id	sid	tid	token	lemma	pos
ap-658	1	1	ap04-bittnar2.vp	ap04-bittnar2.vp	NOUN
ap-658	1	2	1	1	NUM
ap-658	1	3	introduction	introduction	NOUN
ap-658	1	4	it	it	PRON
ap-658	1	5	is	be	AUX
ap-658	1	6	in	in	ADP
ap-658	1	7	a	a	DET
ap-658	1	8	nature	nature	NOUN
ap-658	1	9	of	of	ADP
ap-658	1	10	mankind	mankind	NOUN
ap-658	1	11	to	to	PART
ap-658	1	12	search	search	VERB
ap-658	1	13	for	for	ADP
ap-658	1	14	simplicity	simplicity	NOUN
ap-658	1	15	,	,	PUNCT
ap-658	1	16	efficiency	efficiency	NOUN
ap-658	1	17	and	and	CCONJ
ap-658	1	18	stability	stability	NOUN
ap-658	1	19	.	.	PUNCT
ap-658	2	1	when	when	SCONJ
ap-658	2	2	translated	translate	VERB
ap-658	2	3	into	into	ADP
ap-658	2	4	a	a	DET
ap-658	2	5	computational	computational	ADJ
ap-658	2	6	mechanics	mechanic	NOUN
ap-658	2	7	language	language	NOUN
ap-658	2	8	,	,	PUNCT
ap-658	2	9	a	a	DET
ap-658	2	10	new	new	ADJ
ap-658	2	11	landscape	landscape	NOUN
ap-658	2	12	for	for	ADP
ap-658	2	13	efficient	efficient	ADJ
ap-658	2	14	numerical	numerical	ADJ
ap-658	2	15	schemes	scheme	NOUN
ap-658	2	16	arises	arise	VERB
ap-658	2	17	from	from	ADP
ap-658	2	18	the	the	DET
ap-658	2	19	introduction	introduction	NOUN
ap-658	2	20	of	of	ADP
ap-658	2	21	the	the	DET
ap-658	2	22	multi	multi	ADJ
ap-658	2	23	-	-	NOUN
ap-658	2	24	scale	scale	ADJ
ap-658	2	25	or	or	CCONJ
ap-658	2	26	multilevel	multilevel	ADJ
ap-658	2	27	solution	solution	NOUN
ap-658	2	28	strategies	strategy	NOUN
ap-658	2	29	currently	currently	ADV
ap-658	2	30	at	at	ADP
ap-658	2	31	the	the	DET
ap-658	2	32	forefront	forefront	NOUN
ap-658	2	33	of	of	ADP
ap-658	2	34	engineering	engineering	NOUN
ap-658	2	35	interest	interest	NOUN
ap-658	2	36	when	when	SCONJ
ap-658	2	37	studying	study	VERB
ap-658	2	38	complex	complex	ADJ
ap-658	2	39	heterogeneous	heterogeneous	ADJ
ap-658	2	40	materials	material	NOUN
ap-658	2	41	and	and	CCONJ
ap-658	2	42	structures	structure	NOUN
ap-658	2	43	.	.	PUNCT
ap-658	3	1	to	to	PART
ap-658	3	2	provide	provide	VERB
ap-658	3	3	an	an	DET
ap-658	3	4	illustrative	illustrative	ADJ
ap-658	3	5	example	example	NOUN
ap-658	3	6	of	of	ADP
ap-658	3	7	such	such	DET
ap-658	3	8	a	a	DET
ap-658	3	9	structure	structure	NOUN
ap-658	3	10	,	,	PUNCT
ap-658	3	11	consider	consider	VERB
ap-658	3	12	the	the	DET
ap-658	3	13	multi	multi	ADJ
ap-658	3	14	-	-	ADJ
ap-658	3	15	layered	layered	ADJ
ap-658	3	16	wound	wound	NOUN
ap-658	3	17	composite	composite	ADJ
ap-658	3	18	tube	tube	NOUN
ap-658	3	19	shown	show	VERB
ap-658	3	20	in	in	ADP
ap-658	3	21	fig	fig	NOUN
ap-658	3	22	.	.	PUNCT
ap-658	4	1	1	1	X
ap-658	4	2	.	.	X
ap-658	4	3	an	an	DET
ap-658	4	4	accurate	accurate	ADJ
ap-658	4	5	prediction	prediction	NOUN
ap-658	4	6	of	of	ADP
ap-658	4	7	the	the	DET
ap-658	4	8	mechanical	mechanical	ADJ
ap-658	4	9	response	response	NOUN
ap-658	4	10	of	of	ADP
ap-658	4	11	this	this	DET
ap-658	4	12	particular	particular	ADJ
ap-658	4	13	class	class	NOUN
ap-658	4	14	of	of	ADP
ap-658	4	15	structures	structure	NOUN
ap-658	4	16	inevitably	inevitably	ADV
ap-658	4	17	calls	call	VERB
ap-658	4	18	for	for	ADP
ap-658	4	19	analyses	analysis	NOUN
ap-658	4	20	on	on	ADP
ap-658	4	21	three	three	NUM
ap-658	4	22	widely	widely	ADV
ap-658	4	23	separated	separate	VERB
ap-658	4	24	length	length	NOUN
ap-658	4	25	scales	scale	NOUN
ap-658	4	26	.	.	PUNCT
ap-658	5	1	it	it	PRON
ap-658	5	2	is	be	AUX
ap-658	5	3	now	now	ADV
ap-658	5	4	becoming	becoming	AUX
ap-658	5	5	widely	widely	ADV
ap-658	5	6	accepted	accept	VERB
