	33	plastic	plastic	ADJ
ap-610	377	34	torsion	torsion	NOUN
ap-610	377	35	of	of	ADP
ap-610	377	36	tiny	tiny	ADJ
ap-610	377	37	wires	wire	NOUN
ap-610	377	38	or	or	CCONJ
ap-610	377	39	microbending	microbende	VERB
ap-610	377	40	of	of	ADP
ap-610	377	41	thin	thin	ADJ
ap-610	377	42	films	film	NOUN
ap-610	377	43	.	.	PUNCT
ap-610	378	1	this	this	PRON
ap-610	378	2	is	be	AUX
ap-610	378	3	documented	document	VERB
ap-610	378	4	in	in	ADP
ap-610	378	5	fig	fig	NOUN
ap-610	378	6	.	.	PUNCT
ap-610	379	1	6b	6b	NOUN
ap-610	379	2	,	,	PUNCT
ap-610	379	3	adapted	adapt	VERB
ap-610	379	4	from	from	ADP
ap-610	379	5	fleck	fleck	PROPN
ap-610	379	6	et	et	PROPN
ap-610	379	7	al	al	PROPN
ap-610	379	8	.	.	PROPN
ap-610	379	9	(	(	PUNCT
ap-610	379	10	1994	1994	NUM
ap-610	379	11	)	)	PUNCT
ap-610	379	12	.	.	PUNCT
ap-610	380	1	the	the	DET
ap-610	380	2	figure	figure	NOUN
ap-610	380	3	shows	show	VERB
ap-610	380	4	the	the	DET
ap-610	380	5	dependence	dependence	NOUN
ap-610	380	6	of	of	ADP
ap-610	380	7	the	the	DET
ap-610	380	8	normalized	normalize	VERB
ap-610	380	9	torque	torque	NOUN
ap-610	380	10	,	,	PUNCT
ap-610	380	11	m	m	PRON
ap-610	380	12	d3	d3	PROPN
ap-610	380	13	,	,	PUNCT
ap-610	380	14	on	on	ADP
ap-610	380	15	the	the	DET
ap-610	380	16	normalized	normalize	VERB
ap-610	380	17	angle	angle	NOUN
ap-610	380	18	of	of	ADP
ap-610	380	19	twist	twist	NOUN
ap-610	380	20	,	,	PUNCT
ap-610	380	21	�	�	PROPN
ap-610	380	22	d	d	PROPN
ap-610	380	23	,	,	PUNCT
ap-610	380	24	which	which	PRON
ap-610	380	25	is	be	AUX
ap-610	380	26	equal	equal	ADJ
ap-610	380	27	to	to	ADP
ap-610	380	28	the	the	DET
ap-610	380	29	shear	shear	NOUN
ap-610	380	30	strain	strain	NOUN
ap-610	380	31	on	on	ADP
ap-610	380	32	the	the	DET
ap-610	380	33	wire	wire	NOUN
ap-610	380	34	surface	surface	NOUN
ap-610	380	35	.	.	PUNCT
ap-610	381	1	according	accord	VERB
ap-610	381	2	to	to	ADP
ap-610	381	3	any	any	DET
ap-610	381	4	theory	theory	NOUN
ap-610	381	5	with	with	ADP
ap-610	381	6	stress	stress	NOUN
ap-610	381	7	at	at	ADP
ap-610	381	8	a	a	DET
ap-610	381	9	point	point	NOUN
ap-610	381	10	dependent	dependent	ADJ
ap-610	381	11	on	on	ADP
ap-610	381	12	the	the	DET
ap-610	381	13	history	history	NOUN
ap-610	381	14	of	of	ADP
ap-610	381	15	strain	strain	NOUN
ap-610	381	16	at	at	ADP
ap-610	381	17	that	that	DET
ap-610	381	18	point	point	NOUN
ap-610	381	19	only	only	ADV
ap-610	381	20	,	,	PUNCT
ap-610	381	21	the	the	DET
ap-610	381	22	resulting	result	VERB
ap-610	381	23	curve	curve	NOUN
ap-610	381	24	should	should	AUX
ap-610	381	25	be	be	AUX
ap-610	381	26	independent	independent	ADJ
ap-610	381	27	of	of	ADP
ap-610	381	28	the	the	DET
ap-610	381	29	wire	wire	NOUN
ap-610	381	30	diameter	diameter	NOUN
ap-610	381	31	d.	d.	PROPN
ap-610	381	32	in	in	ADP
ap-610	381	33	reality	reality	NOUN
ap-610	381	34	,	,	PUNCT
ap-610	381	35	this	this	PRON
ap-610	381	36	is	be	AUX
ap-610	381	37	true	true	ADJ
ap-610	381	38	only	only	ADV
ap-610	381	39	for	for	ADP
ap-610	381	40	sufficiently	sufficiently	ADV
ap-610	381	41	thick	thick	ADJ
ap-610	381	42	wires	wire	NOUN
ap-610	381	43	.	.	PUNCT
ap-610	382	1	the	the	DET
ap-610	382	2	figure	figure	NOUN
ap-610	382	3	clearly	clearly	ADV
ap-610	382	4	shows	show	VERB
ap-610	382	5	that	that	SCONJ
ap-610	382	6	for	for	ADP
ap-610	382	7	diameters	diameter	NOUN
ap-610	382	8	in	in	ADP
ap-610	382	9	the	the	DET
ap-610	382	10	order	order	NOUN
ap-610	382	11	of	of	ADP
ap-610	382	12	dozens	dozen	NOUN
ap-610	382	13	of	of	ADP
ap-610	382	14	micrometers	micrometer	NOUN
ap-610	382	15	,	,	PUNCT
ap-610	382	16	the	the	DET
ap-610	382	17	actual	actual	ADJ
ap-610	382	18	response	response	NOUN
ap-610	382	19	after	after	SCONJ
ap-610	382	20	the	the	DET
ap-610	382	21	onset	onset	NOUN
ap-610	382	22	of	of	ADP
ap-610	382	23	yielding	yield	VERB
ap-610	382	24	is	be	AUX
ap-610	382	25	stronger	strong	ADJ
ap-610	382	26	than	than	SCONJ
ap-610	382	27	expected	expect	VERB
ap-610	382	28	.	.	PUNCT
ap-610	383	1	aifantis	aifantis	PROPN
ap-610	383	2	(	(	PUNCT
ap-610	383	3	2003	2003	NUM
ap-610	383	4	)	)	PUNCT
ap-610	383	5	and	and	CCONJ
ap-610	383	6	fleck	fleck	NOUN
ap-610	383	7	and	and	CCONJ
ap-610	383	8	hutchinson	hutchinson	PROPN
ap-610	383	9	(	(	PUNCT
ap-610	383	10	2001	2001	NUM
ap-610	383	11	)	)	PUNCT
ap-610	383	12	have	have	AUX
ap-610	383	13	demonstrated	demonstrate	VERB
ap-610	383	14	that	that	SCONJ
ap-610	383	15	this	this	DET
ap-610	383	16	size	size	NOUN
ap-610	383	17	effect	effect	NOUN
ap-610	383	18	can	can	AUX
ap-610	383	19	be	be	AUX
ap-610	383	20	captured	capture	VERB
ap-610	383	21	by	by	ADP
ap-610	383	22	gradient	gradient	NOUN
ap-610	383	23	plasticity	plasticity	NOUN
ap-610	383	24	theories	theory	NOUN
ap-610	383	25	similar	similar	ADJ
ap-610	383	26	to	to	ADP
ap-610	383	27	the	the	DET
ap-610	383	28	one	one	NOUN
ap-610	383	29	presented	present	VERB
ap-610	383	30	here	here	ADV
ap-610	383	31	.	.	PUNCT
ap-610	384	1	3.4	3.4	NUM
ap-610	384	2	.	.	PUNCT
ap-610	385	1	implicit	implicit	ADJ
ap-610	385	2	gradient	gradient	NOUN
ap-610	385	3	plasticity	plasticity	NOUN
ap-610	385	4	the	the	DET
ap-610	385	5	model	model	NOUN
ap-610	385	6	with	with	ADP
ap-610	385	7	yield	yield	NOUN
ap-610	385	8	stress	stress	NOUN
ap-610	385	9	dependent	dependent	ADJ
ap-610	385	10	on	on	ADP
ap-610	385	11	the	the	DET
ap-610	385	12	second	second	ADJ
ap-610	385	13	gradient	gradient	NOUN
ap-610	385	14	of	of	ADP
ap-610	385	15	cumulative	cumulative	ADJ
ap-610	385	16	plastic	plastic	NOUN
ap-610	385	17	strain	strain	NOUN
ap-610	385	18	falls	fall	VERB
ap-610	385	19	into	into	ADP
ap-610	385	20	the	the	DET
ap-610	385	21	category	category	NOUN
ap-610	385	22	of	of	ADP
ap-610	385	23	explicit	explicit	ADJ
ap-610	385	24	gradient	gradient	NOUN
ap-610	385	25	models	model	NOUN
ap-610	385	26	.	.	PUNCT
ap-610	386	1	recently	recently	ADV
ap-610	386	2	it	it	PRON
ap-610	386	3	turned	turn	VERB
ap-610	386	4	out	out	ADP
ap-610	386	5	that	that	SCONJ
ap-610	386	6	certain	certain	ADJ
ap-610	386	7	advantages	advantage	NOUN
ap-610	386	8	can	can	AUX
ap-610	386	9	be	be	AUX
ap-610	386	10	gained	gain	VERB
ap-610	386	11	by	by	ADP
ap-610	386	12	using	use	VERB
ap-610	386	13	implicit	implicit	ADJ
ap-610	386	14	gradient	gradient	NOUN
ap-610	386	15	formulations	formulation	NOUN
ap-610	386	16	,	,	PUNCT
ap-610	386	17	which	which	PRON
ap-610	386	18	are	be	AUX
ap-610	386	19	closely	closely	ADV
ap-610	386	20	related	relate	VERB
ap-610	386	21	to	to	ADP
ap-610	386	22	integral	integral	ADJ
ap-610	386	23	-	-	PUNCT
ap-610	386	24	type	type	NOUN
ap-610	386	25	nonlocal	nonlocal	ADJ
ap-610	386	26	models	model	NOUN
ap-610	386	27	.	.	PUNCT
ap-610	387	1	a	a	DET
ap-610	387	2	prominent	prominent	ADJ
ap-610	387	3	example	example	NOUN
ap-610	387	4	is	be	AUX
ap-610	387	5	the	the	DET
ap-610	387	6	so	so	ADV
ap-610	387	7	-	-	PUNCT
ap-610	387	8	called	call	VERB
ap-610	387	9	ductile	ductile	NOUN
ap-610	387	10	damage	damage	NOUN
ap-610	387	11	model	model	NOUN
ap-610	387	12	of	of	ADP
ap-610	387	13	geers	geer	NOUN
ap-610	387	14	,	,	PUNCT
ap-610	387	15	engelen	engelen	NOUN
ap-610	387	16	and	and	CCONJ
ap-610	387	17	ubachs	ubach	NOUN
ap-610	387	18	(	(	PUNCT
ap-610	387	19	2001	2001	NUM
ap-610	387	20	)	)	PUNCT
ap-610	387	21	.	.	PUNCT
ap-610	388	1	this	this	DET
ap-610	388	2	model	model	NOUN
ap-610	388	3	introduces	introduce	VERB
ap-610	388	4	the	the	DET
ap-610	388	5	dependence	dependence	NOUN
ap-610	388	6	of	of	ADP
ap-610	388	7	the	the	DET
ap-610	388	8	yield	yield	NOUN
ap-610	388	9	stress	stress	NOUN
ap-610	388	10	on	on	ADP
ap-610	388	11	the	the	DET
ap-610	388	12	nonlocal	nonlocal	ADJ
ap-610	388	13	cumulative	cumulative	ADJ
ap-610	388	14	plastic	plastic	NOUN
ap-610	388	15	strain	strain	NOUN
ap-610	388	16	,	,	PUNCT
ap-610	388	17	�	�	PROPN
ap-610	388	18	,	,	PUNCT
ap-610	388	19	defined	define	VERB
ap-610	388	20	implicitly	implicitly	ADV
ap-610	388	21	as	as	ADP
ap-610	388	22	the	the	DET
ap-610	388	23	solution	solution	NOUN
ap-610	388	24	of	of	ADP
ap-610	388	25	a	a	DET
ap-610	388	26	helmholtz	helmholtz	NOUN
ap-610	388	27	-	-	PUNCT
ap-610	388	28	type	type	NOUN
ap-610	388	29	differential	differential	ADJ
ap-610	388	30	equation	equation	NOUN
ap-610	388	31	with	with	ADP
ap-610	388	32	the	the	DET
ap-610	388	33	local	local	ADJ
ap-610	388	34	cumulative	cumulative	ADJ
ap-610	388	35	plastic	plastic	NOUN
ap-610	388	36	strain	strain	NOUN
ap-610	388	37	on	on	ADP
ap-610	388	38	the	the	DET
ap-610	388	39	right	right	ADJ
ap-610	388	40	-	-	PUNCT
ap-610	388	41	hand	hand	NOUN
ap-610	388	42	side	side	NOUN
ap-610	388	43	.	.	PUNCT
ap-610	389	1	for	for	ADP
ap-610	389	2	a	a	DET
ap-610	389	3	one	one	NUM
ap-610	389	4	-	-	PUNCT
ap-610	389	5	dimensional	dimensional	ADJ
ap-610	389	6	problem	problem	NOUN
ap-610	389	7	,	,	PUNCT
ap-610	389	8	this	this	DET
ap-610	389	9	equation	equation	NOUN
ap-610	389	10	reads	read	VERB
ap-610	389	11	�	�	PROPN
ap-610	389	12	�	�	PROPN
ap-610	389	13	�	�	PROPN
ap-610	389	14	�	�	PROPN
ap-610	389	15	�	�	PROPN
ap-610	389	16	�	�	PROPN
ap-610	389	17	�	�	PROPN
ap-610	389	18	l2	l2	NOUN
ap-610	389	19	,	,	PUNCT
ap-610	389	20	(	(	PUNCT
ap-610	389	21	67	67	NUM
ap-610	389	22	)	)	PUNCT
ap-610	389	23	where	where	SCONJ
ap-610	389	24	l	l	NOUN
ap-610	389	25	is	be	AUX
ap-610	389	26	,	,	PUNCT
ap-610	389	27	as	as	ADV
ap-610	389	28	usual	usual	ADJ
ap-610	389	29	,	,	PUNCT
ap-610	389	30	a	a	DET
ap-610	389	31	model	model	NOUN
ap-610	389	32	parameter	parameter	NOUN
ap-610	389	33	with	with	ADP
ap-610	389	34	the	the	DET
ap-610	389	35	dimension	dimension	NOUN
ap-610	389	36	of	of	ADP
ap-610	389	37	length	length	NOUN
ap-610	389	38	.	.	PUNCT
ap-610	390	1	in	in	ADP
ap-610	390	2	the	the	DET
ap-610	390	3	simplest	simple	ADJ
ap-610	390	4	case	case	NOUN
ap-610	390	5	,	,	PUNCT
ap-610	390	6	one	one	PRON
ap-610	390	7	could	could	AUX
ap-610	390	8	replace	replace	VERB
ap-610	390	9	�	�	PROPN
ap-610	390	10	in	in	ADP
ap-610	390	11	(	(	PUNCT
ap-610	390	12	58)–(59	58)–(59	NOUN
ap-610	390	13	)	)	PUNCT
ap-610	390	14	by	by	ADP
ap-610	390	15	�	�	PROPN
ap-610	390	16	,	,	PUNCT
ap-610	390	17	but	but	CCONJ
ap-610	390	18	such	such	DET
ap-610	390	19	a	a	DET
ap-610	390	20	formulation	formulation	NOUN
ap-610	390	21	would	would	AUX
ap-610	390	22	have	have	VERB
ap-610	390	23	certain	certain	ADJ
ap-610	390	24	deficiencies	deficiency	NOUN
ap-610	390	25	.	.	PUNCT
ap-610	391	1	micromechanical	micromechanical	ADJ
ap-610	391	2	arguments	argument	NOUN
ap-610	391	3	based	base	VERB
ap-610	391	4	on	on	ADP
ap-610	391	5	the	the	DET
ap-610	391	6	idea	idea	NOUN
ap-610	391	7	of	of	ADP
ap-610	391	8	a	a	DET
ap-610	391	9	plastically	plastically	NOUN
ap-610	391	10	hardening	harden	VERB
ap-610	391	11	matrix	matrix	NOUN
ap-610	391	12	weakened	weaken	VERB
ap-610	391	13	by	by	ADP
ap-610	391	14	growing	grow	VERB
ap-610	391	15	voids	voids	NOUN
ap-610	391	16	lead	lead	NOUN
ap-610	391	17	to	to	ADP
ap-610	391	18	the	the	DET
ap-610	391	19	following	follow	VERB
ap-610	391	20	expression	expression	NOUN
ap-610	391	21	for	for	ADP
ap-610	391	22	the	the	DET
ap-610	391	23	yield	yield	NOUN
ap-610	391	24	stress	stress	NOUN
ap-610	391	25	:	:	PUNCT
ap-610	391	26	�	�	PROPN
ap-610	391	27	�	�	PROPN
ap-610	391	28	�	�	PROPN
ap-610	391	29	�	�	PROPN
ap-610	391	30	�	�	PROPN
ap-610	391	31	�	�	PROPN
ap-610	391	32	�	�	PROPN
ap-610	391	33	y	y	PROPN
ap-610	391	34	ph	ph	PROPN
ap-610	391	35	(	(	PUNCT
ap-610	391	36	,	,	PUNCT
ap-610	391	37	)	)	PUNCT
ap-610	391	38	(	(	PUNCT
ap-610	391	39	)	)	PUNCT
ap-610	391	40	[	[	PUNCT
ap-610	391	41	(	(	PUNCT
ap-610	391	42	)	)	PUNCT
ap-610	391	43	]	]	X
ap-610	391	44	�	�	PROPN
ap-610	391	45	�	�	PROPN
ap-610	391	46	�	�	PROPN
ap-610	391	47	0	0	NUM
ap-610	391	48	1	1	NUM
ap-610	391	49	.	.	PUNCT
ap-610	392	1	(	(	PUNCT
ap-610	392	2	68	68	NUM
ap-610	392	3	)	)	PUNCT
ap-610	392	4	here	here	ADV
ap-610	392	5	,	,	PUNCT
ap-610	392	6	the	the	DET
ap-610	392	7	term	term	NOUN
ap-610	392	8	�	�	PROPN
ap-610	392	9	�	�	PROPN
ap-610	392	10	0	0	NUM
ap-610	392	11	�	�	PROPN
ap-610	392	12	h	h	PROPN
ap-610	392	13	represents	represent	VERB
ap-610	392	14	the	the	DET
ap-610	392	15	yield	yield	NOUN
ap-610	392	16	stress	stress	NOUN
ap-610	392	17	of	of	ADP
ap-610	392	18	the	the	DET
ap-610	392	19	matrix	matrix	NOUN
ap-610	392	20	,	,	PUNCT
ap-610	392	21	which	which	PRON
ap-610	392	22	exhibits	exhibit	VERB
ap-610	392	23	hardening	harden	VERB
ap-610	392	24	driven	drive	VERB
ap-610	392	25	by	by	ADP
ap-610	392	26	the	the	DET
ap-610	392	27	local	local	ADJ
ap-610	392	28	value	value	NOUN
ap-610	392	29	of	of	ADP
ap-610	392	30	the	the	DET
ap-610	392	31	cumulative	cumulative	ADJ
ap-610	392	32	plastic	plastic	NOUN
ap-610	392	33	strain	strain	NOUN
ap-610	392	34	,	,	PUNCT
ap-610	392	35	while	while	SCONJ
ap-610	392	36	1	1	NUM
ap-610	392	37	�	�	PROPN
ap-610	392	38	�	�	PROPN
ap-610	392	39	�	�	PROPN
ap-610	392	40	p	p	PROPN
ap-610	392	41	(	(	PUNCT
ap-610	392	42	)	)	PUNCT
ap-610	392	43	is	be	AUX
ap-610	392	44	an	an	DET
ap-610	392	45	integrity	integrity	NOUN
ap-610	392	46	factor	factor	NOUN
ap-610	392	47	taking	take	VERB
ap-610	392	48	into	into	ADP
ap-610	392	49	account	account	NOUN
ap-610	392	50	the	the	DET
ap-610	392	51	reduction	reduction	NOUN
ap-610	392	52	of	of	ADP
ap-610	392	53	the	the	DET
ap-610	392	54	effective	effective	ADJ
ap-610	392	55	area	area	NOUN
ap-610	392	56	by	by	ADP
ap-610	392	57	voids	void	NOUN
ap-610	392	58	that	that	PRON
ap-610	392	59	carry	carry	VERB
ap-610	392	60	no	no	DET
ap-610	392	61	stress	stress	NOUN
ap-610	392	62	.	.	PUNCT
ap-610	393	1	void	void	ADJ
ap-610	393	2	propagation	propagation	NOUN
ap-610	393	3	is	be	AUX
ap-610	393	4	assumed	assume	VERB
ap-610	393	5	to	to	PART
ap-610	393	6	be	be	AUX
ap-610	393	7	driven	drive	VERB
ap-610	393	8	by	by	ADP
ap-610	393	9	the	the	DET
ap-610	393	10	nonlocal	nonlocal	ADJ
ap-610	393	11	cumulative	cumulative	ADJ
ap-610	393	12	plastic	plastic	NOUN
ap-610	393	13	strain	strain	NOUN
ap-610	393	14	,	,	PUNCT
ap-610	393	15	�	�	PROPN
ap-610	393	16	,	,	PUNCT
ap-610	393	17	and	and	CCONJ
ap-610	393	18	is	be	AUX
ap-610	393	19	reflected	reflect	VERB
ap-610	393	20	by	by	ADP
ap-610	393	21	the	the	DET
ap-610	393	22	ductile	ductile	NOUN
ap-610	393	23	damage	damage	NOUN
ap-610	393	24	function	function	NOUN
ap-610	393	25	�	�	PROPN
ap-610	393	26	p	p	NOUN
ap-610	393	27	that	that	PRON
ap-610	393	28	vanishes	vanish	VERB
ap-610	393	29	for	for	ADP
ap-610	393	30	�	�	PROPN
ap-610	393	31	�	�	PROPN
ap-610	393	32	0	0	NUM
ap-610	393	33	and	and	CCONJ
ap-610	393	34	increases	increase	NOUN
ap-610	393	35	later	later	ADV
ap-610	393	36	on	on	ADV
ap-610	393	37	.	.	PUNCT
ap-610	394	1	due	due	ADP
ap-610	394	2	to	to	ADP
ap-610	394	3	the	the	DET
ap-610	394	4	nonlinear	nonlinear	ADJ
ap-610	394	5	format	format	NOUN
ap-610	394	6	of	of	ADP
ap-610	394	7	the	the	DET
ap-610	394	8	hardening	harden	VERB
ap-610	394	9	law	law	NOUN
ap-610	394	10	(	(	PUNCT
ap-610	394	11	68	68	NUM
ap-610	394	12	)	)	PUNCT
ap-610	394	13	,	,	PUNCT
ap-610	394	14	analysis	analysis	NOUN
ap-610	394	15	of	of	ADP
ap-610	394	16	the	the	DET
ap-610	394	17	plastic	plastic	ADJ
ap-610	394	18	strain	strain	NOUN
ap-610	394	19	distribution	distribution	NOUN
ap-610	394	20	in	in	ADP
ap-610	394	21	a	a	DET
ap-610	394	22	general	general	ADJ
ap-610	394	23	state	state	NOUN
ap-610	394	24	would	would	AUX
ap-610	394	25	lead	lead	VERB
ap-610	394	26	to	to	ADP
ap-610	394	27	a	a	DET
ap-610	394	28	nonlinear	nonlinear	ADJ
ap-610	394	29	differential	differential	ADJ
ap-610	394	30	equation	equation	NOUN
ap-610	394	31	.	.	PUNCT
ap-610	395	1	to	to	PART
ap-610	395	2	allow	allow	VERB
ap-610	395	3	for	for	ADP
ap-610	395	4	an	an	DET
ap-610	395	5	analytical	analytical	ADJ
ap-610	395	6	treatment	treatment	NOUN
ap-610	395	7	,	,	PUNCT
ap-610	395	8	we	we	PRON
ap-610	395	9	restrict	restrict	VERB
ap-610	395	10	attention	attention	NOUN
ap-610	395	11	to	to	ADP
ap-610	395	12	the	the	DET
ap-610	395	13	initial	initial	ADJ
ap-610	395	14	distribution	distribution	NOUN
ap-610	395	15	of	of	ADP
ap-610	395	16	the	the	DET
ap-610	395	17	plastic	plastic	ADJ
ap-610	395	18	strain	strain	NOUN
ap-610	395	19	rate	rate	NOUN
ap-610	395	20	.	.	PUNCT
ap-610	396	1	differentiating	differentiate	VERB
ap-610	396	2	(	(	PUNCT
ap-610	396	3	68	68	NUM
ap-610	396	4	)	)	PUNCT
ap-610	396	5	with	with	ADP
ap-610	396	6	respect	respect	NOUN
ap-610	396	7	to	to	ADP
ap-610	396	8	time	time	NOUN
ap-610	396	9	and	and	CCONJ
ap-610	396	10	using	use	VERB
ap-610	396	11	the	the	DET
ap-610	396	12	consistency	consistency	NOUN
ap-610	396	13	condition	condition	NOUN
ap-610	396	14	�	�	PROPN
ap-610	396	15	�	�	PROPN
ap-610	396	16	�	�	PROPN
ap-610	396	17	f	f	PROPN
ap-610	396	18	y	y	PROPN
ap-610	396	19	�	�	PROPN
ap-610	396	20	�	�	PROPN
ap-610	396	21	�	�	PROPN
ap-610	396	22	�	�	PROPN
ap-610	396	23	�	�	PROPN
ap-610	396	24	0	0	NUM
ap-610	396	25	,	,	PUNCT
ap-610	396	26	we	we	PRON
ap-610	396	27	obtain	obtain	VERB
ap-610	396	28	the	the	DET
ap-610	396	29	differential	differential	ADJ
ap-610	396	30	equation	equation	NOUN
ap-610	396	31	h	h	NOUN
ap-610	396	32	hp	hp	VERB
ap-610	397	1	p	p	X
ap-610	397	2	(	(	PUNCT
ap-610	397	3	)	)	PUNCT
ap-610	397	4	�	�	PROPN
ap-610	397	5	(	(	PUNCT
ap-610	397	6	)	)	PUNCT
ap-610	397	7	�	�	PROPN
ap-610	397	8	�	�	PROPN
ap-610	397	9	1	1	NUM
ap-610	397	10	0	0	NUM
ap-610	397	11	�	�	PROPN
ap-610	397	12	�	�	PROPN
ap-610	397	13	�	�	PROPN
ap-610	397	14	�	�	PROPN
ap-610	397	15	�	�	PROPN
ap-610	397	16	�	�	PROPN
ap-610	397	17	�	�	PROPN
ap-610	397	18	�	�	PROPN
ap-610	397	19	�	�	PROPN
ap-610	397	20	�	�	PROPN
ap-610	397	21	�	�	PROPN
ap-610	397	22	�	�	PROPN
ap-610	397	23	d	d	PROPN
ap-610	397	24	d	d	PROPN
ap-610	397	25	.	.	PUNCT
ap-610	398	1	(	(	PUNCT
ap-610	398	2	69	69	NUM
ap-610	398	3	)	)	PUNCT
ap-610	398	4	at	at	ADP
ap-610	398	5	the	the	DET
ap-610	398	6	onset	onset	NOUN
ap-610	398	7	of	of	ADP
ap-610	398	8	yielding	yielding	PROPN
ap-610	398	9	,	,	PUNCT
ap-610	398	10	�	�	PROPN
ap-610	398	11	,	,	PUNCT
ap-610	398	12	�	�	PROPN
ap-610	398	13	and	and	CCONJ
ap-610	398	14	�	�	PROPN
ap-610	398	15	p	p	NOUN
ap-610	398	16	vanish	vanish	VERB
ap-610	398	17	in	in	ADP
ap-610	398	18	the	the	DET
ap-610	398	19	entire	entire	ADJ
ap-610	398	20	layer	layer	NOUN
ap-610	398	21	and	and	CCONJ
ap-610	398	22	the	the	DET
ap-610	398	23	derivative	derivative	ADJ
ap-610	398	24	d	d	PROPN
ap-610	398	25	d	d	PROPN
ap-610	398	26	�	�	PROPN
ap-610	398	27	�	�	PROPN
ap-610	398	28	p	p	PROPN
ap-610	398	29	evaluated	evaluate	VERB
ap-610	398	30	at	at	ADP
ap-610	398	31	�	�	PROPN
ap-610	398	32	�	�	PROPN
ap-610	398	33	0	0	NUM
ap-610	398	34	has	have	VERB
ap-610	398	35	the	the	DET
ap-610	398	36	same	same	ADJ
ap-610	398	37	value	value	NOUN
ap-610	398	38	�	�	NOUN
ap-610	398	39	p	p	NOUN
ap-610	398	40	*	*	PUNCT
ap-610	398	41	at	at	ADV
ap-610	398	42	all	all	DET
ap-610	398	43	points	point	NOUN
ap-610	398	44	x.	x.	NOUN
ap-610	398	45	taking	take	VERB
ap-610	398	46	all	all	DET
ap-610	398	47	this	this	PRON
ap-610	398	48	into	into	ADP
ap-610	398	49	account	account	NOUN
ap-610	398	50	and	and	CCONJ
ap-610	398	51	substituting	substitute	VERB
ap-610	398	52	the	the	DET
ap-610	398	53	rate	rate	NOUN
ap-610	398	54	form	form	NOUN
ap-610	398	55	of	of	ADP
ap-610	398	56	(	(	PUNCT
ap-610	398	57	67	67	NUM
ap-610	398	58	)	)	PUNCT
ap-610	398	59	into	into	ADP
ap-610	398	60	(	(	PUNCT
ap-610	398	61	69	69	NUM
ap-610	398	62	)	)	PUNCT
ap-610	398	63	,	,	PUNCT
ap-610	398	64	we	we	PRON
ap-610	398	65	get	get	VERB
ap-610	398	66	the	the	DET
ap-610	398	67	linear	linear	ADJ
ap-610	398	68	differential	differential	ADJ
ap-610	398	69	equation	equation	NOUN
ap-610	398	70	with	with	ADP
ap-610	398	71	constant	constant	ADJ
ap-610	398	72	coefficients	coefficient	NOUN
ap-610	398	73	,	,	PUNCT
ap-610	398	74	(	(	PUNCT
ap-610	398	75	)	)	PUNCT
ap-610	398	76	�	�	PROPN
ap-610	398	77	�	�	PROPN
ap-610	398	78	�	�	PROPN
ap-610	398	79	*	*	PUNCT
ap-610	398	80	h	h	PROPN
ap-610	398	81	hlp	hlp	PROPN
ap-610	398	82	�	�	PROPN
ap-610	398	83	�	�	PROPN
ap-610	398	84	�	�	PROPN
ap-610	398	85	�	�	PROPN
ap-610	398	86	�	�	PROPN
ap-610	398	87	�	�	PROPN
ap-610	398	88	�	�	PROPN
ap-610	398	89	�	�	PROPN
ap-610	398	90	�	�	PROPN
ap-610	398	91	�	�	PROPN
ap-610	398	92	0	0	NUM
ap-610	398	93	2	2	NUM
ap-610	398	94	.	.	PUNCT
ap-610	399	1	(	(	PUNCT
ap-610	399	2	70	70	NUM
ap-610	399	3	)	)	PUNCT
ap-610	399	4	in	in	ADP
ap-610	399	5	the	the	DET
ap-610	399	6	absence	absence	NOUN
ap-610	399	7	of	of	ADP
ap-610	399	8	body	body	NOUN
ap-610	399	9	forces	force	NOUN
ap-610	399	10	,	,	PUNCT
ap-610	399	11	static	static	ADJ
ap-610	399	12	equilibrium	equilibrium	NOUN
ap-610	399	13	implies	imply	VERB
ap-610	399	14	that	that	SCONJ
ap-610	399	15	the	the	DET
ap-610	399	16	shear	shear	NOUN
ap-610	399	17	stress	stress	NOUN
ap-610	399	18	�	�	PROPN
ap-610	399	19	must	must	AUX
ap-610	399	20	be	be	AUX
ap-610	399	21	uniform	uniform	ADJ
ap-610	399	22	,	,	PUNCT
ap-610	399	23	and	and	CCONJ
ap-610	399	24	so	so	ADV
ap-610	399	25	the	the	DET
ap-610	399	26	right	right	ADJ
ap-610	399	27	-	-	PUNCT
ap-610	399	28	hand	hand	NOUN
ap-610	399	29	side	side	NOUN
ap-610	399	30	in	in	ADP
ap-610	399	31	(	(	PUNCT
ap-610	399	32	70	70	NUM
ap-610	399	33	)	)	PUNCT
ap-610	399	34	is	be	AUX
ap-610	399	35	constant	constant	ADJ
ap-610	399	36	.	.	PUNCT
ap-610	400	1	if	if	SCONJ
ap-610	400	2	h	h	PROPN
ap-610	400	3	p	p	PROPN
ap-610	400	4	�	�	PROPN
ap-610	400	5	�	�	PROPN
ap-610	400	6	�	�	PROPN
ap-610	400	7	�	�	PROPN
ap-610	400	8	0	0	NUM
ap-610	400	9	0	0	NUM
ap-610	400	10	*	*	NOUN
ap-610	400	11	,	,	PUNCT
ap-610	400	12	the	the	DET
ap-610	400	13	general	general	ADJ
ap-610	400	14	solution	solution	NOUN
ap-610	400	15	reads	read	VERB
ap-610	400	16	�	�	PROPN
ap-610	400	17	�	�	PROPN
ap-610	400	18	cosh	cosh	PROPN
ap-610	400	19	sinh	sinh	PROPN
ap-610	400	20	�	�	PROPN
ap-610	400	21	�	�	PROPN
ap-610	400	22	�	�	PROPN
ap-610	400	23	�	�	PROPN
ap-610	400	24	�	�	PROPN
ap-610	400	25	�	�	PROPN
ap-610	400	26	�	�	PROPN
ap-610	400	27	x	x	PUNCT
ap-610	401	1	h	h	NOUN
ap-610	401	2	c	c	NOUN
ap-610	401	3	x	x	X
ap-610	401	4	l	l	NOUN
ap-610	401	5	c	c	NOUN
ap-610	401	6	x	x	SYM
ap-610	401	7	l	l	X
ap-610	401	8	�	�	PROPN
ap-610	401	9	�	�	PROPN
ap-610	401	10	�	�	PROPN
ap-610	401	11	2	2	NUM
ap-610	401	12	1	1	NUM
ap-610	401	13	2	2	NUM
ap-610	401	14	,	,	PUNCT
ap-610	401	15	(	(	PUNCT
ap-610	401	16	71	71	NUM
ap-610	401	17	)	)	PUNCT
ap-610	401	18	where	where	SCONJ
ap-610	401	19	c1	c1	PROPN
ap-610	401	20	and	and	CCONJ
ap-610	401	21	c2	c2	PROPN
ap-610	401	22	are	be	AUX
ap-610	401	23	integration	integration	NOUN
ap-610	401	24	constants	constant	NOUN
ap-610	401	25	and	and	CCONJ
ap-610	401	26	a	a	DET
ap-610	401	27	hp	hp	PROPN
ap-610	401	28	�	�	PROPN
ap-610	401	29	�	�	PROPN
ap-610	401	30	1	1	NUM
ap-610	401	31	0	0	NUM
ap-610	401	32	�	�	PROPN
ap-610	401	33	�	�	PROPN
ap-610	401	34	*	*	PROPN
ap-610	401	35	is	be	AUX
ap-610	401	36	a	a	DET
ap-610	401	37	dimensionless	dimensionless	NOUN
ap-610	401	38	parameter	parameter	NOUN
ap-610	401	39	introduced	introduce	VERB
ap-610	401	40	for	for	ADP
ap-610	401	41	convenience	convenience	NOUN
ap-610	401	42	.	.	PUNCT
ap-610	402	1	©	©	PROPN
ap-610	402	2	czech	czech	PROPN
ap-610	402	3	technical	technical	PROPN
ap-610	402	4	university	university	PROPN
ap-610	402	5	publishing	publishing	NOUN
ap-610	402	6	house	house	NOUN
ap-610	402	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	402	8	27	27	NUM
ap-610	402	9	acta	acta	PROPN
ap-610	402	10	polytechnica	polytechnica	PROPN
ap-610	402	11	vol	vol	NOUN
ap-610	402	12	.	.	PROPN
ap-610	403	1	44	44	NUM
ap-610	403	2	no	no	NOUN
ap-610	403	3	.	.	PUNCT
ap-610	404	1	5–6/2004	5–6/2004	NUM
ap-610	404	2	(	(	PUNCT
ap-610	404	3	a	a	NOUN
ap-610	404	4	)	)	PUNCT
ap-610	404	5	(	(	PUNCT
ap-610	404	6	b	b	X
ap-610	404	7	)	)	PUNCT
ap-610	404	8	fig	fig	NOUN
ap-610	404	9	.	.	PUNCT
ap-610	405	1	6	6	NUM
ap-610	405	2	:	:	PUNCT
ap-610	405	3	(	(	PUNCT
ap-610	405	4	a	a	X
ap-610	405	5	)	)	PUNCT
ap-610	405	6	stress	stress	NOUN
ap-610	405	7	versus	versus	ADP
ap-610	405	8	average	average	ADJ
ap-610	405	9	strain	strain	NOUN
ap-610	405	10	for	for	ADP
ap-610	405	11	different	different	ADJ
ap-610	405	12	thicknesses	thickness	NOUN
ap-610	405	13	of	of	ADP
ap-610	405	14	the	the	DET
ap-610	405	15	shear	shear	NOUN
ap-610	405	16	layer	layer	NOUN
ap-610	405	17	,	,	PUNCT
ap-610	405	18	(	(	PUNCT
ap-610	405	19	b	b	NOUN
ap-610	405	20	)	)	PUNCT
ap-610	405	21	normalized	normalize	VERB
ap-610	405	22	torque	torque	NOUN
ap-610	405	23	,	,	PUNCT
ap-610	405	24	m	m	PROPN
ap-610	405	25	d3	d3	PROPN
ap-610	405	26	,	,	PUNCT
ap-610	405	27	versus	versus	ADP
ap-610	405	28	surface	surface	NOUN
ap-610	405	29	shear	shear	NOUN
ap-610	405	30	strain	strain	NOUN
ap-610	405	31	for	for	ADP
ap-610	405	32	twisted	twisted	ADJ
ap-610	405	33	copper	copper	NOUN
ap-610	405	34	wires	wire	NOUN
ap-610	405	35	of	of	ADP
ap-610	405	36	various	various	ADJ
ap-610	405	37	diameters	diameter	NOUN
ap-610	405	38	d	d	X
ap-610	405	39	(	(	PUNCT
ap-610	405	40	after	after	ADP
ap-610	405	41	fleck	fleck	NOUN
ap-610	405	42	et	et	PROPN
ap-610	405	43	al	al	PROPN
ap-610	405	44	.	.	PROPN
ap-610	405	45	,	,	PUNCT
ap-610	405	46	1994	1994	NUM
ap-610	405	47	)	)	PUNCT
ap-610	405	48	the	the	DET
ap-610	405	49	particular	particular	ADJ
ap-610	405	50	solution	solution	NOUN
ap-610	405	51	depends	depend	VERB
ap-610	405	52	on	on	ADP
ap-610	405	53	the	the	DET
ap-610	405	54	boundary	boundary	ADJ
ap-610	405	55	conditions	condition	NOUN
ap-610	405	56	,	,	PUNCT
ap-610	405	57	which	which	PRON
ap-610	405	58	should	should	AUX
ap-610	405	59	be	be	AUX
ap-610	405	60	formulated	formulate	VERB
ap-610	405	61	in	in	ADP
ap-610	405	62	terms	term	NOUN
ap-610	405	63	of	of	ADP
ap-610	405	64	the	the	DET
ap-610	405	65	nonlocal	nonlocal	ADJ
ap-610	405	66	cumulative	cumulative	ADJ
ap-610	405	67	plastic	plastic	NOUN
ap-610	405	68	strain	strain	NOUN
ap-610	405	69	and	and	CCONJ
ap-610	405	70	its	its	PRON
ap-610	405	71	normal	normal	ADJ
ap-610	405	72	derivative	derivative	NOUN
ap-610	405	73	.	.	PUNCT
ap-610	406	1	for	for	ADP
ap-610	406	2	homogeneous	homogeneous	ADJ
ap-610	406	3	neumann	neumann	PROPN
ap-610	406	4	boundary	boundary	PROPN
ap-610	406	5	conditions	condition	NOUN
ap-610	406	6	,	,	PUNCT
ap-610	406	7	�	�	PROPN
ap-610	406	8	�	�	PROPN
ap-610	406	9	�	�	PROPN
ap-610	406	10	�	�	PROPN
ap-610	406	11	(	(	PUNCT
ap-610	406	12	)	)	PUNCT
ap-610	406	13	l	l	NOUN
ap-610	406	14	2	2	NUM
ap-610	406	15	0	0	NUM
ap-610	406	16	,	,	PUNCT
ap-610	406	17	the	the	DET
ap-610	406	18	integration	integration	NOUN
ap-610	406	19	constants	constant	NOUN
ap-610	406	20	vanish	vanish	VERB
ap-610	406	21	and	and	CCONJ
ap-610	406	22	the	the	DET
ap-610	406	23	solution	solution	NOUN
ap-610	406	24	is	be	AUX
ap-610	406	25	uniform	uniform	ADJ
ap-610	406	26	.	.	PUNCT
ap-610	407	1	consequently	consequently	ADV
ap-610	407	2	,	,	PUNCT
ap-610	407	3	no	no	DET
ap-610	407	4	size	size	NOUN
ap-610	407	5	effect	effect	NOUN
ap-610	407	6	is	be	AUX
ap-610	407	7	predicted	predict	VERB
ap-610	407	8	by	by	ADP
ap-610	407	9	the	the	DET
ap-610	407	10	model	model	NOUN
ap-610	407	11	.	.	PUNCT
ap-610	408	1	this	this	PRON
ap-610	408	2	is	be	AUX
ap-610	408	3	similar	similar	ADJ
ap-610	408	4	to	to	ADP
ap-610	408	5	what	what	PRON
ap-610	408	6	happens	happen	VERB
ap-610	408	7	for	for	ADP
ap-610	408	8	the	the	DET
ap-610	408	9	aifantis	aifantis	ADJ
ap-610	408	10	model	model	NOUN
ap-610	408	11	with	with	ADP
ap-610	408	12	the	the	DET
ap-610	408	13	homogeneous	homogeneous	ADJ
ap-610	408	14	neumann	neumann	PROPN
ap-610	408	15	boundary	boundary	PROPN
ap-610	408	16	conditions	condition	NOUN
ap-610	408	17	�	�	PROPN
ap-610	408	18	�	�	PROPN
ap-610	408	19	�	�	PROPN
ap-610	408	20	�	�	PROPN
ap-610	408	21	(	(	PUNCT
ap-610	408	22	)	)	PUNCT
ap-610	408	23	l	l	NOUN
ap-610	408	24	2	2	NUM
ap-610	408	25	0	0	NUM
ap-610	408	26	.	.	PUNCT
ap-610	409	1	a	a	DET
ap-610	409	2	stiff	stiff	ADJ
ap-610	409	3	boundary	boundary	NOUN
ap-610	409	4	with	with	ADP
ap-610	409	5	a	a	DET
ap-610	409	6	perfect	perfect	ADJ
ap-610	409	7	bond	bond	NOUN
ap-610	409	8	inhibits	inhibit	VERB
ap-610	409	9	propagation	propagation	NOUN
ap-610	409	10	of	of	ADP
ap-610	409	11	voids	voids	NOUN
ap-610	409	12	,	,	PUNCT
ap-610	409	13	which	which	PRON
ap-610	409	14	can	can	AUX
ap-610	409	15	be	be	AUX