ap-658	5	7	that	that	SCONJ
ap-658	5	8	models	model	NOUN
ap-658	5	9	constructed	construct	VERB
ap-658	5	10	on	on	ADP
ap-658	5	11	the	the	DET
ap-658	5	12	basis	basis	NOUN
ap-658	5	13	of	of	ADP
ap-658	5	14	hierarchical	hierarchical	ADJ
ap-658	5	15	or	or	CCONJ
ap-658	5	16	multi	multi	ADJ
ap-658	5	17	-	-	ADJ
ap-658	5	18	scale	scale	ADJ
ap-658	5	19	modeling	modeling	NOUN
ap-658	5	20	offer	offer	VERB
ap-658	5	21	a	a	DET
ap-658	5	22	reliable	reliable	ADJ
ap-658	5	23	route	route	NOUN
ap-658	5	24	in	in	ADP
ap-658	5	25	numerical	numerical	ADJ
ap-658	5	26	investigation	investigation	NOUN
ap-658	5	27	of	of	ADP
ap-658	5	28	deformation	deformation	NOUN
ap-658	5	29	and	and	CCONJ
ap-658	5	30	failure	failure	NOUN
ap-658	5	31	processes	process	NOUN
ap-658	5	32	taking	take	VERB
ap-658	5	33	place	place	NOUN
ap-658	5	34	at	at	ADP
ap-658	5	35	individual	individual	ADJ
ap-658	5	36	scales	scale	NOUN
ap-658	5	37	[	[	X
ap-658	5	38	1–5	1–5	X
ap-658	5	39	]	]	X
ap-658	5	40	.	.	PUNCT
ap-658	6	1	since	since	SCONJ
ap-658	6	2	their	their	PRON
ap-658	6	3	introduction	introduction	NOUN
ap-658	6	4	,	,	PUNCT
ap-658	6	5	the	the	DET
ap-658	6	6	need	need	NOUN
ap-658	6	7	for	for	ADP
ap-658	6	8	a	a	DET
ap-658	6	9	feasible	feasible	ADJ
ap-658	6	10	computational	computational	ADJ
ap-658	6	11	framework	framework	NOUN
ap-658	6	12	has	have	AUX
ap-658	6	13	challenged	challenge	VERB
ap-658	6	14	the	the	DET
ap-658	6	15	applicability	applicability	NOUN
ap-658	6	16	of	of	ADP
ap-658	6	17	various	various	ADJ
ap-658	6	18	numerical	numerical	ADJ
ap-658	6	19	techniques	technique	NOUN
ap-658	6	20	at	at	ADP
ap-658	6	21	individual	individual	ADJ
ap-658	6	22	scales	scale	NOUN
ap-658	6	23	.	.	PUNCT
ap-658	7	1	the	the	DET
ap-658	7	2	high	high	ADJ
ap-658	7	3	cost	cost	NOUN
ap-658	7	4	of	of	ADP
ap-658	7	5	traditional	traditional	ADJ
ap-658	7	6	numerical	numerical	ADJ
ap-658	7	7	techniques	technique	NOUN
ap-658	7	8	,	,	PUNCT
ap-658	7	9	e.g.	e.g.	ADV
ap-658	7	10	,	,	PUNCT
ap-658	7	11	the	the	DET
ap-658	7	12	finite	finite	ADJ
ap-658	7	13	element	element	NOUN
ap-658	7	14	method	method	NOUN
ap-658	7	15	,	,	PUNCT
ap-658	7	16	then	then	ADV
ap-658	7	17	provided	provide	VERB
ap-658	7	18	an	an	DET
ap-658	7	19	opportunity	opportunity	NOUN
ap-658	7	20	for	for	ADP
ap-658	7	21	classical	classical	ADJ
ap-658	7	22	averaging	averaging	NOUN
ap-658	7	23	schemes	scheme	NOUN
ap-658	7	24	as	as	ADP
ap-658	7	25	a	a	DET
ap-658	7	26	cost	cost	NOUN
ap-658	7	27	-	-	PUNCT
ap-658	7	28	effective	effective	ADJ
ap-658	7	29	and	and	CCONJ
ap-658	7	30	computationally	computationally	ADV
ap-658	7	31	simple	simple	ADJ
ap-658	7	32	alternative	alternative	NOUN
ap-658	7	33	.	.	PUNCT
ap-658	8	1	the	the	DET
ap-658	8	2	motivation	motivation	NOUN
ap-658	8	3	for	for	ADP
ap-658	8	4	the	the	DET
ap-658	8	5	present	present	ADJ
ap-658	8	6	paper	paper	NOUN
ap-658	8	7	,	,	PUNCT
ap-658	8	8	in	in	ADP
ap-658	8	9	particular	particular	ADJ
ap-658	8	10	,	,	PUNCT
ap-658	8	11	arises	arise	VERB
ap-658	8	12	from	from	ADP
ap-658	8	13	the	the	DET
ap-658	8	14	idea	idea	NOUN
ap-658	8	15	of	of	ADP
ap-658	8	16	using	use	VERB
ap-658	8	17	the	the	DET
ap-658	8	18	well	well	ADV
ap-658	8	19	-	-	PUNCT
ap-658	8	20	known	know	VERB
ap-658	8	21	variational	variational	ADJ
ap-658	8	22	principles	principle	NOUN
ap-658	8	23	of	of	ADP
ap-658	8	24	hashin	hashin	NOUN
ap-658	8	25	and	and	CCONJ
ap-658	8	26	shtrikman	shtrikman	NOUN
ap-658	8	27	(	(	PUNCT
ap-658	8	28	hs	hs	X