ap-610	409	16	expressed	express	VERB
ap-610	409	17	by	by	ADP
ap-610	409	18	the	the	DET
ap-610	409	19	condition	condition	NOUN
ap-610	409	20	that	that	SCONJ
ap-610	409	21	�	�	PROPN
ap-610	409	22	vanishes	vanish	VERB
ap-610	409	23	at	at	ADP
ap-610	409	24	the	the	DET
ap-610	409	25	boundary	boundary	NOUN
ap-610	409	26	.	.	PUNCT
ap-610	410	1	with	with	ADP
ap-610	410	2	this	this	DET
ap-610	410	3	homogeneous	homogeneous	ADJ
ap-610	410	4	dirichlet	dirichlet	NOUN
ap-610	410	5	condition	condition	NOUN
ap-610	410	6	applied	apply	VERB
ap-610	410	7	at	at	ADP
ap-610	410	8	both	both	DET
ap-610	410	9	parts	part	NOUN
ap-610	410	10	of	of	ADP
ap-610	410	11	the	the	DET
ap-610	410	12	boundary	boundary	NOUN
ap-610	410	13	,	,	PUNCT
ap-610	410	14	the	the	DET
ap-610	410	15	particular	particular	ADJ
ap-610	410	16	solution	solution	NOUN
ap-610	410	17	of	of	ADP
ap-610	410	18	(	(	PUNCT
ap-610	410	19	70	70	NUM
ap-610	410	20	)	)	PUNCT
ap-610	410	21	becomes	become	VERB
ap-610	410	22	�	�	PROPN
ap-610	410	23	(	(	PUNCT
ap-610	410	24	)	)	PUNCT
ap-610	410	25	�	�	PROPN
ap-610	410	26	cosh	cosh	PROPN
ap-610	410	27	(	(	PUNCT
ap-610	410	28	)	)	PUNCT
ap-610	410	29	cosh	cosh	PROPN
ap-610	410	30	(	(	PUNCT
ap-610	410	31	)	)	PUNCT
ap-610	410	32	�	�	PROPN
ap-610	410	33	�	�	PROPN
ap-610	410	34	�	�	PROPN
ap-610	410	35	�	�	PROPN
ap-610	410	36	�	�	PROPN
ap-610	411	1	x	x	PUNCT
ap-610	411	2	h	h	NOUN
ap-610	411	3	x	x	PUNCT
ap-610	411	4	l	l	NOUN
ap-610	411	5	l	l	X
ap-610	411	6	l	l	X
ap-610	411	7	�	�	PROPN
ap-610	411	8	�	�	PROPN
ap-610	411	9	�	�	PROPN
ap-610	411	10	�	�	PROPN
ap-610	411	11	�	�	PROPN
ap-610	411	12	�	�	PROPN
ap-610	411	13	�	�	PROPN
ap-610	411	14	2	2	NUM
ap-610	411	15	1	1	NUM
ap-610	411	16	2	2	NUM
ap-610	411	17	(	(	PUNCT
ap-610	411	18	72	72	NUM
ap-610	411	19	)	)	PUNCT
ap-610	411	20	and	and	CCONJ
ap-610	411	21	the	the	DET
ap-610	411	22	corresponding	corresponding	ADJ
ap-610	411	23	local	local	ADJ
ap-610	411	24	cumulative	cumulative	ADJ
ap-610	411	25	plastic	plastic	NOUN
ap-610	411	26	strain	strain	NOUN
ap-610	411	27	rate	rate	NOUN
ap-610	411	28	is	be	AUX
ap-610	411	29	�	�	PROPN
ap-610	411	30	(	(	PUNCT
ap-610	411	31	)	)	PUNCT
ap-610	411	32	�	�	PROPN
ap-610	411	33	(	(	PUNCT
ap-610	411	34	)	)	PUNCT
ap-610	411	35	cosh	cosh	PROPN
ap-610	411	36	(	(	PUNCT
ap-610	411	37	)	)	PUNCT
ap-610	411	38	cosh	cosh	PROPN
ap-610	411	39	(	(	PUNCT
ap-610	411	40	)	)	PUNCT
ap-610	411	41	�	�	PROPN
ap-610	411	42	�	�	PROPN
ap-610	411	43	�	�	PROPN
ap-610	411	44	�	�	PROPN
ap-610	411	45	�	�	PROPN
ap-610	411	46	�	�	PROPN
ap-610	411	47	x	x	PUNCT
ap-610	411	48	h	h	NOUN
ap-610	411	49	x	x	PUNCT
ap-610	411	50	l	l	NOUN
ap-610	411	51	l	l	X
ap-610	411	52	l	l	X
ap-610	411	53	�	�	PROPN
ap-610	411	54	�	�	PROPN
ap-610	411	55	�	�	PROPN
ap-610	411	56	�	�	PROPN
ap-610	411	57	�	�	PROPN
ap-610	411	58	�	�	PROPN
ap-610	411	59	�	�	PROPN
ap-610	411	60	�	�	PROPN
ap-610	411	61	2	2	NUM
ap-610	411	62	21	21	NUM
ap-610	411	63	1	1	NUM
ap-610	411	64	2	2	NUM
ap-610	411	65	.	.	PUNCT
ap-610	412	1	(	(	PUNCT
ap-610	412	2	73	73	NUM
ap-610	412	3	)	)	PUNCT
ap-610	412	4	following	follow	VERB
ap-610	412	5	the	the	DET
ap-610	412	6	same	same	ADJ
ap-610	412	7	procedure	procedure	NOUN
ap-610	412	8	as	as	ADP
ap-610	412	9	in	in	ADP
ap-610	412	10	section	section	NOUN
ap-610	412	11	3	3	NUM
ap-610	412	12	,	,	PUNCT
ap-610	412	13	we	we	PRON
ap-610	412	14	find	find	VERB
ap-610	412	15	that	that	SCONJ
ap-610	412	16	the	the	DET
ap-610	412	17	shear	shear	NOUN
ap-610	412	18	stress	stress	NOUN
ap-610	412	19	rate	rate	NOUN
ap-610	412	20	is	be	AUX
ap-610	412	21	linked	link	VERB
ap-610	412	22	to	to	ADP
ap-610	412	23	the	the	DET
ap-610	412	24	average	average	ADJ
ap-610	412	25	shear	shear	NOUN
ap-610	412	26	strain	strain	NOUN
ap-610	412	27	rate	rate	NOUN
ap-610	412	28	by	by	ADP
ap-610	412	29	the	the	DET
ap-610	412	30	linear	linear	PROPN
ap-610	412	31	relation	relation	PROPN
ap-610	412	32	�	�	PROPN
ap-610	413	1	~	~	PUNCT
ap-610	413	2	~	~	PUNCT
ap-610	413	3	�	�	PROPN
ap-610	413	4	�	�	PROPN
ap-610	413	5	�	�	PROPN
ap-610	413	6	�	�	PROPN
ap-610	413	7	gep	gep	PROPN
ap-610	413	8	,	,	PUNCT
ap-610	413	9	(	(	PUNCT
ap-610	413	10	74	74	NUM
ap-610	413	11	)	)	PUNCT
ap-610	413	12	where	where	SCONJ
ap-610	413	13	~	~	PUNCT
ap-610	413	14	~g	~g	PUNCT
ap-610	413	15	g	g	NOUN
ap-610	413	16	h	h	PROPN
ap-610	413	17	ep	ep	PROPN
ap-610	413	18	�	�	PROPN
ap-610	413	19	�	�	PROPN
ap-610	413	20	�	�	PROPN
ap-610	413	21	�	�	PROPN
ap-610	413	22	�	�	PROPN
ap-610	413	23	�	�	PROPN
ap-610	413	24	�	�	PROPN
ap-610	413	25	�	�	PROPN
ap-610	413	26	�	�	PROPN
ap-610	413	27	1	1	NUM
ap-610	413	28	1	1	NUM
ap-610	413	29	1	1	NUM
ap-610	413	30	(	(	PUNCT
ap-610	413	31	75	75	NUM
ap-610	413	32	)	)	PUNCT
ap-610	413	33	is	be	AUX
ap-610	413	34	the	the	DET
ap-610	413	35	elastoplastic	elastoplastic	ADJ
ap-610	413	36	shear	shear	NOUN
ap-610	413	37	modulus	modulus	NOUN
ap-610	413	38	and	and	CCONJ
ap-610	413	39	~	~	PUNCT
ap-610	413	40	(	(	PUNCT
ap-610	413	41	)	)	PUNCT
ap-610	413	42	tanh	tanh	PROPN
ap-610	413	43	h	h	PROPN
ap-610	413	44	h	h	PROPN
ap-610	413	45	l	l	NOUN
ap-610	413	46	l	l	NOUN
ap-610	413	47	l	l	X
ap-610	413	48	l	l	X
ap-610	413	49	�	�	PROPN
ap-610	413	50	�	�	PROPN
ap-610	413	51	�	�	PROPN
ap-610	413	52	�	�	PROPN
ap-610	413	53	�	�	PROPN
ap-610	413	54	�	�	PROPN
ap-610	413	55	�	�	PROPN
ap-610	413	56	2	2	NUM
ap-610	413	57	21	21	NUM
ap-610	413	58	1	1	NUM
ap-610	413	59	2	2	NUM
ap-610	413	60	2	2	NUM
ap-610	413	61	(	(	PUNCT
ap-610	413	62	76	76	NUM
ap-610	413	63	)	)	PUNCT
ap-610	413	64	is	be	AUX
ap-610	413	65	the	the	DET
ap-610	413	66	size	size	NOUN
ap-610	413	67	-	-	PUNCT
ap-610	413	68	dependent	dependent	ADJ
ap-610	413	69	hardening	hardening	NOUN
ap-610	413	70	modulus	modulus	NOUN
ap-610	413	71	.	.	PUNCT
ap-610	414	1	for	for	ADP
ap-610	414	2	very	very	ADV
ap-610	414	3	large	large	ADJ
ap-610	414	4	sizes	size	NOUN
ap-610	414	5	l	l	NOUN
ap-610	414	6	,	,	PUNCT
ap-610	414	7	the	the	DET
ap-610	414	8	hardening	harden	VERB
ap-610	414	9	modulus	modulus	NOUN
ap-610	414	10	tends	tend	VERB
ap-610	414	11	to	to	ADP
ap-610	414	12	h	h	VERB
ap-610	414	13	�	�	PROPN
ap-610	414	14	2	2	NUM
ap-610	414	15	,	,	PUNCT
ap-610	414	16	which	which	PRON
ap-610	414	17	is	be	AUX
ap-610	414	18	the	the	DET
ap-610	414	19	value	value	NOUN
ap-610	414	20	corresponding	correspond	VERB
ap-610	414	21	to	to	ADP
ap-610	414	22	the	the	DET
ap-610	414	23	local	local	ADJ
ap-610	414	24	theory	theory	NOUN
ap-610	414	25	with	with	ADP
ap-610	414	26	�	�	PROPN
ap-610	414	27	p	p	PROPN
ap-610	414	28	computed	compute	VERB
ap-610	414	29	from	from	ADP
ap-610	414	30	�	�	PROPN
ap-610	414	31	instead	instead	ADV
ap-610	414	32	of	of	ADP
ap-610	414	33	�	�	PROPN
ap-610	414	34	.	.	PUNCT
ap-610	415	1	for	for	ADP
ap-610	415	2	values	value	NOUN
ap-610	415	3	of	of	ADP
ap-610	415	4	l	l	NOUN
ap-610	415	5	comparable	comparable	ADJ
ap-610	415	6	to	to	ADP
ap-610	415	7	l	l	NOUN
ap-610	415	8	,	,	PUNCT
ap-610	415	9	the	the	DET
ap-610	415	10	hardening	harden	VERB
ap-610	415	11	modulus	modulus	NOUN
ap-610	415	12	increases	increase	NOUN
ap-610	415	13	with	with	ADP
ap-610	415	14	decreasing	decrease	VERB
ap-610	415	15	size	size	NOUN
ap-610	415	16	,	,	PUNCT
ap-610	415	17	which	which	PRON
ap-610	415	18	means	mean	VERB
ap-610	415	19	that	that	SCONJ
ap-610	415	20	the	the	DET
ap-610	415	21	average	average	ADJ
ap-610	415	22	response	response	NOUN
ap-610	415	23	becomes	become	VERB
ap-610	415	24	stiffer	stiff	ADJ
ap-610	415	25	.	.	PUNCT
ap-610	416	1	so	so	ADV
ap-610	416	2	the	the	DET
ap-610	416	3	present	present	ADJ
ap-610	416	4	model	model	NOUN
ap-610	416	5	predicts	predict	VERB
ap-610	416	6	a	a	DET
ap-610	416	7	qualitatively	qualitatively	ADV
ap-610	416	8	similar	similar	ADJ
ap-610	416	9	trend	trend	NOUN
ap-610	416	10	as	as	ADP
ap-610	416	11	the	the	DET
ap-610	416	12	explicit	explicit	ADJ
ap-610	416	13	version	version	NOUN
ap-610	416	14	of	of	ADP
ap-610	416	15	gradient	gradient	ADJ
ap-610	416	16	plasticity	plasticity	NOUN
ap-610	416	17	.	.	PUNCT
ap-610	417	1	the	the	DET
ap-610	417	2	ratio	ratio	NOUN
ap-610	417	3	between	between	ADP
ap-610	417	4	the	the	DET
ap-610	417	5	size	size	NOUN
ap-610	417	6	-	-	PUNCT
ap-610	417	7	dependent	dependent	ADJ
ap-610	417	8	hardening	hardening	NOUN
ap-610	417	9	modulus	modulus	NOUN
ap-610	417	10	and	and	CCONJ
ap-610	417	11	its	its	PRON
ap-610	417	12	large	large	ADJ
ap-610	417	13	-	-	PUNCT
ap-610	417	14	size	size	NOUN
ap-610	417	15	limit	limit	NOUN
ap-610	417	16	is	be	AUX
ap-610	417	17	plotted	plot	VERB
ap-610	417	18	in	in	ADP
ap-610	417	19	fig	fig	NOUN
ap-610	417	20	.	.	PUNCT
ap-610	418	1	7a	7a	NOUN
ap-610	418	2	as	as	ADP
ap-610	418	3	a	a	DET
ap-610	418	4	function	function	NOUN
ap-610	418	5	of	of	ADP
ap-610	418	6	the	the	DET
ap-610	418	7	relative	relative	ADJ
ap-610	418	8	size	size	NOUN
ap-610	418	9	,	,	PUNCT
ap-610	418	10	l	l	PROPN
ap-610	418	11	l	l	NOUN
ap-610	418	12	,	,	PUNCT
ap-610	418	13	for	for	ADP
ap-610	418	14	parameter	parameter	PROPN
ap-610	418	15	�	�	PROPN
ap-610	418	16	�	�	PROPN
ap-610	418	17	05	05	NUM
ap-610	418	18	.	.	PUNCT
ap-610	418	19	.	.	PUNCT
ap-610	419	1	fig	fig	NOUN
ap-610	419	2	.	.	PUNCT
ap-610	420	1	7b	7b	NOUN
ap-610	420	2	shows	show	VERB
ap-610	420	3	the	the	DET
ap-610	420	4	distribution	distribution	NOUN
ap-610	420	5	of	of	ADP
ap-610	420	6	plastic	plastic	ADJ
ap-610	420	7	strain	strain	NOUN
ap-610	420	8	rate	rate	NOUN
ap-610	420	9	across	across	ADP
ap-610	420	10	the	the	DET
ap-610	420	11	layer	layer	NOUN
ap-610	420	12	for	for	ADP
ap-610	420	13	different	different	ADJ
ap-610	420	14	ratios	ratio	NOUN
ap-610	420	15	l	l	X
ap-610	420	16	l.	l.	NOUN
ap-610	420	17	even	even	ADV
ap-610	420	18	though	though	SCONJ
ap-610	420	19	the	the	DET
ap-610	420	20	general	general	ADJ
ap-610	420	21	trends	trend	NOUN
ap-610	420	22	are	be	AUX
ap-610	420	23	the	the	DET
ap-610	420	24	same	same	ADJ
ap-610	420	25	as	as	ADP
ap-610	420	26	for	for	ADP
ap-610	420	27	the	the	DET
ap-610	420	28	explicit	explicit	ADJ
ap-610	420	29	gradient	gradient	NOUN
ap-610	420	30	model	model	NOUN
ap-610	420	31	,	,	PUNCT
ap-610	420	32	certain	certain	ADJ
ap-610	420	33	differences	difference	NOUN
ap-610	420	34	can	can	AUX
ap-610	420	35	be	be	AUX
ap-610	420	36	revealed	reveal	VERB
ap-610	420	37	by	by	ADP
ap-610	420	38	comparing	compare	VERB
ap-610	420	39	fig	fig	NOUN
ap-610	420	40	.	.	PUNCT
ap-610	420	41	7	7	NUM
ap-610	420	42	with	with	ADP
ap-610	420	43	fig	fig	NOUN
ap-610	420	44	.	.	PUNCT
ap-610	421	1	5	5	NUM
ap-610	421	2	.	.	X
ap-610	421	3	for	for	ADP
ap-610	421	4	the	the	DET
ap-610	421	5	explicit	explicit	ADJ
ap-610	421	6	model	model	NOUN
ap-610	421	7	,	,	PUNCT
ap-610	421	8	the	the	DET
ap-610	421	9	hardening	harden	VERB
ap-610	421	10	modulus	modulus	NOUN
ap-610	421	11	tends	tend	VERB
ap-610	421	12	to	to	PART
ap-610	421	13	infinity	infinity	VERB
ap-610	421	14	as	as	SCONJ
ap-610	421	15	the	the	DET
ap-610	421	16	layer	layer	NOUN
ap-610	421	17	thickness	thickness	NOUN
ap-610	421	18	approaches	approach	VERB
ap-610	421	19	zero	zero	NUM
ap-610	421	20	,	,	PUNCT
ap-610	421	21	while	while	SCONJ
ap-610	421	22	for	for	ADP
ap-610	421	23	the	the	DET
ap-610	421	24	implicit	implicit	ADJ
ap-610	421	25	model	model	NOUN
ap-610	421	26	it	it	PRON
ap-610	421	27	tends	tend	VERB
ap-610	421	28	to	to	ADP
ap-610	421	29	a	a	DET
ap-610	421	30	finite	finite	ADJ
ap-610	421	31	value	value	NOUN
ap-610	421	32	.	.	PUNCT
ap-610	422	1	the	the	DET
ap-610	422	2	local	local	ADJ
ap-610	422	3	plastic	plastic	NOUN
ap-610	422	4	strain	strain	NOUN
ap-610	422	5	on	on	ADP
ap-610	422	6	the	the	DET
ap-610	422	7	boundary	boundary	NOUN
ap-610	422	8	is	be	AUX
ap-610	422	9	zero	zero	NUM
ap-610	422	10	for	for	ADP
ap-610	422	11	the	the	DET
ap-610	422	12	explicit	explicit	ADJ
ap-610	422	13	model	model	NOUN
ap-610	422	14	(	(	PUNCT
ap-610	422	15	as	as	SCONJ
ap-610	422	16	dictated	dictate	VERB
ap-610	422	17	by	by	ADP
ap-610	422	18	the	the	DET
ap-610	422	19	boundary	boundary	ADJ
ap-610	422	20	condition	condition	NOUN
ap-610	422	21	)	)	PUNCT
ap-610	422	22	,	,	PUNCT
ap-610	422	23	while	while	SCONJ
ap-610	422	24	for	for	ADP
ap-610	422	25	the	the	DET
ap-610	422	26	implicit	implicit	ADJ
ap-610	422	27	model	model	NOUN
ap-610	422	28	it	it	PRON
ap-610	422	29	is	be	AUX
ap-610	422	30	positive	positive	ADJ
ap-610	422	31	(	(	PUNCT
ap-610	422	32	because	because	SCONJ
ap-610	422	33	the	the	DET
ap-610	422	34	boundary	boundary	ADJ
ap-610	422	35	condition	condition	NOUN
ap-610	422	36	is	be	AUX
ap-610	422	37	formulated	formulate	VERB
ap-610	422	38	in	in	ADP
ap-610	422	39	terms	term	NOUN
ap-610	422	40	of	of	ADP
ap-610	422	41	nonlocal	nonlocal	ADJ
ap-610	422	42	plastic	plastic	ADJ
ap-610	422	43	strain	strain	NOUN
ap-610	422	44	)	)	PUNCT
ap-610	422	45	.	.	PUNCT
ap-610	423	1	for	for	ADP
ap-610	423	2	the	the	DET
ap-610	423	3	explicit	explicit	ADJ
ap-610	423	4	model	model	NOUN
ap-610	423	5	,	,	PUNCT
ap-610	423	6	the	the	DET
ap-610	423	7	profile	profile	NOUN
ap-610	423	8	of	of	ADP
ap-610	423	9	plastic	plastic	ADJ
ap-610	423	10	strain	strain	NOUN
ap-610	423	11	distribution	distribution	NOUN
ap-610	423	12	across	across	ADP
ap-610	423	13	the	the	DET
ap-610	423	14	layer	layer	NOUN
ap-610	423	15	thickness	thickness	NOUN
ap-610	423	16	keeps	keep	VERB
ap-610	423	17	the	the	DET
ap-610	423	18	same	same	ADJ
ap-610	423	19	shape	shape	NOUN
ap-610	423	20	and	and	CCONJ
ap-610	423	21	grows	grow	VERB
ap-610	423	22	proportionally	proportionally	ADV
ap-610	423	23	during	during	ADP
ap-610	423	24	hardening	hardening	NOUN
ap-610	423	25	,	,	PUNCT
ap-610	423	26	while	while	SCONJ
ap-610	423	27	for	for	ADP
ap-610	423	28	the	the	DET
ap-610	423	29	implicit	implicit	ADJ
ap-610	423	30	model	model	NOUN
ap-610	423	31	the	the	DET
ap-610	423	32	analytical	analytical	ADJ
ap-610	423	33	solution	solution	NOUN
ap-610	423	34	covers	cover	VERB
ap-610	423	35	only	only	ADV
ap-610	423	36	the	the	DET
ap-610	423	37	initial	initial	ADJ
ap-610	423	38	distribution	distribution	NOUN
ap-610	423	39	of	of	ADP
ap-610	423	40	the	the	DET
ap-610	423	41	plastic	plastic	ADJ
ap-610	423	42	strain	strain	NOUN
ap-610	423	43	rate	rate	NOUN
ap-610	423	44	and	and	CCONJ
ap-610	423	45	later	later	ADV
ap-610	423	46	the	the	DET
ap-610	423	47	shape	shape	NOUN
ap-610	423	48	of	of	ADP
ap-610	423	49	the	the	DET
ap-610	423	50	profile	profile	NOUN
ap-610	423	51	would	would	AUX
ap-610	423	52	change	change	VERB
ap-610	423	53	.	.	PUNCT
ap-610	424	1	4	4	NUM
ap-610	424	2	strain	strain	NOUN
ap-610	424	3	localization	localization	NOUN
ap-610	424	4	due	due	ADJ
ap-610	424	5	to	to	ADP
ap-610	424	6	softening	soften	VERB
ap-610	424	7	4.1	4.1	NUM
ap-610	424	8	problems	problem	NOUN
ap-610	424	9	with	with	ADP
ap-610	424	10	objective	objective	ADJ
ap-610	424	11	description	description	NOUN
ap-610	424	12	of	of	ADP
ap-610	424	13	softening	soften	VERB
ap-610	424	14	in	in	ADP
ap-610	424	15	many	many	ADJ
ap-610	424	16	structures	structure	NOUN
ap-610	424	17	subjected	subject	VERB
ap-610	424	18	to	to	ADP
ap-610	424	19	high	high	ADJ
ap-610	424	20	levels	level	NOUN
ap-610	424	21	of	of	ADP
ap-610	424	22	solicitation	solicitation	NOUN
ap-610	424	23	,	,	PUNCT
ap-610	424	24	the	the	DET
ap-610	424	25	initially	initially	ADV
ap-610	424	26	smooth	smooth	ADJ
ap-610	424	27	distribution	distribution	NOUN
ap-610	424	28	of	of	ADP
ap-610	424	29	strain	strain	NOUN
ap-610	424	30	at	at	ADP
ap-610	424	31	a	a	DET
ap-610	424	32	certain	certain	ADJ
ap-610	424	33	critical	critical	ADJ
ap-610	424	34	stage	stage	NOUN
ap-610	424	35	abruptly	abruptly	ADV
ap-610	424	36	changes	change	VERB
ap-610	424	37	into	into	ADP
ap-610	424	38	a	a	DET
ap-610	424	39	localized	localized	ADJ
ap-610	424	40	pattern	pattern	NOUN
ap-610	424	41	with	with	ADP
ap-610	424	42	large	large	ADJ
ap-610	424	43	strains	strain	NOUN
ap-610	424	44	concentrated	concentrate	VERB
ap-610	424	45	in	in	ADP
ap-610	424	46	relatively	relatively	ADV
ap-610	424	47	narrow	narrow	ADJ
ap-610	424	48	regions	region	NOUN
ap-610	424	49	.	.	PUNCT
ap-610	425	1	this	this	DET
ap-610	425	2	phenomenon	phenomenon	NOUN
ap-610	425	3	,	,	PUNCT
ap-610	425	4	called	call	VERB
ap-610	425	5	strain	strain	NOUN
ap-610	425	6	localization	localization	NOUN
ap-610	425	7	,	,	PUNCT
ap-610	425	8	can	can	AUX
ap-610	425	9	be	be	AUX
ap-610	425	10	caused	cause	VERB
ap-610	425	11	for	for	ADP
ap-610	425	12	instance	instance	NOUN
ap-610	425	13	by	by	ADP
ap-610	425	14	the	the	DET
ap-610	425	15	softening	soften	VERB
ap-610	425	16	character	character	NOUN
ap-610	425	17	of	of	ADP
ap-610	425	18	the	the	DET
ap-610	425	19	material	material	NOUN
ap-610	425	20	response	response	NOUN
ap-610	425	21	.	.	PUNCT
ap-610	426	1	the	the	DET
ap-610	426	2	general	general	ADJ
ap-610	426	3	definition	definition	NOUN
ap-610	426	4	of	of	ADP
ap-610	426	5	softening	softening	NOUN
ap-610	426	6	is	be	AUX
ap-610	426	7	more	more	ADV
ap-610	426	8	involved	involve	VERB
ap-610	426	9	,	,	PUNCT
ap-610	426	10	but	but	CCONJ
ap-610	426	11	in	in	ADP
ap-610	426	12	the	the	DET
ap-610	426	13	one	one	NUM
ap-610	426	14	-	-	PUNCT
ap-610	426	15	dimensional	dimensional	ADJ
ap-610	426	16	case	case	NOUN
ap-610	426	17	softening	softening	NOUN
ap-610	426	18	means	mean	VERB
ap-610	426	19	decreasing	decrease	VERB
ap-610	426	20	stress	stress	NOUN
ap-610	426	21	at	at	ADP
ap-610	426	22	increasing	increase	VERB
ap-610	426	23	strain	strain	NOUN
ap-610	426	24	.	.	PUNCT
ap-610	427	1	the	the	DET
ap-610	427	2	physical	physical	ADJ
ap-610	427	3	source	source	NOUN
ap-610	427	4	of	of	ADP
ap-610	427	5	softening	softening	NOUN
ap-610	427	6	usually	usually	ADV
ap-610	427	7	resides	reside	VERB
ap-610	427	8	in	in	ADP
ap-610	427	9	the	the	DET
ap-610	427	10	growth	growth	NOUN
ap-610	427	11	and	and	CCONJ
ap-610	427	12	coalescence	coalescence	NOUN
ap-610	427	13	of	of	ADP
ap-610	427	14	defects	defect	NOUN
ap-610	427	15	such	such	ADJ
ap-610	427	16	as	as	ADP
ap-610	427	17	voids	voids	NOUN
ap-610	427	18	or	or	CCONJ
ap-610	427	19	cracks	crack	NOUN
ap-610	427	20	.	.	PUNCT
ap-610	428	1	from	from	ADP
ap-610	428	2	the	the	DET
ap-610	428	3	micromechanical	micromechanical	ADJ
ap-610	428	4	point	point	NOUN
ap-610	428	5	of	of	ADP
ap-610	428	6	view	view	NOUN
ap-610	428	7	,	,	PUNCT
ap-610	428	8	this	this	PRON
ap-610	428	9	means	mean	VERB
ap-610	428	10	that	that	SCONJ
ap-610	428	11	the	the	DET
ap-610	428	12	internal	internal	ADJ
ap-610	428	13	structure	structure	NOUN
ap-610	428	14	of	of	ADP
ap-610	428	15	the	the	DET
ap-610	428	16	material	material	NOUN
ap-610	428	17	is	be	AUX
ap-610	428	18	evolving	evolve	VERB
ap-610	428	19	and	and	CCONJ
ap-610	428	20	the	the	DET
ap-610	428	21	approximate	approximate	ADJ
ap-610	428	22	description	description	NOUN
ap-610	428	23	of	of	ADP
ap-610	428	24	the	the	DET
ap-610	428	25	material	material	NOUN
ap-610	428	26	as	as	ADP
ap-610	428	27	a	a	DET
ap-610	428	28	macroscopically	macroscopically	ADV
ap-610	428	29	homogeneous	homogeneous	ADJ
ap-610	428	30	one	one	PRON
ap-610	428	31	may	may	AUX
ap-610	428	32	become	become	VERB
ap-610	428	33	questionable	questionable	ADJ
ap-610	428	34	.	.	PUNCT
ap-610	429	1	indeed	indeed	ADV
ap-610	429	2	,	,	PUNCT
ap-610	429	3	softening	soften	VERB
ap-610	429	4	incorporated	incorporate	VERB
ap-610	429	5	into	into	ADP
ap-610	429	6	standard	standard	ADJ
ap-610	429	7	inelastic	inelastic	ADJ
ap-610	429	8	continuum	continuum	ADJ
ap-610	429	9	models	model	NOUN
ap-610	429	10	leads	lead	VERB
ap-610	429	11	to	to	ADP
ap-610	429	12	serious	serious	ADJ
ap-610	429	13	mathematical	mathematical	ADJ
ap-610	429	14	and	and	CCONJ
ap-610	429	15	numerical	numerical	ADJ
ap-610	429	16	problems	problem	NOUN
ap-610	429	17	,	,	PUNCT
ap-610	429	18	and	and	CCONJ
ap-610	429	19	enriched	enriched	ADJ
ap-610	429	20	theories	theory	NOUN
ap-610	429	21	are	be	AUX
ap-610	429	22	needed	need	VERB
ap-610	429	23	to	to	PART
ap-610	429	24	provide	provide	VERB
ap-610	429	25	an	an	DET
ap-610	429	26	objective	objective	ADJ
ap-610	429	27	description	description	NOUN
ap-610	429	28	of	of	ADP
ap-610	429	29	the	the	DET
ap-610	429	30	softening	softening	NOUN
ap-610	429	31	process	process	NOUN
ap-610	429	32	.	.	PUNCT
ap-610	430	1	28	28	NUM
ap-610	431	1	©	©	PROPN
ap-610	431	2	czech	czech	PROPN
ap-610	431	3	technical	technical	PROPN
ap-610	431	4	university	university	PROPN
ap-610	431	5	publishing	publishing	NOUN
ap-610	431	6	house	house	NOUN
ap-610	431	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	431	8	acta	acta	PROPN
ap-610	431	9	polytechnica	polytechnica	PROPN
ap-610	431	10	vol	vol	NOUN
ap-610	431	11	.	.	PROPN
ap-610	432	1	44	44	NUM
ap-610	432	2	no	no	NOUN
ap-610	432	3	.	.	PUNCT
ap-610	433	1	5–6/2004	5–6/2004	NUM
ap-610	433	2	(	(	PUNCT
ap-610	433	3	a	a	NOUN
ap-610	433	4	)	)	PUNCT
ap-610	433	5	(	(	PUNCT
ap-610	433	6	b	b	X
ap-610	433	7	)	)	PUNCT
ap-610	433	8	fig	fig	NOUN
ap-610	433	9	.	.	PUNCT
ap-610	434	1	7	7	NUM
ap-610	434	2	:	:	PUNCT
ap-610	434	3	implicit	implicit	ADJ
ap-610	434	4	gradient	gradient	NOUN
ap-610	434	5	plasticity	plasticity	NOUN
ap-610	434	6	:	:	PUNCT
ap-610	434	7	(	(	PUNCT
ap-610	434	8	a	a	X
ap-610	434	9	)	)	PUNCT
ap-610	434	10	dependence	dependence	NOUN
ap-610	434	11	of	of	ADP
ap-610	434	12	the	the	DET
ap-610	434	13	apparent	apparent	ADJ
ap-610	434	14	hardening	harden	VERB
ap-610	434	15	modulus	modulus	NOUN
ap-610	434	16	on	on	ADP
ap-610	434	17	the	the	DET
ap-610	434	18	size	size	NOUN
ap-610	434	19	of	of	ADP
ap-610	434	20	the	the	DET
ap-610	434	21	specimen	speciman	NOUN
ap-610	434	22	(	(	PUNCT
ap-610	434	23	layer	layer	NOUN
ap-610	434	24	thickness	thickness	NOUN
ap-610	434	25	)	)	PUNCT
ap-610	434	26	,	,	PUNCT
ap-610	434	27	(	(	PUNCT
ap-610	434	28	b	b	X
ap-610	434	29	)	)	PUNCT
ap-610	434	30	initial	initial	ADJ
ap-610	434	31	distribution	distribution	NOUN
ap-610	434	32	of	of	ADP
ap-610	434	33	plastic	plastic	ADJ
ap-610	434	34	strain	strain	NOUN
ap-610	434	35	rate	rate	NOUN
ap-610	434	36	across	across	ADP
ap-610	434	37	the	the	DET
ap-610	434	38	layer	layer	NOUN
ap-610	434	39	the	the	DET
ap-610	434	40	essence	essence	NOUN
ap-610	434	41	of	of	ADP
ap-610	434	42	the	the	DET
ap-610	434	43	localization	localization	NOUN
ap-610	434	44	problem	problem	NOUN
ap-610	434	45	will	will	AUX
ap-610	434	46	be	be	AUX
ap-610	434	47	explained	explain	VERB
ap-610	434	48	using	use	VERB
ap-610	434	49	a	a	DET
ap-610	434	50	one	one	NUM
ap-610	434	51	-	-	PUNCT
ap-610	434	52	dimensional	dimensional	ADJ
ap-610	434	53	example	example	NOUN
ap-610	434	54	,	,	PUNCT
ap-610	434	55	which	which	PRON
ap-610	434	56	could	could	AUX
ap-610	434	57	be	be	AUX
ap-610	434	58	interpreted	interpret	VERB
ap-610	434	59	as	as	ADP
ap-610	434	60	localization	localization	NOUN
ap-610	434	61	of	of	ADP
ap-610	434	62	shear	shear	NOUN
ap-610	434	63	strain	strain	NOUN
ap-610	434	64	in	in	ADP
ap-610	434	65	a	a	DET
ap-610	434	66	layer	layer	NOUN
ap-610	434	67	of	of	ADP
ap-610	434	68	elastoplastic	elastoplastic	ADJ
ap-610	434	69	material	material	NOUN
ap-610	434	70	between	between	ADP
ap-610	434	71	two	two	NUM
ap-610	434	72	rigid	rigid	ADJ
ap-610	434	73	plates	plate	NOUN
ap-610	434	74	(	(	PUNCT
ap-610	434	75	already	already	ADV
ap-610	434	76	studied	study	VERB
ap-610	434	77	in	in	ADP
ap-610	434	78	the	the	DET
ap-610	434	79	previous	previous	ADJ
ap-610	434	80	section	section	NOUN
ap-610	434	81	in	in	ADP
ap-610	434	82	the	the	DET
ap-610	434	83	context	context	NOUN
ap-610	434	84	of	of	ADP
ap-610	434	85	size	size	NOUN
ap-610	434	86	effects	effect	NOUN
ap-610	434	87	)	)	PUNCT
ap-610	434	88	.	.	PUNCT
ap-610	435	1	however	however	ADV
ap-610	435	2	,	,	PUNCT
ap-610	435	3	to	to	PART
ap-610	435	4	better	well	ADV
ap-610	435	5	show	show	VERB
ap-610	435	6	various	various	ADJ
ap-610	435	7	facets	facet	NOUN
ap-610	435	8	of	of	ADP
ap-610	435	9	nonlocal	nonlocal	ADJ
ap-610	435	10	theories	theory	NOUN
ap-610	435	11	and	and	CCONJ
ap-610	435	12	their	their	PRON
ap-610	435	13	broad	broad	ADJ
ap-610	435	14	application	application	NOUN
ap-610	435	15	field	field	NOUN
ap-610	435	16	,	,	PUNCT
ap-610	435	17	we	we	PRON
ap-610	435	18	will	will	AUX
ap-610	435	19	discuss	discuss	VERB
ap-610	435	20	the	the	DET
ap-610	435	21	closely	closely	ADV
ap-610	435	22	related	relate	VERB
ap-610	435	23	problem	problem	NOUN
ap-610	435	24	of	of	ADP
ap-610	435	25	a	a	DET
ap-610	435	26	prismatic	prismatic	ADJ
ap-610	435	27	bar	bar	NOUN
ap-610	435	28	of	of	ADP
ap-610	435	29	length	length	NOUN
ap-610	435	30	l	l	NOUN
ap-610	435	31	and	and	CCONJ
ap-610	435	32	cross	cross	ADJ
ap-610	435	33	-	-	ADJ
ap-610	435	34	sectional	sectional	ADJ
ap-610	435	35	area	area	NOUN
ap-610	435	36	a	a	DET
ap-610	435	37	under	under	ADP
ap-610	435	38	uniaxial	uniaxial	ADJ
ap-610	435	39	tension	tension	NOUN
ap-610	435	40	.	.	PUNCT
ap-610	436	1	the	the	DET
ap-610	436	2	bar	bar	NOUN
ap-610	436	3	is	be	AUX
ap-610	436	4	made	make	VERB
ap-610	436	5	of	of	ADP
ap-610	436	6	a	a	DET
ap-610	436	7	softening	soften	VERB
ap-610	436	8	material	material	NOUN
ap-610	436	9	described	describe	VERB
ap-610	436	10	by	by	ADP
ap-610	436	11	a	a	DET
ap-610	436	12	continuum	continuum	ADJ
ap-610	436	13	damage	damage	NOUN
ap-610	436	14	model	model	NOUN
ap-610	436	15	rather	rather	ADV
ap-610	436	16	than	than	ADP
ap-610	436	17	by	by	ADP
ap-610	436	18	an	an	DET
ap-610	436	19	elastoplastic	elastoplastic	ADJ
ap-610	436	20	model	model	NOUN
ap-610	436	21	.	.	PUNCT
ap-610	437	1	damage	damage	NOUN
ap-610	437	2	mechanics	mechanic	NOUN
ap-610	437	3	is	be	AUX
ap-610	437	4	frequently	frequently	ADV
ap-610	437	5	used	use	VERB
ap-610	437	6	for	for	ADP
ap-610	437	7	quasibrittle	quasibrittle	ADJ
ap-610	437	8	materials	material	NOUN
ap-610	437	9	such	such	ADJ
ap-610	437	10	as	as	ADP
ap-610	437	11	concrete	concrete	ADJ
ap-610	437	12	under	under	ADP
ap-610	437	13	predominantly	predominantly	ADV
ap-610	437	14	tensile	tensile	ADJ
ap-610	437	15	loading	loading	NOUN
ap-610	437	16	.	.	PUNCT
ap-610	438	1	many	many	ADJ
ap-610	438	2	results	result	NOUN
ap-610	438	3	and	and	CCONJ
ap-610	438	4	conclusions	conclusion	NOUN
ap-610	438	5	of	of	ADP
ap-610	438	6	the	the	DET
ap-610	438	7	present	present	ADJ
ap-610	438	8	section	section	NOUN
ap-610	438	9	could	could	AUX
ap-610	438	10	be	be	AUX
ap-610	438	11	directly	directly	ADV
ap-610	438	12	reinterpreted	reinterpret	VERB
ap-610	438	13	in	in	ADP
ap-610	438	14	terms	term	NOUN
ap-610	438	15	of	of	ADP
ap-610	438	16	shear	shear	NOUN
ap-610	438	17	bands	band	NOUN
ap-610	438	18	in	in	ADP
ap-610	438	19	ductile	ductile	NOUN
ap-610	438	20	materials	material	NOUN
ap-610	438	21	such	such	ADJ
ap-610	438	22	as	as	ADP
ap-610	438	23	metals	metal	NOUN
ap-610	438	24	or	or	CCONJ
ap-610	438	25	confined	confine	VERB
ap-610	438	26	soils	soil	NOUN
ap-610	438	27	.	.	PUNCT
ap-610	439	1	in	in	ADP
ap-610	439	2	the	the	DET
ap-610	439	3	one	one	NUM
ap-610	439	4	-	-	PUNCT
ap-610	439	5	dimensional	dimensional	ADJ
ap-610	439	6	setting	setting	NOUN
ap-610	439	7	,	,	PUNCT
ap-610	439	8	the	the	DET
ap-610	439	9	stress	stress	NOUN
ap-610	439	10	-	-	PUNCT
ap-610	439	11	strain	strain	NOUN
ap-610	439	12	law	law	NOUN
ap-610	439	13	used	use	VERB
ap-610	439	14	by	by	ADP
ap-610	439	15	the	the	DET
ap-610	439	16	damage	damage	NOUN
ap-610	439	17	model	model	NOUN
ap-610	439	18	reads	read	VERB
ap-610	439	19	�	�	PROPN
ap-610	439	20	�	�	PROPN
ap-610	439	21	�	�	PROPN
ap-610	439	22	(	(	PUNCT
ap-610	439	23	)	)	PUNCT
ap-610	439	24	1	1	NUM
ap-610	439	25	�	�	PROPN
ap-610	439	26	e	e	PROPN
ap-610	439	27	,	,	PUNCT
ap-610	439	28	(	(	PUNCT
ap-610	439	29	77	77	NUM
ap-610	439	30	)	)	PUNCT
ap-610	439	31	where	where	SCONJ
ap-610	439	32	and	and	CCONJ
ap-610	439	33	�	�	PROPN
ap-610	439	34	are	be	AUX
ap-610	439	35	the	the	DET
ap-610	439	36	(	(	PUNCT
ap-610	439	37	normal	normal	ADJ
ap-610	439	38	)	)	PUNCT
ap-610	439	39	stress	stress	NOUN
ap-610	439	40	and	and	CCONJ
ap-610	439	41	strain	strain	NOUN
ap-610	439	42	,	,	PUNCT
ap-610	439	43	e	e	NOUN
ap-610	439	44	is	be	AUX
ap-610	439	45	young	young	ADJ
ap-610	439	46	’s	’s	PART
ap-610	439	47	modulus	modulus	NOUN
ap-610	439	48	of	of	ADP
ap-610	439	49	elasticity	elasticity	NOUN
ap-610	439	50	,	,	PUNCT
ap-610	439	51	and	and	CCONJ
ap-610	439	52	�	�	PROPN
ap-610	439	53	is	be	AUX
ap-610	439	54	a	a	DET
ap-610	439	55	scalar	scalar	ADJ
ap-610	439	56	damage	damage	NOUN
ap-610	439	57	variable	variable	NOUN
ap-610	439	58	characterizing	characterize	VERB
ap-610	439	59	the	the	DET
ap-610	439	60	current	current	ADJ
ap-610	439	61	size	size	NOUN
ap-610	439	62	and	and	CCONJ
ap-610	439	63	density	density	NOUN
ap-610	439	64	of	of	ADP
ap-610	439	65	defects	defect	NOUN
ap-610	439	66	that	that	PRON
ap-610	439	67	reduce	reduce	VERB
ap-610	439	68	the	the	DET
ap-610	439	69	effective	effective	ADJ
ap-610	439	70	area	area	NOUN
ap-610	439	71	capable	capable	ADJ
ap-610	439	72	of	of	ADP
ap-610	439	73	transmitting	transmit	VERB
ap-610	439	74	stress	stress	NOUN
ap-610	439	75	.	.	PUNCT
ap-610	440	1	in	in	ADP
ap-610	440	2	the	the	DET
ap-610	440	3	“	"	PUNCT
ap-610	440	4	virgin	virgin	NOUN
ap-610	440	5	”	"	PUNCT
ap-610	440	6	,	,	PUNCT
ap-610	440	7	undamaged	undamaged	ADJ
ap-610	440	8	state	state	NOUN
ap-610	440	9	of	of	ADP
ap-610	440	10	material	material	NOUN
ap-610	440	11	with	with	ADP
ap-610	440	12	no	no	DET
ap-610	440	13	defects	defect	NOUN
ap-610	440	14	(	(	PUNCT
ap-610	440	15	or	or	CCONJ
ap-610	440	16	with	with	ADP
ap-610	440	17	very	very	ADV
ap-610	440	18	small	small	ADJ
ap-610	440	19	initial	initial	ADJ
ap-610	440	20	defects	defect	NOUN
ap-610	440	21	that	that	PRON
ap-610	440	22	are	be	AUX
ap-610	440	23	incorporated	incorporate	VERB
ap-610	440	24	in	in	ADP
ap-610	440	25	the	the	DET
ap-610	440	26	elastic	elastic	ADJ
ap-610	440	27	modulus	modulus	NOUN
ap-610	440	28	)	)	PUNCT
ap-610	440	29	,	,	PUNCT
ap-610	440	30	the	the	DET
ap-610	440	31	value	value	NOUN
ap-610	440	32	of	of	ADP
ap-610	440	33	the	the	DET
ap-610	440	34	damage	damage	NOUN
ap-610	440	35	parameter	parameter	NOUN
ap-610	440	36	is	be	AUX
ap-610	440	37	zero	zero	NUM
ap-610	440	38	,	,	PUNCT
ap-610	440	39	and	and	CCONJ
ap-610	440	40	it	it	PRON
ap-610	440	41	remains	remain	VERB
ap-610	440	42	zero	zero	NUM
ap-610	440	43	throughout	throughout	ADP
ap-610	440	44	the	the	DET
ap-610	440	45	elastic	elastic	ADJ
ap-610	440	46	stage	stage	NOUN
ap-610	440	47	of	of	ADP
ap-610	440	48	loading	loading	NOUN
ap-610	440	49	.	.	PUNCT
ap-610	441	1	when	when	SCONJ
ap-610	441	2	the	the	DET
ap-610	441	3	elastic	elastic	ADJ
ap-610	441	4	limit	limit	NOUN
ap-610	441	5	is	be	AUX
ap-610	441	6	exceeded	exceed	VERB
ap-610	441	7	,	,	PUNCT
ap-610	441	8	damage	damage	NOUN
ap-610	441	9	starts	start	VERB
ap-610	441	10	growing	grow	VERB
ap-610	441	11	and	and	CCONJ
ap-610	441	12	the	the	DET
ap-610	441	13	elastically	elastically	ADV
ap-610	441	14	computed	compute	VERB
ap-610	441	15	stress	stress	NOUN
ap-610	441	16	e	e	NOUN
ap-610	441	17	�	�	PROPN
ap-610	441	18	is	be	AUX
ap-610	441	19	reduced	reduce	VERB
ap-610	441	20	by	by	ADP
ap-610	441	21	the	the	DET
ap-610	441	22	integrity	integrity	NOUN
ap-610	441	23	factor	factor	NOUN
ap-610	441	24	1	1	NUM
ap-610	441	25	�	�	PROPN
ap-610	441	26	�	�	PROPN
ap-610	441	27	.	.	PUNCT
ap-610	442	1	the	the	DET
ap-610	442	2	limit	limit	NOUN
ap-610	442	3	value	value	NOUN
ap-610	442	4	�	�	PROPN
ap-610	442	5	�	�	PROPN
ap-610	442	6	1	1	NUM
ap-610	442	7	corresponds	correspond	VERB
ap-610	442	8	to	to	ADP
ap-610	442	9	a	a	DET
ap-610	442	10	fully	fully	ADV
ap-610	442	11	damaged	damage	VERB
ap-610	442	12	material	material	NOUN
ap-610	442	13	that	that	PRON
ap-610	442	14	can	can	AUX
ap-610	442	15	no	no	ADV
ap-610	442	16	longer	long	ADV
ap-610	442	17	carry	carry	VERB
ap-610	442	18	any	any	DET
ap-610	442	19	stress	stress	NOUN
ap-610	442	20	.	.	PUNCT
ap-610	443	1	the	the	DET
ap-610	443	2	growth	growth	NOUN
ap-610	443	3	of	of	ADP
ap-610	443	4	damage	damage	NOUN
ap-610	443	5	must	must	AUX
ap-610	443	6	be	be	AUX
ap-610	443	7	described	describe	VERB
ap-610	443	8	by	by	ADP
ap-610	443	9	an	an	DET
ap-610	443	10	appropriate	appropriate	ADJ
ap-610	443	11	damage	damage	NOUN
ap-610	443	12	evolution	evolution	NOUN
ap-610	443	13	law	law	NOUN
ap-610	443	14	for	for	ADP
ap-610	443	15	the	the	DET
ap-610	443	16	internal	internal	ADJ
ap-610	443	17	variable	variable	ADJ
ap-610	443	18	�	�	PROPN
ap-610	443	19	.	.	PUNCT
ap-610	444	1	this	this	DET
ap-610	444	2	law	law	NOUN
ap-610	444	3	could	could	AUX
ap-610	444	4	be	be	AUX
ap-610	444	5	postulated	postulate	VERB
ap-610	444	6	in	in	ADP
ap-610	444	7	the	the	DET
ap-610	444	8	rate	rate	NOUN
ap-610	444	9	form	form	NOUN
ap-610	444	10	,	,	PUNCT
ap-610	444	11	but	but	CCONJ
ap-610	444	12	a	a	DET
ap-610	444	13	particularly	particularly	ADV
ap-610	444	14	simple	simple	ADJ
ap-610	444	15	and	and	CCONJ
ap-610	444	16	practical	practical	ADJ
ap-610	444	17	formulation	formulation	NOUN
ap-610	444	18	is	be	AUX
ap-610	444	19	obtained	obtain	VERB
ap-610	444	20	with	with	ADP
ap-610	444	21	a	a	DET
ap-610	444	22	damage	damage	NOUN
ap-610	444	23	law	law	NOUN
ap-610	444	24	in	in	ADP
ap-610	444	25	the	the	DET
ap-610	444	26	total	total	ADJ
ap-610	444	27	form	form	NOUN
ap-610	444	28	�	�	PROPN
ap-610	444	29	�	�	PROPN
ap-610	444	30	g	g	PROPN
ap-610	444	31	(	(	PUNCT
ap-610	444	32	)	)	PUNCT
ap-610	444	33	�	�	PROPN
ap-610	444	34	,	,	PUNCT
ap-610	444	35	(	(	PUNCT
ap-610	444	36	78	78	NUM
ap-610	444	37	)	)	PUNCT
ap-610	444	38	where	where	SCONJ
ap-610	444	39	�	�	PROPN
ap-610	444	40	corresponds	correspond	VERB
ap-610	444	41	to	to	ADP
ap-610	444	42	the	the	DET
ap-610	444	43	maximum	maximum	ADJ
ap-610	444	44	level	level	NOUN
ap-610	444	45	of	of	ADP
ap-610	444	46	strain	strain	NOUN
ap-610	444	47	reached	reach	VERB
ap-610	444	48	in	in	ADP
ap-610	444	49	the	the	DET
ap-610	444	50	previous	previous	ADJ
ap-610	444	51	history	history	NOUN
ap-610	444	52	of	of	ADP
ap-610	444	53	the	the	DET
ap-610	444	54	material	material	NOUN
ap-610	444	55	.	.	PUNCT
ap-610	445	1	mathematically	mathematically	ADV
ap-610	445	2	,	,	PUNCT
ap-610	445	3	the	the	DET
ap-610	445	4	internal	internal	ADJ
ap-610	445	5	variable	variable	ADJ
ap-610	445	6	�	�	PROPN
ap-610	445	7	is	be	AUX
ap-610	445	8	defined	define	VERB
ap-610	445	9	by	by	ADP
ap-610	445	10	the	the	DET
ap-610	445	11	loading	loading	NOUN
ap-610	445	12	-	-	PUNCT
ap-610	445	13	unloading	unloading	NOUN
ap-610	445	14	conditions	condition	NOUN
ap-610	445	15	�	�	PROPN
ap-610	445	16	,	,	PUNCT
ap-610	445	17	,	,	PUNCT
ap-610	445	18	(	(	PUNCT
ap-610	445	19	)	)	PUNCT
ap-610	445	20	�	�	PROPN
ap-610	445	21	�	�	PROPN
ap-610	445	22	�	�	PROPN
ap-610	445	23	�	�	PROPN
ap-610	445	24	�	�	PROPN
ap-610	445	25	�	�	PROPN
ap-610	445	26	�	�	PROPN
ap-610	445	27	�	�	PROPN
ap-610	445	28	�	�	PROPN
ap-610	445	29	�	�	PROPN
ap-610	445	30	�	�	PROPN
ap-610	445	31	�	�	PROPN
ap-610	445	32	0	0	NUM
ap-610	445	33	0	0	NUM
ap-610	445	34	0	0	NUM
ap-610	445	35	.	.	PUNCT
ap-610	446	1	(	(	PUNCT
ap-610	446	2	79	79	NUM
ap-610	446	3	)	)	PUNCT
ap-610	446	4	during	during	ADP
ap-610	446	5	monotonic	monotonic	ADJ
ap-610	446	6	loading	loading	NOUN
ap-610	446	7	,	,	PUNCT
ap-610	446	8	�	�	PROPN
ap-610	446	9	is	be	AUX
ap-610	446	10	equal	equal	ADJ
ap-610	446	11	to	to	ADP
ap-610	446	12	the	the	DET
ap-610	446	13	strain	strain	PROPN
ap-610	446	14	�	�	PROPN
ap-610	446	15	,	,	PUNCT
ap-610	446	16	and	and	CCONJ
ap-610	446	17	so	so	ADV
ap-610	446	18	the	the	DET
ap-610	446	19	damage	damage	NOUN
ap-610	446	20	evolution	evolution	NOUN
ap-610	446	21	function	function	VERB
ap-610	446	22	g	g	PROPN
ap-610	446	23	that	that	PRON
ap-610	446	24	appears	appear	VERB
ap-610	446	25	in	in	ADP
ap-610	446	26	(	(	PUNCT
ap-610	446	27	78	78	NUM
ap-610	446	28	)	)	PUNCT
ap-610	446	29	can	can	AUX
ap-610	446	30	easily	easily	ADV
ap-610	446	31	be	be	AUX
ap-610	446	32	identified	identify	VERB
ap-610	446	33	from	from	ADP
ap-610	446	34	the	the	DET
ap-610	446	35	monotonic	monotonic	ADJ
ap-610	446	36	stress	stress	NOUN
ap-610	446	37	-	-	PUNCT
ap-610	446	38	strain	strain	NOUN
ap-610	446	39	curve	curve	NOUN
ap-610	446	40	.	.	PUNCT
ap-610	447	1	now	now	ADV
ap-610	447	2	suppose	suppose	VERB
ap-610	447	3	that	that	SCONJ
ap-610	447	4	the	the	DET
ap-610	447	5	stress	stress	NOUN
ap-610	447	6	-	-	PUNCT
ap-610	447	7	strain	strain	NOUN
ap-610	447	8	diagram	diagram	NOUN
ap-610	447	9	is	be	AUX
ap-610	447	10	linear	linear	ADJ
ap-610	447	11	up	up	ADP
ap-610	447	12	to	to	ADP
ap-610	447	13	a	a	DET
ap-610	447	14	certain	certain	ADJ
ap-610	447	15	strain	strain	NOUN
ap-610	447	16	level	level	NOUN
ap-610	447	17	�	�	PROPN
ap-610	447	18	0	0	NUM
ap-610	447	19	,	,	PUNCT
ap-610	447	20	after	after	ADP
ap-610	447	21	which	which	PRON
ap-610	447	22	stress	stress	NOUN
ap-610	447	23	decreases	decrease	VERB
ap-610	447	24	as	as	ADP
ap-610	447	25	a	a	DET
ap-610	447	26	linear	linear	ADJ
ap-610	447	27	function	function	NOUN
ap-610	447	28	of	of	ADP
ap-610	447	29	strain	strain	NOUN
ap-610	447	30	until	until	SCONJ
ap-610	447	31	the	the	DET
ap-610	447	32	zero	zero	NUM
ap-610	447	33	stress	stress	NOUN
ap-610	447	34	level	level	NOUN
ap-610	447	35	is	be	AUX
ap-610	447	36	reached	reach	VERB
ap-610	447	37	at	at	ADP
ap-610	447	38	strain	strain	PROPN
ap-610	447	39	�	�	PROPN
ap-610	447	40	f	f	PROPN
ap-610	447	41	(	(	PUNCT
ap-610	447	42	fig	fig	NOUN
ap-610	447	43	.	.	PUNCT
ap-610	448	1	8a	8a	NUM
ap-610	448	2	)	)	PUNCT
ap-610	448	3	.	.	PUNCT
ap-610	449	1	this	this	DET
ap-610	449	2	linear	linear	NOUN
ap-610	449	3	softening	soften	VERB
ap-610	449	4	model	model	NOUN
ap-610	449	5	can	can	AUX
ap-610	449	6	be	be	AUX
ap-610	449	7	considered	consider	VERB
ap-610	449	8	as	as	ADP
ap-610	449	9	the	the	DET
ap-610	449	10	simplest	simple	ADJ
ap-610	449	11	description	description	NOUN
ap-610	449	12	of	of	ADP
ap-610	449	13	concrete	concrete	ADJ
ap-610	449	14	cracking	crack	VERB
ap-610	449	15	under	under	ADP
ap-610	449	16	tension	tension	NOUN
ap-610	449	17	.	.	PUNCT
ap-610	450	1	due	due	ADP
ap-610	450	2	to	to	ADP
ap-610	450	3	the	the	DET
ap-610	450	4	heterogeneous	heterogeneous	ADJ
ap-610	450	5	and	and	CCONJ
ap-610	450	6	quasibrittle	quasibrittle	ADJ
ap-610	450	7	nature	nature	NOUN
ap-610	450	8	of	of	ADP
ap-610	450	9	the	the	DET
ap-610	450	10	material	material	NOUN
ap-610	450	11	,	,	PUNCT
ap-610	450	12	a	a	DET
ap-610	450	13	contiguous	contiguous	ADJ
ap-610	450	14	stress	stress	NOUN
ap-610	450	15	-	-	PUNCT
ap-610	450	16	free	free	ADJ
ap-610	450	17	crack	crack	NOUN
ap-610	450	18	across	across	ADP
ap-610	450	19	the	the	DET
ap-610	450	20	entire	entire	ADJ
ap-610	450	21	section	section	NOUN
ap-610	450	22	of	of	ADP
ap-610	450	23	a	a	DET
ap-610	450	24	bar	bar	NOUN
ap-610	450	25	does	do	AUX
ap-610	450	26	not	not	PART
ap-610	450	27	form	form	VERB
ap-610	450	28	instantaneously	instantaneously	ADV
ap-610	450	29	but	but	CCONJ
ap-610	450	30	is	be	AUX
ap-610	450	31	obtained	obtain	VERB
ap-610	450	32	as	as	ADP
ap-610	450	33	the	the	DET
ap-610	450	34	final	final	ADJ
ap-610	450	35	result	result	NOUN
ap-610	450	36	of	of	ADP
ap-610	450	37	propagation	propagation	NOUN
ap-610	450	38	and	and	CCONJ
ap-610	450	39	coalescence	coalescence	NOUN
ap-610	450	40	of	of	ADP
ap-610	450	41	many	many	ADJ
ap-610	450	42	smaller	small	ADJ
ap-610	450	43	cracks	crack	NOUN
ap-610	450	44	.	.	PUNCT
ap-610	451	1	consequently	consequently	ADV
ap-610	451	2	,	,	PUNCT
ap-610	451	3	even	even	ADV
ap-610	451	4	after	after	ADP
ap-610	451	5	the	the	DET
ap-610	451	6	onset	onset	NOUN
ap-610	451	7	of	of	ADP
ap-610	451	8	cracking	crack	VERB
ap-610	451	9	the	the	DET
ap-610	451	10	bar	bar	NOUN
ap-610	451	11	can	can	AUX
ap-610	451	12	still	still	ADV
ap-610	451	13	transmit	transmit	VERB
ap-610	451	14	a	a	DET
ap-610	451	15	certain	certain	ADJ
ap-610	451	16	force	force	NOUN
ap-610	451	17	but	but	CCONJ
ap-610	451	18	its	its	PRON
ap-610	451	19	residual	residual	ADJ
ap-610	451	20	strength	strength	NOUN
ap-610	451	21	decreases	decrease	VERB
ap-610	451	22	as	as	SCONJ
ap-610	451	23	the	the	DET
ap-610	451	24	cracks	crack	NOUN
ap-610	451	25	evolve	evolve	VERB
ap-610	451	26	.	.	PUNCT
ap-610	452	1	under	under	ADP
ap-610	452	2	static	static	ADJ
ap-610	452	3	loading	loading	NOUN
ap-610	452	4	and	and	CCONJ
ap-610	452	5	in	in	ADP
ap-610	452	6	the	the	DET
ap-610	452	7	absence	absence	NOUN
ap-610	452	8	of	of	ADP
ap-610	452	9	body	body	NOUN
ap-610	452	10	forces	force	NOUN
ap-610	452	11	,	,	PUNCT
ap-610	452	12	the	the	DET
ap-610	452	13	stress	stress	NOUN
ap-610	452	14	in	in	ADP
ap-610	452	15	the	the	DET
ap-610	452	16	bar	bar	NOUN
ap-610	452	17	must	must	AUX
ap-610	452	18	be	be	AUX
ap-610	452	19	uniformly	uniformly	ADV
ap-610	452	20	distributed	distribute	VERB
ap-610	452	21	.	.	PUNCT
ap-610	453	1	in	in	ADP
ap-610	453	2	the	the	DET
ap-610	453	3	elastic	elastic	ADJ
ap-610	453	4	range	range	NOUN
ap-610	453	5	,	,	PUNCT
ap-610	453	6	strain	strain	NOUN
ap-610	453	7	is	be	AUX
ap-610	453	8	a	a	DET
ap-610	453	9	unique	unique	ADJ
ap-610	453	10	function	function	NOUN
ap-610	453	11	of	of	ADP
ap-610	453	12	stress	stress	NOUN
ap-610	453	13	,	,	PUNCT
ap-610	453	14	and	and	CCONJ
ap-610	453	15	so	so	ADV
ap-610	453	16	the	the	DET
ap-610	453	17	strain	strain	NOUN
ap-610	453	18	distribution	distribution	NOUN
ap-610	453	19	must	must	AUX
ap-610	453	20	be	be	AUX
ap-610	453	21	uniform	uniform	ADJ
ap-610	453	22	as	as	ADV
ap-610	453	23	well	well	ADV
ap-610	453	24	.	.	PUNCT
ap-610	454	1	when	when	SCONJ
ap-610	454	2	the	the	DET
ap-610	454	3	peak	peak	NOUN
ap-610	454	4	stress	stress	NOUN
ap-610	454	5	(	(	PUNCT
ap-610	454	6	tensile	tensile	NOUN
ap-610	454	7	strength	strength	NOUN
ap-610	454	8	)	)	PUNCT
ap-610	454	9	ft	ft	PROPN
ap-610	454	10	is	be	AUX
ap-610	454	11	attained	attain	VERB
ap-610	454	12	,	,	PUNCT
ap-610	454	13	the	the	DET
ap-610	454	14	uniqueness	uniqueness	NOUN
ap-610	454	15	of	of	ADP
ap-610	454	16	the	the	DET
ap-610	454	17	response	response	NOUN
ap-610	454	18	is	be	AUX
ap-610	454	19	lost	lose	VERB
ap-610	454	20	.	.	PUNCT
ap-610	455	1	stress	stress	NOUN
ap-610	455	2	must	must	AUX
ap-610	455	3	still	still	ADV
ap-610	455	4	remain	remain	VERB
ap-610	455	5	uniform	uniform	ADJ
ap-610	455	6	and	and	CCONJ
ap-610	455	7	it	it	PRON
ap-610	455	8	can	can	AUX
ap-610	455	9	only	only	ADV
ap-610	455	10	decrease	decrease	VERB
ap-610	455	11	,	,	PUNCT
ap-610	455	12	but	but	CCONJ
ap-610	455	13	a	a	DET
ap-610	455	14	given	give	VERB
ap-610	455	15	stress	stress	NOUN
ap-610	455	16	level	level	NOUN
ap-610	455	17	can	can	AUX
ap-610	455	18	be	be	AUX
ap-610	455	19	reached	reach	VERB
ap-610	455	20	either	either	CCONJ
ap-610	455	21	by	by	ADP
ap-610	455	22	further	far	ADV
ap-610	455	23	stretching	stretch	VERB
ap-610	455	24	the	the	DET
ap-610	455	25	material	material	NOUN
ap-610	455	26	into	into	ADP
ap-610	455	27	the	the	DET
ap-610	455	28	softening	soften	VERB
ap-610	455	29	regime	regime	NOUN
ap-610	455	30	,	,	PUNCT
ap-610	455	31	or	or	CCONJ
ap-610	455	32	by	by	ADP
ap-610	455	33	elastic	elastic	ADJ
ap-610	455	34	unloading	unloading	NOUN
ap-610	455	35	.	.	PUNCT
ap-610	456	1	consequently	consequently	ADV
ap-610	456	2	,	,	PUNCT
ap-610	456	3	there	there	PRON
ap-610	456	4	are	be	VERB
ap-610	456	5	many	many	ADJ
ap-610	456	6	different	different	ADJ
ap-610	456	7	spatial	spatial	ADJ
ap-610	456	8	distributions	distribution	NOUN
ap-610	456	9	of	of	ADP
ap-610	456	10	the	the	DET
ap-610	456	11	strain	strain	NOUN
ap-610	456	12	increments	increment	NOUN
ap-610	456	13	that	that	PRON
ap-610	456	14	lead	lead	VERB
ap-610	456	15	to	to	ADP
ap-610	456	16	the	the	DET
ap-610	456	17	same	same	ADJ
ap-610	456	18	uniform	uniform	ADJ
ap-610	456	19	stress	stress	NOUN
ap-610	456	20	decrement	decrement	ADJ
ap-610	456	21	and	and	CCONJ
ap-610	456	22	thus	thus	ADV
ap-610	456	23	represent	represent	VERB
ap-610	456	24	a	a	DET
ap-610	456	25	valid	valid	ADJ
ap-610	456	26	solution	solution	NOUN
ap-610	456	27	satisfying	satisfy	VERB
ap-610	456	28	the	the	DET
ap-610	456	29	equilibrium	equilibrium	NOUN
ap-610	456	30	equation	equation	NOUN
ap-610	456	31	and	and	CCONJ
ap-610	456	32	the	the	DET
ap-610	456	33	constitutive	constitutive	ADJ
ap-610	456	34	law	law	NOUN
ap-610	456	35	.	.	PUNCT
ap-610	457	1	the	the	DET
ap-610	457	2	compatibility	compatibility	NOUN
ap-610	457	3	equations	equation	NOUN
ap-610	457	4	do	do	AUX
ap-610	457	5	not	not	PART
ap-610	457	6	represent	represent	VERB
ap-610	457	7	any	any	DET
ap-610	457	8	important	important	ADJ
ap-610	457	9	constraint	constraint	NOUN
ap-610	457	10	in	in	ADP
ap-610	457	11	the	the	DET
ap-610	457	12	one	one	NUM
ap-610	457	13	-	-	PUNCT
ap-610	457	14	dimensional	dimensional	ADJ
ap-610	457	15	case	case	NOUN
ap-610	457	16	,	,	PUNCT
ap-610	457	17	because	because	SCONJ
ap-610	457	18	the	the	DET
ap-610	457	19	strain	strain	NOUN
ap-610	457	20	field	field	NOUN
ap-610	457	21	can	can	AUX
ap-610	457	22	always	always	ADV
ap-610	457	23	be	be	AUX
ap-610	457	24	integrated	integrate	VERB
ap-610	457	25	to	to	PART
ap-610	457	26	yield	yield	VERB
ap-610	457	27	the	the	DET
ap-610	457	28	displacement	displacement	ADJ
ap-610	457	29	field	field	NOUN
ap-610	457	30	.	.	PUNCT
ap-610	458	1	for	for	ADP
ap-610	458	2	example	example	NOUN
ap-610	458	3	,	,	PUNCT
ap-610	458	4	the	the	DET
ap-610	458	5	material	material	NOUN
ap-610	458	6	can	can	AUX
ap-610	458	7	be	be	AUX
ap-610	458	8	softening	soften	VERB
ap-610	458	9	in	in	ADP
ap-610	458	10	an	an	DET
ap-610	458	11	interval	interval	NOUN
ap-610	458	12	of	of	ADP
ap-610	458	13	length	length	NOUN
ap-610	458	14	ls	ls	PROPN
ap-610	458	15	and	and	CCONJ
ap-610	458	16	unloading	unload	VERB
ap-610	458	17	everywhere	everywhere	ADV
ap-610	458	18	else	else	ADV
ap-610	458	19	.	.	PUNCT
ap-610	459	1	when	when	SCONJ
ap-610	459	2	the	the	DET
ap-610	459	3	stress	stress	NOUN
ap-610	459	4	is	be	AUX
ap-610	459	5	completely	completely	ADV
ap-610	459	6	relaxed	relaxed	ADJ
ap-610	459	7	to	to	ADP
ap-610	459	8	zero	zero	NUM
ap-610	459	9	,	,	PUNCT
ap-610	459	10	the	the	DET
ap-610	459	11	strain	strain	NOUN
ap-610	459	12	in	in	ADP
ap-610	459	13	the	the	DET
ap-610	459	14	softening	soften	VERB
ap-610	459	15	region	region	NOUN
ap-610	459	16	is	be	AUX
ap-610	459	17	�	�	PROPN
ap-610	459	18	f	f	PROPN
ap-610	459	19	and	and	CCONJ
ap-610	459	20	the	the	DET
ap-610	459	21	strain	strain	NOUN
ap-610	459	22	in	in	ADP
ap-610	459	23	the	the	DET
ap-610	459	24	unloading	unloading	NOUN
ap-610	459	25	region	region	NOUN
ap-610	459	26	vanishes;	vanishes;	VERB
ap-610	459	27	the	the	DET
ap-610	459	28	total	total	ADJ
ap-610	459	29	elongation	elongation	NOUN
ap-610	459	30	of	of	ADP
ap-610	459	31	the	the	DET
ap-610	459	32	bar	bar	NOUN
ap-610	459	33	is	be	AUX
ap-610	459	34	therefore	therefore	ADV
ap-610	459	35	u	u	PROPN
ap-610	459	36	ls	ls	PROPN
ap-610	459	37	f	f	PROPN
ap-610	459	38	�	�	PROPN
ap-610	459	39	�	�	PROPN
ap-610	459	40	.	.	PUNCT
ap-610	460	1	the	the	DET
ap-610	460	2	length	length	NOUN
ap-610	460	3	ls	ls	PROPN
ap-610	460	4	remains	remain	VERB
ap-610	460	5	undetermined	undetermined	ADJ
ap-610	460	6	,	,	PUNCT
ap-610	460	7	and	and	CCONJ
ap-610	460	8	it	it	PRON
ap-610	460	9	can	can	AUX
ap-610	460	10	have	have	VERB
ap-610	460	11	any	any	DET
ap-610	460	12	value	value	NOUN
ap-610	460	13	between	between	ADP
ap-610	460	14	0	0	NUM
ap-610	460	15	and	and	CCONJ
ap-610	460	16	l.	l.	PROPN
ap-610	460	17	this	this	PRON
ap-610	460	18	means	mean	VERB
ap-610	460	19	that	that	SCONJ
ap-610	460	20	the	the	DET
ap-610	460	21	problem	problem	NOUN
ap-610	460	22	has	have	VERB
ap-610	460	23	infinitely	infinitely	ADV
ap-610	460	24	many	many	ADJ
ap-610	460	25	solutions;	solutions;	NOUN
ap-610	460	26	the	the	DET
ap-610	460	27	corresponding	corresponding	ADJ
ap-610	460	28	post	post	ADJ
ap-610	460	29	-	-	ADJ
ap-610	460	30	peak	peak	ADJ
ap-610	460	31	branches	branch	NOUN
ap-610	460	32	of	of	ADP
ap-610	460	33	the	the	DET
ap-610	460	34	load	load	NOUN
ap-610	460	35	-	-	PUNCT
ap-610	460	36	displacement	displacement	ADJ
ap-610	460	37	diagram	diagram	NOUN
ap-610	460	38	fill	fill	VERB
ap-610	460	39	the	the	DET
ap-610	460	40	fan	fan	NOUN
ap-610	460	41	shown	show	VERB
ap-610	460	42	in	in	ADP
ap-610	460	43	fig	fig	NOUN
ap-610	460	44	.	.	PUNCT
ap-610	461	1	8b	8b	NUM
ap-610	461	2	.	.	PUNCT
ap-610	462	1	the	the	DET
ap-610	462	2	ambiguity	ambiguity	NOUN
ap-610	462	3	is	be	AUX
ap-610	462	4	removed	remove	VERB
ap-610	462	5	if	if	SCONJ
ap-610	462	6	imperfections	imperfection	NOUN
ap-610	462	7	are	be	AUX
ap-610	462	8	taken	take	VERB
ap-610	462	9	into	into	ADP
ap-610	462	10	account	account	NOUN
ap-610	462	11	.	.	PUNCT
ap-610	463	1	real	real	ADJ
ap-610	463	2	material	material	NOUN
ap-610	463	3	properties	property	NOUN
ap-610	463	4	and	and	CCONJ
ap-610	463	5	sectional	sectional	ADJ
ap-610	463	6	dimensions	dimension	NOUN
ap-610	463	7	can	can	AUX
ap-610	463	8	not	not	PART
ap-610	463	9	be	be	AUX
ap-610	463	10	perfectly	perfectly	ADV
ap-610	463	11	uniform	uniform	ADJ
ap-610	463	12	.	.	PUNCT
ap-610	464	1	suppose	suppose	VERB
ap-610	464	2	that	that	SCONJ
ap-610	464	3	the	the	DET
ap-610	464	4	strength	strength	NOUN
ap-610	464	5	in	in	ADP
ap-610	464	6	a	a	DET
ap-610	464	7	small	small	ADJ
ap-610	464	8	region	region	NOUN
ap-610	464	9	is	be	AUX
ap-610	464	10	slightly	slightly	ADV
ap-610	464	11	lower	low	ADJ
ap-610	464	12	than	than	ADP
ap-610	464	13	in	in	ADP
ap-610	464	14	the	the	DET
ap-610	464	15	remaining	remain	VERB
ap-610	464	16	portion	portion	NOUN
ap-610	464	17	of	of	ADP
ap-610	464	18	the	the	DET
ap-610	464	19	bar	bar	NOUN
ap-610	464	20	.	.	PUNCT
ap-610	465	1	when	when	SCONJ
ap-610	465	2	the	the	DET
ap-610	465	3	applied	apply	VERB
ap-610	465	4	stress	stress	NOUN
ap-610	465	5	reaches	reach	VERB
ap-610	465	6	the	the	DET
ap-610	465	7	reduced	reduce	VERB
ap-610	465	8	strength	strength	NOUN
ap-610	465	9	,	,	PUNCT
ap-610	465	10	softening	softening	NOUN
ap-610	465	11	starts	start	NOUN
ap-610	465	12	and	and	CCONJ
ap-610	465	13	the	the	DET
ap-610	465	14	stress	stress	NOUN
ap-610	465	15	decreases	decrease	VERB
ap-610	465	16	.	.	PUNCT
ap-610	466	1	consequently	consequently	ADV
ap-610	466	2	,	,	PUNCT
ap-610	466	3	the	the	DET
ap-610	466	4	material	material	NOUN
ap-610	466	5	outside	outside	ADP
ap-610	466	6	the	the	DET
ap-610	466	7	weaker	weak	ADJ
ap-610	466	8	region	region	NOUN
ap-610	466	9	must	must	AUX
ap-610	466	10	unload	unload	VERB
ap-610	466	11	elastically	elastically	ADV
ap-610	466	12	,	,	PUNCT
ap-610	466	13	because	because	SCONJ
ap-610	466	14	its	its	PRON
ap-610	466	15	strength	strength	NOUN
ap-610	466	16	has	have	AUX
ap-610	466	17	not	not	PART
ap-610	466	18	been	be	AUX
ap-610	466	19	exhausted	exhaust	VERB
ap-610	466	20	.	.	PUNCT
ap-610	467	1	this	this	PRON
ap-610	467	2	leads	lead	VERB
ap-610	467	3	to	to	ADP
ap-610	467	4	the	the	DET
ap-610	467	5	conclusion	conclusion	NOUN
ap-610	467	6	that	that	SCONJ
ap-610	467	7	the	the	DET
ap-610	467	8	size	size	NOUN
ap-610	467	9	of	of	ADP
ap-610	467	10	the	the	DET
ap-610	467	11	softening	soften	VERB
ap-610	467	12	region	region	NOUN
ap-610	467	13	can	can	AUX
ap-610	467	14	not	not	PART
ap-610	467	15	exceed	exceed	VERB
ap-610	467	16	the	the	DET
ap-610	467	17	size	size	NOUN
ap-610	467	18	of	of	ADP
ap-610	467	19	the	the	DET
ap-610	467	20	region	region	NOUN
ap-610	467	21	with	with	ADP
ap-610	467	22	minimum	minimum	NOUN
ap-610	467	23	strength	strength	NOUN
ap-610	467	24	.	.	PUNCT
ap-610	468	1	such	such	DET
ap-610	468	2	a	a	DET
ap-610	468	3	region	region	NOUN
ap-610	468	4	can	can	AUX
ap-610	468	5	be	be	AUX
ap-610	468	6	arbitrarily	arbitrarily	ADV
ap-610	468	7	small	small	ADJ
ap-610	468	8	,	,	PUNCT
ap-610	468	9	and	and	CCONJ
ap-610	468	10	the	the	DET
ap-610	468	11	corresponding	correspond	VERB
ap-610	468	12	softening	soften	VERB
ap-610	468	13	©	©	PROPN
ap-610	468	14	czech	czech	PROPN
ap-610	468	15	technical	technical	PROPN
ap-610	468	16	university	university	PROPN
ap-610	468	17	publishing	publishing	NOUN
ap-610	468	18	house	house	NOUN
ap-610	468	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	468	20	29	29	NUM
ap-610	468	21	acta	acta	PROPN
ap-610	468	22	polytechnica	polytechnica	PROPN
ap-610	468	23	vol	vol	NOUN
ap-610	468	24	.	.	PROPN
ap-610	469	1	44	44	NUM
ap-610	470	1	no	no	NOUN
ap-610	470	2	.	.	PUNCT
ap-610	471	1	5–6/2004	5–6/2004	NUM
ap-610	471	2	(	(	PUNCT
ap-610	471	3	a	a	NOUN
ap-610	471	4	)	)	PUNCT
ap-610	471	5	(	(	PUNCT
ap-610	471	6	b	b	X
ap-610	471	7	)	)	PUNCT
ap-610	471	8	fig	fig	NOUN
ap-610	471	9	.	.	PUNCT
ap-610	472	1	8	8	NUM
ap-610	472	2	:	:	PUNCT
ap-610	472	3	(	(	PUNCT
ap-610	472	4	a	a	X
ap-610	472	5	)	)	PUNCT
ap-610	472	6	stress	stress	NOUN
ap-610	472	7	-	-	PUNCT
ap-610	472	8	strain	strain	NOUN
ap-610	472	9	diagram	diagram	NOUN
ap-610	472	10	with	with	ADP
ap-610	472	11	linear	linear	PROPN
ap-610	472	12	softening	softening	NOUN
ap-610	472	13	,	,	PUNCT
ap-610	472	14	(	(	PUNCT
ap-610	472	15	b	b	X
ap-610	472	16	)	)	PUNCT
ap-610	472	17	fan	fan	NOUN
ap-610	472	18	of	of	ADP
ap-610	472	19	possible	possible	ADJ
ap-610	472	20	post	post	ADJ
ap-610	472	21	-	-	ADJ
ap-610	472	22	peak	peak	ADJ
ap-610	472	23	branches	branch	NOUN
ap-610	472	24	of	of	ADP
ap-610	472	25	the	the	DET
ap-610	472	26	load	load	NOUN
ap-610	472	27	-	-	PUNCT
ap-610	472	28	displacement	displacement	ADJ
ap-610	472	29	diagram	diagram	NOUN
ap-610	472	30	branch	branch	NOUN
ap-610	472	31	can	can	AUX
ap-610	472	32	be	be	AUX
ap-610	472	33	arbitrarily	arbitrarily	ADV
ap-610	472	34	close	close	ADJ
ap-610	472	35	to	to	ADP
ap-610	472	36	the	the	DET
ap-610	472	37	elastic	elastic	ADJ
ap-610	472	38	branch	branch	NOUN
ap-610	472	39	of	of	ADP
ap-610	472	40	the	the	DET
ap-610	472	41	load	load	NOUN
ap-610	472	42	-	-	PUNCT
ap-610	472	43	displacement	displacement	NOUN
ap-610	472	44	diagram	diagram	NOUN
ap-610	472	45	.	.	PUNCT
ap-610	473	1	thus	thus	ADV
ap-610	473	2	the	the	DET
ap-610	473	3	standard	standard	ADJ
ap-610	473	4	strain	strain	NOUN
ap-610	473	5	-	-	PUNCT
ap-610	473	6	softening	soften	VERB
ap-610	473	7	continuum	continuum	ADJ
ap-610	473	8	formulation	formulation	NOUN
ap-610	473	9	leads	lead	VERB
ap-610	473	10	to	to	ADP
ap-610	473	11	a	a	DET
ap-610	473	12	solution	solution	NOUN
ap-610	473	13	that	that	PRON
ap-610	473	14	has	have	VERB
ap-610	473	15	several	several	ADJ
ap-610	473	16	pathological	pathological	ADJ
ap-610	473	17	features	feature	NOUN
ap-610	473	18	:	:	PUNCT
ap-610	473	19	(	(	PUNCT
ap-610	473	20	i	i	NOUN
ap-610	473	21	)	)	PUNCT
ap-610	473	22	the	the	DET
ap-610	473	23	softening	soften	VERB
ap-610	473	24	region	region	NOUN
ap-610	473	25	is	be	AUX
ap-610	473	26	infinitely	infinitely	ADV
ap-610	473	27	small;	small;	NOUN
ap-610	473	28	(	(	PUNCT
ap-610	473	29	ii	ii	NOUN
ap-610	473	30	)	)	PUNCT
ap-610	473	31	the	the	DET
ap-610	473	32	load	load	NOUN
ap-610	473	33	-	-	PUNCT
ap-610	473	34	displacement	displacement	ADJ
ap-610	473	35	diagram	diagram	NOUN
ap-610	473	36	always	always	ADV
ap-610	473	37	exhibits	exhibit	VERB
ap-610	473	38	snapback	snapback	NOUN
ap-610	473	39	,	,	PUNCT
ap-610	473	40	independently	independently	ADV
ap-610	473	41	of	of	ADP
ap-610	473	42	the	the	DET
ap-610	473	43	structural	structural	ADJ
ap-610	473	44	size	size	NOUN
ap-610	473	45	and	and	CCONJ
ap-610	473	46	of	of	ADP
ap-610	473	47	the	the	DET
ap-610	473	48	material	material	ADJ
ap-610	473	49	ductility;	ductility;	NOUN
ap-610	473	50	(	(	PUNCT
ap-610	473	51	iii	iii	NOUN
ap-610	473	52	)	)	PUNCT
ap-610	473	53	the	the	DET
ap-610	473	54	total	total	ADJ
ap-610	473	55	amount	amount	NOUN
ap-610	473	56	of	of	ADP
ap-610	473	57	energy	energy	NOUN
ap-610	473	58	dissipated	dissipate	VERB
ap-610	473	59	during	during	ADP
ap-610	473	60	the	the	DET
ap-610	473	61	failure	failure	NOUN
ap-610	473	62	process	process	NOUN
ap-610	473	63	is	be	AUX
ap-610	473	64	zero	zero	NUM
ap-610	473	65	.	.	PUNCT
ap-610	474	1	from	from	ADP
ap-610	474	2	the	the	DET
ap-610	474	3	mathematical	mathematical	ADJ
ap-610	474	4	point	point	NOUN
ap-610	474	5	of	of	ADP
ap-610	474	6	view	view	NOUN
ap-610	474	7	,	,	PUNCT
ap-610	474	8	these	these	DET
ap-610	474	9	annoying	annoying	ADJ
ap-610	474	10	features	feature	NOUN
ap-610	474	11	are	be	AUX
ap-610	474	12	related	relate	VERB
ap-610	474	13	to	to	ADP
ap-610	474	14	the	the	DET
ap-610	474	15	so	so	ADV
ap-610	474	16	-	-	PUNCT
ap-610	474	17	called	call	VERB
ap-610	474	18	loss	loss	NOUN
ap-610	474	19	of	of	ADP
ap-610	474	20	ellipticity	ellipticity	NOUN
ap-610	474	21	of	of	ADP
ap-610	474	22	the	the	DET
ap-610	474	23	governing	govern	VERB