ap-658	8	29	)	)	PUNCT
ap-658	9	1	[	[	X
ap-658	9	2	6	6	NUM
ap-658	9	3	]	]	PUNCT
ap-658	9	4	when	when	SCONJ
ap-658	9	5	studying	study	VERB
ap-658	9	6	the	the	DET
ap-658	9	7	behavior	behavior	NOUN
ap-658	9	8	of	of	ADP
ap-658	9	9	a	a	DET
ap-658	9	10	composite	composite	NOUN
ap-658	9	11	on	on	ADP
ap-658	9	12	the	the	DET
ap-658	9	13	level	level	NOUN
ap-658	9	14	of	of	ADP
ap-658	9	15	individual	individual	ADJ
ap-658	9	16	constituents	constituent	NOUN
ap-658	9	17	,	,	PUNCT
ap-658	9	18	fig	fig	NOUN
ap-658	9	19	.	.	PUNCT
ap-658	10	1	1c	1c	NOUN
ap-658	10	2	.	.	PUNCT
ap-658	11	1	assuming	assume	VERB
ap-658	11	2	that	that	SCONJ
ap-658	11	3	the	the	DET
ap-658	11	4	material	material	ADJ
ap-658	11	5	response	response	NOUN
ap-658	11	6	of	of	ADP
ap-658	11	7	a	a	DET
ap-658	11	8	two	two	NUM
ap-658	11	9	-	-	PUNCT
ap-658	11	10	phase	phase	NOUN
ap-658	11	11	composite	composite	ADJ
ap-658	11	12	system	system	NOUN
ap-658	11	13	is	be	AUX
ap-658	11	14	well	well	ADV
ap-658	11	15	described	describe	VERB
ap-658	11	16	by	by	ADP
ap-658	11	17	volume	volume	NOUN
ap-658	11	18	averages	average	NOUN
ap-658	11	19	of	of	ADP
ap-658	11	20	local	local	ADJ
ap-658	11	21	fields	field	NOUN
ap-658	11	22	,	,	PUNCT
ap-658	11	23	all	all	DET
ap-658	11	24	these	these	DET
ap-658	11	25	methods	method	NOUN
ap-658	11	26	including	include	VERB
ap-658	11	27	the	the	DET
ap-658	11	28	hs	hs	PROPN
ap-658	11	29	principles	principle	NOUN
ap-658	11	30	can	can	AUX
ap-658	11	31	be	be	AUX
ap-658	11	32	conveniently	conveniently	ADV
ap-658	11	33	referred	refer	VERB
ap-658	11	34	to	to	ADP
ap-658	11	35	as	as	ADP
ap-658	11	36	two	two	NUM
ap-658	11	37	point	point	NOUN
ap-658	11	38	averaging	average	VERB
ap-658	11	39	schemes	scheme	NOUN
ap-658	11	40	.	.	PUNCT
ap-658	12	1	a	a	DET
ap-658	12	2	comprehensive	comprehensive	ADJ
ap-658	12	3	overview	overview	NOUN
ap-658	12	4	of	of	ADP
ap-658	12	5	various	various	ADJ
ap-658	12	6	micromechanical	micromechanical	ADJ
ap-658	12	7	techniques	technique	NOUN
ap-658	12	8	can	can	AUX
ap-658	12	9	be	be	AUX
ap-658	12	10	found	find	VERB
ap-658	12	11	in	in	ADP
ap-658	12	12	[	[	X
ap-658	12	13	7	7	NUM
ap-658	12	14	]	]	PUNCT
ap-658	12	15	.	.	PUNCT
ap-658	13	1	an	an	DET
ap-658	13	2	extension	extension	NOUN
ap-658	13	3	to	to	ADP
ap-658	13	4	the	the	DET
ap-658	13	5	loading	loading	NOUN
ap-658	13	6	conditions	condition	NOUN
ap-658	13	7	that	that	PRON
ap-658	13	8	promote	promote	VERB
ap-658	13	9	inelastic	inelastic	ADJ
ap-658	13	10	deformation	deformation	NOUN
ap-658	13	11	is	be	AUX
ap-658	13	12	presented	present	VERB
ap-658	13	13	in	in	ADP
ap-658	13	14	[	[	X
ap-658	13	15	8–14	8–14	PROPN
ap-658	13	16	]	]	X
ap-658	13	17	.	.	PUNCT
ap-658	14	1	a	a	DET
ap-658	14	2	number	number	NOUN
ap-658	14	3	of	of	ADP
ap-658	14	4	studies	study	NOUN
ap-658	14	5	,	,	PUNCT
ap-658	14	6	however	however	ADV
ap-658	14	7	,	,	PUNCT
ap-658	14	8	have	have	AUX
ap-658	14	9	revealed	reveal	VERB
ap-658	14	10	the	the	DET
ap-658	14	11	main	main	ADJ
ap-658	14	12	drawback	drawback	NOUN
ap-658	14	13	of	of	ADP
ap-658	14	14	the	the	DET
ap-658	14	15	so	so	ADV
ap-658	14	16	called	call	VERB
ap-658	14	17	“	"	PUNCT
ap-658	14	18	elastic	elastic	ADJ
ap-658	14	19	localization	localization	NOUN
ap-658	14	20	rule	rule	NOUN
ap-658	14	21	”	"	PUNCT
ap-658	14	22	for	for	ADP
ap-658	14	23	the	the	DET
ap-658	14	24	evaluation	evaluation	NOUN
ap-658	14	25	of	of	ADP
ap-658	14	26	local	local	ADJ
ap-658	14	27	stress	stress	NOUN
ap-658	14	28	and	and	CCONJ