ap-610	474	24	differential	differential	ADJ
ap-610	474	25	equation	equation	NOUN
ap-610	474	26	.	.	PUNCT
ap-610	475	1	in	in	ADP
ap-610	475	2	the	the	DET
ap-610	475	3	present	present	ADJ
ap-610	475	4	one	one	NUM
ap-610	475	5	-	-	PUNCT
ap-610	475	6	dimensional	dimensional	ADJ
ap-610	475	7	setting	setting	NOUN
ap-610	475	8	,	,	PUNCT
ap-610	475	9	loss	loss	NOUN
ap-610	475	10	of	of	ADP
ap-610	475	11	ellipticity	ellipticity	NOUN
ap-610	475	12	occurs	occur	VERB
ap-610	475	13	when	when	SCONJ
ap-610	475	14	the	the	DET
ap-610	475	15	tangent	tangent	NOUN
ap-610	475	16	modulus	modulus	NOUN
ap-610	475	17	ceases	cease	VERB
ap-610	475	18	to	to	PART
ap-610	475	19	be	be	AUX
ap-610	475	20	positive	positive	ADJ
ap-610	475	21	,	,	PUNCT
ap-610	475	22	i.e.	i.e.	X
ap-610	475	23	,	,	PUNCT
ap-610	475	24	it	it	PRON
ap-610	475	25	coincides	coincide	VERB
ap-610	475	26	with	with	ADP
ap-610	475	27	the	the	DET
ap-610	475	28	onset	onset	NOUN
ap-610	475	29	of	of	ADP
ap-610	475	30	softening	soften	VERB
ap-610	475	31	(	(	PUNCT
ap-610	475	32	this	this	PRON
ap-610	475	33	is	be	AUX
ap-610	475	34	not	not	PART
ap-610	475	35	always	always	ADV
ap-610	475	36	the	the	DET
ap-610	475	37	case	case	NOUN
ap-610	475	38	in	in	ADP
ap-610	475	39	multiple	multiple	ADJ
ap-610	475	40	dimensions	dimension	NOUN
ap-610	475	41	)	)	PUNCT
ap-610	475	42	.	.	PUNCT
ap-610	476	1	the	the	DET
ap-610	476	2	boundary	boundary	ADJ
ap-610	476	3	value	value	NOUN
ap-610	476	4	problem	problem	NOUN
ap-610	476	5	becomes	become	VERB
ap-610	476	6	ill	ill	ADV
ap-610	476	7	-	-	PUNCT
ap-610	476	8	posed	pose	VERB
ap-610	476	9	,	,	PUNCT
ap-610	476	10	i.e.	i.e.	X
ap-610	476	11	,	,	PUNCT
ap-610	476	12	it	it	PRON
ap-610	476	13	does	do	AUX
ap-610	476	14	not	not	PART
ap-610	476	15	have	have	VERB
ap-610	476	16	a	a	DET
ap-610	476	17	unique	unique	ADJ
ap-610	476	18	solution	solution	NOUN
ap-610	476	19	with	with	ADP
ap-610	476	20	continuous	continuous	ADJ
ap-610	476	21	dependence	dependence	NOUN
ap-610	476	22	on	on	ADP
ap-610	476	23	the	the	DET
ap-610	476	24	given	give	VERB
ap-610	476	25	data	datum	NOUN
ap-610	476	26	.	.	PUNCT
ap-610	477	1	from	from	ADP
ap-610	477	2	the	the	DET
ap-610	477	3	numerical	numerical	ADJ
ap-610	477	4	point	point	NOUN
ap-610	477	5	of	of	ADP
ap-610	477	6	view	view	NOUN
ap-610	477	7	,	,	PUNCT
ap-610	477	8	ill	ill	ADJ
ap-610	477	9	-	-	PUNCT
ap-610	477	10	posedness	posedness	NOUN
ap-610	477	11	is	be	AUX
ap-610	477	12	manifested	manifest	VERB
ap-610	477	13	by	by	ADP
ap-610	477	14	pathological	pathological	ADJ
ap-610	477	15	sensitivity	sensitivity	NOUN
ap-610	477	16	of	of	ADP
ap-610	477	17	the	the	DET
ap-610	477	18	results	result	NOUN
ap-610	477	19	to	to	ADP
ap-610	477	20	the	the	DET
ap-610	477	21	size	size	NOUN
ap-610	477	22	of	of	ADP
ap-610	477	23	finite	finite	ADJ
ap-610	477	24	elements	element	NOUN
ap-610	477	25	.	.	PUNCT
ap-610	478	1	for	for	ADP
ap-610	478	2	example	example	NOUN
ap-610	478	3	,	,	PUNCT
ap-610	478	4	suppose	suppose	VERB
ap-610	478	5	that	that	SCONJ
ap-610	478	6	the	the	DET
ap-610	478	7	bar	bar	NOUN
ap-610	478	8	is	be	AUX
ap-610	478	9	discretized	discretize	VERB
ap-610	478	10	by	by	ADP
ap-610	478	11	ne	ne	X
ap-610	478	12	twonode	twonode	NOUN
ap-610	478	13	elements	element	NOUN
ap-610	478	14	with	with	ADP
ap-610	478	15	linear	linear	ADJ
ap-610	478	16	displacement	displacement	ADJ
ap-610	478	17	interpolation	interpolation	NOUN
ap-610	478	18	.	.	PUNCT
ap-610	479	1	if	if	SCONJ
ap-610	479	2	the	the	DET
ap-610	479	3	numerical	numerical	ADJ
ap-610	479	4	algorithm	algorithm	NOUN
ap-610	479	5	properly	properly	ADV
ap-610	479	6	captures	capture	VERB
ap-610	479	7	the	the	DET
ap-610	479	8	most	most	ADV
ap-610	479	9	localized	localized	ADJ
ap-610	479	10	solution	solution	NOUN
ap-610	479	11	,	,	PUNCT
ap-610	479	12	the	the	DET
ap-610	479	13	softening	soften	VERB
ap-610	479	14	region	region	NOUN
ap-610	479	15	extends	extend	VERB
ap-610	479	16	over	over	ADP
ap-610	479	17	one	one	NUM
ap-610	479	18	element	element	NOUN
ap-610	479	19	,	,	PUNCT
ap-610	479	20	and	and	CCONJ
ap-610	479	21	we	we	PRON
ap-610	479	22	have	have	VERB
ap-610	479	23	l	l	NOUN
ap-610	479	24	l	l	X
ap-610	479	25	ns	ns	X
ap-610	479	26	e	e	PROPN
ap-610	479	27	�	�	PROPN
ap-610	479	28	.	.	PUNCT
ap-610	480	1	the	the	DET
ap-610	480	2	slope	slope	NOUN
ap-610	480	3	of	of	ADP
ap-610	480	4	the	the	DET
ap-610	480	5	post	post	ADJ
ap-610	480	6	-	-	ADJ
ap-610	480	7	peak	peak	ADJ
ap-610	480	8	branch	branch	NOUN
ap-610	480	9	therefore	therefore	ADV
ap-610	480	10	strongly	strongly	ADV
ap-610	480	11	depends	depend	VERB
ap-610	480	12	on	on	ADP
ap-610	480	13	the	the	DET
ap-610	480	14	number	number	NOUN
ap-610	480	15	of	of	ADP
ap-610	480	16	elements	element	NOUN
ap-610	480	17	,	,	PUNCT
ap-610	480	18	and	and	CCONJ
ap-610	480	19	it	it	PRON
ap-610	480	20	approaches	approach	VERB
ap-610	480	21	the	the	DET
ap-610	480	22	initial	initial	ADJ
ap-610	480	23	elastic	elastic	ADJ
ap-610	480	24	slope	slope	NOUN
ap-610	480	25	as	as	SCONJ
ap-610	480	26	the	the	DET
ap-610	480	27	number	number	NOUN
ap-610	480	28	of	of	ADP
ap-610	480	29	elements	element	NOUN
ap-610	480	30	tends	tend	VERB
ap-610	480	31	to	to	ADP
ap-610	480	32	infinity;	infinity;	NOUN
ap-610	480	33	see	see	VERB
ap-610	480	34	fig	fig	NOUN
ap-610	480	35	.	.	PUNCT
ap-610	481	1	9a	9a	NOUN
ap-610	481	2	,	,	PUNCT
ap-610	481	3	constructed	construct	VERB
ap-610	481	4	for	for	ADP
ap-610	481	5	a	a	DET
ap-610	481	6	linear	linear	ADJ
ap-610	481	7	softening	soften	VERB
ap-610	481	8	law	law	NOUN
ap-610	481	9	with	with	ADP
ap-610	481	10	�	�	PROPN
ap-610	481	11	�	�	PROPN
ap-610	481	12	f	f	PROPN
ap-610	481	13	0	0	NUM
ap-610	481	14	20	20	NUM
ap-610	481	15	�	�	PROPN
ap-610	481	16	.	.	PUNCT
ap-610	482	1	the	the	DET
ap-610	482	2	strain	strain	NOUN
ap-610	482	3	profiles	profile	NOUN
ap-610	482	4	at	at	ADP
ap-610	482	5	u	u	PROPN
ap-610	482	6	l	l	NOUN
ap-610	482	7	�	�	PROPN
ap-610	482	8	2	2	NUM
ap-610	482	9	0	0	NUM
ap-610	482	10	�	�	PROPN
ap-610	482	11	for	for	ADP
ap-610	482	12	various	various	ADJ
ap-610	482	13	mesh	mesh	NOUN
ap-610	482	14	refinements	refinement	NOUN
ap-610	482	15	are	be	AUX
ap-610	482	16	plotted	plot	VERB
ap-610	482	17	in	in	ADP
ap-610	482	18	fig	fig	NOUN
ap-610	482	19	.	.	PUNCT
ap-610	483	1	9b	9b	NOUN
ap-610	483	2	(	(	PUNCT
ap-610	483	3	under	under	ADP
ap-610	483	4	the	the	DET
ap-610	483	5	assumption	assumption	NOUN
ap-610	483	6	that	that	SCONJ
ap-610	483	7	the	the	DET
ap-610	483	8	weakest	weak	ADJ
ap-610	483	9	spot	spot	NOUN
ap-610	483	10	is	be	AUX
ap-610	483	11	located	locate	VERB
ap-610	483	12	at	at	ADP
ap-610	483	13	the	the	DET
ap-610	483	14	center	center	NOUN
ap-610	483	15	of	of	ADP
ap-610	483	16	the	the	DET
ap-610	483	17	bar	bar	NOUN
ap-610	483	18	)	)	PUNCT
ap-610	483	19	.	.	PUNCT
ap-610	484	1	in	in	ADP
ap-610	484	2	the	the	DET
ap-610	484	3	limit	limit	NOUN
ap-610	484	4	,	,	PUNCT
ap-610	484	5	the	the	DET
ap-610	484	6	profiles	profile	NOUN
ap-610	484	7	tend	tend	VERB
ap-610	484	8	to	to	ADP
ap-610	484	9	2	2	NUM
ap-610	484	10	20l	20l	NOUN
ap-610	484	11	x	x	SYM
ap-610	484	12	l	l	X
ap-610	484	13	�	�	PROPN
ap-610	484	14	�	�	PROPN
ap-610	484	15	(	(	PUNCT
ap-610	484	16	)	)	PUNCT
ap-610	484	17	�	�	PROPN
ap-610	484	18	where	where	SCONJ
ap-610	484	19	�	�	PROPN
ap-610	484	20	denotes	denote	VERB
ap-610	484	21	the	the	DET
ap-610	484	22	dirac	dirac	NOUN
ap-610	484	23	distribution	distribution	NOUN
ap-610	484	24	.	.	PUNCT
ap-610	485	1	the	the	DET
ap-610	485	2	limit	limit	NOUN
ap-610	485	3	solution	solution	NOUN
ap-610	485	4	represents	represent	VERB
ap-610	485	5	a	a	DET
ap-610	485	6	displacement	displacement	ADJ
ap-610	485	7	jump	jump	NOUN
ap-610	485	8	at	at	ADP
ap-610	485	9	the	the	DET
ap-610	485	10	center	center	NOUN
ap-610	485	11	,	,	PUNCT
ap-610	485	12	with	with	ADP
ap-610	485	13	zero	zero	NUM
ap-610	485	14	strain	strain	NOUN
ap-610	485	15	everywhere	everywhere	ADV
ap-610	485	16	else	else	ADV
ap-610	485	17	.	.	PUNCT
ap-610	486	1	4.2	4.2	NUM
ap-610	486	2	nonlocal	nonlocal	ADJ
ap-610	486	3	formulation	formulation	NOUN
ap-610	486	4	serving	serve	VERB
ap-610	486	5	as	as	ADP
ap-610	486	6	localization	localization	NOUN
ap-610	486	7	limiter	limiter	NOUN
ap-610	486	8	in	in	ADP
ap-610	486	9	real	real	ADJ
ap-610	486	10	materials	material	NOUN
ap-610	486	11	,	,	PUNCT
ap-610	486	12	inelastic	inelastic	ADJ
ap-610	486	13	processes	process	NOUN
ap-610	486	14	typically	typically	ADV
ap-610	486	15	localize	localize	VERB
ap-610	486	16	in	in	ADP
ap-610	486	17	narrow	narrow	ADJ
ap-610	486	18	bands	band	NOUN
ap-610	486	19	that	that	PRON
ap-610	486	20	initially	initially	ADV
ap-610	486	21	have	have	VERB
ap-610	486	22	a	a	DET
ap-610	486	23	small	small	ADJ
ap-610	486	24	but	but	CCONJ
ap-610	486	25	nonzero	nonzero	ADJ
ap-610	486	26	width	width	PROPN
ap-610	486	27	.	.	PUNCT
ap-610	487	1	propagation	propagation	NOUN
ap-610	487	2	and	and	CCONJ
ap-610	487	3	coalescence	coalescence	NOUN
ap-610	487	4	of	of	ADP
ap-610	487	5	microdefects	microdefect	NOUN
ap-610	487	6	in	in	ADP
ap-610	487	7	the	the	DET
ap-610	487	8	localization	localization	NOUN
ap-610	487	9	band	band	NOUN
ap-610	487	10	can	can	AUX
ap-610	487	11	eventually	eventually	ADV
ap-610	487	12	lead	lead	VERB
ap-610	487	13	to	to	ADP
ap-610	487	14	the	the	DET
ap-610	487	15	formation	formation	NOUN
ap-610	487	16	of	of	ADP
ap-610	487	17	a	a	DET
ap-610	487	18	displacement	displacement	ADJ
ap-610	487	19	discontinuity	discontinuity	NOUN
ap-610	487	20	,	,	PUNCT
ap-610	487	21	e.g.	e.g.	ADV
ap-610	487	22	,	,	PUNCT
ap-610	487	23	of	of	ADP
ap-610	487	24	a	a	DET
ap-610	487	25	macroscopic	macroscopic	ADJ
ap-610	487	26	stress	stress	NOUN
ap-610	487	27	-	-	PUNCT
ap-610	487	28	free	free	ADJ
ap-610	487	29	crack	crack	NOUN
ap-610	487	30	or	or	CCONJ
ap-610	487	31	a	a	DET
ap-610	487	32	sharp	sharp	ADJ
ap-610	487	33	slip	slip	NOUN
ap-610	487	34	line	line	NOUN
ap-610	487	35	.	.	PUNCT
ap-610	488	1	the	the	DET
ap-610	488	2	initial	initial	ADJ
ap-610	488	3	thickness	thickness	NOUN
ap-610	488	4	of	of	ADP
ap-610	488	5	the	the	DET
ap-610	488	6	localization	localization	NOUN
ap-610	488	7	band	band	NOUN
ap-610	488	8	depends	depend	VERB
ap-610	488	9	on	on	ADP
ap-610	488	10	the	the	DET
ap-610	488	11	material	material	NOUN
ap-610	488	12	microstructure	microstructure	NOUN
ap-610	488	13	and	and	CCONJ
ap-610	488	14	is	be	AUX
ap-610	488	15	usually	usually	ADV
ap-610	488	16	of	of	ADP
ap-610	488	17	the	the	DET
ap-610	488	18	same	same	ADJ
ap-610	488	19	order	order	NOUN
ap-610	488	20	of	of	ADP
ap-610	488	21	magnitude	magnitude	NOUN
ap-610	488	22	as	as	ADP
ap-610	488	23	the	the	DET
ap-610	488	24	characteristic	characteristic	ADJ
ap-610	488	25	material	material	NOUN
ap-610	488	26	length	length	NOUN
ap-610	488	27	,	,	PUNCT
ap-610	488	28	determined	determine	VERB
ap-610	488	29	by	by	ADP
ap-610	488	30	the	the	DET
ap-610	488	31	size	size	NOUN
ap-610	488	32	or	or	CCONJ
ap-610	488	33	spacing	spacing	NOUN
ap-610	488	34	of	of	ADP
ap-610	488	35	dominant	dominant	ADJ
ap-610	488	36	heterogeneities	heterogeneity	NOUN
ap-610	488	37	.	.	PUNCT
ap-610	489	1	therefore	therefore	ADV
ap-610	489	2	,	,	PUNCT
ap-610	489	3	it	it	PRON
ap-610	489	4	is	be	AUX
ap-610	489	5	natural	natural	ADJ
ap-610	489	6	to	to	PART
ap-610	489	7	expect	expect	VERB
ap-610	489	8	that	that	SCONJ
ap-610	489	9	enriched	enrich	VERB
ap-610	489	10	continuum	continuum	ADJ
ap-610	489	11	theories	theory	NOUN
ap-610	489	12	can	can	AUX
ap-610	489	13	better	well	ADV
ap-610	489	14	reflect	reflect	VERB
ap-610	489	15	the	the	DET
ap-610	489	16	actual	actual	ADJ
ap-610	489	17	deformation	deformation	NOUN
ap-610	489	18	and	and	CCONJ
ap-610	489	19	failure	failure	NOUN
ap-610	489	20	processes	process	NOUN
ap-610	489	21	and	and	CCONJ
ap-610	489	22	restore	restore	VERB
ap-610	489	23	mathematical	mathematical	ADJ
ap-610	489	24	well	well	ADJ
ap-610	489	25	-	-	PUNCT
ap-610	489	26	posedness	posedness	NOUN
ap-610	489	27	of	of	ADP
ap-610	489	28	the	the	DET
ap-610	489	29	boundary	boundary	ADJ
ap-610	489	30	value	value	NOUN
ap-610	489	31	problem	problem	NOUN
ap-610	489	32	.	.	PUNCT
ap-610	490	1	indeed	indeed	ADV
ap-610	490	2	,	,	PUNCT
ap-610	490	3	when	when	SCONJ
ap-610	490	4	properly	properly	ADV
ap-610	490	5	formulated	formulate	VERB
ap-610	490	6	,	,	PUNCT
ap-610	490	7	nonlocal	nonlocal	ADJ
ap-610	490	8	or	or	CCONJ
ap-610	490	9	gradient	gradient	ADJ
ap-610	490	10	enrichments	enrichment	NOUN
ap-610	490	11	regularize	regularize	VERB
ap-610	490	12	the	the	DET
ap-610	490	13	problem	problem	NOUN
ap-610	490	14	in	in	ADP
ap-610	490	15	the	the	DET
ap-610	490	16	sense	sense	NOUN
ap-610	490	17	that	that	SCONJ
ap-610	490	18	the	the	DET
ap-610	490	19	resulting	result	VERB
ap-610	490	20	strain	strain	NOUN
ap-610	490	21	field	field	NOUN
ap-610	490	22	is	be	AUX
ap-610	490	23	highly	highly	ADV
ap-610	490	24	concentrated	concentrated	ADJ
ap-610	490	25	in	in	ADP
ap-610	490	26	certain	certain	ADJ
ap-610	490	27	narrow	narrow	ADJ
ap-610	490	28	zones	zone	NOUN
ap-610	490	29	but	but	CCONJ
ap-610	490	30	remains	remain	VERB
ap-610	490	31	continuous	continuous	ADJ
ap-610	490	32	.	.	PUNCT
ap-610	491	1	the	the	DET
ap-610	491	2	corresponding	corresponding	ADJ
ap-610	491	3	numerical	numerical	ADJ
ap-610	491	4	solutions	solution	NOUN
ap-610	491	5	converge	converge	VERB
ap-610	491	6	upon	upon	SCONJ
ap-610	491	7	mesh	mesh	NOUN
ap-610	491	8	refinement	refinement	NOUN
ap-610	491	9	to	to	ADP
ap-610	491	10	a	a	DET
ap-610	491	11	physically	physically	ADV
ap-610	491	12	meaningful	meaningful	ADJ
ap-610	491	13	limit	limit	NOUN
ap-610	491	14	,	,	PUNCT
ap-610	491	15	and	and	CCONJ
ap-610	491	16	the	the	DET
ap-610	491	17	numerical	numerical	ADJ
ap-610	491	18	results	result	NOUN
ap-610	491	19	do	do	AUX
ap-610	491	20	not	not	PART
ap-610	491	21	suffer	suffer	VERB
ap-610	491	22	by	by	ADP
ap-610	491	23	pathological	pathological	ADJ
ap-610	491	24	sensitivity	sensitivity	NOUN
ap-610	491	25	to	to	ADP
ap-610	491	26	the	the	DET
ap-610	491	27	discretization	discretization	NOUN
ap-610	491	28	.	.	PUNCT
ap-610	492	1	enrichments	enrichment	NOUN
ap-610	492	2	that	that	PRON
ap-610	492	3	prevent	prevent	VERB
ap-610	492	4	localization	localization	NOUN
ap-610	492	5	of	of	ADP
ap-610	492	6	strain	strain	NOUN
ap-610	492	7	into	into	ADP
ap-610	492	8	arbitrarily	arbitrarily	ADV
ap-610	492	9	small	small	ADJ
ap-610	492	10	regions	region	NOUN
ap-610	492	11	are	be	AUX
ap-610	492	12	called	call	VERB
ap-610	492	13	localization	localization	NOUN
ap-610	492	14	limiters	limiter	NOUN
ap-610	492	15	.	.	PUNCT
ap-610	493	1	nonlocal	nonlocal	ADJ
ap-610	493	2	material	material	NOUN
ap-610	493	3	models	model	NOUN
ap-610	493	4	of	of	ADP
ap-610	493	5	the	the	DET
ap-610	493	6	integral	integral	ADJ
ap-610	493	7	type	type	NOUN
ap-610	493	8	were	be	AUX
ap-610	493	9	first	first	ADV
ap-610	493	10	exploited	exploit	VERB
ap-610	493	11	as	as	ADP
ap-610	493	12	localization	localization	NOUN
ap-610	493	13	limiters	limiter	NOUN
ap-610	493	14	in	in	ADP
ap-610	493	15	the	the	DET
ap-610	493	16	1980s	1980s	NUM
ap-610	493	17	.	.	PUNCT
ap-610	494	1	after	after	ADP
ap-610	494	2	some	some	DET
ap-610	494	3	preliminary	preliminary	ADJ
ap-610	494	4	formulations	formulation	NOUN
ap-610	494	5	exploiting	exploit	VERB
ap-610	494	6	the	the	DET
ap-610	494	7	concept	concept	NOUN
ap-610	494	8	of	of	ADP
ap-610	494	9	an	an	DET
ap-610	494	10	imbricate	imbricate	ADJ
ap-610	494	11	continuum	continuum	X
ap-610	494	12	(	(	PUNCT
ap-610	494	13	bažant	bažant	PROPN
ap-610	494	14	,	,	PUNCT
ap-610	494	15	belytschko	belytschko	PROPN
ap-610	494	16	and	and	CCONJ
ap-610	494	17	chang	chang	PROPN
ap-610	494	18	,	,	PUNCT
ap-610	494	19	1984	1984	NUM
ap-610	494	20	)	)	PUNCT
ap-610	494	21	,	,	PUNCT
ap-610	494	22	the	the	DET
ap-610	494	23	nonlocal	nonlocal	ADJ
ap-610	494	24	damage	damage	NOUN
ap-610	494	25	theory	theory	NOUN
ap-610	494	26	emerged	emerge	VERB
ap-610	494	27	(	(	PUNCT
ap-610	494	28	pijaudier	pijaudier	NOUN
ap-610	494	29	-	-	PUNCT
ap-610	494	30	cabot	cabot	PROPN
ap-610	494	31	and	and	CCONJ
ap-610	494	32	bažant	bažant	NOUN
ap-610	494	33	,	,	PUNCT
ap-610	494	34	1987	1987	NUM
ap-610	494	35	)	)	PUNCT
ap-610	494	36	.	.	PUNCT
ap-610	495	1	nonlocal	nonlocal	ADJ
ap-610	495	2	formulations	formulation	NOUN
ap-610	495	3	were	be	AUX
ap-610	495	4	then	then	ADV
ap-610	495	5	developed	develop	VERB
ap-610	495	6	for	for	ADP
ap-610	495	7	a	a	DET
ap-610	495	8	number	number	NOUN
ap-610	495	9	of	of	ADP
ap-610	495	10	constitutive	constitutive	ADJ
ap-610	495	11	theories	theory	NOUN
ap-610	495	12	,	,	PUNCT
ap-610	495	13	including	include	VERB
ap-610	495	14	softening	soften	VERB
ap-610	495	15	plasticity	plasticity	NOUN
ap-610	495	16	,	,	PUNCT
ap-610	495	17	smeared	smear	VERB
ap-610	495	18	cracking	cracking	NOUN
ap-610	495	19	,	,	PUNCT
ap-610	495	20	microplane	microplane	NOUN
ap-610	495	21	models	model	NOUN
ap-610	495	22	,	,	PUNCT
ap-610	495	23	etc	etc	X
ap-610	495	24	.	.	X
ap-610	495	25	for	for	ADP
ap-610	495	26	a	a	DET
ap-610	495	27	list	list	NOUN
ap-610	495	28	of	of	ADP
ap-610	495	29	references	reference	NOUN
ap-610	495	30	,	,	PUNCT
ap-610	495	31	see	see	VERB
ap-610	495	32	e.g.	e.g.	ADV
ap-610	495	33	bažant	bažant	NOUN
ap-610	495	34	and	and	CCONJ
ap-610	495	35	jirásek	jirásek	NOUN
ap-610	495	36	(	(	PUNCT
ap-610	495	37	2002	2002	NUM
ap-610	495	38	)	)	PUNCT
ap-610	495	39	or	or	CCONJ
ap-610	495	40	chapter	chapter	NOUN
ap-610	495	41	26	26	NUM
ap-610	495	42	in	in	ADP
ap-610	495	43	jirásek	jirásek	NOUN
ap-610	495	44	and	and	CCONJ
ap-610	495	45	bažant	bažant	ADJ
ap-610	495	46	(	(	PUNCT
ap-610	495	47	2002	2002	NUM
ap-610	495	48	)	)	PUNCT
ap-610	495	49	.	.	PUNCT
ap-610	496	1	generally	generally	ADV
ap-610	496	2	speaking	speak	VERB
ap-610	496	3	,	,	PUNCT
ap-610	496	4	the	the	DET
ap-610	496	5	nonlocal	nonlocal	ADJ
ap-610	496	6	approach	approach	NOUN
ap-610	496	7	consists	consist	VERB
ap-610	496	8	in	in	ADP
ap-610	496	9	replacing	replace	VERB
ap-610	496	10	a	a	DET
ap-610	496	11	certain	certain	ADJ
ap-610	496	12	variable	variable	NOUN
ap-610	496	13	by	by	ADP
ap-610	496	14	its	its	PRON
ap-610	496	15	nonlocal	nonlocal	ADJ
ap-610	496	16	counterpart	counterpart	NOUN
ap-610	496	17	obtained	obtain	VERB
ap-610	496	18	by	by	ADP
ap-610	496	19	weighted	weight	VERB
ap-610	496	20	averaging	average	VERB
ap-610	496	21	over	over	ADP
ap-610	496	22	a	a	DET
ap-610	496	23	spatial	spatial	ADJ
ap-610	496	24	neighborhood	neighborhood	NOUN
ap-610	496	25	of	of	ADP
ap-610	496	26	each	each	DET
ap-610	496	27	point	point	NOUN
ap-610	496	28	under	under	ADP
ap-610	496	29	consideration	consideration	NOUN
ap-610	496	30	.	.	PUNCT
ap-610	497	1	in	in	ADP
ap-610	497	2	nonlocal	nonlocal	ADJ
ap-610	497	3	elasticity	elasticity	NOUN
ap-610	497	4	,	,	PUNCT
ap-610	497	5	the	the	DET
ap-610	497	6	averaged	average	VERB
ap-610	497	7	quantity	quantity	NOUN
ap-610	497	8	is	be	AUX
ap-610	497	9	usually	usually	ADV
ap-610	497	10	the	the	DET
ap-610	497	11	strain	strain	NOUN
ap-610	497	12	.	.	PUNCT
ap-610	498	1	nonlocal	nonlocal	ADJ
ap-610	498	2	elastic	elastic	ADJ
ap-610	498	3	models	model	NOUN
ap-610	498	4	can	can	AUX
ap-610	498	5	correctly	correctly	ADV
ap-610	498	6	reflect	reflect	VERB
ap-610	498	7	the	the	DET
ap-610	498	8	experimentally	experimentally	ADV
ap-610	498	9	observed	observe	VERB
ap-610	498	10	dispersion	dispersion	NOUN
ap-610	498	11	of	of	ADP
ap-610	498	12	short	short	ADJ
ap-610	498	13	elastic	elastic	ADJ
ap-610	498	14	waves	wave	NOUN
ap-610	498	15	.	.	PUNCT
ap-610	499	1	however	however	ADV
ap-610	499	2	,	,	PUNCT
ap-610	499	3	in	in	ADP
ap-610	499	4	typical	typical	ADJ
ap-610	499	5	structural	structural	ADJ
ap-610	499	6	applications	application	NOUN
ap-610	499	7	,	,	PUNCT
ap-610	499	8	the	the	DET
ap-610	499	9	strain	strain	NOUN
ap-610	499	10	in	in	ADP
ap-610	499	11	the	the	DET
ap-610	499	12	elastic	elastic	ADJ
ap-610	499	13	regime	regime	NOUN
ap-610	499	14	remains	remains	AUX
ap-610	499	15	relatively	relatively	ADV
ap-610	499	16	smoothly	smoothly	ADV
ap-610	499	17	distributed	distribute	VERB
ap-610	499	18	(	(	PUNCT
ap-610	499	19	with	with	ADP
ap-610	499	20	the	the	DET
ap-610	499	21	exception	exception	NOUN
ap-610	499	22	of	of	ADP
ap-610	499	23	stress	stress	ADJ
ap-610	499	24	concentrations	concentration	NOUN
ap-610	499	25	and	and	CCONJ
ap-610	499	26	singularities	singularity	NOUN
ap-610	499	27	around	around	ADP
ap-610	499	28	specific	specific	ADJ
ap-610	499	29	points	point	NOUN
ap-610	499	30	,	,	PUNCT
ap-610	499	31	e.g.	e.g.	ADV
ap-610	499	32	,	,	PUNCT
ap-610	499	33	tips	tip	NOUN
ap-610	499	34	of	of	ADP
ap-610	499	35	pre	pre	ADJ
ap-610	499	36	-	-	ADJ
ap-610	499	37	existing	exist	VERB
ap-610	499	38	sharp	sharp	ADJ
ap-610	499	39	cracks	crack	NOUN
ap-610	499	40	)	)	PUNCT
ap-610	499	41	.	.	PUNCT
ap-610	500	1	steep	steep	ADJ
ap-610	500	2	strain	strain	NOUN
ap-610	500	3	gradients	gradient	NOUN
ap-610	500	4	appear	appear	VERB
ap-610	500	5	only	only	ADV
ap-610	500	6	after	after	ADP
ap-610	500	7	the	the	DET
ap-610	500	8	onset	onset	NOUN
ap-610	500	9	of	of	ADP
ap-610	500	10	localization	localization	NOUN
ap-610	500	11	and	and	CCONJ
ap-610	500	12	are	be	AUX
ap-610	500	13	accompanied	accompany	VERB
ap-610	500	14	by	by	ADP
ap-610	500	15	highly	highly	ADV
ap-610	500	16	nonuniform	nonuniform	ADJ
ap-610	500	17	distribution	distribution	NOUN
ap-610	500	18	of	of	ADP
ap-610	500	19	damage	damage	NOUN
ap-610	500	20	.	.	PUNCT
ap-610	501	1	therefore	therefore	ADV
ap-610	501	2	,	,	PUNCT
ap-610	501	3	most	most	ADJ
ap-610	501	4	nonlocal	nonlocal	ADJ
ap-610	501	5	models	model	NOUN
ap-610	501	6	serving	serve	VERB
ap-610	501	7	as	as	SCONJ
ap-610	501	8	localization	localization	NOUN
ap-610	501	9	limiters	limiter	NOUN
ap-610	501	10	reduce	reduce	VERB
ap-610	501	11	to	to	ADP
ap-610	501	12	standard	standard	ADJ
ap-610	501	13	local	local	ADJ
ap-610	501	14	elasticity	elasticity	NOUN
ap-610	501	15	at	at	ADP
ap-610	501	16	low	low	ADJ
ap-610	501	17	strain	strain	NOUN
ap-610	501	18	levels	level	NOUN
ap-610	501	19	,	,	PUNCT
ap-610	501	20	and	and	CCONJ
ap-610	501	21	the	the	DET
ap-610	501	22	nonlocal	nonlocal	ADJ
ap-610	501	23	effects	effect	NOUN
ap-610	501	24	are	be	AUX
ap-610	501	25	considered	consider	VERB
ap-610	501	26	only	only	ADV
ap-610	501	27	in	in	ADP
ap-610	501	28	the	the	DET
ap-610	501	29	inelastic	inelastic	ADJ
ap-610	501	30	regime	regime	NOUN
ap-610	501	31	.	.	PUNCT
ap-610	502	1	for	for	ADP
ap-610	502	2	instance	instance	NOUN
ap-610	502	3	,	,	PUNCT
ap-610	502	4	one	one	NUM
ap-610	502	5	widely	widely	ADV
ap-610	502	6	used	use	VERB
ap-610	502	7	nonlocal	nonlocal	ADJ
ap-610	502	8	damage	damage	NOUN
ap-610	502	9	formulation	formulation	NOUN
ap-610	502	10	replaces	replace	VERB
ap-610	502	11	the	the	DET
ap-610	502	12	strain	strain	NOUN
ap-610	502	13	in	in	ADP
ap-610	502	14	the	the	DET
ap-610	502	15	loading	loading	NOUN
ap-610	502	16	-	-	PUNCT
ap-610	502	17	unloading	unloading	NOUN
ap-610	502	18	conditions	condition	NOUN
ap-610	502	19	(	(	PUNCT
ap-610	502	20	79	79	NUM
ap-610	502	21	)	)	PUNCT
ap-610	502	22	by	by	ADP
ap-610	502	23	its	its	PRON
ap-610	502	24	nonlocal	nonlocal	ADJ
ap-610	502	25	average	average	NOUN
ap-610	502	26	,	,	PUNCT
ap-610	502	27	�	�	PROPN
ap-610	502	28	,	,	PUNCT
ap-610	502	29	while	while	SCONJ
ap-610	502	30	strain	strain	ADJ
ap-610	502	31	entering	enter	VERB
ap-610	502	32	the	the	DET
ap-610	502	33	stress	stress	NOUN
ap-610	502	34	-	-	PUNCT
ap-610	502	35	strain	strain	NOUN
ap-610	502	36	law	law	NOUN
ap-610	502	37	(	(	PUNCT
ap-610	502	38	77	77	NUM
ap-610	502	39	)	)	PUNCT
ap-610	502	40	is	be	AUX
ap-610	502	41	still	still	ADV
ap-610	502	42	considered	consider	VERB
ap-610	502	43	as	as	ADP
ap-610	502	44	local	local	ADJ
ap-610	502	45	.	.	PUNCT
ap-610	503	1	according	accord	VERB
ap-610	503	2	to	to	ADP
ap-610	503	3	the	the	DET
ap-610	503	4	modified	modify	VERB
ap-610	503	5	loading	loading	NOUN
ap-610	503	6	-	-	PUNCT
ap-610	503	7	unloading	unloading	NOUN
ap-610	503	8	conditions	condition	NOUN
ap-610	503	9	,	,	PUNCT
ap-610	503	10	�	�	PROPN
ap-610	503	11	,	,	PUNCT
ap-610	503	12	,	,	PUNCT
ap-610	503	13	(	(	PUNCT
ap-610	503	14	)	)	PUNCT
ap-610	503	15	�	�	PROPN
ap-610	503	16	�	�	PROPN
ap-610	503	17	�	�	PROPN
ap-610	503	18	�	�	PROPN
ap-610	503	19	�	�	PROPN
ap-610	503	20	�	�	PROPN
ap-610	503	21	�	�	PROPN
ap-610	503	22	�	�	PROPN
ap-610	503	23	�	�	PROPN
ap-610	503	24	�	�	PROPN
ap-610	503	25	�	�	PROPN
ap-610	503	26	�	�	PROPN
ap-610	503	27	0	0	NUM
ap-610	503	28	0	0	NUM
ap-610	503	29	0	0	NUM
ap-610	503	30	,	,	PUNCT
ap-610	503	31	(	(	PUNCT
ap-610	503	32	80	80	NUM
ap-610	503	33	)	)	PUNCT
ap-610	503	34	30	30	NUM
ap-610	503	35	©	©	PROPN
ap-610	503	36	czech	czech	PROPN
ap-610	503	37	technical	technical	PROPN
ap-610	503	38	university	university	PROPN
ap-610	503	39	publishing	publishing	NOUN
ap-610	503	40	house	house	NOUN
ap-610	503	41	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	503	42	acta	acta	PROPN
ap-610	503	43	polytechnica	polytechnica	PROPN
ap-610	503	44	vol	vol	NOUN
ap-610	503	45	.	.	PROPN
ap-610	504	1	44	44	NUM
ap-610	504	2	no	no	NOUN
ap-610	504	3	.	.	PUNCT
ap-610	505	1	5–6/2004	5–6/2004	NUM
ap-610	505	2	(	(	PUNCT
ap-610	505	3	a	a	NOUN
ap-610	505	4	)	)	PUNCT
ap-610	505	5	(	(	PUNCT
ap-610	505	6	b	b	X
ap-610	505	7	)	)	PUNCT
ap-610	505	8	fig	fig	NOUN
ap-610	505	9	.	.	PUNCT
ap-610	506	1	9	9	NUM
ap-610	506	2	:	:	PUNCT
ap-610	506	3	pathological	pathological	ADJ
ap-610	506	4	effects	effect	NOUN
ap-610	506	5	of	of	ADP
ap-610	506	6	mesh	mesh	NOUN
ap-610	506	7	refinement	refinement	NOUN
ap-610	506	8	on	on	ADP
ap-610	506	9	the	the	DET
ap-610	506	10	numerical	numerical	ADJ
ap-610	506	11	results	result	NOUN
ap-610	506	12	obtained	obtain	VERB
ap-610	506	13	with	with	ADP
ap-610	506	14	the	the	DET
ap-610	506	15	local	local	ADJ
ap-610	506	16	damage	damage	NOUN
ap-610	506	17	model	model	NOUN
ap-610	506	18	:	:	PUNCT
ap-610	506	19	mesh	mesh	NOUN
ap-610	506	20	-	-	PUNCT
ap-610	506	21	dependence	dependence	NOUN
ap-610	506	22	of	of	ADP
ap-610	506	23	(	(	PUNCT
ap-610	506	24	a	a	PRON
ap-610	506	25	)	)	PUNCT
ap-610	506	26	load	load	NOUN
ap-610	506	27	-	-	PUNCT
ap-610	506	28	displacement	displacement	NOUN
ap-610	506	29	diagrams	diagram	NOUN
ap-610	506	30	,	,	PUNCT
ap-610	506	31	(	(	PUNCT
ap-610	506	32	b	b	X
ap-610	506	33	)	)	PUNCT
ap-610	506	34	strain	strain	NOUN
ap-610	506	35	profiles	profile	NOUN
ap-610	506	36	the	the	DET
ap-610	506	37	internal	internal	ADJ
ap-610	506	38	variable	variable	ADJ
ap-610	506	39	�	�	PROPN
ap-610	506	40	has	have	VERB
ap-610	506	41	the	the	DET
ap-610	506	42	meaning	meaning	NOUN
ap-610	506	43	of	of	ADP
ap-610	506	44	the	the	DET
ap-610	506	45	largest	large	ADJ
ap-610	506	46	previously	previously	ADV
ap-610	506	47	reached	reach	VERB
ap-610	506	48	value	value	NOUN
ap-610	506	49	of	of	ADP
ap-610	506	50	nonlocal	nonlocal	ADJ
ap-610	506	51	strain	strain	NOUN
ap-610	506	52	.	.	PUNCT
ap-610	507	1	if	if	SCONJ
ap-610	507	2	strain	strain	NOUN
ap-610	507	3	has	have	VERB
ap-610	507	4	a	a	DET
ap-610	507	5	tendency	tendency	NOUN
ap-610	507	6	to	to	PART
ap-610	507	7	localize	localize	VERB
ap-610	507	8	in	in	ADP
ap-610	507	9	a	a	DET
ap-610	507	10	very	very	ADV
ap-610	507	11	narrow	narrow	ADJ
ap-610	507	12	region	region	NOUN
ap-610	507	13	,	,	PUNCT
ap-610	507	14	e.g.	e.g.	ADV
ap-610	507	15	,	,	PUNCT
ap-610	507	16	in	in	ADP
ap-610	507	17	one	one	NUM
ap-610	507	18	single	single	ADJ
ap-610	507	19	cross	cross	NOUN
ap-610	507	20	section	section	NOUN
ap-610	507	21	,	,	PUNCT
ap-610	507	22	the	the	DET
ap-610	507	23	nonlocal	nonlocal	ADJ
ap-610	507	24	strain	strain	NOUN
ap-610	507	25	becomes	become	VERB
ap-610	507	26	high	high	ADJ
ap-610	507	27	not	not	PART
ap-610	507	28	only	only	ADV
ap-610	507	29	in	in	ADP
ap-610	507	30	this	this	DET
ap-610	507	31	region	region	NOUN
ap-610	507	32	but	but	CCONJ
ap-610	507	33	also	also	ADV
ap-610	507	34	in	in	ADP
ap-610	507	35	its	its	PRON
ap-610	507	36	close	close	ADJ
ap-610	507	37	neighborhood	neighborhood	NOUN
ap-610	507	38	.	.	PUNCT
ap-610	508	1	this	this	PRON
ap-610	508	2	leads	lead	VERB
ap-610	508	3	to	to	ADP
ap-610	508	4	damage	damage	NOUN
ap-610	508	5	growth	growth	NOUN
ap-610	508	6	in	in	ADP
ap-610	508	7	that	that	DET
ap-610	508	8	neighborhood	neighborhood	NOUN
ap-610	508	9	,	,	PUNCT
ap-610	508	10	and	and	CCONJ
ap-610	508	11	the	the	DET
ap-610	508	12	local	local	ADJ
ap-610	508	13	strain	strain	NOUN
ap-610	508	14	at	at	ADP
ap-610	508	15	the	the	DET
ap-610	508	16	damaged	damage	VERB
ap-610	508	17	points	point	NOUN
ap-610	508	18	must	must	AUX
ap-610	508	19	be	be	AUX
ap-610	508	20	increased	increase	VERB
ap-610	508	21	in	in	ADP
ap-610	508	22	order	order	NOUN
ap-610	508	23	to	to	PART
ap-610	508	24	keep	keep	VERB
ap-610	508	25	the	the	DET
ap-610	508	26	stress	stress	NOUN
ap-610	508	27	distribution	distribution	NOUN
ap-610	508	28	uniform	uniform	NOUN
ap-610	508	29	.	.	PUNCT
ap-610	509	1	by	by	ADP
ap-610	509	2	this	this	DET
ap-610	509	3	mechanism	mechanism	NOUN
ap-610	509	4	,	,	PUNCT
ap-610	509	5	strain	strain	NOUN
ap-610	509	6	and	and	CCONJ
ap-610	509	7	damage	damage	NOUN
ap-610	509	8	are	be	AUX
ap-610	509	9	prevented	prevent	VERB
ap-610	509	10	from	from	ADP
ap-610	509	11	localizing	localize	VERB
ap-610	509	12	into	into	ADP
ap-610	509	13	a	a	DET
ap-610	509	14	single	single	ADJ
ap-610	509	15	cross	cross	NOUN
ap-610	509	16	section	section	NOUN
ap-610	509	17	.	.	PUNCT
ap-610	510	1	the	the	DET
ap-610	510	2	localized	localized	ADJ
ap-610	510	3	region	region	NOUN
ap-610	510	4	always	always	ADV
ap-610	510	5	has	have	VERB
ap-610	510	6	a	a	DET
ap-610	510	7	certain	certain	ADJ
ap-610	510	8	finite	finite	ADJ
ap-610	510	9	size	size	NOUN
ap-610	510	10	,	,	PUNCT
ap-610	510	11	controlled	control	VERB
ap-610	510	12	by	by	ADP
ap-610	510	13	the	the	DET
ap-610	510	14	length	length	NOUN
ap-610	510	15	parameter	parameter	NOUN
ap-610	510	16	that	that	PRON
ap-610	510	17	appears	appear	VERB
ap-610	510	18	in	in	ADP
ap-610	510	19	the	the	DET
ap-610	510	20	definition	definition	NOUN
ap-610	510	21	of	of	ADP
ap-610	510	22	the	the	DET
ap-610	510	23	nonlocal	nonlocal	ADJ
ap-610	510	24	weight	weight	NOUN
ap-610	510	25	function	function	NOUN
ap-610	510	26	.	.	PUNCT
ap-610	511	1	4.3	4.3	NUM
ap-610	511	2	localization	localization	NOUN
ap-610	511	3	analysis	analysis	NOUN
ap-610	511	4	the	the	DET
ap-610	511	5	initial	initial	ADJ
ap-610	511	6	bifurcation	bifurcation	NOUN
ap-610	511	7	from	from	ADP
ap-610	511	8	a	a	DET
ap-610	511	9	uniform	uniform	ADJ
ap-610	511	10	state	state	NOUN
ap-610	511	11	can	can	AUX
ap-610	511	12	be	be	AUX
ap-610	511	13	studied	study	VERB
ap-610	511	14	analytically	analytically	ADV
ap-610	511	15	under	under	ADP
ap-610	511	16	the	the	DET
ap-610	511	17	simplified	simplified	ADJ
ap-610	511	18	assumption	assumption	NOUN
ap-610	511	19	that	that	SCONJ
ap-610	511	20	the	the	DET
ap-610	511	21	strain	strain	NOUN
ap-610	511	22	keeps	keep	VERB
ap-610	511	23	increasing	increase	VERB
ap-610	511	24	at	at	ADP
ap-610	511	25	all	all	DET
ap-610	511	26	points	point	NOUN
ap-610	511	27	both	both	PRON
ap-610	511	28	for	for	ADP
ap-610	511	29	the	the	DET
ap-610	511	30	fundamental	fundamental	ADJ
ap-610	511	31	uniform	uniform	ADJ
ap-610	511	32	solution	solution	NOUN
ap-610	511	33	and	and	CCONJ
ap-610	511	34	the	the	DET
ap-610	511	35	bifurcated	bifurcated	ADJ
ap-610	511	36	nonuniform	nonuniform	NOUN
ap-610	511	37	solution	solution	NOUN
ap-610	511	38	.	.	PUNCT
ap-610	512	1	if	if	SCONJ
ap-610	512	2	the	the	DET
ap-610	512	3	bifurcated	bifurcated	ADJ
ap-610	512	4	solution	solution	NOUN
ap-610	512	5	is	be	AUX
ap-610	512	6	considered	consider	VERB
ap-610	512	7	as	as	ADP
ap-610	512	8	a	a	DET
ap-610	512	9	small	small	ADJ
ap-610	512	10	perturbation	perturbation	NOUN
ap-610	512	11	of	of	ADP
ap-610	512	12	the	the	DET
ap-610	512	13	uniform	uniform	ADJ
ap-610	512	14	solution	solution	NOUN
ap-610	512	15	,	,	PUNCT
ap-610	512	16	the	the	DET
ap-610	512	17	stress	stress	NOUN
ap-610	512	18	perturbation	perturbation	NOUN
ap-610	512	19	�	�	PROPN
ap-610	512	20	can	can	AUX
ap-610	512	21	be	be	AUX
ap-610	512	22	linked	link	VERB
ap-610	512	23	to	to	ADP
ap-610	512	24	the	the	DET
ap-610	512	25	strain	strain	NOUN
ap-610	512	26	perturbation	perturbation	NOUN
ap-610	512	27	�	�	NOUN
ap-610	512	28	�	�	PROPN
ap-610	512	29	by	by	ADP
ap-610	512	30	the	the	DET
ap-610	512	31	linearized	linearize	VERB
ap-610	512	32	equation	equation	NOUN
ap-610	512	33	�	�	PROPN
ap-610	512	34	�	�	PROPN
ap-610	512	35	�	�	PROPN
ap-610	512	36	�	�	PROPN
ap-610	512	37	�	�	PROPN
ap-610	512	38	�	�	PROPN
ap-610	512	39	�	�	PROPN
ap-610	512	40	�	�	PROPN
ap-610	512	41	(	(	PUNCT
ap-610	512	42	)	)	SYM
ap-610	512	43	1	1	NUM
ap-610	512	44	�	�	PROPN
ap-610	512	45	�	�	PROPN
ap-610	512	46	e	e	ADP
ap-610	512	47	e	e	X
ap-610	512	48	(	(	PUNCT
ap-610	512	49	81	81	NUM
ap-610	512	50	)	)	PUNCT
ap-610	512	51	and	and	CCONJ
ap-610	512	52	the	the	DET
ap-610	512	53	perturbation	perturbation	NOUN
ap-610	512	54	of	of	ADP
ap-610	512	55	the	the	DET
ap-610	512	56	damage	damage	NOUN
ap-610	512	57	field	field	NOUN
ap-610	512	58	�	�	PROPN
ap-610	512	59	�	�	PROPN
ap-610	512	60	is	be	AUX
ap-610	512	61	linked	link	VERB
ap-610	512	62	to	to	ADP
ap-610	512	63	the	the	DET
ap-610	512	64	strain	strain	NOUN
ap-610	512	65	perturbation	perturbation	NOUN
ap-610	512	66	by	by	ADP
ap-610	512	67	the	the	DET
ap-610	512	68	nonlocal	nonlocal	ADJ
ap-610	512	69	relation	relation	NOUN
ap-610	512	70	�	�	PROPN
ap-610	512	71	�	�	PROPN
ap-610	512	72	�	�	PROPN
ap-610	512	73	�	�	PROPN
ap-610	512	74	�	�	PROPN
ap-610	512	75	(	(	PUNCT
ap-610	512	76	)	)	PUNCT
ap-610	512	77	(	(	PUNCT
ap-610	512	78	,	,	PUNCT
ap-610	512	79	)	)	PUNCT
ap-610	512	80	(	(	PUNCT
ap-610	513	1	)	)	PUNCT
ap-610	513	2	*	*	PUNCT
ap-610	513	3	x	x	X
ap-610	513	4	g	g	NOUN
ap-610	513	5	x	x	SYM
ap-610	513	6	l	l	X
ap-610	513	7	�	�	PROPN
ap-610	513	8	�	�	PROPN
ap-610	513	9	d	d	PROPN
ap-610	513	10	,	,	PUNCT
ap-610	513	11	(	(	PUNCT
ap-610	513	12	82	82	NUM
ap-610	513	13	)	)	PUNCT
ap-610	513	14	where	where	SCONJ
ap-610	513	15	g	g	NOUN
ap-610	513	16	*	*	PROPN
ap-610	513	17	is	be	AUX
ap-610	513	18	the	the	DET
ap-610	513	19	derivative	derivative	NOUN
ap-610	513	20	of	of	ADP
ap-610	513	21	the	the	DET
ap-610	513	22	damage	damage	NOUN
ap-610	513	23	function	function	NOUN
ap-610	513	24	g	g	NOUN
ap-610	513	25	with	with	ADP
ap-610	513	26	respect	respect	NOUN
ap-610	513	27	to	to	ADP
ap-610	513	28	its	its	PRON
ap-610	513	29	argument	argument	NOUN
ap-610	513	30	�	�	PROPN
ap-610	513	31	evaluated	evaluate	VERB
ap-610	513	32	for	for	ADP
ap-610	513	33	the	the	DET
ap-610	513	34	fundamental	fundamental	ADJ
ap-610	513	35	(	(	PUNCT
ap-610	513	36	uniform	uniform	ADJ
ap-610	513	37	)	)	PUNCT
ap-610	513	38	solution	solution	NOUN
ap-610	513	39	and	and	CCONJ
ap-610	513	40	therefore	therefore	ADV
ap-610	513	41	independent	independent	ADJ
ap-610	513	42	of	of	ADP
ap-610	513	43	the	the	DET
ap-610	513	44	spatial	spatial	ADJ
ap-610	513	45	coordinate	coordinate	NOUN
ap-610	513	46	.	.	PUNCT
ap-610	514	1	even	even	ADV
ap-610	514	2	though	though	SCONJ
ap-610	514	3	the	the	DET
ap-610	514	4	fundamental	fundamental	ADJ
ap-610	514	5	solution	solution	NOUN
ap-610	514	6	is	be	AUX
ap-610	514	7	considered	consider	VERB
ap-610	514	8	as	as	ADP
ap-610	514	9	static	static	ADJ
ap-610	514	10	,	,	PUNCT
ap-610	514	11	we	we	PRON
ap-610	514	12	will	will	AUX
ap-610	514	13	analyze	analyze	VERB
ap-610	514	14	the	the	DET
ap-610	514	15	evolution	evolution	NOUN
ap-610	514	16	of	of	ADP
ap-610	514	17	the	the	DET
ap-610	514	18	perturbation	perturbation	NOUN
ap-610	514	19	as	as	ADP
ap-610	514	20	a	a	DET
ap-610	514	21	dynamic	dynamic	ADJ
ap-610	514	22	process	process	NOUN
ap-610	514	23	.	.	PUNCT
ap-610	515	1	this	this	DET
ap-610	515	2	approach	approach	NOUN
ap-610	515	3	provides	provide	VERB
ap-610	515	4	more	more	ADJ
ap-610	515	5	insight	insight	NOUN
ap-610	515	6	into	into	ADP
ap-610	515	7	the	the	DET
ap-610	515	8	localization	localization	NOUN
ap-610	515	9	phenomena	phenomena	NOUN
ap-610	515	10	.	.	PUNCT
ap-610	516	1	in	in	ADP
ap-610	516	2	dynamics	dynamic	NOUN
ap-610	516	3	,	,	PUNCT
ap-610	516	4	the	the	DET
ap-610	516	5	stress	stress	NOUN
ap-610	516	6	perturbation	perturbation	NOUN
ap-610	516	7	and	and	CCONJ
ap-610	516	8	the	the	DET
ap-610	516	9	displacement	displacement	ADJ
ap-610	516	10	perturbation	perturbation	NOUN
ap-610	516	11	must	must	AUX
ap-610	516	12	satisfy	satisfy	VERB
ap-610	516	13	the	the	DET
ap-610	516	14	equation	equation	NOUN
ap-610	516	15	of	of	ADP
ap-610	516	16	motion	motion	NOUN
ap-610	516	17	�	�	PROPN
ap-610	516	18	�	�	PROPN
ap-610	516	19	�	�	PROPN
ap-610	516	20	�	�	PROPN
ap-610	516	21	�	�	PROPN
ap-610	516	22	u	u	PROPN
ap-610	516	23	�	�	PROPN
ap-610	516	24	�	�	PROPN
ap-610	516	25	�	�	PROPN
ap-610	516	26	0	0	NUM
ap-610	516	27	.	.	PUNCT
ap-610	517	1	(	(	PUNCT
ap-610	517	2	83	83	NUM
ap-610	517	3	)	)	PUNCT
ap-610	517	4	for	for	ADP
ap-610	517	5	an	an	DET
ap-610	517	6	infinite	infinite	ADJ
ap-610	517	7	body	body	NOUN
ap-610	517	8	and	and	CCONJ
ap-610	517	9	nonlocal	nonlocal	ADJ
ap-610	517	10	weight	weight	NOUN
ap-610	517	11	function	function	NOUN
ap-610	517	12	in	in	ADP
ap-610	517	13	the	the	DET
ap-610	517	14	form	form	NOUN
ap-610	517	15	�	�	PROPN
ap-610	517	16	�	�	PROPN
ap-610	517	17	(	(	PUNCT
ap-610	517	18	,	,	PUNCT
ap-610	517	19	)	)	PUNCT
ap-610	517	20	(	(	PUNCT
ap-610	517	21	)	)	PUNCT
ap-610	517	22	x	x	X
ap-610	517	23	x	x	X
ap-610	517	24	�	�	PROPN
ap-610	517	25	�	�	PROPN
ap-610	517	26	0	0	NUM
ap-610	517	27	,	,	PUNCT
ap-610	517	28	the	the	DET
ap-610	517	29	assumed	assume	VERB
ap-610	517	30	solution	solution	NOUN
ap-610	517	31	for	for	ADP
ap-610	517	32	�	�	PROPN
ap-610	517	33	u	u	NOUN
ap-610	517	34	in	in	ADP
ap-610	517	35	the	the	DET
ap-610	517	36	form	form	NOUN
ap-610	517	37	of	of	ADP
ap-610	517	38	a	a	DET
ap-610	517	39	harmonic	harmonic	ADJ
ap-610	517	40	wave	wave	NOUN
ap-610	517	41	substituted	substitute	VERB
ap-610	517	42	into	into	ADP
ap-610	517	43	(	(	PUNCT
ap-610	517	44	81)–(83	81)–(83	NUM
ap-610	517	45	)	)	PUNCT
ap-610	517	46	leads	lead	VERB
ap-610	517	47	to	to	ADP
ap-610	517	48	the	the	DET
ap-610	517	49	dispersion	dispersion	NOUN
ap-610	517	50	equation	equation	NOUN
ap-610	517	51	�	�	PROPN
ap-610	517	52	�	�	PROPN
ap-610	517	53	�	�	PROPN
ap-610	517	54	�	�	PROPN
ap-610	517	55	�	�	PROPN
ap-610	517	56	�	�	PROPN
ap-610	517	57	�	�	PROPN
ap-610	517	58	�	�	PROPN
ap-610	517	59	�	�	PROPN
ap-610	517	60	2	2	NUM
ap-610	517	61	2	2	NUM
ap-610	517	62	2	2	NUM
ap-610	517	63	01	01	NUM
ap-610	517	64	0	0	NUM
ap-610	517	65	(	(	PUNCT
ap-610	517	66	)	)	PUNCT
ap-610	517	67	(	(	PUNCT
ap-610	517	68	)	)	PUNCT
ap-610	517	69	*	*	PUNCT
ap-610	518	1	*	*	PUNCT
ap-610	518	2	�	�	PROPN
ap-610	518	3	ek	ek	AUX
ap-610	518	4	g	g	PROPN
ap-610	518	5	e	e	PROPN
ap-610	518	6	k	k	PROPN
ap-610	518	7	k	k	X
ap-610	518	8	,	,	PUNCT
ap-610	518	9	(	(	PUNCT
ap-610	518	10	84	84	NUM
ap-610	518	11	)	)	PUNCT
ap-610	518	12	where	where	SCONJ
ap-610	518	13	�	�	PROPN
ap-610	518	14	is	be	AUX
ap-610	518	15	the	the	DET
ap-610	518	16	circular	circular	ADJ
ap-610	518	17	frequency	frequency	NOUN
ap-610	518	18	of	of	ADP
ap-610	518	19	the	the	DET
ap-610	518	20	wave	wave	NOUN
ap-610	518	21	(	(	PUNCT
ap-610	518	22	not	not	PART
ap-610	518	23	to	to	PART
ap-610	518	24	be	be	AUX
ap-610	518	25	confused	confuse	VERB
ap-610	518	26	with	with	ADP
ap-610	518	27	the	the	DET
ap-610	518	28	damage	damage	NOUN
ap-610	518	29	variable	variable	NOUN
ap-610	518	30	�	�	PROPN
ap-610	518	31	)	)	PUNCT
ap-610	518	32	,	,	PUNCT
ap-610	518	33	k	k	PROPN
ap-610	518	34	is	be	AUX
ap-610	518	35	the	the	DET
ap-610	518	36	wave	wave	NOUN
ap-610	518	37	number	number	NOUN
ap-610	518	38	,	,	PUNCT
ap-610	518	39	and	and	CCONJ
ap-610	518	40	�	�	PROPN
ap-610	518	41	0	0	NUM
ap-610	518	42	*	*	PUNCT
ap-610	518	43	is	be	AUX
ap-610	518	44	the	the	DET
ap-610	518	45	fourier	fourier	ADJ
ap-610	518	46	image	image	NOUN
ap-610	518	47	of	of	ADP
ap-610	518	48	the	the	DET
ap-610	518	49	weight	weight	NOUN
ap-610	518	50	function	function	NOUN
ap-610	518	51	.	.	PUNCT
ap-610	519	1	the	the	DET
ap-610	519	2	resulting	result	VERB
ap-610	519	3	dispersion	dispersion	NOUN
ap-610	519	4	law	law	NOUN
ap-610	519	5	reads	read	VERB
ap-610	519	6	�	�	PROPN
ap-610	519	7	�	�	PROPN
ap-610	519	8	�	�	PROPN
ap-610	519	9	�	�	PROPN
ap-610	519	10	�	�	PROPN
ap-610	519	11	�	�	PROPN
ap-610	519	12	c	c	PROPN
ap-610	519	13	k	k	PROPN
ap-610	519	14	g	g	PROPN
ap-610	519	15	k0	k0	PROPN
ap-610	519	16	01	01	NUM
ap-610	519	17	�	�	PROPN
ap-610	519	18	*	*	PUNCT
ap-610	519	19	*	*	PUNCT
ap-610	519	20	(	(	PUNCT
ap-610	519	21	)	)	PUNCT
ap-610	519	22	.	.	PUNCT
ap-610	520	1	(	(	PUNCT
ap-610	520	2	85	85	NUM
ap-610	520	3	)	)	PUNCT
ap-610	520	4	the	the	DET
ap-610	520	5	fourier	fourier	NOUN
ap-610	520	6	image	image	NOUN
ap-610	520	7	�	�	PROPN
ap-610	520	8	0	0	NUM
ap-610	520	9	*	*	PUNCT
ap-610	520	10	has	have	VERB
ap-610	520	11	a	a	DET
ap-610	520	12	unit	unit	NOUN
ap-610	520	13	value	value	NOUN
ap-610	520	14	at	at	ADP
ap-610	520	15	k	k	PROPN
ap-610	520	16	�	�	PROPN
ap-610	520	17	0	0	NUM
ap-610	520	18	and	and	CCONJ
ap-610	520	19	smaller	small	ADJ
ap-610	520	20	values	value	NOUN
ap-610	520	21	at	at	ADP
ap-610	520	22	positive	positive	ADJ
ap-610	520	23	wave	wave	NOUN
ap-610	520	24	numbers	number	NOUN
ap-610	520	25	k.	k.	VERB
ap-610	521	1	so	so	ADV
ap-610	521	2	if	if	SCONJ
ap-610	521	3	1	1	NUM
ap-610	521	4	0	0	NUM
ap-610	521	5	�	�	PROPN
ap-610	521	6	�	�	PROPN
ap-610	521	7	�	�	PROPN
ap-610	521	8	�	�	PROPN
ap-610	521	9	g	g	PROPN
ap-610	521	10	*	*	PROPN
ap-610	521	11	�	�	PROPN
ap-610	521	12	,	,	PUNCT
ap-610	521	13	all	all	DET
ap-610	521	14	wave	wave	NOUN
ap-610	521	15	numbers	number	NOUN
ap-610	521	16	have	have	VERB
ap-610	521	17	real	real	ADJ
ap-610	521	18	positive	positive	ADJ
ap-610	521	19	frequencies	frequency	NOUN
ap-610	521	20	and	and	CCONJ
ap-610	521	21	a	a	DET
ap-610	521	22	small	small	ADJ
ap-610	521	23	perturbation	perturbation	NOUN
ap-610	521	24	of	of	ADP
ap-610	521	25	an	an	DET
ap-610	521	26	arbitrary	arbitrary	ADJ
ap-610	521	27	shape	shape	NOUN
ap-610	521	28	propagates	propagate	VERB
ap-610	521	29	through	through	ADP
ap-610	521	30	the	the	DET
ap-610	521	31	body	body	NOUN
ap-610	521	32	but	but	CCONJ
ap-610	521	33	does	do	AUX
ap-610	521	34	not	not	PART
ap-610	521	35	grow	grow	VERB
ap-610	521	36	in	in	ADP
ap-610	521	37	magnitude	magnitude	NOUN
ap-610	521	38	.	.	PUNCT
ap-610	522	1	if	if	SCONJ
ap-610	522	2	1	1	NUM
ap-610	522	3	0	0	NUM
ap-610	522	4	�	�	PROPN
ap-610	522	5	�	�	PROPN
ap-610	522	6	�	�	PROPN
ap-610	522	7	�	�	PROPN
ap-610	522	8	g	g	PROPN
ap-610	522	9	*	*	PROPN
ap-610	522	10	�	�	PROPN
ap-610	522	11	,	,	PUNCT
ap-610	522	12	there	there	PRON
ap-610	522	13	exists	exist	VERB
ap-610	522	14	a	a	DET
ap-610	522	15	band	band	NOUN
ap-610	522	16	of	of	ADP
ap-610	522	17	low	low	ADJ
ap-610	522	18	wave	wave	NOUN
ap-610	522	19	numbers	number	NOUN
ap-610	522	20	between	between	ADP
ap-610	522	21	zero	zero	NUM
ap-610	522	22	and	and	CCONJ
ap-610	522	23	a	a	DET
ap-610	522	24	positive	positive	ADJ
ap-610	522	25	limit	limit	NOUN
ap-610	522	26	kcrit	kcrit	NOUN
ap-610	522	27	for	for	ADP
ap-610	522	28	which	which	PRON
ap-610	522	29	the	the	DET
ap-610	522	30	frequencies	frequency	NOUN
ap-610	522	31	are	be	AUX
ap-610	522	32	imaginary	imaginary	ADJ
ap-610	522	33	.	.	PUNCT
ap-610	523	1	this	this	PRON
ap-610	523	2	indicates	indicate	VERB
ap-610	523	3	an	an	DET
ap-610	523	4	instability	instability	NOUN
ap-610	523	5	if	if	SCONJ
ap-610	523	6	the	the	DET
ap-610	523	7	perturbation	perturbation	NOUN
ap-610	523	8	contains	contain	VERB
ap-610	523	9	a	a	DET
ap-610	523	10	component	component	NOUN
ap-610	523	11	with	with	ADP
ap-610	523	12	a	a	DET
ap-610	523	13	sufficiently	sufficiently	ADV
ap-610	523	14	long	long	ADJ
ap-610	523	15	wavelength	wavelength	NOUN
ap-610	523	16	.	.	PUNCT
ap-610	524	1	in	in	ADP
ap-610	524	2	statics	statics	PROPN
ap-610	524	3	,	,	PUNCT
ap-610	524	4	a	a	DET
ap-610	524	5	stationary	stationary	ADJ
ap-610	524	6	wave	wave	NOUN
ap-610	524	7	of	of	ADP
ap-610	524	8	wavelength	wavelength	NOUN
ap-610	524	9	2	2	NUM
ap-610	524	10	�	�	PROPN
ap-610	524	11	kcrit	kcrit	NOUN
ap-610	524	12	can	can	AUX
ap-610	524	13	be	be	AUX
ap-610	524	14	superimposed	superimpose	VERB
ap-610	524	15	on	on	ADP
ap-610	524	16	the	the	DET
ap-610	524	17	fundamental	fundamental	ADJ
ap-610	524	18	uniform	uniform	ADJ
ap-610	524	19	solution	solution	NOUN
ap-610	524	20	without	without	ADP
ap-610	524	21	violating	violate	VERB
ap-610	524	22	the	the	DET
ap-610	524	23	equilibrium	equilibrium	NOUN
ap-610	524	24	condition	condition	NOUN
ap-610	524	25	.	.	PUNCT
ap-610	525	1	the	the	DET
ap-610	525	2	critical	critical	ADJ
ap-610	525	3	wave	wave	NOUN
ap-610	525	4	number	number	NOUN
ap-610	525	5	can	can	AUX
ap-610	525	6	be	be	AUX
ap-610	525	7	determined	determine	VERB
ap-610	525	8	from	from	ADP
ap-610	525	9	the	the	DET
ap-610	525	10	condition	condition	NOUN
ap-610	525	11	�	�	PROPN
ap-610	525	12	�	�	PROPN
ap-610	525	13	0	0	NUM
ap-610	525	14	.	.	PUNCT
ap-610	526	1	in	in	ADP
ap-610	526	2	a	a	DET
ap-610	526	3	monotonic	monotonic	ADJ
ap-610	526	4	loading	loading	NOUN
ap-610	526	5	process	process	NOUN
ap-610	526	6	,	,	PUNCT
ap-610	526	7	the	the	DET
ap-610	526	8	damage	damage	NOUN
ap-610	526	9	variable	variable	ADJ
ap-610	526	10	�	�	PROPN
ap-610	526	11	is	be	AUX
ap-610	526	12	a	a	DET
ap-610	526	13	function	function	NOUN
ap-610	526	14	of	of	ADP
ap-610	526	15	strain	strain	NOUN
ap-610	526	16	,	,	PUNCT
ap-610	526	17	�	�	PROPN
ap-610	526	18	�	�	PROPN
ap-610	526	19	�	�	PROPN
ap-610	526	20	g	g	PROPN
ap-610	526	21	(	(	PUNCT
ap-610	526	22	)	)	PUNCT
ap-610	526	23	,	,	PUNCT
ap-610	526	24	and	and	CCONJ
ap-610	526	25	also	also	ADV
ap-610	526	26	the	the	DET
ap-610	526	27	derivative	derivative	ADJ
ap-610	526	28	g	g	PROPN
ap-610	526	29	g*	g*	PROPN
ap-610	526	30	�	�	PROPN
ap-610	526	31	d	d	SYM
ap-610	526	32	d	d	PROPN
ap-610	526	33	�	�	PROPN
ap-610	526	34	is	be	AUX
ap-610	526	35	a	a	DET
ap-610	526	36	function	function	NOUN
ap-610	526	37	of	of	ADP
ap-610	526	38	strain	strain	NOUN
ap-610	526	39	.	.	PUNCT
ap-610	527	1	the	the	DET
ap-610	527	2	expression	expression	NOUN
ap-610	527	3	under	under	ADP
ap-610	527	4	the	the	DET
ap-610	527	5	square	square	ADJ
ap-610	527	6	root	root	NOUN
ap-610	527	7	in	in	ADP
ap-610	527	8	(	(	PUNCT
ap-610	527	9	85	85	NUM
ap-610	527	10	)	)	PUNCT
ap-610	527	11	vanishes	vanish	VERB
ap-610	527	12	for	for	ADP
ap-610	527	13	the	the	DET
ap-610	527	14	wave	wave	NOUN
ap-610	527	15	number	number	NOUN
ap-610	527	16	satisfying	satisfy	VERB
ap-610	527	17	the	the	DET
ap-610	527	18	condition	condition	NOUN
ap-610	527	19	�	�	PROPN
ap-610	527	20	�	�	PROPN
ap-610	527	21	�	�	PROPN
ap-610	527	22	�	�	PROPN
ap-610	527	23	�	�	PROPN
ap-610	527	24	0	0	NUM
ap-610	527	25	1	1	NUM
ap-610	527	26	*	*	PRON
ap-610	527	27	(	(	PUNCT
ap-610	527	28	)	)	PUNCT
ap-610	527	29	(	(	PUNCT
ap-610	527	30	)	)	PUNCT
ap-610	527	31	(	(	PUNCT
ap-610	527	32	)	)	PUNCT
ap-610	527	33	k	k	PROPN
ap-610	527	34	g	g	PROPN
ap-610	527	35	gcrit	gcrit	PROPN
ap-610	527	36	�	�	PROPN
ap-610	527	37	�	�	PROPN
ap-610	527	38	d	d	PROPN
ap-610	527	39	d	d	PROPN
ap-610	527	40	.	.	PUNCT
ap-610	528	1	(	(	PUNCT
ap-610	528	2	86	86	NUM
ap-610	528	3	)	)	PUNCT
ap-610	528	4	for	for	ADP
ap-610	528	5	a	a	DET
ap-610	528	6	given	give	VERB
ap-610	528	7	damage	damage	NOUN
ap-610	528	8	function	function	NOUN
ap-610	528	9	g	g	NOUN
ap-610	528	10	and	and	CCONJ
ap-610	528	11	nonlocal	nonlocal	ADJ
ap-610	528	12	weight	weight	NOUN
ap-610	528	13	function	function	NOUN
ap-610	528	14	�	�	PROPN
ap-610	528	15	0	0	NUM
ap-610	528	16	,	,	PUNCT
ap-610	528	17	this	this	DET
ap-610	528	18	equation	equation	NOUN
ap-610	528	19	can	can	AUX
ap-610	528	20	be	be	AUX
ap-610	528	21	solved	solve	VERB
ap-610	528	22	(	(	PUNCT
ap-610	528	23	either	either	CCONJ
ap-610	528	24	analytically	analytically	ADV
ap-610	528	25	or	or	CCONJ
ap-610	528	26	numerically	numerically	ADV
ap-610	528	27	)	)	PUNCT
ap-610	528	28	and	and	CCONJ
ap-610	528	29	the	the	DET
ap-610	528	30	critical	critical	ADJ
ap-610	528	31	wavelength	wavelength	NOUN
ap-610	528	32	l	l	PROPN
ap-610	528	33	kcrit	kcrit	PROPN
ap-610	528	34	crit	crit	PROPN
ap-610	528	35	�	�	PROPN
ap-610	528	36	2	2	NUM
ap-610	528	37	�	�	PROPN
ap-610	528	38	can	can	AUX
ap-610	528	39	be	be	AUX
ap-610	528	40	determined	determine	VERB
ap-610	528	41	as	as	ADP
ap-610	528	42	a	a	DET
ap-610	528	43	function	function	NOUN
ap-610	528	44	of	of	ADP
ap-610	528	45	strain	strain	NOUN
ap-610	528	46	.	.	PUNCT
ap-610	529	1	for	for	ADP
ap-610	529	2	instance	instance	NOUN
ap-610	529	3	,	,	PUNCT
ap-610	529	4	for	for	ADP
ap-610	529	5	an	an	DET
ap-610	529	6	exponential	exponential	ADJ
ap-610	529	7	softening	soften	VERB
ap-610	529	8	curve	curve	NOUN
ap-610	529	9	(	(	PUNCT
ap-610	529	10	more	more	ADV
ap-610	529	11	realistic	realistic	ADJ
ap-610	529	12	for	for	ADP
ap-610	529	13	concrete	concrete	ADJ
ap-610	529	14	than	than	ADP
ap-610	529	15	the	the	DET
ap-610	529	16	linear	linear	ADJ
ap-610	529	17	one	one	NUM
ap-610	529	18	)	)	PUNCT
ap-610	529	19	,	,	PUNCT
ap-610	529	20	the	the	DET
ap-610	529	21	damage	damage	NOUN
ap-610	529	22	function	function	NOUN
ap-610	529	23	is	be	AUX
ap-610	529	24	given	give	VERB
ap-610	529	25	by	by	ADP
ap-610	529	26	g	g	PROPN
ap-610	529	27	f	f	PROPN
ap-610	529	28	(	(	PUNCT
ap-610	529	29	)	)	PUNCT
ap-610	529	30	exp	exp	NOUN
ap-610	529	31	�	�	PROPN
ap-610	529	32	�	�	PROPN
ap-610	529	33	�	�	PROPN
ap-610	529	34	�	�	PROPN
ap-610	529	35	�	�	PROPN
ap-610	529	36	�	�	PROPN
ap-610	529	37	�	�	PROPN
ap-610	529	38	�	�	PROPN
ap-610	529	39	�	�	PROPN
ap-610	529	40	�	�	PROPN
ap-610	529	41	�	�	PROPN
ap-610	529	42	�	�	PROPN
ap-610	529	43	�	�	PROPN
ap-610	529	44	�	�	PROPN
ap-610	529	45	�	�	PROPN
ap-610	529	46	�	�	PROPN
ap-610	529	47	�	�	PROPN
ap-610	529	48	�	�	PROPN
ap-610	529	49	�	�	PROPN
ap-610	529	50	�	�	PROPN
ap-610	529	51	1	1	NUM
ap-610	529	52	0	0	NUM
ap-610	529	53	0	0	NUM
ap-610	529	54	0	0	NUM
ap-610	529	55	(	(	PUNCT
ap-610	529	56	87	87	NUM
ap-610	529	57	)	)	PUNCT
ap-610	529	58	where	where	SCONJ
ap-610	529	59	�	�	PROPN
ap-610	529	60	0	0	PROPN
ap-610	529	61	is	be	AUX
ap-610	529	62	the	the	DET
ap-610	529	63	limit	limit	NOUN
ap-610	529	64	elastic	elastic	ADJ
ap-610	529	65	strain	strain	NOUN
ap-610	529	66	and	and	CCONJ
ap-610	529	67	�	�	PROPN
ap-610	529	68	f	f	PROPN
ap-610	529	69	is	be	AUX
ap-610	529	70	another	another	DET
ap-610	529	71	parameter	parameter	NOUN
ap-610	529	72	controlling	control	VERB
ap-610	529	73	the	the	DET
ap-610	529	74	slope	slope	NOUN
ap-610	529	75	of	of	ADP
ap-610	529	76	the	the	DET
ap-610	529	77	softening	soften	VERB
ap-610	529	78	curve	curve	NOUN
ap-610	529	79	.	.	PUNCT
ap-610	530	1	substituting	substitute	VERB
ap-610	530	2	(	(	PUNCT
ap-610	530	3	87	87	NUM
ap-610	530	4	)	)	PUNCT
ap-610	530	5	and	and	CCONJ
ap-610	530	6	the	the	DET
ap-610	530	7	fourier	fourier	NOUN
ap-610	530	8	image	image	NOUN
ap-610	530	9	�	�	PROPN
ap-610	530	10	0	0	NUM
ap-610	530	11	2	2	NUM
ap-610	530	12	2	2	NUM
ap-610	530	13	4	4	NUM
ap-610	530	14	*	*	NUM
ap-610	530	15	(	(	PUNCT
ap-610	530	16	)	)	PUNCT
ap-610	530	17	exp	exp	NOUN
ap-610	530	18	(	(	PUNCT
ap-610	530	19	)	)	PUNCT
ap-610	530	20	k	k	PROPN
ap-610	531	1	k	k	PROPN
ap-610	531	2	a	a	DET
ap-610	531	3	�	�	PROPN
ap-610	531	4	�	�	PROPN
ap-610	531	5	of	of	ADP
ap-610	531	6	the	the	DET
ap-610	531	7	gauss	gauss	ADJ
ap-610	531	8	-	-	PUNCT
ap-610	531	9	like	like	ADJ
ap-610	531	10	weight	weight	NOUN
ap-610	531	11	function	function	NOUN
ap-610	531	12	(	(	PUNCT
ap-610	531	13	52	52	NUM
ap-610	531	14	)	)	PUNCT
ap-610	531	15	into	into	ADP
ap-610	531	16	(	(	PUNCT
ap-610	531	17	86	86	NUM
ap-610	531	18	)	)	PUNCT
ap-610	531	19	,	,	PUNCT
ap-610	531	20	we	we	PRON
ap-610	531	21	obtain	obtain	VERB
ap-610	531	22	l	l	PROPN
ap-610	531	23	k	k	PROPN
ap-610	531	24	a	a	DET
ap-610	531	25	crit	crit	NOUN
ap-610	531	26	crit	crit	PROPN
ap-610	531	27	f	f	PROPN
ap-610	531	28	�	�	PROPN
ap-610	531	29	�	�	PROPN
ap-610	531	30	�	�	PROPN
ap-610	531	31	�	�	PROPN
ap-610	531	32	�	�	PROPN
ap-610	531	33	�	�	PROPN
ap-610	531	34	�	�	PROPN
ap-610	531	35	�	�	PROPN
ap-610	531	36	�	�	PROPN
ap-610	531	37	�	�	PROPN
ap-610	531	38	�	�	PROPN
ap-610	531	39	�	�	PROPN
ap-610	531	40	2	2	NUM
ap-610	531	41	1	1	NUM
ap-610	531	42	0	0	NUM
ap-610	531	43	�	�	PROPN
ap-610	531	44	�	�	PROPN
ap-610	531	45	�	�	PROPN
ap-610	531	46	�	�	PROPN
ap-610	531	47	�	�	PROPN
ap-610	531	48	ln	ln	PROPN
ap-610	531	49	.	.	PUNCT
ap-610	532	1	(	(	PUNCT
ap-610	532	2	88	88	NUM
ap-610	532	3	)	)	PUNCT
ap-610	532	4	of	of	ADP
ap-610	532	5	course	course	NOUN
ap-610	532	6	,	,	PUNCT
ap-610	532	7	this	this	DET
ap-610	532	8	expression	expression	NOUN
ap-610	532	9	is	be	AUX
ap-610	532	10	valid	valid	ADJ
ap-610	532	11	only	only	ADV
ap-610	532	12	in	in	ADP
ap-610	532	13	the	the	DET
ap-610	532	14	inelastic	inelastic	ADJ
ap-610	532	15	range	range	NOUN
ap-610	532	16	,	,	PUNCT
ap-610	532	17	i.e.	i.e.	X
ap-610	532	18	,	,	PUNCT
ap-610	532	19	for	for	ADP
ap-610	532	20	�	�	PROPN
ap-610	532	21	�	�	PROPN
ap-610	532	22	�	�	PROPN
ap-610	532	23	0	0	NUM
ap-610	532	24	.	.	PUNCT
ap-610	533	1	for	for	ADP
ap-610	533	2	the	the	DET
ap-610	533	3	present	present	ADJ
ap-610	533	4	damage	damage	NOUN
ap-610	533	5	function	function	NOUN
ap-610	533	6	(	(	PUNCT
ap-610	533	7	87	87	NUM
ap-610	533	8	)	)	PUNCT
ap-610	533	9	,	,	PUNCT
ap-610	533	10	the	the	DET
ap-610	533	11	elastic	elastic	ADJ
ap-610	533	12	limit	limit	NOUN
ap-610	533	13	coincides	coincide	VERB
ap-610	533	14	with	with	ADP
ap-610	533	15	the	the	DET
ap-610	533	16	peak	peak	NOUN
ap-610	533	17	of	of	ADP
ap-610	533	18	the	the	DET
ap-610	533	19	stress	stress	NOUN
ap-610	533	20	-	-	PUNCT
ap-610	533	21	strain	strain	NOUN
ap-610	533	22	curve	curve	NOUN
ap-610	533	23	.	.	PUNCT
ap-610	534	1	if	if	SCONJ
ap-610	534	2	,	,	PUNCT
ap-610	534	3	for	for	ADP
ap-610	534	4	instance	instance	NOUN
ap-610	534	5	,	,	PUNCT
ap-610	534	6	�	�	PROPN
ap-610	534	7	�	�	PROPN
ap-610	534	8	f	f	PROPN
ap-610	534	9	�	�	PROPN
ap-610	534	10	11	11	NUM
ap-610	534	11	0	0	NUM
ap-610	534	12	,	,	PUNCT
ap-610	534	13	the	the	DET
ap-610	534	14	critical	critical	ADJ
ap-610	534	15	wavelength	wavelength	NOUN
ap-610	534	16	for	for	ADP
ap-610	534	17	the	the	DET
ap-610	534	18	uniform	uniform	ADJ
ap-610	534	19	state	state	NOUN
ap-610	534	20	at	at	ADP
ap-610	534	21	peak	peak	NOUN
ap-610	534	22	stress	stress	NOUN
ap-610	534	23	is	be	AUX
ap-610	534	24	l	l	PROPN
ap-610	534	25	a	a	DET
ap-610	534	26	acrit	acrit	PROPN
ap-610	534	27	�	�	PROPN
ap-610	534	28	�	�	PROPN
ap-610	534	29	�	�	PROPN
ap-610	534	30	ln	ln	NOUN
ap-610	534	31	.	.	PUNCT
ap-610	535	1	.11	.11	NUM
ap-610	535	2	10176	10176	NUM
ap-610	535	3	.	.	PUNCT
ap-610	536	1	this	this	DET
ap-610	536	2	example	example	NOUN
ap-610	536	3	shows	show	VERB
ap-610	536	4	that	that	SCONJ
ap-610	536	5	the	the	DET
ap-610	536	6	critical	critical	ADJ
ap-610	536	7	wavelength	wavelength	NOUN
ap-610	536	8	is	be	AUX
ap-610	536	9	proportional	proportional	ADJ
ap-610	536	10	to	to	ADP
ap-610	536	11	the	the	DET
ap-610	536	12	model	model	NOUN
ap-610	536	13	parameter	parameter	NOUN
ap-610	536	14	that	that	PRON
ap-610	536	15	plays	play	VERB
ap-610	536	16	the	the	DET
ap-610	536	17	role	role	NOUN
ap-610	536	18	of	of	ADP
ap-610	536	19	the	the	DET
ap-610	536	20	internal	internal	ADJ
ap-610	536	21	material	material	NOUN
ap-610	536	22	length	length	NOUN
ap-610	536	23	(	(	PUNCT
ap-610	536	24	and	and	CCONJ
ap-610	536	25	is	be	AUX
ap-610	536	26	often	often	ADV
ap-610	536	27	denoted	denote	VERB
ap-610	536	28	as	as	ADP
ap-610	536	29	l	l	NOUN
ap-610	536	30	)	)	PUNCT
ap-610	536	31	.	.	PUNCT
ap-610	537	1	in	in	ADP
ap-610	537	2	an	an	DET
ap-610	537	3	infinite	infinite	ADJ
ap-610	537	4	bar	bar	NOUN
ap-610	537	5	at	at	ADP
ap-610	537	6	peak	peak	NOUN
ap-610	537	7	stress	stress	NOUN
ap-610	537	8	,	,	PUNCT
ap-610	537	9	the	the	DET
ap-610	537	10	appearance	appearance	NOUN
ap-610	537	11	of	of	ADP
ap-610	537	12	a	a	DET
ap-610	537	13	stationary	stationary	ADJ
ap-610	537	14	wave	wave	NOUN
ap-610	537	15	of	of	ADP
ap-610	537	16	wavelength	wavelength	NOUN
ap-610	537	17	lcrit	lcrit	NOUN
ap-610	537	18	corresponds	correspond	VERB
ap-610	537	19	to	to	ADP
ap-610	537	20	a	a	DET
ap-610	537	21	particular	particular	ADJ