ap-658	14	29	strain	strain	VERB
ap-658	14	30	averages	average	NOUN
ap-658	14	31	with	with	ADP
ap-658	14	32	the	the	DET
ap-658	14	33	two	two	NUM
ap-658	14	34	-	-	PUNCT
ap-658	14	35	point	point	NOUN
ap-658	14	36	averaging	average	VERB
ap-658	14	37	schemes	scheme	NOUN
ap-658	14	38	.	.	PUNCT
ap-658	15	1	in	in	ADP
ap-658	15	2	particular	particular	ADJ
ap-658	15	3	,	,	PUNCT
ap-658	15	4	defining	define	VERB
ap-658	15	5	the	the	DET
ap-658	15	6	localization	localization	NOUN
ap-658	15	7	rules	rule	NOUN
ap-658	15	8	based	base	VERB
ap-658	15	9	on	on	ADP
ap-658	15	10	the	the	DET
ap-658	15	11	elastic	elastic	ADJ
ap-658	15	12	or	or	CCONJ
ap-658	15	13	tangent	tangent	ADJ
ap-658	15	14	behavior	behavior	NOUN
ap-658	15	15	of	of	ADP
ap-658	15	16	individual	individual	ADJ
ap-658	15	17	phases	phase	NOUN
ap-658	16	1	[	[	X
ap-658	16	2	8	8	NUM
ap-658	16	3	]	]	PUNCT
ap-658	16	4	yields	yield	VERB
ap-658	16	5	a	a	DET
ap-658	16	6	macroscopic	macroscopic	ADJ
ap-658	16	7	response	response	NOUN
ap-658	16	8	that	that	PRON
ap-658	16	9	is	be	AUX
ap-658	16	10	significantly	significantly	ADV
ap-658	16	11	stiffer	stiff	ADJ
ap-658	16	12	than	than	ADP
ap-658	16	13	that	that	PRON
ap-658	16	14	provided	provide	VERB
ap-658	16	15	by	by	ADP
ap-658	16	16	the	the	DET
ap-658	16	17	finite	finite	PROPN
ap-658	16	18	element	element	NOUN
ap-658	16	19	method	method	NOUN
ap-658	16	20	or	or	CCONJ
ap-658	16	21	a	a	DET
ap-658	16	22	sufficiently	sufficiently	ADV
ap-658	16	23	refined	refine	VERB
ap-658	16	24	transformation	transformation	NOUN
ap-658	16	25	field	field	NOUN
ap-658	16	26	analysis	analysis	NOUN
ap-658	16	27	[	[	X
ap-658	16	28	13	13	NUM
ap-658	16	29	]	]	PUNCT
ap-658	16	30	.	.	PUNCT
ap-658	17	1	a	a	DET
ap-658	17	2	number	number	NOUN
ap-658	17	3	of	of	ADP
ap-658	17	4	approaches	approach	NOUN
ap-658	17	5	have	have	AUX
ap-658	17	6	been	be	AUX
ap-658	17	7	proposed	propose	VERB
ap-658	17	8	to	to	PART
ap-658	17	9	address	address	VERB
ap-658	17	10	this	this	DET
ap-658	17	11	task	task	NOUN
ap-658	17	12	with	with	ADP
ap-658	17	13	the	the	DET
ap-658	17	14	main	main	ADJ
ap-658	17	15	goal	goal	NOUN
ap-658	17	16	of	of	ADP
ap-658	17	17	improving	improve	VERB
ap-658	17	18	the	the	DET
ap-658	17	19	way	way	NOUN
ap-658	17	20	the	the	DET
ap-658	17	21	macro200	macro200	PROPN
ap-658	17	22	©	©	PROPN
ap-658	17	23	czech	czech	PROPN
ap-658	17	24	technical	technical	PROPN
ap-658	17	25	university	university	PROPN
ap-658	17	26	publishing	publishing	NOUN
ap-658	17	27	house	house	NOUN
ap-658	17	28	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	17	29	acta	acta	PROPN
ap-658	17	30	polytechnica	polytechnica	PROPN
ap-658	17	31	vol	vol	NOUN
ap-658	17	32	.	.	PROPN
ap-658	18	1	44	44	NUM
ap-658	18	2	no.5–6/2004	no.5–6/2004	NOUN
ap-658	18	3	on	on	ADP
ap-658	18	4	adequacy	adequacy	NOUN
ap-658	18	5	of	of	ADP
ap-658	18	6	two	two	NUM
ap-658	18	7	-	-	PUNCT
ap-658	18	8	point	point	NOUN
ap-658	18	9	averaging	average	VERB
ap-658	18	10	schemes	scheme	NOUN
ap-658	18	11	for	for	ADP
ap-658	18	12	composites	composite	NOUN
ap-658	18	13	with	with	ADP
ap-658	18	14	nonlinear	nonlinear	ADJ
ap-658	18	15	viscoelastic	viscoelastic	ADJ
ap-658	18	16	phases	phase	NOUN
ap-658	18	17	j.	j.	PROPN
ap-658	18	18	zeman	zeman	PROPN
ap-658	18	19	,	,	PUNCT
ap-658	18	20	r.	r.	PROPN
ap-658	18	21	valenta	valenta	PROPN
ap-658	18	22	,	,	PUNCT
ap-658	18	23	m.	m.	NOUN
ap-658	18	24	šejnoha	šejnoha	PROPN
ap-658	18	25	finite	finite	PROPN