ap-610	537	22	periodic	periodic	ADJ
ap-610	537	23	localization	localization	NOUN
ap-610	537	24	pattern	pattern	NOUN
ap-610	537	25	.	.	PUNCT
ap-610	538	1	in	in	ADP
ap-610	538	2	reality	reality	NOUN
ap-610	538	3	,	,	PUNCT
ap-610	538	4	there	there	PRON
ap-610	538	5	exists	exist	VERB
ap-610	538	6	an	an	DET
ap-610	538	7	energetically	energetically	ADV
ap-610	538	8	more	more	ADV
ap-610	538	9	favorable	favorable	ADJ
ap-610	538	10	localization	localization	NOUN
ap-610	538	11	pattern	pattern	NOUN
ap-610	538	12	that	that	PRON
ap-610	538	13	is	be	AUX
ap-610	538	14	not	not	PART
ap-610	538	15	periodic	periodic	ADJ
ap-610	538	16	but	but	CCONJ
ap-610	538	17	is	be	AUX
ap-610	538	18	concentrated	concentrate	VERB
ap-610	538	19	into	into	ADP
ap-610	538	20	one	one	NUM
ap-610	538	21	single	single	ADJ
ap-610	538	22	interval	interval	NOUN
ap-610	538	23	of	of	ADP
ap-610	538	24	length	length	NOUN
ap-610	538	25	slightly	slightly	ADV
ap-610	538	26	below	below	ADP
ap-610	538	27	the	the	DET
ap-610	538	28	critical	critical	ADJ
ap-610	538	29	wavelength	wavelength	NOUN
ap-610	538	30	.	.	PUNCT
ap-610	539	1	the	the	DET
ap-610	539	2	exact	exact	ADJ
ap-610	539	3	size	size	NOUN
ap-610	539	4	of	of	ADP
ap-610	539	5	the	the	DET
ap-610	539	6	localized	localized	ADJ
ap-610	539	7	zone	zone	NOUN
ap-610	539	8	could	could	AUX
ap-610	539	9	be	be	AUX
ap-610	539	10	solved	solve	VERB
ap-610	539	11	from	from	ADP
ap-610	539	12	a	a	DET
ap-610	539	13	fredholm	fredholm	ADJ
ap-610	539	14	integral	integral	ADJ
ap-610	539	15	equation	equation	NOUN
ap-610	539	16	of	of	ADP
ap-610	539	17	the	the	DET
ap-610	539	18	second	second	ADJ
ap-610	539	19	kind	kind	NOUN
ap-610	539	20	combined	combine	VERB
ap-610	539	21	with	with	ADP
ap-610	539	22	the	the	DET
ap-610	539	23	complementarity	complementarity	NOUN
ap-610	539	24	conditions	condition	NOUN
ap-610	539	25	,	,	PUNCT
ap-610	539	26	but	but	CCONJ
ap-610	539	27	since	since	SCONJ
ap-610	539	28	the	the	DET
ap-610	539	29	solution	solution	NOUN
ap-610	539	30	is	be	AUX
ap-610	539	31	not	not	PART
ap-610	539	32	available	available	ADJ
ap-610	539	33	in	in	ADP
ap-610	539	34	closed	closed	ADJ
ap-610	539	35	form	form	NOUN
ap-610	539	36	,	,	PUNCT
ap-610	539	37	we	we	PRON
ap-610	539	38	will	will	AUX
ap-610	539	39	not	not	PART
ap-610	539	40	elaborate	elaborate	VERB
ap-610	539	41	on	on	ADP
ap-610	539	42	that	that	PRON
ap-610	539	43	.	.	PUNCT
ap-610	540	1	if	if	SCONJ
ap-610	540	2	the	the	DET
ap-610	540	3	bar	bar	NOUN
ap-610	540	4	is	be	AUX
ap-610	540	5	finite	finite	ADJ
ap-610	540	6	but	but	CCONJ
ap-610	540	7	longer	long	ADJ
ap-610	540	8	than	than	ADP
ap-610	540	9	lcrit	lcrit	NOUN
ap-610	540	10	,	,	PUNCT
ap-610	540	11	it	it	PRON
ap-610	540	12	can	can	AUX
ap-610	540	13	be	be	AUX
ap-610	540	14	expected	expect	VERB
ap-610	540	15	that	that	SCONJ
ap-610	540	16	at	at	ADP
ap-610	540	17	peak	peak	NOUN
ap-610	540	18	stress	stress	VERB
ap-610	540	19	the	the	DET
ap-610	540	20	subsequent	subsequent	ADJ
ap-610	540	21	increments	increment	NOUN
ap-610	540	22	of	of	ADP
ap-610	540	23	strain	strain	NOUN
ap-610	540	24	localize	localize	VERB
ap-610	540	25	into	into	ADP
ap-610	540	26	a	a	DET
ap-610	540	27	band	band	NOUN
ap-610	540	28	of	of	ADP
ap-610	540	29	thickness	thickness	NOUN
ap-610	540	30	approximately	approximately	ADV
ap-610	540	31	equal	equal	ADJ
ap-610	540	32	to	to	PART
ap-610	540	33	lcrit	lcrit	VERB
ap-610	540	34	.	.	PUNCT
ap-610	541	1	for	for	ADP
ap-610	541	2	shorter	short	ADJ
ap-610	541	3	bars	bar	NOUN
ap-610	541	4	,	,	PUNCT
ap-610	541	5	localization	localization	NOUN
ap-610	541	6	can	can	AUX
ap-610	541	7	be	be	AUX
ap-610	541	8	delayed	delay	VERB
ap-610	541	9	and	and	CCONJ
ap-610	541	10	the	the	DET
ap-610	541	11	actual	actual	ADJ
ap-610	541	12	behavior	behavior	NOUN
ap-610	541	13	depends	depend	VERB
ap-610	541	14	on	on	ADP
ap-610	541	15	the	the	DET
ap-610	541	16	specific	specific	ADJ
ap-610	541	17	form	form	NOUN
ap-610	541	18	of	of	ADP
ap-610	541	19	the	the	DET
ap-610	541	20	nonlocal	nonlocal	ADJ
ap-610	541	21	averaging	averaging	NOUN
ap-610	541	22	operator	operator	NOUN
ap-610	541	23	around	around	ADP
ap-610	541	24	the	the	DET
ap-610	541	25	boundaries	boundary	NOUN
ap-610	541	26	.	.	PUNCT
ap-610	542	1	however	however	ADV
ap-610	542	2	,	,	PUNCT
ap-610	542	3	in	in	ADP
ap-610	542	4	general	general	ADJ
ap-610	542	5	it	it	PRON
ap-610	542	6	can	can	AUX
ap-610	542	7	be	be	AUX
ap-610	542	8	expected	expect	VERB
ap-610	542	9	that	that	SCONJ
ap-610	542	10	localization	localization	NOUN
ap-610	542	11	occurs	occur	VERB
ap-610	542	12	when	when	SCONJ
ap-610	542	13	the	the	DET
ap-610	542	14	critical	critical	ADJ
ap-610	542	15	wavelength	wavelength	NOUN
ap-610	542	16	becomes	become	VERB
ap-610	542	17	approximately	approximately	ADV
ap-610	542	18	equal	equal	ADJ
ap-610	542	19	to	to	ADP
ap-610	542	20	the	the	DET
ap-610	542	21	bar	bar	NOUN
ap-610	542	22	length	length	NOUN
ap-610	542	23	.	.	PUNCT
ap-610	543	1	as	as	SCONJ
ap-610	543	2	shown	show	VERB
ap-610	543	3	in	in	ADP
ap-610	543	4	fig	fig	NOUN
ap-610	543	5	.	.	PUNCT
ap-610	544	1	10a	10a	NOUN
ap-610	544	2	,	,	PUNCT
ap-610	544	3	the	the	DET
ap-610	544	4	critical	critical	ADJ
ap-610	544	5	wavelength	wavelength	NOUN
ap-610	544	6	monotonically	monotonically	ADV
ap-610	544	7	decreases	decrease	VERB
ap-610	544	8	with	with	ADP
ap-610	544	9	increasing	increase	VERB
ap-610	544	10	strain	strain	NOUN
ap-610	544	11	and	and	CCONJ
ap-610	544	12	asymptotically	asymptotically	ADV
ap-610	544	13	tends	tend	VERB
ap-610	544	14	to	to	ADP
ap-610	544	15	zero	zero	NUM
ap-610	544	16	.	.	PUNCT
ap-610	545	1	this	this	DET
ap-610	545	2	property	property	NOUN
ap-610	545	3	has	have	VERB
ap-610	545	4	important	important	ADJ
ap-610	545	5	implications	implication	NOUN
ap-610	545	6	for	for	ADP
ap-610	545	7	the	the	DET
ap-610	545	8	evolution	evolution	NOUN
ap-610	545	9	of	of	ADP
ap-610	545	10	the	the	DET
ap-610	545	11	localized	localized	ADJ
ap-610	545	12	strain	strain	NOUN
ap-610	545	13	©	©	PROPN
ap-610	545	14	czech	czech	PROPN
ap-610	545	15	technical	technical	PROPN
ap-610	545	16	university	university	PROPN
ap-610	545	17	publishing	publishing	NOUN
ap-610	545	18	house	house	NOUN
ap-610	545	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	545	20	31	31	NUM
ap-610	545	21	acta	acta	PROPN
ap-610	545	22	polytechnica	polytechnica	PROPN
ap-610	545	23	vol	vol	NOUN
ap-610	545	24	.	.	PROPN
ap-610	546	1	44	44	NUM
ap-610	547	1	no	no	NOUN
ap-610	547	2	.	.	PUNCT
ap-610	548	1	5–6/2004	5–6/2004	NUM
ap-610	548	2	profile	profile	NOUN
ap-610	548	3	–	–	PUNCT
ap-610	548	4	it	it	PRON
ap-610	548	5	indicates	indicate	VERB
ap-610	548	6	that	that	SCONJ
ap-610	548	7	the	the	DET
ap-610	548	8	active	active	ADJ
ap-610	548	9	zone	zone	NOUN
ap-610	548	10	in	in	ADP
ap-610	548	11	which	which	PRON
ap-610	548	12	strains	strain	NOUN
ap-610	548	13	are	be	AUX
ap-610	548	14	increasing	increase	VERB
ap-610	548	15	tends	tend	VERB
ap-610	548	16	to	to	PART
ap-610	548	17	shrink	shrink	VERB
ap-610	548	18	during	during	ADP
ap-610	548	19	the	the	DET
ap-610	548	20	loading	loading	NOUN
ap-610	548	21	process	process	NOUN
ap-610	548	22	.	.	PUNCT
ap-610	549	1	such	such	DET
ap-610	549	2	a	a	DET
ap-610	549	3	trend	trend	NOUN
ap-610	549	4	has	have	AUX
ap-610	549	5	indeed	indeed	ADV
ap-610	549	6	been	be	AUX
ap-610	549	7	confirmed	confirm	VERB
ap-610	549	8	by	by	ADP
ap-610	549	9	numerical	numerical	ADJ
ap-610	549	10	simulations	simulation	NOUN
ap-610	549	11	.	.	PUNCT
ap-610	550	1	4.4	4.4	NUM
ap-610	550	2	mesh	mesh	NOUN
ap-610	550	3	sensitivity	sensitivity	NOUN
ap-610	550	4	and	and	CCONJ
ap-610	550	5	size	size	NOUN
ap-610	550	6	effect	effect	PROPN
ap-610	550	7	fig	fig	NOUN
ap-610	550	8	.	.	PUNCT
ap-610	551	1	10b	10b	NOUN
ap-610	551	2	shows	show	VERB
ap-610	551	3	the	the	DET
ap-610	551	4	load	load	NOUN
ap-610	551	5	-	-	PUNCT
ap-610	551	6	displacement	displacement	ADJ
ap-610	551	7	diagram	diagram	NOUN
ap-610	551	8	for	for	ADP
ap-610	551	9	strain	strain	NOUN
ap-610	551	10	localization	localization	NOUN
ap-610	551	11	in	in	ADP
ap-610	551	12	a	a	DET
ap-610	551	13	bar	bar	NOUN
ap-610	551	14	under	under	ADP
ap-610	551	15	uniaxial	uniaxial	ADJ
ap-610	551	16	tension	tension	NOUN
ap-610	551	17	,	,	PUNCT
ap-610	551	18	calculated	calculate	VERB
ap-610	551	19	by	by	ADP
ap-610	551	20	the	the	DET
ap-610	551	21	finite	finite	PROPN
ap-610	551	22	element	element	NOUN
ap-610	551	23	method	method	NOUN
ap-610	551	24	using	use	VERB
ap-610	551	25	a	a	DET
ap-610	551	26	nonlocal	nonlocal	ADJ
ap-610	551	27	damage	damage	NOUN
ap-610	551	28	model	model	NOUN
ap-610	551	29	with	with	ADP
ap-610	551	30	the	the	DET
ap-610	551	31	weight	weight	NOUN
ap-610	551	32	function	function	NOUN
ap-610	551	33	(	(	PUNCT
ap-610	551	34	53	53	NUM
ap-610	551	35	)	)	PUNCT
ap-610	551	36	and	and	CCONJ
ap-610	551	37	with	with	ADP
ap-610	551	38	the	the	DET
ap-610	551	39	exponential	exponential	ADJ
ap-610	551	40	damage	damage	NOUN
ap-610	551	41	function	function	NOUN
ap-610	551	42	(	(	PUNCT
ap-610	551	43	87	87	NUM
ap-610	551	44	)	)	PUNCT
ap-610	551	45	.	.	PUNCT
ap-610	552	1	as	as	ADP
ap-610	552	2	the	the	DET
ap-610	552	3	number	number	NOUN
ap-610	552	4	of	of	ADP
ap-610	552	5	elements	element	NOUN
ap-610	552	6	nel	nel	PROPN
ap-610	552	7	increases	increase	NOUN
ap-610	552	8	,	,	PUNCT
ap-610	552	9	the	the	DET
ap-610	552	10	load	load	NOUN
ap-610	552	11	-	-	PUNCT
ap-610	552	12	displacement	displacement	NOUN
ap-610	552	13	curve	curve	NOUN
ap-610	552	14	rapidly	rapidly	ADV
ap-610	552	15	converges	converge	VERB
ap-610	552	16	to	to	ADP
ap-610	552	17	the	the	DET
ap-610	552	18	exact	exact	ADJ
ap-610	552	19	solution	solution	NOUN
ap-610	552	20	.	.	PUNCT
ap-610	553	1	convergence	convergence	NOUN
ap-610	553	2	of	of	ADP
ap-610	553	3	strain	strain	NOUN
ap-610	553	4	and	and	CCONJ
ap-610	553	5	damage	damage	NOUN
ap-610	553	6	profiles	profile	NOUN
ap-610	553	7	generated	generate	VERB
ap-610	553	8	by	by	ADP
ap-610	553	9	an	an	DET
ap-610	553	10	applied	apply	VERB
ap-610	553	11	displacement	displacement	ADJ
ap-610	553	12	u	u	PROPN
ap-610	553	13	l	l	NOUN
ap-610	553	14	�	�	PROPN
ap-610	553	15	2	2	NUM
ap-610	553	16	0	0	NUM
ap-610	553	17	�	�	PROPN
ap-610	553	18	is	be	AUX
ap-610	553	19	documented	document	VERB
ap-610	553	20	in	in	ADP
ap-610	553	21	fig	fig	NOUN
ap-610	553	22	.	.	PUNCT
ap-610	554	1	10c	10c	NOUN
ap-610	554	2	,	,	PUNCT
ap-610	554	3	d.	d.	NOUN
ap-610	554	4	in	in	ADP
ap-610	554	5	contrast	contrast	NOUN
ap-610	554	6	to	to	ADP
ap-610	554	7	the	the	DET
ap-610	554	8	local	local	ADJ
ap-610	554	9	model	model	NOUN
ap-610	554	10	,	,	PUNCT
ap-610	554	11	the	the	DET
ap-610	554	12	process	process	NOUN
ap-610	554	13	zone	zone	NOUN
ap-610	554	14	does	do	AUX
ap-610	554	15	not	not	PART
ap-610	554	16	shrink	shrink	VERB
ap-610	554	17	to	to	ADP
ap-610	554	18	a	a	DET
ap-610	554	19	single	single	ADJ
ap-610	554	20	point	point	NOUN
ap-610	554	21	as	as	SCONJ
ap-610	554	22	the	the	DET
ap-610	554	23	mesh	mesh	NOUN
ap-610	554	24	is	be	AUX
ap-610	554	25	refined	refine	VERB
ap-610	554	26	.	.	PUNCT
ap-610	555	1	its	its	PRON
ap-610	555	2	size	size	NOUN
ap-610	555	3	is	be	AUX
ap-610	555	4	controlled	control	VERB
ap-610	555	5	by	by	ADP
ap-610	555	6	parameter	parameter	NOUN
ap-610	555	7	that	that	PRON
ap-610	555	8	sets	set	VERB
ap-610	555	9	the	the	DET
ap-610	555	10	internal	internal	ADJ
ap-610	555	11	length	length	NOUN
ap-610	555	12	scale	scale	NOUN
ap-610	555	13	.	.	PUNCT
ap-610	556	1	this	this	DET
ap-610	556	2	example	example	NOUN
ap-610	556	3	demonstrates	demonstrate	VERB
ap-610	556	4	that	that	SCONJ
ap-610	556	5	the	the	DET
ap-610	556	6	nonlocal	nonlocal	ADJ
ap-610	556	7	formulation	formulation	NOUN
ap-610	556	8	serves	serve	VERB
ap-610	556	9	as	as	ADP
ap-610	556	10	a	a	DET
ap-610	556	11	localization	localization	NOUN
ap-610	556	12	limiter	limiter	NOUN
ap-610	556	13	and	and	CCONJ
ap-610	556	14	provides	provide	VERB
ap-610	556	15	an	an	DET
ap-610	556	16	objective	objective	ADJ
ap-610	556	17	description	description	NOUN
ap-610	556	18	of	of	ADP
ap-610	556	19	the	the	DET
ap-610	556	20	localization	localization	NOUN
ap-610	556	21	process	process	NOUN
ap-610	556	22	,	,	PUNCT
ap-610	556	23	with	with	ADP
ap-610	556	24	no	no	DET
ap-610	556	25	pathological	pathological	ADJ
ap-610	556	26	sensitivity	sensitivity	NOUN
ap-610	556	27	of	of	ADP
ap-610	556	28	the	the	DET
ap-610	556	29	numerical	numerical	ADJ
ap-610	556	30	results	result	NOUN
ap-610	556	31	to	to	ADP
ap-610	556	32	the	the	DET
ap-610	556	33	discretization	discretization	NOUN
ap-610	556	34	.	.	PUNCT
ap-610	557	1	another	another	DET
ap-610	557	2	important	important	ADJ
ap-610	557	3	advantage	advantage	NOUN
ap-610	557	4	of	of	ADP
ap-610	557	5	nonlocal	nonlocal	ADJ
ap-610	557	6	softening	softening	NOUN
ap-610	557	7	models	model	NOUN
ap-610	557	8	is	be	AUX
ap-610	557	9	that	that	SCONJ
ap-610	557	10	they	they	PRON
ap-610	557	11	can	can	AUX
ap-610	557	12	realistically	realistically	ADV
ap-610	557	13	describe	describe	VERB
ap-610	557	14	the	the	DET
ap-610	557	15	size	size	NOUN
ap-610	557	16	effect	effect	NOUN
ap-610	557	17	on	on	ADP
ap-610	557	18	nominal	nominal	ADJ
ap-610	557	19	strength	strength	NOUN
ap-610	557	20	of	of	ADP
ap-610	557	21	quasibrittle	quasibrittle	ADJ
ap-610	557	22	materials	material	NOUN
ap-610	557	23	.	.	PUNCT
ap-610	558	1	the	the	DET
ap-610	558	2	nominal	nominal	ADJ
ap-610	558	3	strength	strength	NOUN
ap-610	558	4	is	be	AUX
ap-610	558	5	understood	understand	VERB
ap-610	558	6	as	as	ADP
ap-610	558	7	the	the	DET
ap-610	558	8	peak	peak	NOUN
ap-610	558	9	load	load	NOUN
ap-610	558	10	divided	divide	VERB
ap-610	558	11	by	by	ADP
ap-610	558	12	a	a	DET
ap-610	558	13	characteristic	characteristic	ADJ
ap-610	558	14	area	area	NOUN
ap-610	558	15	of	of	ADP
ap-610	558	16	the	the	DET
ap-610	558	17	structure	structure	NOUN
ap-610	558	18	.	.	PUNCT
ap-610	559	1	according	accord	VERB
ap-610	559	2	to	to	ADP
ap-610	559	3	the	the	DET
ap-610	559	4	standard	standard	ADJ
ap-610	559	5	(	(	PUNCT
ap-610	559	6	local	local	ADJ
ap-610	559	7	)	)	PUNCT
ap-610	559	8	version	version	NOUN
ap-610	559	9	of	of	ADP
ap-610	559	10	perfect	perfect	ADJ
ap-610	559	11	plasticity	plasticity	NOUN
ap-610	559	12	theory	theory	NOUN
ap-610	559	13	,	,	PUNCT
ap-610	559	14	the	the	DET
ap-610	559	15	nominal	nominal	ADJ
ap-610	559	16	strength	strength	NOUN
ap-610	559	17	for	for	ADP
ap-610	559	18	a	a	DET
ap-610	559	19	set	set	NOUN
ap-610	559	20	of	of	ADP
ap-610	559	21	geometrically	geometrically	ADV
ap-610	559	22	similar	similar	ADJ
ap-610	559	23	structures	structure	NOUN
ap-610	559	24	of	of	ADP
ap-610	559	25	different	different	ADJ
ap-610	559	26	sizes	size	NOUN
ap-610	559	27	should	should	AUX
ap-610	559	28	be	be	AUX
ap-610	559	29	the	the	DET
ap-610	559	30	same	same	ADJ
ap-610	559	31	,	,	PUNCT
ap-610	559	32	independent	independent	ADJ
ap-610	559	33	of	of	ADP
ap-610	559	34	the	the	DET
ap-610	559	35	size	size	NOUN
ap-610	559	36	.	.	PUNCT
ap-610	560	1	for	for	ADP
ap-610	560	2	instance	instance	NOUN
ap-610	560	3	,	,	PUNCT
ap-610	560	4	for	for	ADP
ap-610	560	5	a	a	DET
ap-610	560	6	beam	beam	NOUN
ap-610	560	7	of	of	ADP
ap-610	560	8	a	a	DET
ap-610	560	9	rectangular	rectangular	ADJ
ap-610	560	10	cross	cross	NOUN
ap-610	560	11	section	section	NOUN
ap-610	560	12	,	,	PUNCT
ap-610	560	13	subjected	subject	VERB
ap-610	560	14	to	to	ADP
ap-610	560	15	three	three	NUM
ap-610	560	16	-	-	PUNCT
ap-610	560	17	point	point	NOUN
ap-610	560	18	bending	bending	NOUN
ap-610	560	19	,	,	PUNCT
ap-610	560	20	the	the	DET
ap-610	560	21	plastic	plastic	ADJ
ap-610	560	22	collapse	collapse	NOUN
ap-610	560	23	load	load	NOUN
ap-610	560	24	is	be	AUX
ap-610	560	25	f	f	PROPN
ap-610	560	26	m	m	PROPN
ap-610	560	27	l	l	NOUN
ap-610	561	1	bd	bd	PROPN
ap-610	561	2	l	l	NOUN
ap-610	561	3	p	p	NOUN
ap-610	561	4	0	0	NUM
ap-610	561	5	2	2	NUM
ap-610	561	6	04	04	NUM
ap-610	561	7	�	�	PROPN
ap-610	561	8	�	�	PROPN
ap-610	561	9	,	,	PUNCT
ap-610	561	10	(	(	PUNCT
ap-610	561	11	89	89	NUM
ap-610	561	12	)	)	PUNCT
ap-610	561	13	where	where	SCONJ
ap-610	561	14	b	b	NOUN
ap-610	561	15	is	be	AUX
ap-610	561	16	the	the	DET
ap-610	561	17	width	width	NOUN
ap-610	561	18	and	and	CCONJ
ap-610	561	19	d	d	X
ap-610	561	20	the	the	DET
ap-610	561	21	depth	depth	NOUN
ap-610	561	22	of	of	ADP
ap-610	561	23	the	the	DET
ap-610	561	24	cross	cross	NOUN
ap-610	561	25	section	section	NOUN
ap-610	561	26	,	,	PUNCT
ap-610	561	27	l	l	PROPN
ap-610	561	28	is	be	AUX
ap-610	561	29	the	the	DET
ap-610	561	30	span	span	NOUN
ap-610	561	31	,	,	PUNCT
ap-610	561	32	mp	mp	PROPN
ap-610	561	33	is	be	AUX
ap-610	561	34	the	the	DET
ap-610	561	35	plastic	plastic	ADJ
ap-610	561	36	limit	limit	NOUN
ap-610	561	37	moment	moment	NOUN
ap-610	561	38	of	of	ADP
ap-610	561	39	the	the	DET
ap-610	561	40	cross	cross	NOUN
ap-610	561	41	section	section	NOUN
ap-610	561	42	,	,	PUNCT
ap-610	561	43	and	and	CCONJ
ap-610	561	44	0	0	NUM
ap-610	561	45	is	be	AUX
ap-610	561	46	the	the	DET
ap-610	561	47	yield	yield	NOUN
ap-610	561	48	stress	stress	NOUN
ap-610	561	49	.	.	PUNCT
ap-610	562	1	the	the	DET
ap-610	562	2	nominal	nominal	ADJ
ap-610	562	3	strength	strength	NOUN
ap-610	562	4	defined	define	VERB
ap-610	562	5	as	as	ADP
ap-610	562	6	the	the	DET
ap-610	562	7	peak	peak	NOUN
ap-610	562	8	load	load	NOUN
ap-610	562	9	divided	divide	VERB
ap-610	562	10	by	by	ADP
ap-610	562	11	the	the	DET
ap-610	562	12	cross	cross	ADJ
ap-610	562	13	-	-	ADJ
ap-610	562	14	sectional	sectional	ADJ
ap-610	562	15	area	area	NOUN
ap-610	562	16	,	,	PUNCT
ap-610	562	17	n	n	PROPN
ap-610	562	18	f	f	PROPN
ap-610	562	19	bd	bd	PROPN
ap-610	562	20	d	d	PROPN
ap-610	562	21	l	l	PROPN
ap-610	562	22	�	�	PROPN
ap-610	562	23	�	�	PROPN
ap-610	562	24	0	0	NUM
ap-610	562	25	0	0	NUM
ap-610	563	1	(	(	PUNCT
ap-610	563	2	90	90	NUM
ap-610	563	3	)	)	PUNCT
ap-610	563	4	is	be	AUX
ap-610	563	5	equal	equal	ADJ
ap-610	563	6	to	to	ADP
ap-610	563	7	the	the	DET
ap-610	563	8	material	material	NOUN
ap-610	563	9	property	property	NOUN
ap-610	563	10	0	0	PUNCT
ap-610	563	11	multiplied	multiply	VERB
ap-610	563	12	by	by	ADP
ap-610	563	13	the	the	DET
ap-610	563	14	geometrical	geometrical	ADJ
ap-610	563	15	factor	factor	NOUN
ap-610	563	16	d	d	PROPN
ap-610	563	17	l	l	PROPN
ap-610	563	18	,	,	PUNCT
ap-610	563	19	which	which	PRON
ap-610	563	20	depends	depend	VERB
ap-610	563	21	only	only	ADV
ap-610	563	22	on	on	ADP
ap-610	563	23	the	the	DET
ap-610	563	24	shape	shape	NOUN
ap-610	563	25	of	of	ADP
ap-610	563	26	the	the	DET
ap-610	563	27	structure	structure	NOUN
ap-610	563	28	but	but	CCONJ
ap-610	563	29	not	not	PART
ap-610	563	30	on	on	ADP
ap-610	563	31	its	its	PRON
ap-610	563	32	size	size	NOUN
ap-610	563	33	(	(	PUNCT
ap-610	563	34	assuming	assume	VERB
ap-610	563	35	proportional	proportional	ADJ
ap-610	563	36	scaling	scaling	NOUN
ap-610	563	37	of	of	ADP
ap-610	563	38	all	all	DET
ap-610	563	39	structural	structural	ADJ
ap-610	563	40	dimensions	dimension	NOUN
ap-610	563	41	for	for	ADP
ap-610	563	42	three	three	NUM
ap-610	563	43	-	-	PUNCT
ap-610	563	44	dimensional	dimensional	ADJ
ap-610	563	45	similarity	similarity	NOUN
ap-610	563	46	,	,	PUNCT
ap-610	563	47	or	or	CCONJ
ap-610	563	48	at	at	ADP
ap-610	563	49	least	least	ADJ
ap-610	563	50	of	of	ADP
ap-610	563	51	the	the	DET
ap-610	563	52	in	in	ADP
ap-610	563	53	-	-	PUNCT
ap-610	563	54	plane	plane	NOUN
ap-610	563	55	dimensions	dimension	NOUN
ap-610	563	56	l	l	PROPN
ap-610	563	57	and	and	CCONJ
ap-610	563	58	d	d	PROPN
ap-610	563	59	for	for	ADP
ap-610	563	60	two	two	NUM
ap-610	563	61	-	-	PUNCT
ap-610	563	62	dimensional	dimensional	ADJ
ap-610	563	63	similarity	similarity	NOUN
ap-610	563	64	)	)	PUNCT
ap-610	563	65	.	.	PUNCT
ap-610	564	1	in	in	ADP
ap-610	564	2	contrast	contrast	NOUN
ap-610	564	3	to	to	ADP
ap-610	564	4	elastic	elastic	ADJ
ap-610	564	5	-	-	PUNCT
ap-610	564	6	perfectly	perfectly	ADV
ap-610	564	7	plastic	plastic	ADJ
ap-610	564	8	structures	structure	NOUN
ap-610	564	9	,	,	PUNCT
ap-610	564	10	structures	structure	NOUN
ap-610	564	11	made	make	VERB
ap-610	564	12	of	of	ADP
ap-610	564	13	quasibrittle	quasibrittle	ADJ
ap-610	564	14	materials	material	NOUN
ap-610	564	15	often	often	ADV
ap-610	564	16	exhibit	exhibit	VERB
ap-610	564	17	a	a	DET
ap-610	564	18	strong	strong	ADJ
ap-610	564	19	size	size	NOUN
ap-610	564	20	dependence	dependence	NOUN
ap-610	564	21	of	of	ADP
ap-610	564	22	the	the	DET
ap-610	564	23	nominal	nominal	ADJ
ap-610	564	24	strength	strength	NOUN
ap-610	564	25	.	.	PUNCT
ap-610	565	1	for	for	ADP
ap-610	565	2	certain	certain	ADJ
ap-610	565	3	specimen	speciman	NOUN
ap-610	565	4	geometries	geometry	NOUN
ap-610	565	5	with	with	ADP
ap-610	565	6	initial	initial	ADJ
ap-610	565	7	notches	notch	NOUN
ap-610	565	8	scaled	scale	VERB
ap-610	565	9	proportionally	proportionally	ADV
ap-610	565	10	to	to	ADP
ap-610	565	11	other	other	ADJ
ap-610	565	12	structural	structural	ADJ
ap-610	565	13	dimensions	dimension	NOUN
ap-610	565	14	,	,	PUNCT
ap-610	565	15	the	the	DET
ap-610	565	16	large	large	ADJ
ap-610	565	17	-	-	PUNCT
ap-610	565	18	size	size	NOUN
ap-610	565	19	limit	limit	NOUN
ap-610	565	20	is	be	AUX
ap-610	565	21	adequately	adequately	ADV
ap-610	565	22	described	describe	VERB
ap-610	565	23	by	by	ADP
ap-610	565	24	linear	linear	ADJ
ap-610	565	25	elastic	elastic	ADJ
ap-610	565	26	fracture	fracture	NOUN
ap-610	565	27	mechanics	mechanic	NOUN
ap-610	565	28	,	,	PUNCT
ap-610	565	29	32	32	NUM
ap-610	565	30	©	©	PROPN
ap-610	565	31	czech	czech	PROPN
ap-610	565	32	technical	technical	PROPN
ap-610	565	33	university	university	PROPN
ap-610	565	34	publishing	publishing	NOUN
ap-610	565	35	house	house	NOUN
ap-610	565	36	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	565	37	acta	acta	PROPN
ap-610	565	38	polytechnica	polytechnica	PROPN
ap-610	565	39	vol	vol	NOUN
ap-610	565	40	.	.	PROPN
ap-610	566	1	44	44	NUM
ap-610	567	1	no	no	NOUN
ap-610	567	2	.	.	PUNCT
ap-610	568	1	5–6/2004	5–6/2004	NUM
ap-610	568	2	(	(	PUNCT
ap-610	568	3	a	a	NOUN
ap-610	568	4	)	)	PUNCT
ap-610	568	5	(	(	PUNCT
ap-610	568	6	b	b	X
ap-610	568	7	)	)	PUNCT
ap-610	568	8	(	(	PUNCT
ap-610	568	9	c	c	X
ap-610	568	10	)	)	PUNCT
ap-610	568	11	(	(	PUNCT
ap-610	568	12	d	d	X
ap-610	568	13	)	)	PUNCT
ap-610	568	14	fig	fig	NOUN
ap-610	568	15	.	.	PUNCT
ap-610	569	1	10	10	NUM
ap-610	569	2	:	:	PUNCT
ap-610	569	3	nonlocal	nonlocal	ADJ
ap-610	569	4	damage	damage	NOUN
ap-610	569	5	model	model	NOUN
ap-610	569	6	:	:	PUNCT
ap-610	569	7	(	(	PUNCT
ap-610	569	8	a	a	X
ap-610	569	9	)	)	PUNCT
ap-610	569	10	critical	critical	ADJ
ap-610	569	11	wavelength	wavelength	NOUN
ap-610	569	12	as	as	ADP
ap-610	569	13	a	a	DET
ap-610	569	14	function	function	NOUN
ap-610	569	15	of	of	ADP
ap-610	569	16	strain	strain	NOUN
ap-610	569	17	(	(	PUNCT
ap-610	569	18	for	for	ADP
ap-610	569	19	reference	reference	NOUN
ap-610	569	20	,	,	PUNCT
ap-610	569	21	the	the	DET
ap-610	569	22	stress	stress	NOUN
ap-610	569	23	-	-	PUNCT
ap-610	569	24	strain	strain	NOUN
ap-610	569	25	curve	curve	NOUN
ap-610	569	26	is	be	AUX
ap-610	569	27	plotted	plot	VERB
ap-610	569	28	by	by	ADP
ap-610	569	29	the	the	DET
ap-610	569	30	dashed	dash	VERB
ap-610	569	31	line	line	NOUN
ap-610	569	32	)	)	PUNCT
ap-610	569	33	,	,	PUNCT
ap-610	569	34	(	(	PUNCT
ap-610	569	35	b	b	X
ap-610	569	36	)	)	PUNCT
ap-610	569	37	convergence	convergence	NOUN
ap-610	569	38	of	of	ADP
ap-610	569	39	load	load	NOUN
ap-610	569	40	-	-	PUNCT
ap-610	569	41	displacement	displacement	NOUN
ap-610	569	42	diagram	diagram	NOUN
ap-610	569	43	,	,	PUNCT
ap-610	569	44	(	(	PUNCT
ap-610	569	45	c	c	X
ap-610	569	46	)	)	PUNCT
ap-610	569	47	convergence	convergence	NOUN
ap-610	569	48	of	of	ADP
ap-610	569	49	strain	strain	NOUN
ap-610	569	50	profile	profile	NOUN
ap-610	569	51	,	,	PUNCT
ap-610	569	52	(	(	PUNCT
ap-610	569	53	d	d	X
ap-610	569	54	)	)	PUNCT
ap-610	569	55	convergence	convergence	NOUN
ap-610	569	56	of	of	ADP
ap-610	569	57	damage	damage	NOUN
ap-610	569	58	profile	profile	NOUN
ap-610	569	59	;	;	PUNCT
ap-610	569	60	nel	nel	PROPN
ap-610	569	61	�	�	PROPN
ap-610	569	62	number	number	NOUN
ap-610	569	63	of	of	ADP
ap-610	569	64	elements	element	NOUN
ap-610	569	65	which	which	PRON
ap-610	569	66	predicts	predict	VERB
ap-610	569	67	proportionality	proportionality	NOUN
ap-610	569	68	of	of	ADP
ap-610	569	69	the	the	DET
ap-610	569	70	nominal	nominal	ADJ
ap-610	569	71	strength	strength	NOUN
ap-610	569	72	to	to	ADP
ap-610	569	73	1	1	NUM
ap-610	569	74	d.	d.	NOUN
ap-610	569	75	the	the	DET
ap-610	569	76	transition	transition	NOUN
ap-610	569	77	between	between	ADP
ap-610	569	78	no	no	DET
ap-610	569	79	size	size	NOUN
ap-610	569	80	effect	effect	NOUN
ap-610	569	81	for	for	ADP
ap-610	569	82	small	small	ADJ
ap-610	569	83	sizes	size	NOUN
ap-610	569	84	and	and	CCONJ
ap-610	569	85	strong	strong	ADJ
ap-610	569	86	size	size	NOUN
ap-610	569	87	effect	effect	NOUN
ap-610	569	88	for	for	ADP
ap-610	569	89	large	large	ADJ
ap-610	569	90	sizes	size	NOUN
ap-610	569	91	can	can	AUX
ap-610	569	92	be	be	AUX
ap-610	569	93	approximated	approximate	VERB
ap-610	569	94	by	by	ADP
ap-610	569	95	bažant	bažant	PROPN
ap-610	569	96	’s	’s	PART
ap-610	569	97	(	(	PUNCT
ap-610	569	98	1984	1984	NUM
ap-610	569	99	)	)	PUNCT
ap-610	569	100	formula	formula	NOUN
ap-610	569	101	n	n	CCONJ
ap-610	569	102	n	n	NOUN
ap-610	569	103	d	d	PROPN
ap-610	569	104	d	d	X
ap-610	569	105	�	�	PROPN
ap-610	569	106	�	�	PROPN
ap-610	569	107	0	0	NUM
ap-610	569	108	0	0	NUM
ap-610	569	109	1	1	NUM
ap-610	569	110	,	,	PUNCT
ap-610	569	111	(	(	PUNCT
ap-610	569	112	91	91	NUM
ap-610	569	113	)	)	PUNCT
ap-610	569	114	where	where	SCONJ
ap-610	569	115	d0	d0	NOUN
ap-610	569	116	and	and	CCONJ
ap-610	569	117	n0	n0	NUM
ap-610	569	118	are	be	AUX
ap-610	569	119	parameters	parameter	NOUN
ap-610	569	120	to	to	PART
ap-610	569	121	be	be	AUX
ap-610	569	122	determined	determine	VERB
ap-610	569	123	by	by	ADP
ap-610	569	124	fitting	fitting	NOUN
ap-610	569	125	of	of	ADP
ap-610	569	126	the	the	DET
ap-610	569	127	experimental	experimental	ADJ
ap-610	569	128	results	result	NOUN
ap-610	569	129	.	.	PUNCT
ap-610	570	1	the	the	DET
ap-610	570	2	transitional	transitional	ADJ
ap-610	570	3	size	size	NOUN
ap-610	570	4	effect	effect	NOUN
ap-610	570	5	characteristic	characteristic	NOUN
ap-610	570	6	of	of	ADP
ap-610	570	7	quasibrittle	quasibrittle	ADJ
ap-610	570	8	structures	structure	NOUN
ap-610	570	9	is	be	AUX
ap-610	570	10	nicely	nicely	ADV
ap-610	570	11	reproduced	reproduce	VERB
ap-610	570	12	by	by	ADP
ap-610	570	13	nonlocal	nonlocal	ADJ
ap-610	570	14	softening	softening	NOUN
ap-610	570	15	models	model	NOUN
ap-610	570	16	,	,	PUNCT
ap-610	570	17	if	if	SCONJ
ap-610	570	18	the	the	DET
ap-610	570	19	model	model	NOUN
ap-610	570	20	parameters	parameter	NOUN
ap-610	570	21	are	be	AUX
ap-610	570	22	chosen	choose	VERB
ap-610	570	23	correctly	correctly	ADV
ap-610	570	24	.	.	PUNCT
ap-610	571	1	as	as	ADP
ap-610	571	2	an	an	DET
ap-610	571	3	example	example	NOUN
ap-610	571	4	,	,	PUNCT
ap-610	571	5	consider	consider	VERB
ap-610	571	6	the	the	DET
ap-610	571	7	compact	compact	ADJ
ap-610	571	8	tension	tension	NOUN
ap-610	571	9	test	test	NOUN
ap-610	571	10	of	of	ADP
ap-610	571	11	concrete	concrete	ADJ
ap-610	571	12	depicted	depict	VERB
ap-610	571	13	in	in	ADP
ap-610	571	14	fig	fig	NOUN
ap-610	571	15	.	.	PUNCT
ap-610	572	1	11a	11a	NOUN
ap-610	572	2	.	.	PUNCT
ap-610	573	1	the	the	DET
ap-610	573	2	experimental	experimental	ADJ
ap-610	573	3	results	result	NOUN
ap-610	573	4	obtained	obtain	VERB
ap-610	573	5	by	by	ADP
ap-610	573	6	wittmann	wittmann	PROPN
ap-610	573	7	,	,	PUNCT
ap-610	573	8	mihashi	mihashi	NOUN
ap-610	573	9	and	and	CCONJ
ap-610	573	10	nomura	nomura	NOUN
ap-610	573	11	(	(	PUNCT
ap-610	573	12	1990	1990	NUM
ap-610	573	13	)	)	PUNCT
ap-610	573	14	are	be	AUX
ap-610	573	15	shown	show	VERB
ap-610	573	16	in	in	ADP
ap-610	573	17	the	the	DET
ap-610	573	18	logarithmic	logarithmic	ADJ
ap-610	573	19	size	size	NOUN
ap-610	573	20	effect	effect	NOUN
ap-610	573	21	diagram	diagram	NOUN
ap-610	573	22	in	in	ADP
ap-610	573	23	fig	fig	NOUN
ap-610	573	24	.	.	PUNCT
ap-610	574	1	11b	11b	NOUN
ap-610	574	2	,	,	PUNCT
ap-610	574	3	along	along	ADP
ap-610	574	4	with	with	ADP
ap-610	574	5	the	the	DET
ap-610	574	6	optimal	optimal	ADJ
ap-610	574	7	fit	fit	NOUN
ap-610	574	8	by	by	ADP
ap-610	574	9	formula	formula	NOUN
ap-610	574	10	(	(	PUNCT
ap-610	574	11	91	91	NUM
ap-610	574	12	)	)	PUNCT
ap-610	574	13	and	and	CCONJ
ap-610	574	14	the	the	DET
ap-610	574	15	results	result	NOUN
ap-610	574	16	of	of	ADP
ap-610	574	17	numerical	numerical	ADJ
ap-610	574	18	simulations	simulation	NOUN
ap-610	574	19	.	.	PUNCT
ap-610	575	1	the	the	DET
ap-610	575	2	role	role	NOUN
ap-610	575	3	of	of	ADP
ap-610	575	4	the	the	DET
ap-610	575	5	characteristic	characteristic	ADJ
ap-610	575	6	structural	structural	ADJ
ap-610	575	7	size	size	NOUN
ap-610	575	8	d	d	X
ap-610	575	9	is	be	AUX
ap-610	575	10	played	play	VERB
ap-610	575	11	by	by	ADP
ap-610	575	12	the	the	DET
ap-610	575	13	ligament	ligament	NOUN
ap-610	575	14	length	length	NOUN
ap-610	575	15	,	,	PUNCT
ap-610	575	16	and	and	CCONJ
ap-610	575	17	the	the	DET
ap-610	575	18	nominal	nominal	ADJ
ap-610	575	19	strength	strength	NOUN
ap-610	575	20	is	be	AUX
ap-610	575	21	defined	define	VERB
ap-610	575	22	as	as	ADP
ap-610	575	23	the	the	DET
ap-610	575	24	peak	peak	NOUN
ap-610	575	25	load	load	NOUN
ap-610	575	26	divided	divide	VERB
ap-610	575	27	by	by	ADP
ap-610	575	28	the	the	DET
ap-610	575	29	ligament	ligament	NOUN
ap-610	575	30	area	area	NOUN
ap-610	575	31	,	,	PUNCT
ap-610	575	32	bd	bd	PROPN
ap-610	575	33	,	,	PUNCT
ap-610	575	34	where	where	SCONJ
ap-610	575	35	b	b	NOUN
ap-610	575	36	is	be	AUX
ap-610	575	37	the	the	DET
ap-610	575	38	out	out	ADJ
ap-610	575	39	-	-	PUNCT
ap-610	575	40	of	of	ADP
ap-610	575	41	-	-	PUNCT
ap-610	575	42	plane	plane	NOUN
ap-610	575	43	thickness	thickness	NOUN
ap-610	575	44	of	of	ADP
ap-610	575	45	the	the	DET
ap-610	575	46	specimen	speciman	NOUN
ap-610	575	47	.	.	PUNCT
ap-610	576	1	the	the	DET
ap-610	576	2	experimentally	experimentally	ADV
ap-610	576	3	measured	measure	VERB
ap-610	576	4	size	size	NOUN
ap-610	576	5	effect	effect	NOUN
ap-610	576	6	can	can	AUX
ap-610	576	7	be	be	AUX
ap-610	576	8	accurately	accurately	ADV
ap-610	576	9	reproduced	reproduce	VERB
ap-610	576	10	by	by	ADP
ap-610	576	11	a	a	DET
ap-610	576	12	nonlocal	nonlocal	ADJ
ap-610	576	13	isotropic	isotropic	ADJ
ap-610	576	14	damage	damage	NOUN
ap-610	576	15	model	model	NOUN
ap-610	576	16	with	with	ADP
ap-610	576	17	different	different	ADJ
ap-610	576	18	combinations	combination	NOUN
ap-610	576	19	of	of	ADP
ap-610	576	20	internal	internal	ADJ
ap-610	576	21	length	length	NOUN
ap-610	576	22	parameter	parameter	NOUN
ap-610	576	23	a	a	PRON
ap-610	576	24	and	and	CCONJ
ap-610	576	25	parameter	parameter	PROPN
ap-610	576	26	�	�	PROPN
ap-610	576	27	f	f	PROPN
ap-610	576	28	of	of	ADP
ap-610	576	29	the	the	DET
ap-610	576	30	damage	damage	NOUN
ap-610	576	31	function	function	NOUN
ap-610	576	32	(	(	PUNCT
ap-610	576	33	86	86	NUM
ap-610	576	34	)	)	PUNCT
ap-610	576	35	.	.	PUNCT
ap-610	577	1	if	if	SCONJ
ap-610	577	2	one	one	NUM
ap-610	577	3	parameter	parameter	NOUN
ap-610	577	4	is	be	AUX
ap-610	577	5	fixed	fix	VERB
ap-610	577	6	,	,	PUNCT
ap-610	577	7	the	the	DET
ap-610	577	8	other	other	ADJ
ap-610	577	9	can	can	AUX
ap-610	577	10	be	be	AUX
ap-610	577	11	determined	determine	VERB
ap-610	577	12	by	by	ADP
ap-610	577	13	optimal	optimal	ADJ
ap-610	577	14	fitting	fitting	NOUN
ap-610	577	15	,	,	PUNCT
ap-610	577	16	but	but	CCONJ
ap-610	577	17	both	both	DET
ap-610	577	18	parameters	parameter	NOUN
ap-610	577	19	can	can	AUX
ap-610	577	20	not	not	PART
ap-610	577	21	be	be	AUX
ap-610	577	22	determined	determine	VERB
ap-610	577	23	simultaneously	simultaneously	ADV
ap-610	577	24	from	from	ADP
ap-610	577	25	the	the	DET
ap-610	577	26	size	size	NOUN
ap-610	577	27	effect	effect	NOUN
ap-610	577	28	on	on	ADP
ap-610	577	29	nominal	nominal	ADJ
ap-610	577	30	strength	strength	NOUN
ap-610	577	31	only	only	ADV
ap-610	577	32	.	.	PUNCT
ap-610	578	1	a	a	DET
ap-610	578	2	unique	unique	ADJ
ap-610	578	3	parameter	parameter	NOUN
ap-610	578	4	identification	identification	NOUN
ap-610	578	5	requires	require	VERB
ap-610	578	6	additional	additional	ADJ
ap-610	578	7	information	information	NOUN
ap-610	578	8	such	such	ADJ
ap-610	578	9	as	as	ADP
ap-610	578	10	the	the	DET
ap-610	578	11	distribution	distribution	NOUN
ap-610	578	12	of	of	ADP
ap-610	578	13	strain	strain	NOUN
ap-610	578	14	or	or	CCONJ
ap-610	578	15	damage	damage	NOUN
ap-610	578	16	in	in	ADP
ap-610	578	17	the	the	DET
ap-610	578	18	process	process	NOUN
ap-610	578	19	zone	zone	NOUN
ap-610	578	20	(	(	PUNCT
ap-610	578	21	geers	geer	NOUN
ap-610	578	22	,	,	PUNCT
ap-610	578	23	de	de	X
ap-610	578	24	borst	borst	X
ap-610	578	25	,	,	PUNCT
ap-610	578	26	brekelmans	brekelman	NOUN
ap-610	578	27	and	and	CCONJ
ap-610	578	28	peerlings	peerling	NOUN
ap-610	578	29	,	,	PUNCT
ap-610	578	30	1999	1999	NUM
ap-610	578	31	)	)	PUNCT
ap-610	578	32	or	or	CCONJ
ap-610	578	33	the	the	DET
ap-610	578	34	size	size	NOUN
ap-610	578	35	effect	effect	NOUN
ap-610	578	36	on	on	ADP
ap-610	578	37	fracture	fracture	PROPN
ap-610	578	38	energy	energy	NOUN
ap-610	578	39	(	(	PUNCT
ap-610	578	40	jirásek	jirásek	NOUN
ap-610	578	41	,	,	PUNCT
ap-610	578	42	rolshoven	rolshoven	ADJ
ap-610	578	43	and	and	CCONJ
ap-610	578	44	grassl	grassl	VERB
ap-610	578	45	,	,	PUNCT
ap-610	578	46	2004	2004	NUM
ap-610	578	47	)	)	PUNCT
ap-610	578	48	.	.	PUNCT
ap-610	579	1	5	5	NUM
ap-610	579	2	concluding	concluding	NOUN
ap-610	579	3	remarks	remark	VERB
ap-610	579	4	the	the	DET
ap-610	579	5	common	common	ADJ
ap-610	579	6	denominator	denominator	NOUN
ap-610	579	7	of	of	ADP
ap-610	579	8	all	all	DET
ap-610	579	9	examples	example	NOUN
ap-610	579	10	presented	present	VERB
ap-610	579	11	in	in	ADP
ap-610	579	12	the	the	DET
ap-610	579	13	preceding	precede	VERB
ap-610	579	14	sections	section	NOUN
ap-610	579	15	is	be	AUX
ap-610	579	16	that	that	SCONJ
ap-610	579	17	the	the	DET
ap-610	579	18	characteristic	characteristic	ADJ
ap-610	579	19	wavelength	wavelength	NOUN
ap-610	579	20	of	of	ADP
ap-610	579	21	the	the	DET
ap-610	579	22	deformation	deformation	NOUN
ap-610	579	23	field	field	NOUN
ap-610	579	24	becomes	become	VERB
ap-610	579	25	comparable	comparable	ADJ
ap-610	579	26	to	to	ADP
ap-610	579	27	the	the	DET
ap-610	579	28	characteristic	characteristic	ADJ
ap-610	579	29	size	size	NOUN
ap-610	579	30	of	of	ADP
ap-610	579	31	the	the	DET
ap-610	579	32	internal	internal	ADJ
ap-610	579	33	material	material	NOUN
ap-610	579	34	structure	structure	NOUN
ap-610	579	35	.	.	PUNCT
ap-610	580	1	here	here	ADV
ap-610	580	2	,	,	PUNCT
ap-610	580	3	the	the	DET
ap-610	580	4	notion	notion	NOUN
ap-610	580	5	of	of	ADP
ap-610	580	6	characteristic	characteristic	ADJ
ap-610	580	7	wavelength	wavelength	NOUN
ap-610	580	8	has	have	VERB
ap-610	580	9	to	to	PART
ap-610	580	10	be	be	AUX
ap-610	580	11	understood	understand	VERB
ap-610	580	12	in	in	ADP
ap-610	580	13	a	a	DET
ap-610	580	14	broad	broad	ADJ
ap-610	580	15	sense	sense	NOUN
ap-610	580	16	,	,	PUNCT
ap-610	580	17	not	not	PART
ap-610	580	18	only	only	ADV
ap-610	580	19	as	as	ADP
ap-610	580	20	the	the	DET
ap-610	580	21	spatial	spatial	ADJ
ap-610	580	22	period	period	NOUN
ap-610	580	23	of	of	ADP
ap-610	580	24	a	a	DET
ap-610	580	25	dynamic	dynamic	ADJ
ap-610	580	26	phenomenon	phenomenon	NOUN
ap-610	580	27	but	but	CCONJ
ap-610	580	28	also	also	ADV
ap-610	580	29	as	as	ADP
ap-610	580	30	the	the	DET
ap-610	580	31	length	length	NOUN
ap-610	580	32	on	on	ADP
ap-610	580	33	which	which	PRON
ap-610	580	34	the	the	DET
ap-610	580	35	value	value	NOUN
ap-610	580	36	of	of	ADP
ap-610	580	37	strain	strain	NOUN
ap-610	580	38	changes	change	NOUN
ap-610	580	39	substantially	substantially	ADV
ap-610	580	40	in	in	ADP
ap-610	580	41	static	static	ADJ
ap-610	580	42	problems	problem	NOUN
ap-610	580	43	.	.	PUNCT
ap-610	581	1	such	such	DET
ap-610	581	2	a	a	DET
ap-610	581	3	more	more	ADV
ap-610	581	4	general	general	ADJ
ap-610	581	5	definition	definition	NOUN
ap-610	581	6	could	could	AUX
ap-610	581	7	be	be	AUX
ap-610	581	8	based	base	VERB
ap-610	581	9	e.g.	e.g.	ADV
ap-610	581	10	on	on	ADP
ap-610	581	11	a	a	DET
ap-610	581	12	suitably	suitably	ADV
ap-610	581	13	normalized	normalize	VERB
ap-610	581	14	ratio	ratio	NOUN
ap-610	581	15	between	between	ADP
ap-610	581	16	the	the	DET
ap-610	581	17	maximum	maximum	ADJ
ap-610	581	18	strain	strain	NOUN
ap-610	581	19	and	and	CCONJ
ap-610	581	20	the	the	DET
ap-610	581	21	maximum	maximum	ADJ
ap-610	581	22	strain	strain	NOUN
ap-610	581	23	gradient	gradient	NOUN
ap-610	581	24	(	(	PUNCT
ap-610	581	25	both	both	CCONJ
ap-610	581	26	in	in	ADP
ap-610	581	27	absolute	absolute	ADJ
ap-610	581	28	values	value	NOUN
ap-610	581	29	)	)	PUNCT
ap-610	581	30	.	.	PUNCT
ap-610	582	1	thus	thus	ADV
ap-610	582	2	the	the	DET
ap-610	582	3	characteristic	characteristic	ADJ
ap-610	582	4	wavelength	wavelength	NOUN
ap-610	582	5	is	be	AUX
ap-610	582	6	necessarily	necessarily	ADV
ap-610	582	7	close	close	ADJ
ap-610	582	8	to	to	ADP
ap-610	582	9	the	the	DET
ap-610	582	10	internal	internal	ADJ
ap-610	582	11	material	material	NOUN
ap-610	582	12	length	length	NOUN
ap-610	582	13	if	if	SCONJ
ap-610	582	14	the	the	DET
ap-610	582	15	size	size	NOUN
ap-610	582	16	of	of	ADP
ap-610	582	17	the	the	DET
ap-610	582	18	specimen	speciman	NOUN
ap-610	582	19	is	be	AUX
ap-610	582	20	not	not	PART
ap-610	582	21	much	much	ADV
ap-610	582	22	larger	large	ADJ
ap-610	582	23	than	than	ADP
ap-610	582	24	the	the	DET
ap-610	582	25	size	size	NOUN
ap-610	582	26	and	and	CCONJ
ap-610	582	27	spacing	spacing	NOUN
ap-610	582	28	of	of	ADP
ap-610	582	29	major	major	ADJ
ap-610	582	30	heterogeneities	heterogeneity	NOUN
ap-610	582	31	,	,	PUNCT
ap-610	582	32	or	or	CCONJ
ap-610	582	33	if	if	SCONJ
ap-610	582	34	strain	strain	NOUN
ap-610	582	35	localizes	localize	VERB
ap-610	582	36	due	due	ADP
ap-610	582	37	to	to	ADP
ap-610	582	38	softening	soften	VERB
ap-610	582	39	.	.	PUNCT
ap-610	583	1	the	the	DET
ap-610	583	2	enrichment	enrichment	NOUN
ap-610	583	3	terms	term	NOUN
ap-610	583	4	introduced	introduce	VERB
ap-610	583	5	by	by	ADP
ap-610	583	6	various	various	ADJ
ap-610	583	7	generalized	generalized	ADJ
ap-610	583	8	continuum	continuum	ADJ
ap-610	583	9	theories	theory	NOUN
ap-610	583	10	have	have	VERB
ap-610	583	11	a	a	DET
ap-610	583	12	differential	differential	ADJ
ap-610	583	13	or	or	CCONJ
ap-610	583	14	integral	integral	ADJ
ap-610	583	15	character	character	NOUN
ap-610	583	16	,	,	PUNCT
ap-610	583	17	but	but	CCONJ
ap-610	583	18	all	all	PRON
ap-610	583	19	of	of	ADP
ap-610	583	20	them	they	PRON
ap-610	583	21	can	can	AUX
ap-610	583	22	be	be	AUX
ap-610	583	23	considered	consider	VERB
ap-610	583	24	as	as	ADP
ap-610	583	25	nonlocal	nonlocal	ADJ
ap-610	583	26	,	,	PUNCT
ap-610	583	27	at	at	ADP
ap-610	583	28	least	least	ADJ
ap-610	583	29	in	in	ADP
ap-610	583	30	the	the	DET
ap-610	583	31	weak	weak	ADJ
ap-610	583	32	sense	sense	NOUN
ap-610	583	33	.	.	PUNCT
ap-610	584	1	they	they	PRON
ap-610	584	2	always	always	ADV
ap-610	584	3	introduce	introduce	VERB
ap-610	584	4	a	a	DET
ap-610	584	5	model	model	NOUN
ap-610	584	6	parameter	parameter	NOUN
ap-610	584	7	with	with	ADP
ap-610	584	8	the	the	DET
ap-610	584	9	dimension	dimension	NOUN
ap-610	584	10	of	of	ADP
ap-610	584	11	length	length	NOUN
ap-610	584	12	,	,	PUNCT
ap-610	584	13	which	which	PRON
ap-610	584	14	reflects	reflect	VERB
ap-610	584	15	the	the	DET
ap-610	584	16	internal	internal	ADJ
ap-610	584	17	length	length	NOUN
ap-610	584	18	scale	scale	NOUN
ap-610	584	19	of	of	ADP
ap-610	584	20	the	the	DET
ap-610	584	21	material	material	NOUN
ap-610	584	22	.	.	PUNCT
ap-610	585	1	three	three	NUM
ap-610	585	2	typical	typical	ADJ
ap-610	585	3	cases	case	NOUN
ap-610	585	4	covered	cover	VERB
ap-610	585	5	here	here	ADV
ap-610	585	6	encompass	encompass	VERB
ap-610	585	7	static	static	ADJ
ap-610	585	8	and	and	CCONJ
ap-610	585	9	dynamic	dynamic	ADJ
ap-610	585	10	phenomena	phenomenon	NOUN
ap-610	585	11	,	,	PUNCT
ap-610	585	12	linear	linear	ADJ
ap-610	585	13	and	and	CCONJ
ap-610	585	14	nonlinear	nonlinear	ADJ
ap-610	585	15	behavior	behavior	NOUN
ap-610	585	16	,	,	PUNCT
ap-610	585	17	and	and	CCONJ
ap-610	585	18	three	three	NUM
ap-610	585	19	classes	class	NOUN
ap-610	585	20	of	of	ADP
ap-610	585	21	material	material	NOUN
ap-610	585	22	laws	law	NOUN
ap-610	585	23	,	,	PUNCT
ap-610	585	24	namely	namely	ADV
ap-610	585	25	elasticity	elasticity	NOUN
ap-610	585	26	,	,	PUNCT
ap-610	585	27	plasticity	plasticity	NOUN
ap-610	585	28	and	and	CCONJ
ap-610	585	29	continuum	continuum	ADJ
ap-610	585	30	damage	damage	NOUN
ap-610	585	31	mechanics	mechanic	NOUN
ap-610	585	32	.	.	PUNCT
ap-610	586	1	this	this	PRON
ap-610	586	2	shows	show	VERB
ap-610	586	3	that	that	SCONJ
ap-610	586	4	the	the	DET
ap-610	586	5	nonlocal	nonlocal	ADJ
ap-610	586	6	enrichments	enrichment	NOUN
ap-610	586	7	can	can	AUX
ap-610	586	8	be	be	AUX
ap-610	586	9	useful	useful	ADJ
ap-610	586	10	in	in	ADP
ap-610	586	11	a	a	DET
ap-610	586	12	wide	wide	ADJ
ap-610	586	13	range	range	NOUN
ap-610	586	14	of	of	ADP
ap-610	586	15	mechanical	mechanical	ADJ
ap-610	586	16	problems	problem	NOUN
ap-610	586	17	.	.	PUNCT
ap-610	587	1	unfortunately	unfortunately	ADV
ap-610	587	2	,	,	PUNCT
ap-610	587	3	so	so	ADV
ap-610	587	4	far	far	ADV
ap-610	587	5	there	there	PRON
ap-610	587	6	is	be	VERB
ap-610	587	7	no	no	DET
ap-610	587	8	general	general	ADJ
ap-610	587	9	and	and	CCONJ
ap-610	587	10	universally	universally	ADV
ap-610	587	11	accepted	accept	VERB
ap-610	587	12	theory	theory	NOUN
ap-610	587	13	covering	cover	VERB
ap-610	587	14	this	this	DET
ap-610	587	15	entire	entire	ADJ
ap-610	587	16	range	range	NOUN
ap-610	587	17	within	within	ADP
ap-610	587	18	one	one	NUM
ap-610	587	19	unified	unified	ADJ
ap-610	587	20	framework	framework	NOUN
ap-610	587	21	.	.	PUNCT
ap-610	588	1	even	even	ADV
ap-610	588	2	though	though	SCONJ
ap-610	588	3	the	the	DET
ap-610	588	4	first	first	ADJ
ap-610	588	5	nonlocal	nonlocal	ADJ
ap-610	588	6	theories	theory	NOUN
ap-610	588	7	were	be	AUX
ap-610	588	8	pioneered	pioneer	VERB
ap-610	588	9	in	in	ADP
ap-610	588	10	the	the	DET
ap-610	588	11	1960s	1960	NOUN
ap-610	588	12	,	,	PUNCT
ap-610	588	13	there	there	ADV
ap-610	588	14	many	many	ADJ
ap-610	588	15	problems	problem	NOUN
ap-610	588	16	remain	remain	VERB
ap-610	588	17	open	open	ADJ
ap-610	588	18	and	and	CCONJ
ap-610	588	19	many	many	ADJ
ap-610	588	20	issues	issue	NOUN
ap-610	588	21	unresolved	unresolve	VERB
ap-610	588	22	.	.	PUNCT
ap-610	589	1	some	some	PRON
ap-610	589	2	of	of	ADP
ap-610	589	3	the	the	DET
ap-610	589	4	most	most	ADV
ap-610	589	5	challenging	challenging	ADJ
ap-610	589	6	questions	question	NOUN
ap-610	589	7	include	include	VERB
ap-610	589	8	the	the	DET
ap-610	589	9	correct	correct	ADJ
ap-610	589	10	formulation	formulation	NOUN
ap-610	589	11	of	of	ADP
ap-610	589	12	boundary	boundary	ADJ
ap-610	589	13	conditions	condition	NOUN
ap-610	589	14	,	,	PUNCT
ap-610	589	15	micromechanical	micromechanical	ADJ
ap-610	589	16	justification	justification	NOUN
ap-610	589	17	of	of	ADP
ap-610	589	18	models	model	NOUN
ap-610	589	19	with	with	ADP
ap-610	589	20	nonlocal	nonlocal	ADJ
ap-610	589	21	internal	internal	ADJ
ap-610	589	22	variables	variable	NOUN
ap-610	589	23	,	,	PUNCT
ap-610	589	24	or	or	CCONJ
ap-610	589	25	identification	identification	NOUN
ap-610	589	26	techniques	technique	NOUN
ap-610	589	27	for	for	ADP
ap-610	589	28	the	the	DET
ap-610	589	29	internal	internal	ADJ
ap-610	589	30	length	length	NOUN
ap-610	589	31	parameter	parameter	NOUN
ap-610	589	32	and	and	CCONJ
ap-610	589	33	its	its	PRON
ap-610	589	34	possible	possible	ADJ
ap-610	589	35	evolution	evolution	NOUN
ap-610	589	36	.	.	PUNCT
ap-610	590	1	references	reference	NOUN
ap-610	590	2	[	[	X
ap-610	590	3	1	1	NUM
ap-610	590	4	]	]	X
ap-610	590	5	aifantis	aifantis	PROPN
ap-610	590	6	e.	e.	PROPN
ap-610	590	7	c.	c.	PROPN
ap-610	590	8	:	:	PUNCT
ap-610	590	9	“	"	PUNCT
ap-610	590	10	on	on	ADP
ap-610	590	11	the	the	DET
ap-610	590	12	microstructural	microstructural	ADJ
ap-610	590	13	origin	origin	NOUN
ap-610	590	14	of	of	ADP
ap-610	590	15	certain	certain	ADJ
ap-610	590	16	inelastic	inelastic	ADJ
ap-610	590	17	models	model	NOUN
ap-610	590	18	.	.	PUNCT
ap-610	590	19	”	"	PUNCT
ap-610	591	1	journal	journal	NOUN
ap-610	591	2	of	of	ADP
ap-610	591	3	engineering	engineering	NOUN
ap-610	591	4	mechanics	mechanic	NOUN
ap-610	591	5	and	and	CCONJ
ap-610	591	6	technology	technology	NOUN
ap-610	591	7	,	,	PUNCT
ap-610	591	8	asme	asme	PROPN
ap-610	591	9	,	,	PUNCT
ap-610	591	10	vol	vol	NOUN
ap-610	591	11	.	.	PROPN
ap-610	591	12	106	106	NUM
ap-610	591	13	(	(	PUNCT
ap-610	591	14	1984	1984	NUM
ap-610	591	15	)	)	PUNCT
ap-610	591	16	,	,	PUNCT
ap-610	592	1	p.	p.	NOUN
ap-610	592	2	326–330	326–330	NUM
ap-610	592	3	.	.	PUNCT
ap-610	593	1	[	[	X
ap-610	593	2	2	2	NUM
ap-610	593	3	]	]	X
ap-610	593	4	aifantis	aifantis	PROPN
ap-610	593	5	e.	e.	PROPN
ap-610	593	6	c.	c.	PROPN
ap-610	593	7	:	:	PUNCT
ap-610	593	8	“	"	PUNCT
ap-610	593	9	update	update	NOUN
ap-610	593	10	on	on	ADP
ap-610	593	11	a	a	DET
ap-610	593	12	class	class	NOUN
ap-610	593	13	of	of	ADP
ap-610	593	14	gradient	gradient	NOUN
ap-610	593	15	theories	theory	NOUN
ap-610	593	16	.	.	PUNCT
ap-610	593	17	”	"	PUNCT
ap-610	593	18	mechanics	mechanic	NOUN
ap-610	593	19	of	of	ADP
ap-610	593	20	materials	material	NOUN
ap-610	593	21	,	,	PUNCT
ap-610	593	22	vol	vol	NOUN
ap-610	593	23	.	.	PROPN
ap-610	593	24	35	35	NUM
ap-610	593	25	(	(	PUNCT
ap-610	593	26	2003	2003	NUM
ap-610	593	27	)	)	PUNCT
ap-610	593	28	,	,	PUNCT
ap-610	593	29	p.	p.	NOUN
ap-610	593	30	259–280	259–280	NUM
ap-610	593	31	.	.	PUNCT
ap-610	594	1	[	[	X
ap-610	594	2	3	3	X
ap-610	594	3	]	]	PUNCT
ap-610	594	4	askes	ask	VERB
ap-610	594	5	h.	h.	PROPN
ap-610	594	6	,	,	PUNCT
ap-610	594	7	metrikine	metrikine	NOUN
ap-610	594	8	a.	a.	PROPN
ap-610	594	9	v.	v.	PROPN
ap-610	594	10	:	:	PUNCT
ap-610	594	11	“	"	PUNCT
ap-610	594	12	one	one	NUM
ap-610	594	13	-	-	PUNCT
ap-610	594	14	dimensional	dimensional	ADJ
ap-610	594	15	dynamically	dynamically	ADV
ap-610	594	16	consistent	consistent	ADJ
ap-610	594	17	gradient	gradient	NOUN
ap-610	594	18	elasticity	elasticity	NOUN
ap-610	594	19	models	model	NOUN
ap-610	594	20	derived	derive	VERB
ap-610	594	21	from	from	ADP
ap-610	594	22	a	a	DET
ap-610	594	23	discrete	discrete	ADJ
ap-610	594	24	microstructure	microstructure	NOUN
ap-610	594	25	.	.	PUNCT
ap-610	595	1	part	part	NOUN
ap-610	595	2	2	2	NUM
ap-610	595	3	:	:	PUNCT
ap-610	595	4	static	static	ADJ
ap-610	595	5	and	and	CCONJ
ap-610	595	6	dynamic	dynamic	ADJ
ap-610	595	7	response	response	NOUN
ap-610	595	8	.	.	PUNCT
ap-610	595	9	”	"	PUNCT
ap-610	596	1	european	european	PROPN
ap-610	596	2	journal	journal	PROPN
ap-610	596	3	of	of	ADP
ap-610	596	4	mechanics	mechanic	NOUN
ap-610	596	5	a	a	PRON
ap-610	596	6	,	,	PUNCT
ap-610	596	7	vol	vol	NOUN
ap-610	596	8	.	.	PROPN
ap-610	596	9	21	21	NUM
ap-610	596	10	(	(	PUNCT
ap-610	596	11	2002	2002	NUM
ap-610	596	12	)	)	PUNCT
ap-610	596	13	,	,	PUNCT
ap-610	596	14	p.	p.	NOUN
ap-610	596	15	573–588	573–588	NUM
ap-610	596	16	.	.	PUNCT
ap-610	597	1	©	©	PROPN
ap-610	597	2	czech	czech	PROPN
ap-610	597	3	technical	technical	PROPN
ap-610	597	4	university	university	PROPN
ap-610	597	5	publishing	publishing	NOUN
ap-610	597	6	house	house	NOUN
ap-610	597	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	597	8	33	33	NUM
ap-610	597	9	acta	acta	PROPN
ap-610	597	10	polytechnica	polytechnica	PROPN
ap-610	597	11	vol	vol	NOUN
ap-610	597	12	.	.	PROPN
ap-610	598	1	44	44	NUM
ap-610	598	2	no	no	NOUN
ap-610	598	3	.	.	PUNCT
ap-610	599	1	5–6/2004	5–6/2004	NUM
ap-610	599	2	(	(	PUNCT
ap-610	599	3	a	a	NOUN
ap-610	599	4	)	)	PUNCT
ap-610	599	5	(	(	PUNCT
ap-610	599	6	b	b	X
ap-610	599	7	)	)	PUNCT
ap-610	599	8	fig	fig	NOUN
ap-610	599	9	.	.	PUNCT
ap-610	600	1	11	11	NUM
ap-610	600	2	:	:	PUNCT
ap-610	600	3	(	(	PUNCT
ap-610	600	4	a	a	X
ap-610	600	5	)	)	PUNCT
ap-610	600	6	compact	compact	ADJ
ap-610	600	7	tension	tension	NOUN
ap-610	600	8	specimen	speciman	NOUN
ap-610	600	9	,	,	PUNCT
ap-610	600	10	(	(	PUNCT
ap-610	600	11	b	b	NOUN
ap-610	600	12	)	)	PUNCT
ap-610	600	13	size	size	NOUN
ap-610	600	14	effect	effect	NOUN
ap-610	600	15	diagram	diagram	NOUN
ap-610	601	1	[	[	X
ap-610	601	2	4	4	X
ap-610	601	3	]	]	PUNCT
ap-610	601	4	bažant	bažant	PROPN
ap-610	601	5	z.	z.	PROPN
ap-610	601	6	p.	p.	PROPN
ap-610	601	7	:	:	PUNCT
ap-610	601	8	“	"	PUNCT
ap-610	601	9	size	size	NOUN
ap-610	601	10	effect	effect	NOUN
ap-610	601	11	in	in	ADP
ap-610	601	12	blunt	blunt	ADJ
ap-610	601	13	fracture	fracture	NOUN
ap-610	601	14	:	:	PUNCT
ap-610	602	1	concrete	concrete	ADJ
ap-610	602	2	,	,	PUNCT
ap-610	602	3	rock	rock	NOUN
ap-610	602	4	,	,	PUNCT
ap-610	602	5	metal	metal	NOUN
ap-610	602	6	.	.	PUNCT
ap-610	602	7	”	"	PUNCT
ap-610	603	1	journal	journal	NOUN
ap-610	603	2	of	of	ADP
ap-610	603	3	engineering	engineering	NOUN
ap-610	603	4	mechanics	mechanic	NOUN
ap-610	603	5	,	,	PUNCT
ap-610	603	6	asce	asce	NOUN
ap-610	603	7	,	,	PUNCT
ap-610	603	8	vol	vol	NOUN
ap-610	603	9	.	.	PUNCT
ap-610	604	1	110	110	NUM
ap-610	604	2	(	(	PUNCT
ap-610	604	3	1984	1984	NUM
ap-610	604	4	)	)	PUNCT
ap-610	604	5	,	,	PUNCT
ap-610	605	1	p.	p.	NOUN
ap-610	605	2	518–535	518–535	NUM
ap-610	605	3	.	.	PUNCT
ap-610	606	1	[	[	X
ap-610	606	2	5	5	NUM
ap-610	606	3	]	]	PUNCT
ap-610	606	4	bažant	bažant	PROPN
ap-610	606	5	z.	z.	PROPN
ap-610	606	6	p.	p.	PROPN
ap-610	606	7	,	,	PUNCT
ap-610	606	8	chang	chang	PROPN
ap-610	606	9	,	,	PUNCT
ap-610	606	10	t.-p	t.-p	PROPN
ap-610	606	11	.	.	PUNCT
ap-610	606	12	:	:	PUNCT
ap-610	606	13	“	"	PUNCT
ap-610	606	14	instability	instability	NOUN
ap-610	606	15	of	of	ADP
ap-610	606	16	nonlocal	nonlocal	ADJ
ap-610	606	17	continuum	continuum	ADJ
ap-610	606	18	and	and	CCONJ
ap-610	606	19	strain	strain	ADJ
ap-610	606	20	averaging	average	VERB
ap-610	606	21	.	.	PUNCT
ap-610	606	22	”	"	PUNCT
ap-610	606	23	journal	journal	NOUN
ap-610	606	24	of	of	ADP
ap-610	606	25	engineering	engineering	NOUN
ap-610	606	26	mechanics	mechanic	NOUN
ap-610	606	27	,	,	PUNCT
ap-610	606	28	asce	asce	NOUN
ap-610	606	29	,	,	PUNCT
ap-610	606	30	vol	vol	NOUN
ap-610	606	31	.	.	PUNCT
ap-610	607	1	110	110	NUM
ap-610	607	2	(	(	PUNCT
ap-610	607	3	1984	1984	NUM
ap-610	607	4	)	)	PUNCT
ap-610	607	5	,	,	PUNCT
ap-610	607	6	p.	p.	NOUN
ap-610	607	7	2015–2035	2015–2035	NUM
ap-610	607	8	.	.	PUNCT
ap-610	608	1	[	[	X
ap-610	608	2	6	6	NUM
ap-610	608	3	]	]	PUNCT
ap-610	608	4	bažant	bažant	PROPN
ap-610	608	5	z.	z.	PROPN
ap-610	608	6	p.	p.	PROPN
ap-610	608	7	,	,	PUNCT
ap-610	608	8	jirásek	jirásek	PROPN
ap-610	608	9	m.	m.	NOUN
ap-610	608	10	:	:	PUNCT
ap-610	608	11	“	"	PUNCT
ap-610	608	12	nonlocal	nonlocal	ADJ
ap-610	608	13	integral	integral	ADJ
ap-610	608	14	formulations	formulation	NOUN
ap-610	608	15	of	of	ADP
ap-610	608	16	plasticity	plasticity	NOUN
ap-610	608	17	and	and	CCONJ
ap-610	608	18	damage	damage	NOUN
ap-610	608	19	:	:	PUNCT
ap-610	608	20	survey	survey	NOUN
ap-610	608	21	of	of	ADP
ap-610	608	22	progress	progress	NOUN
ap-610	608	23	.	.	PUNCT
ap-610	608	24	”	"	PUNCT
ap-610	608	25	journal	journal	NOUN
ap-610	608	26	of	of	ADP
ap-610	608	27	engineering	engineering	NOUN
ap-610	608	28	mechanics	mechanic	NOUN
ap-610	608	29	,	,	PUNCT
ap-610	608	30	asce	asce	NOUN
ap-610	608	31	,	,	PUNCT
ap-610	608	32	vol	vol	NOUN
ap-610	608	33	.	.	PROPN
ap-610	608	34	128	128	NUM
ap-610	608	35	(	(	PUNCT
ap-610	608	36	2002	2002	NUM
ap-610	608	37	)	)	PUNCT
ap-610	608	38	,	,	PUNCT
ap-610	608	39	p.	p.	NOUN
ap-610	608	40	1119–1149	1119–1149	NUM
ap-610	608	41	.	.	PUNCT
ap-610	609	1	[	[	X
ap-610	609	2	7	7	X
ap-610	609	3	]	]	X
ap-610	609	4	bažant	bažant	PROPN
ap-610	609	5	z.	z.	PROPN
ap-610	609	6	p.	p.	PROPN
ap-610	609	7	,	,	PUNCT
ap-610	609	8	belytschko	belytschko	PROPN
ap-610	609	9	t.	t.	PROPN
ap-610	609	10	b.	b.	PROPN
ap-610	609	11	,	,	PUNCT
ap-610	609	12	chang	chang	PROPN
ap-610	609	13	,	,	PUNCT
ap-610	609	14	t.-p	t.-p	PROPN
ap-610	609	15	.	.	PUNCT
ap-610	609	16	:	:	PUNCT
ap-610	609	17	“	"	PUNCT
ap-610	609	18	continuum	continuum	ADJ
ap-610	609	19	model	model	NOUN
ap-610	609	20	for	for	ADP
ap-610	609	21	strain	strain	NOUN
ap-610	609	22	softening	soften	VERB
ap-610	609	23	.	.	PUNCT
ap-610	609	24	”	"	PUNCT
ap-610	609	25	journal	journal	NOUN
ap-610	609	26	of	of	ADP
ap-610	609	27	engineering	engineering	NOUN
ap-610	609	28	mechanics	mechanic	NOUN
ap-610	609	29	,	,	PUNCT
ap-610	609	30	asce	asce	NOUN
ap-610	609	31	,	,	PUNCT
ap-610	609	32	vol	vol	NOUN
ap-610	609	33	.	.	PUNCT
ap-610	610	1	110	110	NUM
ap-610	610	2	(	(	PUNCT
ap-610	610	3	1984	1984	NUM
ap-610	610	4	)	)	PUNCT
ap-610	610	5	,	,	PUNCT
ap-610	611	1	p.	p.	NOUN
ap-610	611	2	1666–1692	1666–1692	NUM
ap-610	611	3	.	.	PUNCT
ap-610	612	1	[	[	X
ap-610	612	2	8	8	X
ap-610	612	3	]	]	X
ap-610	612	4	eringen	eringen	PROPN
ap-610	612	5	a.	a.	PROPN
ap-610	612	6	c.	c.	PROPN
ap-610	612	7	:	:	PUNCT
ap-610	612	8	“	"	PUNCT
ap-610	612	9	linear	linear	ADJ
ap-610	612	10	theory	theory	NOUN
ap-610	612	11	of	of	ADP
ap-610	612	12	nonlocal	nonlocal	ADJ
ap-610	612	13	elasticity	elasticity	NOUN
ap-610	612	14	and	and	CCONJ
ap-610	612	15	dispersion	dispersion	NOUN
ap-610	612	16	of	of	ADP
ap-610	612	17	plane	plane	NOUN
ap-610	612	18	waves	wave	NOUN
ap-610	612	19	.	.	PUNCT
ap-610	612	20	”	"	PUNCT
ap-610	613	1	international	international	ADJ
ap-610	613	2	journal	journal	NOUN
ap-610	613	3	of	of	ADP
ap-610	613	4	engineering	engineering	NOUN
ap-610	613	5	science	science	NOUN
ap-610	613	6	,	,	PUNCT
ap-610	613	7	vol	vol	NOUN
ap-610	613	8	.	.	PROPN
ap-610	614	1	10	10	NUM
ap-610	614	2	(	(	PUNCT
ap-610	614	3	1972	1972	NUM
ap-610	614	4	)	)	PUNCT
ap-610	614	5	,	,	PUNCT
ap-610	615	1	p.	p.	NOUN
ap-610	615	2	425–435	425–435	NUM
ap-610	615	3	.	.	PUNCT
ap-610	616	1	[	[	X
ap-610	616	2	9	9	NUM
ap-610	616	3	]	]	PUNCT
ap-610	616	4	fish	fish	NOUN
ap-610	616	5	j.	j.	PROPN
ap-610	616	6	,	,	PUNCT
ap-610	616	7	chen	chen	PROPN
ap-610	616	8	w.	w.	PROPN
ap-610	616	9	,	,	PUNCT
ap-610	616	10	nagai	nagai	PROPN
ap-610	616	11	,	,	PUNCT
ap-610	616	12	g.	g.	PROPN
ap-610	616	13	:	:	PUNCT
ap-610	616	14	“	"	PUNCT
ap-610	616	15	nonlocal	nonlocal	ADJ
ap-610	616	16	dispersive	dispersive	ADJ
ap-610	616	17	model	model	NOUN
ap-610	616	18	for	for	ADP
ap-610	616	19	wave	wave	NOUN
ap-610	616	20	propagation	propagation	NOUN
ap-610	616	21	in	in	ADP
ap-610	616	22	heterogeneous	heterogeneous	ADJ
ap-610	616	23	media	medium	NOUN
ap-610	616	24	.	.	PUNCT
ap-610	617	1	part	part	NOUN
ap-610	617	2	1	1	NUM
ap-610	617	3	:	:	PUNCT
ap-610	617	4	one	one	NUM
ap-610	617	5	-	-	PUNCT
ap-610	617	6	dimensional	dimensional	ADJ
ap-610	617	7	case	case	NOUN
ap-610	617	8	.	.	PUNCT
ap-610	617	9	”	"	PUNCT
ap-610	618	1	international	international	ADJ
ap-610	618	2	journal	journal	NOUN
ap-610	618	3	for	for	ADP
ap-610	618	4	numerical	numerical	ADJ
ap-610	618	5	methods	method	NOUN
ap-610	618	6	in	in	ADP
ap-610	618	7	engineering	engineering	NOUN
ap-610	618	8	,	,	PUNCT
ap-610	618	9	vol	vol	NOUN
ap-610	618	10	.	.	PROPN
ap-610	618	11	54	54	NUM
ap-610	618	12	(	(	PUNCT
ap-610	618	13	2002a	2002a	NUM
ap-610	618	14	)	)	PUNCT
ap-610	618	15	,	,	PUNCT
ap-610	618	16	p.	p.	NOUN
ap-610	618	17	331–346	331–346	NUM
ap-610	618	18	.	.	PUNCT
ap-610	619	1	[	[	X
ap-610	619	2	10	10	NUM
ap-610	619	3	]	]	X
ap-610	619	4	fish	fish	NOUN
ap-610	619	5	j.	j.	PROPN
ap-610	619	6	,	,	PUNCT
ap-610	619	7	chen	chen	PROPN
ap-610	619	8	w.	w.	PROPN
ap-610	619	9	,	,	PUNCT
ap-610	619	10	nagai	nagai	PROPN
ap-610	619	11	g.	g.	PROPN
ap-610	619	12	:	:	PUNCT
ap-610	619	13	“	"	PUNCT
ap-610	619	14	nonlocal	nonlocal	ADJ
ap-610	619	15	dispersive	dispersive	ADJ
ap-610	619	16	model	model	NOUN
ap-610	619	17	for	for	ADP
ap-610	619	18	wave	wave	NOUN
ap-610	619	19	propagation	propagation	NOUN
ap-610	619	20	in	in	ADP
ap-610	619	21	heterogeneous	heterogeneous	ADJ
ap-610	619	22	media	medium	NOUN
ap-610	619	23	.	.	PUNCT
ap-610	620	1	part	part	NOUN
ap-610	620	2	2	2	NUM
ap-610	620	3	:	:	PUNCT
ap-610	620	4	multi	multi	ADJ
ap-610	620	5	-	-	ADJ
ap-610	620	6	dimensional	dimensional	ADJ
ap-610	620	7	case	case	NOUN
ap-610	620	8	.	.	PUNCT
ap-610	620	9	”	"	PUNCT
ap-610	621	1	international	international	ADJ
ap-610	621	2	journal	journal	NOUN