ap-658	18	26	element	element	NOUN
ap-658	18	27	simulations	simulation	NOUN
ap-658	18	28	on	on	ADP
ap-658	18	29	fibrous	fibrous	ADJ
ap-658	18	30	composites	composite	NOUN
ap-658	18	31	with	with	ADP
ap-658	18	32	nonlinear	nonlinear	ADJ
ap-658	18	33	viscoelastic	viscoelastic	ADJ
ap-658	18	34	response	response	NOUN
ap-658	18	35	of	of	ADP
ap-658	18	36	the	the	DET
ap-658	18	37	matrix	matrix	NOUN
ap-658	18	38	phase	phase	NOUN
ap-658	18	39	are	be	AUX
ap-658	18	40	performed	perform	VERB
ap-658	18	41	to	to	PART
ap-658	18	42	explain	explain	VERB
ap-658	18	43	why	why	SCONJ
ap-658	18	44	so	so	ADV
ap-658	18	45	called	call	VERB
ap-658	18	46	two	two	NUM
ap-658	18	47	-	-	PUNCT
ap-658	18	48	point	point	NOUN
ap-658	18	49	averaging	averaging	NOUN
ap-658	18	50	schemes	scheme	NOUN
ap-658	18	51	may	may	AUX
ap-658	18	52	fail	fail	VERB
ap-658	18	53	to	to	PART
ap-658	18	54	deliver	deliver	VERB
ap-658	18	55	a	a	DET
ap-658	18	56	realistic	realistic	ADJ
ap-658	18	57	macroscopic	macroscopic	ADJ
ap-658	18	58	response	response	NOUN
ap-658	18	59	.	.	PUNCT
ap-658	19	1	nevertheless	nevertheless	ADV
ap-658	19	2	,	,	PUNCT
ap-658	19	3	the	the	DET
ap-658	19	4	potential	potential	NOUN
ap-658	19	5	of	of	ADP
ap-658	19	6	two	two	NUM
ap-658	19	7	-	-	PUNCT
ap-658	19	8	point	point	NOUN
ap-658	19	9	averaging	average	VERB
ap-658	19	10	schemes	scheme	NOUN
ap-658	19	11	(	(	PUNCT
ap-658	19	12	the	the	DET
ap-658	19	13	overall	overall	ADJ
ap-658	19	14	response	response	NOUN
ap-658	19	15	estimated	estimate	VERB
ap-658	19	16	in	in	ADP
ap-658	19	17	terms	term	NOUN
ap-658	19	18	of	of	ADP
ap-658	19	19	localized	localized	ADJ
ap-658	19	20	averages	average	NOUN
ap-658	19	21	of	of	ADP
ap-658	19	22	a	a	DET
ap-658	19	23	two	two	NUM
ap-658	19	24	-	-	PUNCT
ap-658	19	25	phase	phase	NOUN
ap-658	19	26	composite	composite	ADJ
ap-658	19	27	medium	medium	NOUN
ap-658	19	28	)	)	PUNCT
ap-658	19	29	has	have	AUX
ap-658	19	30	been	be	AUX
ap-658	19	31	put	put	VERB
ap-658	19	32	forward	forward	ADV
ap-658	19	33	in	in	ADP
ap-658	19	34	number	number	NOUN
ap-658	19	35	of	of	ADP
ap-658	19	36	studies	study	NOUN
ap-658	19	37	either	either	CCONJ
ap-658	19	38	in	in	ADP
ap-658	19	39	its	its	PRON
ap-658	19	40	original	original	ADJ
ap-658	19	41	format	format	NOUN
ap-658	19	42	or	or	CCONJ
ap-658	19	43	modified	modify	VERB
ap-658	19	44	to	to	PART
ap-658	19	45	overcome	overcome	VERB
ap-658	19	46	the	the	DET
ap-658	19	47	inherited	inherit	VERB
ap-658	19	48	stiffness	stiffness	NOUN
ap-658	19	49	of	of	ADP
ap-658	19	50	classical	classical	ADJ
ap-658	19	51	”	"	PUNCT
ap-658	19	52	elastic	elastic	ADJ
ap-658	19	53	”	"	PUNCT
ap-658	19	54	localization	localization	NOUN
ap-658	19	55	rules	rule	NOUN
ap-658	19	56	.	.	PUNCT
ap-658	20	1	however	however	ADV
ap-658	20	2	,	,	PUNCT
ap-658	20	3	when	when	SCONJ
ap-658	20	4	the	the	DET
ap-658	20	5	material	material	NOUN
ap-658	20	6	model	model	NOUN
ap-658	20	7	and	and	CCONJ
ap-658	20	8	geometry	geometry	NOUN
ap-658	20	9	of	of	ADP
ap-658	20	10	the	the	DET
ap-658	20	11	microstructure	microstructure	NOUN
ap-658	20	12	promote	promote	NOUN
ap-658	20	13	the	the	DET
ap-658	20	14	formation	formation	NOUN
ap-658	20	15	of	of	ADP
ap-658	20	16	shear	shear	NOUN
ap-658	20	17	bands	band	NOUN
ap-658	20	18	,	,	PUNCT
ap-658	20	19	none	none	NOUN
ap-658	20	20	of	of	ADP
ap-658	20	21	the	the	DET
ap-658	20	22	existing	exist	VERB
ap-658	20	23	two	two	NUM
ap-658	20	24	-	-	PUNCT
ap-658	20	25	point	point	NOUN
ap-658	20	26	averaging	averaging	NOUN
ap-658	20	27	schemes	scheme	NOUN
ap-658	20	28	will	will	AUX
ap-658	20	29	provide	provide	VERB
ap-658	20	30	an	an	DET
ap-658	20	31	adequate	adequate	ADJ
ap-658	20	32	macroscopic	macroscopic	ADJ
ap-658	20	33	response	response	NOUN
ap-658	20	34	,	,	PUNCT
ap-658	20	35	since	since	SCONJ
ap-658	20	36	they	they	PRON
ap-658	20	37	all	all	PRON
ap-658	20	38	fail	fail	VERB
ap-658	20	39	to	to	PART
ap-658	20	40	capture	capture	VERB
ap-658	20	41	the	the	DET
ap-658	20	42	above	above	ADJ
ap-658	20	43	phenomenon	phenomenon	NOUN
ap-658	20	44	.	.	PUNCT
ap-658	21	1	several	several	ADJ
ap-658	21	2	examples	example	NOUN
ap-658	21	3	are	be	AUX
ap-658	21	4	presented	present	VERB
ap-658	21	5	here	here	ADV
ap-658	21	6	to	to	PART
ap-658	21	7	support	support	VERB
ap-658	21	8	this	this	DET
ap-658	21	9	statement	statement	NOUN
ap-658	21	10	.	.	PUNCT
ap-658	22	1	keywords	keyword	NOUN
ap-658	22	2	:	:	PUNCT
ap-658	22	3	fiber	fiber	NOUN
ap-658	22	4	-	-	PUNCT
ap-658	22	5	reinforced	reinforce	VERB
ap-658	22	6	composite	composite	ADJ
ap-658	22	7	materials	material	NOUN
ap-658	22	8	,	,	PUNCT
ap-658	22	9	microstructure	microstructure	NOUN
ap-658	22	10	,	,	PUNCT
ap-658	22	11	nonlinear	nonlinear	ADJ
ap-658	22	12	viscoelastic	viscoelastic	ADJ
ap-658	22	13	behavior	behavior	NOUN
ap-658	22	14	,	,	PUNCT
ap-658	22	15	leonov	leonov	NOUN
ap-658	22	16	model	model	NOUN
ap-658	22	17	,	,	PUNCT
ap-658	22	18	energy	energy	NOUN
ap-658	22	19	methods	method	NOUN
ap-658	22	20	,	,	PUNCT
ap-658	22	21	finite	finite	NOUN
ap-658	22	22	element	element	NOUN
ap-658	22	23	modeling	modeling	NOUN
ap-658	22	24	.	.	PUNCT
ap-658	23	1	macro	macro	ADJ
ap-658	23	2	-	-	NOUN
ap-658	23	3	scale	scale	NOUN
ap-658	23	4	m	m	NOUN
ap-658	23	5	»	»	NOUN
ap-658	23	6	meso	meso	NOUN
ap-658	23	7	-	-	PUNCT
ap-658	23	8	scale	scale	NOUN
ap-658	23	9	mm	mm	INTJ
ap-658	23	10	»	»	PUNCT
ap-658	23	11	micro	micro	NOUN
ap-658	23	12	-	-	NOUN
ap-658	23	13	scale	scale	ADJ
ap-658	23	14	m	m	NOUN
ap-658	23	15	»	»	NOUN
ap-658	23	16	m	m	NOUN
ap-658	23	17	fig	fig	NOUN
ap-658	23	18	.	.	PUNCT
ap-658	24	1	1	1	NUM
ap-658	24	2	:	:	PUNCT
ap-658	24	3	an	an	DET
ap-658	24	4	example	example	NOUN
ap-658	24	5	of	of	ADP
ap-658	24	6	three	three	NUM
ap-658	24	7	-	-	PUNCT
ap-658	24	8	scale	scale	NOUN
ap-658	24	9	modeling	modeling	NOUN
ap-658	24	10	scopic	scopic	NOUN
ap-658	24	11	strains	strain	NOUN
ap-658	24	12	or	or	CCONJ
ap-658	24	13	stresses	stress	NOUN
ap-658	24	14	are	be	AUX
ap-658	24	15	redistributed	redistribute	VERB
ap-658	24	16	into	into	ADP
ap-658	24	17	the	the	DET
ap-658	24	18	individual	individual	ADJ
ap-658	24	19	phases	phase	NOUN
ap-658	24	20	.	.	PUNCT
ap-658	25	1	this	this	PRON
ap-658	25	2	led	lead	VERB
ap-658	25	3	to	to	ADP
ap-658	25	4	the	the	DET
ap-658	25	5	appearance	appearance	NOUN
ap-658	25	6	of	of	ADP
ap-658	25	7	alternative	alternative	ADJ
ap-658	25	8	methods	method	NOUN
ap-658	25	9	,	,	PUNCT
ap-658	25	10	based	base	VERB
ap-658	25	11	on	on	ADP
ap-658	25	12	different	different	ADJ
ap-658	25	13	linearization	linearization	NOUN
ap-658	25	14	of	of	ADP
ap-658	25	15	the	the	DET
ap-658	25	16	governing	govern	VERB
ap-658	25	17	non	non	ADJ
ap-658	25	18	-	-	ADJ
ap-658	25	19	linear	linear	ADJ
ap-658	25	20	problem	problem	NOUN
ap-658	25	21	such	such	ADJ
ap-658	25	22	as	as	ADP
ap-658	25	23	the	the	DET
ap-658	25	24	secant	secant	ADJ
ap-658	25	25	,	,	PUNCT
ap-658	25	26	modified	modified	ADJ