ap-610	621	3	for	for	ADP
ap-610	621	4	numerical	numerical	ADJ
ap-610	621	5	methods	method	NOUN
ap-610	621	6	in	in	ADP
ap-610	621	7	engineering	engineering	NOUN
ap-610	621	8	,	,	PUNCT
ap-610	621	9	vol	vol	NOUN
ap-610	621	10	.	.	PROPN
ap-610	621	11	54	54	NUM
ap-610	621	12	(	(	PUNCT
ap-610	621	13	2002b	2002b	NUM
ap-610	621	14	)	)	PUNCT
ap-610	621	15	,	,	PUNCT
ap-610	621	16	p.	p.	NOUN
ap-610	621	17	347–363	347–363	NUM
ap-610	621	18	.	.	PUNCT
ap-610	622	1	[	[	X
ap-610	622	2	11	11	NUM
ap-610	622	3	]	]	SYM
ap-610	622	4	fleck	fleck	NOUN
ap-610	622	5	n.	n.	PROPN
ap-610	622	6	a.	a.	PROPN
ap-610	622	7	,	,	PUNCT
ap-610	622	8	hutchinson	hutchinson	PROPN
ap-610	622	9	j.	j.	PROPN
ap-610	622	10	w.	w.	PROPN
ap-610	622	11	:	:	PUNCT
ap-610	622	12	“	"	PUNCT
ap-610	622	13	a	a	DET
ap-610	622	14	reformulation	reformulation	NOUN
ap-610	622	15	of	of	ADP
ap-610	622	16	strain	strain	NOUN
ap-610	622	17	gradient	gradient	NOUN
ap-610	622	18	plasticity	plasticity	NOUN
ap-610	622	19	.	.	PUNCT
ap-610	622	20	”	"	PUNCT
ap-610	622	21	journal	journal	NOUN
ap-610	622	22	of	of	ADP
ap-610	622	23	the	the	DET
ap-610	622	24	mechanics	mechanic	NOUN
ap-610	622	25	and	and	CCONJ
ap-610	622	26	physics	physic	NOUN
ap-610	622	27	of	of	ADP
ap-610	622	28	solids	solid	NOUN
ap-610	622	29	,	,	PUNCT
ap-610	622	30	vol	vol	NOUN
ap-610	622	31	.	.	PROPN
ap-610	622	32	49	49	NUM
ap-610	622	33	(	(	PUNCT
ap-610	622	34	2001	2001	NUM
ap-610	622	35	)	)	PUNCT
ap-610	622	36	,	,	PUNCT
ap-610	622	37	p.	p.	NOUN
ap-610	622	38	2245–2271	2245–2271	NUM
ap-610	622	39	.	.	PUNCT
ap-610	623	1	[	[	X
ap-610	623	2	12	12	NUM
ap-610	623	3	]	]	PUNCT
ap-610	623	4	fleck	fleck	NOUN
ap-610	623	5	n.	n.	PROPN
ap-610	623	6	a.	a.	PROPN
ap-610	623	7	,	,	PUNCT
ap-610	623	8	muller	muller	PROPN
ap-610	623	9	g.	g.	PROPN
ap-610	623	10	m.	m.	PROPN
ap-610	623	11	,	,	PUNCT
ap-610	623	12	ashby	ashby	PROPN
ap-610	623	13	m.	m.	PROPN
ap-610	623	14	f.	f.	PROPN
ap-610	623	15	,	,	PUNCT
ap-610	623	16	hutchinson	hutchinson	PROPN
ap-610	623	17	j.	j.	PROPN
ap-610	623	18	w.	w.	PROPN
ap-610	623	19	:	:	PUNCT
ap-610	623	20	“	"	PUNCT
ap-610	623	21	strain	strain	VERB
ap-610	623	22	gradient	gradient	ADJ
ap-610	623	23	plasticity	plasticity	NOUN
ap-610	623	24	:	:	PUNCT
ap-610	623	25	theory	theory	NOUN
ap-610	623	26	and	and	CCONJ
ap-610	623	27	experiment	experiment	NOUN
ap-610	623	28	.	.	PUNCT
ap-610	623	29	”	"	PUNCT
ap-610	624	1	acta	acta	PROPN
ap-610	624	2	metallurgica	metallurgica	PROPN
ap-610	624	3	et	et	PROPN
ap-610	624	4	materialia	materialia	PROPN
ap-610	624	5	,	,	PUNCT
ap-610	624	6	vol	vol	NOUN
ap-610	624	7	.	.	PUNCT
ap-610	625	1	42	42	NUM
ap-610	625	2	(	(	PUNCT
ap-610	625	3	1994	1994	NUM
ap-610	625	4	)	)	PUNCT
ap-610	625	5	,	,	PUNCT
ap-610	626	1	p.	p.	NOUN
ap-610	626	2	475–487	475–487	NUM
ap-610	626	3	.	.	PUNCT
ap-610	627	1	[	[	X
ap-610	627	2	13	13	NUM
ap-610	627	3	]	]	PUNCT
ap-610	627	4	geers	geer	NOUN
ap-610	627	5	m.	m.	NOUN
ap-610	627	6	g.	g.	PROPN
ap-610	627	7	d.	d.	PROPN
ap-610	627	8	,	,	PUNCT
ap-610	627	9	de	de	PROPN
ap-610	627	10	borst	borst	PROPN
ap-610	627	11	r.	r.	PROPN
ap-610	627	12	,	,	PUNCT
ap-610	627	13	brekelmans	brekelman	VERB
ap-610	627	14	w.	w.	PROPN
ap-610	627	15	a.	a.	PROPN
ap-610	627	16	m.	m.	PROPN
ap-610	627	17	,	,	PUNCT
ap-610	628	1	peerlings	peerlings	PROPN
ap-610	628	2	r.	r.	PROPN
ap-610	628	3	h.	h.	PROPN
ap-610	628	4	j.	j.	PROPN
ap-610	628	5	:	:	PUNCT
ap-610	628	6	“	"	PUNCT
ap-610	628	7	validation	validation	NOUN
ap-610	628	8	and	and	CCONJ
ap-610	628	9	internal	internal	ADJ
ap-610	628	10	length	length	NOUN
ap-610	628	11	scale	scale	NOUN
ap-610	628	12	determination	determination	NOUN
ap-610	628	13	for	for	ADP
ap-610	628	14	a	a	DET
ap-610	628	15	gradient	gradient	ADJ
ap-610	628	16	damage	damage	NOUN
ap-610	628	17	model	model	NOUN
ap-610	628	18	:	:	PUNCT
ap-610	628	19	application	application	NOUN
ap-610	628	20	to	to	ADP
ap-610	628	21	short	short	ADJ
ap-610	628	22	glass	glass	NOUN
ap-610	628	23	-	-	PUNCT
ap-610	628	24	fibre	fibre	NOUN
ap-610	628	25	-	-	PUNCT
ap-610	628	26	reinforced	reinforce	VERB
ap-610	628	27	polypropylene	polypropylene	NOUN
ap-610	628	28	.	.	PUNCT
ap-610	628	29	”	"	PUNCT
ap-610	629	1	international	international	ADJ
ap-610	629	2	journal	journal	NOUN
ap-610	629	3	of	of	ADP
ap-610	629	4	solids	solid	NOUN
ap-610	629	5	and	and	CCONJ
ap-610	629	6	structures	structure	NOUN
ap-610	629	7	,	,	PUNCT
ap-610	629	8	vol	vol	NOUN
ap-610	629	9	.	.	PROPN
ap-610	629	10	36	36	NUM
ap-610	629	11	(	(	PUNCT
ap-610	629	12	1999	1999	NUM
ap-610	629	13	)	)	PUNCT
ap-610	629	14	,	,	PUNCT
ap-610	629	15	p.	p.	NOUN
ap-610	629	16	2557–2583	2557–2583	NUM
ap-610	629	17	.	.	PUNCT
ap-610	630	1	[	[	X
ap-610	630	2	14	14	NUM
ap-610	630	3	]	]	X
ap-610	630	4	geers	geer	NOUN
ap-610	630	5	m.	m.	NOUN
ap-610	630	6	g.	g.	PROPN
ap-610	630	7	d.	d.	PROPN
ap-610	630	8	,	,	PUNCT
ap-610	630	9	engelen	engelen	PROPN
ap-610	630	10	r.	r.	PROPN
ap-610	630	11	a.	a.	PROPN
ap-610	630	12	b.	b.	PROPN
ap-610	630	13	,	,	PUNCT
ap-610	630	14	ubachs	ubachs	PROPN
ap-610	630	15	r.	r.	PROPN
ap-610	630	16	j.	j.	PROPN
ap-610	630	17	m.	m.	PROPN
ap-610	630	18	:	:	PUNCT
ap-610	630	19	“	"	PUNCT
ap-610	630	20	on	on	ADP
ap-610	630	21	the	the	DET
ap-610	630	22	numerical	numerical	ADJ
ap-610	630	23	modelling	modelling	NOUN
ap-610	630	24	of	of	ADP
ap-610	630	25	ductile	ductile	NOUN
ap-610	630	26	damage	damage	NOUN
ap-610	630	27	with	with	ADP
ap-610	630	28	an	an	DET
ap-610	630	29	implicit	implicit	ADJ
ap-610	630	30	gradient	gradient	NOUN
ap-610	630	31	-	-	PUNCT
ap-610	630	32	enhanced	enhance	VERB
ap-610	630	33	formulation	formulation	NOUN
ap-610	630	34	.	.	PUNCT
ap-610	630	35	”	"	PUNCT
ap-610	631	1	revue	revue	PROPN
ap-610	631	2	européenne	européenne	PROPN
ap-610	631	3	des	des	PROPN
ap-610	631	4	éléments	éléments	PROPN
ap-610	631	5	finis	finis	PROPN
ap-610	631	6	,	,	PUNCT
ap-610	631	7	vol	vol	NOUN
ap-610	631	8	.	.	PROPN
ap-610	631	9	10	10	NUM
ap-610	631	10	(	(	PUNCT
ap-610	631	11	2001	2001	NUM
ap-610	631	12	)	)	PUNCT
ap-610	631	13	,	,	PUNCT
ap-610	631	14	p.	p.	NOUN
ap-610	631	15	173–191	173–191	NUM
ap-610	631	16	.	.	PUNCT
ap-610	632	1	[	[	X
ap-610	632	2	15	15	NUM
ap-610	632	3	]	]	X
ap-610	632	4	green	green	PROPN
ap-610	632	5	a.	a.	PROPN
ap-610	632	6	e.	e.	PROPN
ap-610	632	7	,	,	PUNCT
ap-610	632	8	rivlin	rivlin	PROPN
ap-610	632	9	r.	r.	PROPN
ap-610	632	10	s.	s.	PROPN
ap-610	632	11	:	:	PUNCT
ap-610	632	12	“	"	PUNCT
ap-610	632	13	simple	simple	ADJ
ap-610	632	14	force	force	NOUN
ap-610	632	15	and	and	CCONJ
ap-610	632	16	stress	stress	NOUN
ap-610	632	17	multipoles	multipole	NOUN
ap-610	632	18	.	.	PUNCT
ap-610	632	19	”	"	PUNCT
ap-610	633	1	archive	archive	NOUN
ap-610	633	2	for	for	ADP
ap-610	633	3	rational	rational	ADJ
ap-610	633	4	mechanics	mechanic	NOUN
ap-610	633	5	and	and	CCONJ
ap-610	633	6	analysis	analysis	NOUN
ap-610	633	7	,	,	PUNCT
ap-610	633	8	vol	vol	NOUN
ap-610	633	9	.	.	PUNCT
ap-610	634	1	16	16	NUM
ap-610	634	2	(	(	PUNCT
ap-610	634	3	1964	1964	NUM
ap-610	634	4	)	)	PUNCT
ap-610	634	5	,	,	PUNCT
ap-610	635	1	p.	p.	NOUN
ap-610	635	2	325–353	325–353	NUM
ap-610	635	3	.	.	PUNCT
ap-610	636	1	[	[	X
ap-610	636	2	16	16	NUM
ap-610	636	3	]	]	X
ap-610	636	4	jirásek	jirásek	NOUN
ap-610	636	5	m.	m.	NOUN
ap-610	636	6	,	,	PUNCT
ap-610	636	7	bažant	bažant	PROPN
ap-610	636	8	z.	z.	PROPN
ap-610	636	9	p.	p.	PROPN
ap-610	636	10	:	:	PUNCT
ap-610	636	11	“	"	PUNCT
ap-610	636	12	inelastic	inelastic	ADJ
ap-610	636	13	analysis	analysis	NOUN
ap-610	636	14	of	of	ADP
ap-610	636	15	structures	structure	NOUN
ap-610	636	16	.	.	PUNCT
ap-610	636	17	”	"	PUNCT
ap-610	637	1	john	john	PROPN
ap-610	637	2	wiley	wiley	PROPN
ap-610	637	3	and	and	CCONJ
ap-610	637	4	sons	son	NOUN
ap-610	637	5	,	,	PUNCT
ap-610	637	6	chichester	chichester	PROPN
ap-610	637	7	,	,	PUNCT
ap-610	637	8	u.k	u.k	PROPN
ap-610	637	9	.	.	PROPN
ap-610	637	10	,	,	PUNCT
ap-610	637	11	2002	2002	NUM
ap-610	637	12	.	.	PUNCT
ap-610	638	1	[	[	X
ap-610	638	2	17	17	NUM
ap-610	638	3	]	]	X
ap-610	638	4	jirásek	jirásek	NOUN
ap-610	638	5	m.	m.	NOUN
ap-610	638	6	,	,	PUNCT
ap-610	638	7	rolshoven	rolshoven	ADJ
ap-610	638	8	,	,	PUNCT
ap-610	638	9	grassl	grassl	VERB
ap-610	638	10	,	,	PUNCT
ap-610	638	11	p.	p.	NOUN
ap-610	638	12	:	:	PUNCT
ap-610	638	13	“	"	PUNCT
ap-610	638	14	size	size	NOUN
ap-610	638	15	effect	effect	NOUN
ap-610	638	16	on	on	ADP
ap-610	638	17	fracture	fracture	NOUN
ap-610	638	18	energy	energy	NOUN
ap-610	638	19	induced	induce	VERB
ap-610	638	20	by	by	ADP
ap-610	638	21	nonlocality	nonlocality	NOUN
ap-610	638	22	.	.	PUNCT
ap-610	638	23	”	"	PUNCT
ap-610	639	1	international	international	ADJ
ap-610	639	2	journal	journal	NOUN
ap-610	639	3	for	for	ADP
ap-610	639	4	numerical	numerical	ADJ
ap-610	639	5	and	and	CCONJ
ap-610	639	6	analytical	analytical	ADJ
ap-610	639	7	methods	method	NOUN
ap-610	639	8	in	in	ADP
ap-610	639	9	engineering	engineering	NOUN
ap-610	639	10	,	,	PUNCT
ap-610	639	11	vol	vol	NOUN
ap-610	639	12	.	.	PROPN
ap-610	639	13	28	28	NUM
ap-610	639	14	(	(	PUNCT
ap-610	639	15	2004	2004	NUM
ap-610	639	16	)	)	PUNCT
ap-610	639	17	,	,	PUNCT
ap-610	639	18	in	in	ADP
ap-610	639	19	press	press	NOUN
ap-610	639	20	.	.	PUNCT
ap-610	640	1	[	[	X
ap-610	640	2	18	18	NUM
ap-610	640	3	]	]	X
ap-610	640	4	lakes	lakes	PROPN
ap-610	640	5	r.	r.	PROPN
ap-610	640	6	s.	s.	PROPN
ap-610	640	7	:	:	PUNCT
ap-610	640	8	“	"	PUNCT
ap-610	640	9	experimental	experimental	ADJ
ap-610	640	10	microelasticity	microelasticity	NOUN
ap-610	640	11	of	of	ADP
ap-610	640	12	two	two	NUM
ap-610	640	13	porous	porous	ADJ
ap-610	640	14	solids	solid	NOUN
ap-610	640	15	.	.	PUNCT
ap-610	640	16	”	"	PUNCT
ap-610	641	1	international	international	ADJ
ap-610	641	2	journal	journal	NOUN
ap-610	641	3	of	of	ADP
ap-610	641	4	solids	solid	NOUN
ap-610	641	5	and	and	CCONJ
ap-610	641	6	structures	structure	NOUN
ap-610	641	7	,	,	PUNCT
ap-610	641	8	vol	vol	NOUN
ap-610	641	9	.	.	PROPN
ap-610	641	10	22	22	NUM
ap-610	641	11	(	(	PUNCT
ap-610	641	12	1986	1986	NUM
ap-610	641	13	)	)	PUNCT
ap-610	641	14	,	,	PUNCT
ap-610	641	15	p.	p.	NOUN
ap-610	641	16	55–63	55–63	NUM
ap-610	641	17	.	.	PUNCT
ap-610	642	1	[	[	X
ap-610	642	2	19	19	NUM
ap-610	642	3	]	]	X
ap-610	642	4	ma	ma	PROPN
ap-610	642	5	q.	q.	PROPN
ap-610	642	6	,	,	PUNCT
ap-610	642	7	clarke	clarke	PROPN
ap-610	642	8	d.	d.	PROPN
ap-610	642	9	r.	r.	PROPN
ap-610	642	10	:	:	PUNCT
ap-610	642	11	“	"	PUNCT
ap-610	642	12	size	size	VERB
ap-610	642	13	dependent	dependent	ADJ
ap-610	642	14	hardness	hardness	NOUN
ap-610	642	15	in	in	ADP
ap-610	642	16	silver	silver	ADJ
ap-610	642	17	single	single	ADJ
ap-610	642	18	crystals	crystal	NOUN
ap-610	642	19	.	.	PUNCT
ap-610	642	20	”	"	PUNCT
ap-610	642	21	journal	journal	NOUN
ap-610	642	22	of	of	ADP
ap-610	642	23	materials	material	NOUN
ap-610	642	24	research	research	NOUN
ap-610	642	25	,	,	PUNCT
ap-610	642	26	vol	vol	NOUN
ap-610	642	27	.	.	PROPN
ap-610	642	28	10	10	NUM
ap-610	642	29	(	(	PUNCT
ap-610	642	30	1995	1995	NUM
ap-610	642	31	)	)	PUNCT
ap-610	642	32	,	,	PUNCT
ap-610	642	33	p.	p.	NOUN
ap-610	642	34	853–863	853–863	NUM
ap-610	642	35	.	.	PUNCT
ap-610	643	1	[	[	X
ap-610	643	2	20	20	NUM
ap-610	643	3	]	]	X
ap-610	643	4	metrikine	metrikine	NOUN
ap-610	643	5	a.	a.	PROPN
ap-610	643	6	v.	v.	PROPN
ap-610	643	7	,	,	PUNCT
ap-610	643	8	askes	ask	VERB
ap-610	643	9	h.	h.	PROPN
ap-610	643	10	:	:	PUNCT
ap-610	643	11	“	"	PUNCT
ap-610	643	12	one	one	NUM
ap-610	643	13	-	-	PUNCT
ap-610	643	14	dimensional	dimensional	ADJ
ap-610	643	15	dynamically	dynamically	ADV
ap-610	643	16	consistent	consistent	ADJ
ap-610	643	17	gradient	gradient	NOUN
ap-610	643	18	elasticity	elasticity	NOUN
ap-610	643	19	models	model	NOUN
ap-610	643	20	derived	derive	VERB
ap-610	643	21	from	from	ADP
ap-610	643	22	a	a	DET
ap-610	643	23	discrete	discrete	ADJ
ap-610	643	24	microstructure	microstructure	NOUN
ap-610	643	25	.	.	PUNCT
ap-610	644	1	part	part	NOUN
ap-610	644	2	1	1	NUM
ap-610	644	3	:	:	PUNCT
ap-610	644	4	generic	generic	ADJ
ap-610	644	5	formulation	formulation	NOUN
ap-610	644	6	.	.	PUNCT
ap-610	644	7	”	"	PUNCT
ap-610	645	1	european	european	PROPN
ap-610	645	2	journal	journal	PROPN
ap-610	645	3	of	of	ADP
ap-610	645	4	mechanics	mechanic	NOUN
ap-610	645	5	a	a	PRON
ap-610	645	6	,	,	PUNCT
ap-610	645	7	vol	vol	NOUN
ap-610	645	8	.	.	PROPN
ap-610	645	9	21	21	NUM
ap-610	645	10	(	(	PUNCT
ap-610	645	11	2002	2002	NUM
ap-610	645	12	)	)	PUNCT
ap-610	645	13	,	,	PUNCT
ap-610	645	14	p.	p.	NOUN
ap-610	645	15	555–572	555–572	NUM
ap-610	645	16	.	.	PUNCT
ap-610	646	1	[	[	X
ap-610	646	2	21	21	NUM
ap-610	646	3	]	]	X
ap-610	646	4	mindlin	mindlin	PROPN
ap-610	646	5	r.	r.	PROPN
ap-610	646	6	d.	d.	PROPN
ap-610	646	7	:	:	PUNCT
ap-610	646	8	“	"	PUNCT
ap-610	646	9	micro	micro	NOUN
ap-610	646	10	-	-	NOUN
ap-610	646	11	structure	structure	NOUN
ap-610	646	12	in	in	ADP
ap-610	646	13	linear	linear	PROPN
ap-610	646	14	elasticity	elasticity	NOUN
ap-610	646	15	.	.	PUNCT
ap-610	646	16	”	"	PUNCT
ap-610	647	1	archive	archive	NOUN
ap-610	647	2	for	for	ADP
ap-610	647	3	rational	rational	ADJ
ap-610	647	4	mechanics	mechanic	NOUN
ap-610	647	5	and	and	CCONJ
ap-610	647	6	analysis	analysis	NOUN
ap-610	647	7	,	,	PUNCT
ap-610	647	8	vol	vol	NOUN
ap-610	647	9	.	.	PUNCT
ap-610	648	1	16	16	NUM
ap-610	648	2	(	(	PUNCT
ap-610	648	3	1964	1964	NUM
ap-610	648	4	)	)	PUNCT
ap-610	648	5	,	,	PUNCT
ap-610	648	6	p.	p.	NOUN
ap-610	648	7	51–78	51–78	NUM
ap-610	648	8	.	.	PUNCT
ap-610	649	1	[	[	X
ap-610	649	2	22	22	NUM
ap-610	649	3	]	]	X
ap-610	649	4	mindlin	mindlin	PROPN
ap-610	649	5	r.	r.	PROPN
ap-610	649	6	d.	d.	PROPN
ap-610	649	7	:	:	PUNCT
ap-610	649	8	“	"	PUNCT
ap-610	649	9	second	second	ADJ
ap-610	649	10	gradient	gradient	NOUN
ap-610	649	11	of	of	ADP
ap-610	649	12	strain	strain	NOUN
ap-610	649	13	and	and	CCONJ
ap-610	649	14	surface	surface	NOUN
ap-610	649	15	tension	tension	NOUN
ap-610	649	16	in	in	ADP
ap-610	649	17	linear	linear	PROPN
ap-610	649	18	elasticity	elasticity	NOUN
ap-610	649	19	.	.	PUNCT
ap-610	649	20	”	"	PUNCT
ap-610	650	1	international	international	ADJ
ap-610	650	2	journal	journal	NOUN
ap-610	650	3	of	of	ADP
ap-610	650	4	solids	solid	NOUN
ap-610	650	5	and	and	CCONJ
ap-610	650	6	structures	structure	NOUN
ap-610	650	7	,	,	PUNCT
ap-610	650	8	vol	vol	NOUN
ap-610	650	9	.	.	PROPN
ap-610	650	10	1	1	NUM
ap-610	650	11	(	(	PUNCT
ap-610	650	12	1965	1965	NUM
ap-610	650	13	)	)	PUNCT
ap-610	650	14	,	,	PUNCT
ap-610	651	1	p.	p.	NOUN
ap-610	651	2	417–438	417–438	NUM
ap-610	651	3	.	.	PUNCT
ap-610	652	1	[	[	X
ap-610	652	2	23	23	NUM
ap-610	652	3	]	]	X
ap-610	652	4	morrison	morrison	PROPN
ap-610	652	5	j.	j.	PROPN
ap-610	652	6	l.	l.	PROPN
ap-610	652	7	m.	m.	PROPN
ap-610	652	8	:	:	PUNCT
ap-610	652	9	“	"	PUNCT
ap-610	652	10	the	the	DET
ap-610	652	11	yield	yield	NOUN
ap-610	652	12	of	of	ADP
ap-610	652	13	mild	mild	ADJ
ap-610	652	14	steel	steel	NOUN
ap-610	652	15	with	with	ADP
ap-610	652	16	particular	particular	ADJ
ap-610	652	17	reference	reference	NOUN
ap-610	652	18	to	to	ADP
ap-610	652	19	the	the	DET
ap-610	652	20	effect	effect	NOUN
ap-610	652	21	of	of	ADP
ap-610	652	22	size	size	NOUN
ap-610	652	23	of	of	ADP
ap-610	652	24	specimen	speciman	NOUN
ap-610	652	25	.	.	PUNCT
ap-610	652	26	”	"	PUNCT
ap-610	653	1	proceedings	proceeding	NOUN
ap-610	653	2	of	of	ADP
ap-610	653	3	the	the	DET
ap-610	653	4	institute	institute	PROPN
ap-610	653	5	of	of	ADP
ap-610	653	6	mechanical	mechanical	ADJ
ap-610	653	7	engineers	engineer	NOUN
ap-610	653	8	,	,	PUNCT
ap-610	653	9	vol	vol	NOUN
ap-610	653	10	.	.	PROPN
ap-610	653	11	142	142	NUM
ap-610	653	12	(	(	PUNCT
ap-610	653	13	1939	1939	NUM
ap-610	653	14	)	)	PUNCT
ap-610	653	15	,	,	PUNCT
ap-610	653	16	p.	p.	NOUN
ap-610	653	17	193–223	193–223	NUM
ap-610	653	18	.	.	PUNCT
ap-610	654	1	[	[	X
ap-610	654	2	24	24	NUM
ap-610	654	3	]	]	X
ap-610	654	4	nagai	nagai	PROPN
ap-610	654	5	g.	g.	PROPN
ap-610	654	6	,	,	PUNCT
ap-610	654	7	fish	fish	PROPN
ap-610	654	8	j.	j.	PROPN
ap-610	654	9	,	,	PUNCT
ap-610	654	10	watanabe	watanabe	PROPN
ap-610	654	11	k.	k.	PROPN
ap-610	654	12	:	:	PUNCT
ap-610	654	13	“	"	PUNCT
ap-610	654	14	stabilized	stabilize	VERB
ap-610	654	15	nonlocal	nonlocal	ADJ
ap-610	654	16	model	model	NOUN
ap-610	654	17	for	for	ADP
ap-610	654	18	wave	wave	NOUN
ap-610	654	19	propagation	propagation	NOUN
ap-610	654	20	in	in	ADP
ap-610	654	21	heterogeneous	heterogeneous	ADJ
ap-610	654	22	media	medium	NOUN
ap-610	654	23	.	.	PUNCT
ap-610	654	24	”	"	PUNCT
ap-610	655	1	computational	computational	ADJ
ap-610	655	2	mechanics	mechanic	NOUN
ap-610	655	3	,	,	PUNCT
ap-610	655	4	vol	vol	NOUN
ap-610	655	5	.	.	PROPN
ap-610	655	6	33	33	NUM
ap-610	655	7	(	(	PUNCT
ap-610	655	8	2004	2004	NUM
ap-610	655	9	)	)	PUNCT
ap-610	655	10	,	,	PUNCT
ap-610	655	11	p.	p.	NOUN
ap-610	655	12	144–153	144–153	NUM
ap-610	655	13	.	.	PUNCT
ap-610	656	1	[	[	X
ap-610	656	2	25	25	NUM
ap-610	656	3	]	]	X
ap-610	656	4	nix	nix	PROPN
ap-610	656	5	w.	w.	PROPN
ap-610	656	6	d.	d.	PROPN
ap-610	656	7	:	:	PUNCT
ap-610	656	8	“	"	PUNCT
ap-610	656	9	mechanical	mechanical	ADJ
ap-610	656	10	properties	property	NOUN
ap-610	656	11	of	of	ADP
ap-610	656	12	thin	thin	ADJ
ap-610	656	13	films	film	NOUN
ap-610	656	14	.	.	PUNCT
ap-610	656	15	”	"	PUNCT
ap-610	656	16	metallurgical	metallurgical	ADJ
ap-610	656	17	transactions	transaction	NOUN
ap-610	656	18	,	,	PUNCT
ap-610	656	19	vol	vol	NOUN
ap-610	656	20	.	.	NOUN
ap-610	656	21	20a	20a	NOUN
ap-610	656	22	(	(	PUNCT
ap-610	656	23	1989	1989	NUM
ap-610	656	24	)	)	PUNCT
ap-610	656	25	,	,	PUNCT
ap-610	656	26	p.	p.	NOUN
ap-610	656	27	2217–2245	2217–2245	NUM
ap-610	656	28	.	.	PUNCT
ap-610	657	1	[	[	X
ap-610	657	2	26	26	NUM
ap-610	657	3	]	]	PUNCT
ap-610	657	4	pijaudier	pijaudier	NOUN
ap-610	657	5	-	-	PUNCT
ap-610	657	6	cabot	cabot	PROPN
ap-610	657	7	g.	g.	PROPN
ap-610	657	8	,	,	PUNCT
ap-610	657	9	bažant	bažant	PROPN
ap-610	657	10	z.	z.	PROPN
ap-610	657	11	p.	p.	PROPN
ap-610	657	12	:	:	PUNCT
ap-610	657	13	“	"	PUNCT
ap-610	657	14	nonlocal	nonlocal	ADJ
ap-610	657	15	damage	damage	NOUN
ap-610	657	16	theory	theory	NOUN
ap-610	657	17	.	.	PUNCT
ap-610	657	18	”	"	PUNCT
ap-610	657	19	journal	journal	NOUN
ap-610	657	20	of	of	ADP
ap-610	657	21	engineering	engineering	NOUN
ap-610	657	22	mechanics	mechanic	NOUN
ap-610	657	23	,	,	PUNCT
ap-610	657	24	asce	asce	NOUN
ap-610	657	25	,	,	PUNCT
ap-610	657	26	vol	vol	NOUN
ap-610	657	27	.	.	PROPN
ap-610	657	28	113	113	NUM
ap-610	657	29	(	(	PUNCT
ap-610	657	30	1987	1987	NUM
ap-610	657	31	)	)	PUNCT
ap-610	657	32	,	,	PUNCT
ap-610	657	33	p.	p.	NOUN
ap-610	657	34	1512–1533	1512–1533	NUM
ap-610	657	35	.	.	PUNCT
ap-610	658	1	[	[	X
ap-610	658	2	27	27	NUM
ap-610	658	3	]	]	X
ap-610	658	4	poole	poole	PROPN
ap-610	658	5	w.	w.	PROPN
ap-610	658	6	j.	j.	PROPN
ap-610	658	7	,	,	PUNCT
ap-610	658	8	ashby	ashby	PROPN
ap-610	658	9	m.	m.	PROPN
ap-610	658	10	f.	f.	PROPN
ap-610	658	11	,	,	PUNCT
ap-610	658	12	fleck	fleck	PROPN
ap-610	658	13	n.	n.	PROPN
ap-610	658	14	a.	a.	PROPN
ap-610	658	15	:	:	PUNCT
ap-610	658	16	“	"	PUNCT
ap-610	658	17	microhardness	microhardness	ADJ
ap-610	658	18	of	of	ADP
ap-610	658	19	annealed	annealed	ADJ
ap-610	658	20	and	and	CCONJ
ap-610	658	21	work	work	NOUN
ap-610	658	22	-	-	PUNCT
ap-610	658	23	hardened	harden	VERB
ap-610	658	24	copper	copper	NOUN
ap-610	658	25	polycrystals	polycrystal	NOUN
ap-610	658	26	.	.	PUNCT
ap-610	658	27	”	"	PUNCT
ap-610	659	1	scripta	scripta	PROPN
ap-610	659	2	metallurgica	metallurgica	VERB
ap-610	659	3	et	et	PROPN
ap-610	659	4	materialia	materialia	PROPN
ap-610	659	5	,	,	PUNCT
ap-610	659	6	vol	vol	NOUN
ap-610	659	7	.	.	PUNCT
ap-610	660	1	34	34	NUM
ap-610	660	2	(	(	PUNCT
ap-610	660	3	1996	1996	NUM
ap-610	660	4	)	)	PUNCT
ap-610	660	5	,	,	PUNCT
ap-610	661	1	p.	p.	NOUN
ap-610	661	2	559–564	559–564	NUM
ap-610	661	3	.	.	PUNCT
ap-610	662	1	[	[	X
ap-610	662	2	28	28	NUM
ap-610	662	3	]	]	X
ap-610	662	4	rogula	rogula	NOUN
ap-610	662	5	d.	d.	PROPN
ap-610	662	6	:	:	PUNCT
ap-610	662	7	“	"	PUNCT
ap-610	662	8	introduction	introduction	NOUN
ap-610	662	9	to	to	ADP
ap-610	662	10	nonlocal	nonlocal	ADJ
ap-610	662	11	theory	theory	NOUN
ap-610	662	12	of	of	ADP
ap-610	662	13	material	material	ADJ
ap-610	662	14	media	medium	NOUN
ap-610	662	15	”	"	PUNCT
ap-610	662	16	,	,	PUNCT
ap-610	662	17	in	in	ADP
ap-610	662	18	d.	d.	PROPN
ap-610	662	19	rogula	rogula	PROPN
ap-610	662	20	(	(	PUNCT
ap-610	662	21	ed	ed	NOUN
ap-610	662	22	.	.	PUNCT
ap-610	662	23	)	)	PUNCT
ap-610	662	24	,	,	PUNCT
ap-610	662	25	nonlocal	nonlocal	ADJ
ap-610	662	26	theory	theory	NOUN
ap-610	662	27	of	of	ADP
ap-610	662	28	material	material	ADJ
ap-610	662	29	media	medium	NOUN
ap-610	662	30	,	,	PUNCT
ap-610	662	31	no	no	INTJ
ap-610	662	32	.	.	NOUN
ap-610	662	33	268	268	NUM
ap-610	662	34	in	in	ADP
ap-610	662	35	cism	cism	NOUN
ap-610	662	36	courses	course	NOUN
ap-610	662	37	and	and	CCONJ
ap-610	662	38	lectures	lecture	NOUN
ap-610	662	39	,	,	PUNCT
ap-610	662	40	springer	springer	NOUN
ap-610	662	41	verlag	verlag	NOUN
ap-610	662	42	,	,	PUNCT
ap-610	662	43	wien	wien	PROPN
ap-610	662	44	and	and	CCONJ
ap-610	662	45	new	new	PROPN
ap-610	662	46	york	york	PROPN
ap-610	662	47	,	,	PUNCT
ap-610	662	48	1982	1982	NUM
ap-610	662	49	,	,	PUNCT
ap-610	662	50	p.	p.	NOUN
ap-610	662	51	125–222	125–222	NUM
ap-610	662	52	.	.	PUNCT
ap-610	663	1	[	[	X
ap-610	663	2	29	29	NUM
ap-610	663	3	]	]	X
ap-610	663	4	shu	shu	PROPN
ap-610	663	5	j.	j.	PROPN
ap-610	663	6	y.	y.	PROPN
ap-610	663	7	,	,	PUNCT
ap-610	663	8	fleck	fleck	PROPN
ap-610	663	9	n.	n.	PROPN
ap-610	663	10	a.	a.	PROPN
ap-610	663	11	,	,	PUNCT
ap-610	663	12	van	van	PROPN
ap-610	663	13	der	der	PROPN
ap-610	663	14	giessen	giessen	PROPN
ap-610	663	15	e.	e.	PROPN
ap-610	663	16	,	,	PUNCT
ap-610	663	17	needleman	needleman	PROPN
ap-610	663	18	a.	a.	PROPN
ap-610	663	19	:	:	PUNCT
ap-610	663	20	“	"	PUNCT
ap-610	663	21	boundary	boundary	ADJ
ap-610	663	22	layers	layer	NOUN
ap-610	663	23	in	in	ADP
ap-610	663	24	constrained	constrain	VERB
ap-610	663	25	plastic	plastic	NOUN
ap-610	663	26	flow	flow	NOUN
ap-610	663	27	:	:	PUNCT
ap-610	663	28	comparison	comparison	NOUN
ap-610	663	29	of	of	ADP
ap-610	663	30	nonlocal	nonlocal	ADJ
ap-610	663	31	and	and	CCONJ
ap-610	663	32	discrete	discrete	ADJ
ap-610	663	33	dislocation	dislocation	NOUN
ap-610	663	34	platicity	platicity	NOUN
ap-610	663	35	.	.	PUNCT
ap-610	663	36	”	"	PUNCT
ap-610	663	37	journal	journal	NOUN
ap-610	663	38	of	of	ADP
ap-610	663	39	the	the	DET
ap-610	663	40	mechanics	mechanic	NOUN
ap-610	663	41	and	and	CCONJ
ap-610	663	42	physics	physic	NOUN
ap-610	663	43	of	of	ADP
ap-610	663	44	solids	solid	NOUN
ap-610	663	45	,	,	PUNCT
ap-610	663	46	vol	vol	NOUN
ap-610	663	47	.	.	PROPN
ap-610	663	48	49	49	NUM
ap-610	663	49	(	(	PUNCT
ap-610	663	50	2001	2001	NUM
ap-610	663	51	)	)	PUNCT
ap-610	663	52	,	,	PUNCT
ap-610	663	53	p.	p.	NOUN
ap-610	663	54	1361–1395	1361–1395	NUM
ap-610	663	55	.	.	PUNCT
ap-610	664	1	[	[	X
ap-610	664	2	30	30	NUM
ap-610	664	3	]	]	X
ap-610	664	4	stolken	stolken	PROPN
ap-610	664	5	j.	j.	PROPN
ap-610	664	6	s.	s.	PROPN
ap-610	664	7	,	,	PUNCT
ap-610	664	8	evans	evans	PROPN
ap-610	664	9	a.	a.	PROPN
ap-610	664	10	g.	g.	PROPN
ap-610	664	11	:	:	PUNCT
ap-610	664	12	“	"	PUNCT
ap-610	664	13	a	a	DET
ap-610	664	14	microbend	microbend	NOUN
ap-610	664	15	test	test	NOUN
ap-610	664	16	method	method	NOUN
ap-610	664	17	for	for	ADP
ap-610	664	18	measuring	measure	VERB
ap-610	664	19	the	the	DET
ap-610	664	20	plasticity	plasticity	NOUN
ap-610	664	21	length	length	NOUN
ap-610	664	22	scale	scale	NOUN
ap-610	664	23	.	.	PUNCT
ap-610	664	24	”	"	PUNCT
ap-610	665	1	acta	acta	PROPN
ap-610	665	2	metallurgica	metallurgica	PROPN
ap-610	665	3	et	et	PROPN
ap-610	665	4	materialia	materialia	PROPN
ap-610	665	5	,	,	PUNCT
ap-610	665	6	vol	vol	NOUN
ap-610	665	7	.	.	PROPN
ap-610	666	1	46	46	NUM
ap-610	666	2	(	(	PUNCT
ap-610	666	3	1998	1998	NUM
ap-610	666	4	)	)	PUNCT
ap-610	666	5	,	,	PUNCT
ap-610	667	1	p.	p.	NOUN
ap-610	667	2	5109–5115	5109–5115	NUM
ap-610	667	3	.	.	PUNCT
ap-610	668	1	[	[	X
ap-610	668	2	31	31	NUM
ap-610	668	3	]	]	PUNCT
ap-610	668	4	toupin	toupin	PROPN
ap-610	668	5	r.	r.	PROPN
ap-610	668	6	a.	a.	NOUN
ap-610	668	7	:	:	PUNCT
ap-610	668	8	“	"	PUNCT
ap-610	668	9	elastic	elastic	ADJ
ap-610	668	10	materials	material	NOUN
ap-610	668	11	with	with	ADP
ap-610	668	12	couple	couple	NOUN
ap-610	668	13	-	-	PUNCT
ap-610	668	14	stresses	stress	NOUN
ap-610	668	15	.	.	PUNCT
ap-610	668	16	”	"	PUNCT
ap-610	669	1	archive	archive	NOUN
ap-610	669	2	for	for	ADP
ap-610	669	3	rational	rational	ADJ
ap-610	669	4	mechanics	mechanic	NOUN
ap-610	669	5	and	and	CCONJ
ap-610	669	6	analysis	analysis	NOUN
ap-610	669	7	,	,	PUNCT
ap-610	669	8	vol	vol	NOUN
ap-610	669	9	.	.	PROPN
ap-610	669	10	11	11	NUM
ap-610	669	11	(	(	PUNCT
ap-610	669	12	1962	1962	NUM
ap-610	669	13	)	)	PUNCT
ap-610	669	14	,	,	PUNCT
ap-610	669	15	p.	p.	PROPN
ap-610	669	16	385–414	385–414	NUM
ap-610	669	17	.	.	PUNCT
ap-610	670	1	[	[	X
ap-610	670	2	32	32	NUM
ap-610	670	3	]	]	PUNCT
ap-610	670	4	wittmann	wittmann	PROPN
ap-610	670	5	f.	f.	PROPN
ap-610	670	6	h.	h.	PROPN
ap-610	670	7	,	,	PUNCT
ap-610	670	8	mihashi	mihashi	PROPN
ap-610	670	9	h.	h.	PROPN
ap-610	670	10	,	,	PUNCT
ap-610	670	11	nomura	nomura	NOUN
ap-610	670	12	n.	n.	NOUN
ap-610	670	13	:	:	PUNCT
ap-610	670	14	“	"	PUNCT
ap-610	670	15	size	size	NOUN
ap-610	670	16	effect	effect	NOUN
ap-610	670	17	on	on	ADP
ap-610	670	18	fracture	fracture	NOUN
ap-610	670	19	energy	energy	NOUN
ap-610	670	20	of	of	ADP
ap-610	670	21	concrete	concrete	NOUN
ap-610	670	22	.	.	PUNCT
ap-610	670	23	”	"	PUNCT
ap-610	671	1	engineering	engineering	NOUN
ap-610	671	2	fracture	fracture	NOUN
ap-610	671	3	mechanics	mechanic	NOUN
ap-610	671	4	,	,	PUNCT
ap-610	671	5	vol	vol	NOUN
ap-610	671	6	.	.	PROPN
ap-610	671	7	35	35	NUM
ap-610	671	8	(	(	PUNCT
ap-610	671	9	1990	1990	NUM
ap-610	671	10	)	)	PUNCT
ap-610	671	11	,	,	PUNCT
ap-610	672	1	p.	p.	NOUN
ap-610	672	2	107–115	107–115	NUM
ap-610	672	3	.	.	PUNCT
ap-610	673	1	[	[	X
ap-610	673	2	33	33	NUM
ap-610	673	3	]	]	X
ap-610	673	4	yarnel	yarnel	PROPN
ap-610	673	5	j.	j.	PROPN
ap-610	673	6	l.	l.	PROPN
ap-610	673	7	,	,	PUNCT
ap-610	673	8	warren	warren	PROPN
ap-610	673	9	j.	j.	PROPN
ap-610	673	10	l.	l.	PROPN
ap-610	673	11	,	,	PUNCT
ap-610	673	12	koenig	koenig	PROPN
ap-610	673	13	s.	s.	PROPN
ap-610	673	14	h.	h.	PROPN
ap-610	673	15	:	:	PUNCT
ap-610	673	16	in	in	ADP
ap-610	673	17	lattice	lattice	NOUN
ap-610	673	18	dynamics	dynamic	NOUN
ap-610	673	19	,	,	PUNCT
ap-610	673	20	r.	r.	PROPN
ap-610	673	21	f.	f.	PROPN
ap-610	673	22	wallis	wallis	PROPN
ap-610	673	23	(	(	PUNCT
ap-610	673	24	ed	ed	NOUN
ap-610	673	25	.	.	PUNCT
ap-610	673	26	)	)	PUNCT
ap-610	673	27	,	,	PUNCT
ap-610	673	28	pergamon	pergamon	PROPN
ap-610	673	29	press	press	PROPN
ap-610	673	30	,	,	PUNCT
ap-610	673	31	1965	1965	NUM
ap-610	673	32	,	,	PUNCT
ap-610	673	33	p.	p.	NOUN
ap-610	673	34	57	57	NUM
ap-610	673	35	.	.	PUNCT
ap-610	673	36	milan	milan	PROPN
ap-610	673	37	jirásek	jirásek	PROPN
ap-610	673	38	laboratory	laboratory	PROPN
ap-610	673	39	of	of	ADP
ap-610	673	40	structural	structural	ADJ
ap-610	673	41	and	and	CCONJ
ap-610	673	42	continuum	continuum	ADJ
ap-610	673	43	mechanics	mechanic	NOUN
ap-610	673	44	swiss	swiss	PROPN
ap-610	673	45	federal	federal	PROPN
ap-610	673	46	institute	institute	PROPN
ap-610	673	47	of	of	ADP
ap-610	673	48	technology	technology	PROPN
ap-610	673	49	at	at	ADP
ap-610	673	50	lausanne	lausanne	PROPN
ap-610	673	51	(	(	PUNCT
ap-610	673	52	epfl	epfl	PROPN
ap-610	673	53	)	)	PUNCT
ap-610	673	54	1015	1015	NUM
ap-610	673	55	lausanne	lausanne	PROPN
ap-610	673	56	,	,	PUNCT
ap-610	673	57	switzerland	switzerland	PROPN
ap-610	673	58	34	34	NUM
ap-610	674	1	©	©	PROPN
ap-610	674	2	czech	czech	PROPN
ap-610	674	3	technical	technical	PROPN
ap-610	674	4	university	university	PROPN
ap-610	674	5	publishing	publishing	NOUN
ap-610	674	6	house	house	NOUN
ap-610	674	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-610	674	8	acta	acta	PROPN
ap-610	674	9	polytechnica	polytechnica	PROPN
ap-610	674	10	vol	vol	NOUN
ap-610	674	11	.	.	PROPN
ap-610	675	1	44	44	NUM
ap-610	675	2	no	no	NOUN
ap-610	675	3	.	.	PUNCT
ap-610	676	1	5–6/2004	5–6/2004	NUM