ap-658	25	27	secant	secant	ADJ
ap-658	25	28	and	and	CCONJ
ap-658	25	29	affine	affine	NOUN
ap-658	25	30	methods	method	NOUN
ap-658	25	31	[	[	X
ap-658	25	32	11	11	NUM
ap-658	25	33	,	,	PUNCT
ap-658	25	34	12	12	NUM
ap-658	25	35	]	]	PUNCT
ap-658	25	36	.	.	PUNCT
ap-658	26	1	another	another	DET
ap-658	26	2	example	example	NOUN
ap-658	26	3	are	be	AUX
ap-658	26	4	the	the	DET
ap-658	26	5	second	second	ADJ
ap-658	26	6	-	-	PUNCT
ap-658	26	7	order	order	NOUN
ap-658	26	8	variational	variational	ADJ
ap-658	26	9	estimates	estimate	NOUN
ap-658	26	10	for	for	ADP
ap-658	26	11	material	material	NOUN
ap-658	26	12	systems	system	NOUN
ap-658	26	13	described	describe	VERB
ap-658	26	14	by	by	ADP
ap-658	26	15	convex	convex	PROPN
ap-658	26	16	potentials	potential	NOUN
ap-658	26	17	[	[	X
ap-658	26	18	11	11	NUM
ap-658	26	19	]	]	PUNCT
ap-658	26	20	.	.	PUNCT
ap-658	27	1	a	a	DET
ap-658	27	2	drawback	drawback	NOUN
ap-658	27	3	of	of	ADP
ap-658	27	4	the	the	DET
ap-658	27	5	previously	previously	ADV
ap-658	27	6	mentioned	mention	VERB
ap-658	27	7	methods	method	NOUN
ap-658	27	8	when	when	SCONJ
ap-658	27	9	presented	present	VERB
ap-658	27	10	in	in	ADP
ap-658	27	11	the	the	DET
ap-658	27	12	framework	framework	NOUN
ap-658	27	13	of	of	ADP
ap-658	27	14	incremental	incremental	ADJ
ap-658	27	15	formulation	formulation	NOUN
ap-658	27	16	is	be	AUX
ap-658	27	17	the	the	DET
ap-658	27	18	need	need	NOUN
ap-658	27	19	for	for	ADP
ap-658	27	20	the	the	DET
ap-658	27	21	solution	solution	NOUN
ap-658	27	22	of	of	ADP
ap-658	27	23	a	a	DET
ap-658	27	24	nonlinear	nonlinear	ADJ
ap-658	27	25	system	system	NOUN
ap-658	27	26	of	of	ADP
ap-658	27	27	equations	equation	NOUN
ap-658	27	28	for	for	ADP
ap-658	27	29	each	each	DET
ap-658	27	30	load	load	NOUN
ap-658	27	31	increment	increment	NOUN
ap-658	27	32	.	.	PUNCT
ap-658	28	1	a	a	DET
ap-658	28	2	remedy	remedy	NOUN
ap-658	28	3	has	have	AUX
ap-658	28	4	been	be	AUX
ap-658	28	5	offered	offer	VERB
ap-658	28	6	in	in	ADP
ap-658	28	7	[	[	X
ap-658	28	8	13	13	NUM
ap-658	28	9	]	]	PUNCT
ap-658	28	10	where	where	SCONJ
ap-658	28	11	the	the	DET
ap-658	28	12	classical	classical	ADJ
ap-658	28	13	“	"	PUNCT
ap-658	28	14	total	total	ADJ
ap-658	28	15	localization	localization	NOUN
ap-658	28	16	rule	rule	NOUN
ap-658	28	17	”	"	PUNCT
ap-658	28	18	presented	present	VERB
ap-658	28	19	in	in	ADP
ap-658	28	20	the	the	DET
ap-658	28	21	framework	framework	NOUN
ap-658	28	22	of	of	ADP
ap-658	28	23	transformation	transformation	NOUN
ap-658	28	24	field	field	NOUN
ap-658	28	25	analysis	analysis	NOUN
ap-658	28	26	but	but	CCONJ
ap-658	28	27	enhanced	enhance	VERB
ap-658	28	28	by	by	ADP
ap-658	28	29	corrected	correct	VERB
ap-658	28	30	values	value	NOUN
ap-658	28	31	for	for	SCONJ
ap-658	28	32	the	the	DET
ap-658	28	33	eigenstrains	eigenstrain	NOUN
ap-658	28	34	to	to	PART
ap-658	28	35	soften	soften	VERB
ap-658	28	36	the	the	DET
ap-658	28	37	localization	localization	NOUN
ap-658	28	38	rule	rule	NOUN
ap-658	28	39	was	be	AUX
ap-658	28	40	proposed	propose	VERB
ap-658	28	41	.	.	PUNCT
ap-658	29	1	although	although	SCONJ
ap-658	29	2	appealing	appeal	VERB
ap-658	29	3	in	in	ADP
ap-658	29	4	the	the	DET
ap-658	29	5	macroscopic	macroscopic	ADJ
ap-658	29	6	response	response	NOUN
ap-658	29	7	that	that	SCONJ
ap-658	29	8	they	they	PRON
ap-658	29	9	deliver	deliver	VERB
ap-658	29	10	,	,	PUNCT
ap-658	29	11	most	most	ADJ
ap-658	29	12	of	of	ADP
ap-658	29	13	the	the	DET
ap-658	29	14	above	above	ADJ
ap-658	29	15	methods	method	NOUN
ap-658	29	16	require	require	VERB
ap-658	29	17	the	the	DET
ap-658	29	18	existence	existence	NOUN
ap-658	29	19	of	of	ADP
ap-658	29	20	instantaneous	instantaneous	ADJ
ap-658	29	21	or	or	CCONJ
ap-658	29	22	asymptotic	asymptotic	ADJ
ap-658	29	23	tangent	tangent	NOUN
ap-658	29	24	stiffness	stiffness	NOUN
ap-658	29	25	,	,	PUNCT
ap-658	29	26	which	which	PRON
ap-658	29	27	is	be	AUX
ap-658	29	28	not	not	PART
ap-658	29	29	always	always	ADV
ap-658	29	30	available	available	ADJ
ap-658	29	31	,	,	PUNCT
ap-658	29	32	so	so	SCONJ
ap-658	29	33	that	that	SCONJ
ap-658	29	34	an	an	DET
ap-658	29	35	extension	extension	NOUN
ap-658	29	36	to	to	ADP
ap-658	29	37	more	more	ADV
ap-658	29	38	complex	complex	ADJ
ap-658	29	39	and/or	and/or	CCONJ
ap-658	29	40	rate	rate	NOUN
ap-658	29	41	-	-	PUNCT
ap-658	29	42	dependent	dependent	ADJ
ap-658	29	43	constitutive	constitutive	ADJ
ap-658	29	44	laws	law	NOUN
ap-658	29	45	might	might	AUX
ap-658	29	46	not	not	PART
ap-658	29	47	be	be	AUX
ap-658	29	48	an	an	DET
ap-658	29	49	easy	easy	ADJ
ap-658	29	50	task	task	NOUN
ap-658	29	51	[	[	X
ap-658	29	52	14	14	NUM
ap-658	29	53	]	]	PUNCT
ap-658	29	54	.	.	PUNCT
ap-658	30	1	in	in	ADP
ap-658	30	2	this	this	DET
ap-658	30	3	work	work	NOUN
ap-658	30	4	in	in	ADP
ap-658	30	5	particular	particular	ADJ
ap-658	30	6	the	the	DET
ap-658	30	7	authors	author	NOUN
ap-658	30	8	examined	examine	VERB
ap-658	30	9	the	the	DET
ap-658	30	10	use	use	NOUN
ap-658	30	11	of	of	ADP
ap-658	30	12	the	the	DET
ap-658	30	13	two	two	NUM
ap-658	30	14	-	-	PUNCT
ap-658	30	15	point	point	NOUN
ap-658	30	16	averaging	averaging	NOUN
ap-658	30	17	scheme	scheme	NOUN
ap-658	30	18	in	in	ADP
ap-658	30	19	conjunction	conjunction	NOUN
ap-658	30	20	with	with	ADP
ap-658	30	21	the	the	DET
ap-658	30	22	extended	extended	ADJ
ap-658	30	23	hs	hs	NOUN
ap-658	30	24	principles	principle	NOUN
ap-658	30	25	for	for	ADP
ap-658	30	26	modeling	modeling	NOUN
ap-658	30	27	of	of	ADP
ap-658	30	28	unidirectional	unidirectional	ADJ
ap-658	30	29	composites	composite	NOUN
ap-658	30	30	with	with	ADP
ap-658	30	31	a	a	DET
ap-658	30	32	disordered	disordered	ADJ
ap-658	30	33	microstructure	microstructure	NOUN
ap-658	30	34	.	.	PUNCT
ap-658	31	1	when	when	SCONJ
ap-658	31	2	allowing	allow	VERB
ap-658	31	3	for	for	ADP
ap-658	31	4	a	a	DET
ap-658	31	5	nonlinear	nonlinear	ADJ
ap-658	31	6	viscoelastic	viscoelastic	ADJ
ap-658	31	7	response	response	NOUN
ap-658	31	8	of	of	ADP
ap-658	31	9	the	the	DET
ap-658	31	10	matrix	matrix	NOUN
ap-658	31	11	phase	phase	NOUN
ap-658	31	12	,	,	PUNCT
ap-658	31	13	a	a	DET
ap-658	31	14	rather	rather	ADV
ap-658	31	15	surprising	surprising	ADJ
ap-658	31	16	phenomenon	phenomenon	NOUN
ap-658	31	17	was	be	AUX
ap-658	31	18	observed	observe	VERB
ap-658	31	19	suggesting	suggest	VERB
ap-658	31	20	severe	severe	ADJ
ap-658	31	21	limitations	limitation	NOUN
ap-658	31	22	in	in	ADP
ap-658	31	23	the	the	DET
ap-658	31	24	application	application	NOUN
ap-658	31	25	of	of	ADP
ap-658	31	26	two	two	NUM
ap-658	31	27	-	-	PUNCT
ap-658	31	28	point	point	NOUN
ap-658	31	29	averaging	average	VERB
ap-658	31	30	schemes	scheme	NOUN
ap-658	31	31	.	.	PUNCT
ap-658	32	1	to	to	PART
ap-658	32	2	introduce	introduce	VERB
ap-658	32	3	the	the	DET
ap-658	32	4	subject	subject	NOUN
ap-658	32	5	we	we	PRON
ap-658	32	6	recall	recall	VERB
ap-658	32	7	the	the	DET
ap-658	32	8	essential	essential	ADJ
ap-658	32	9	conclusions	conclusion	NOUN
ap-658	32	10	put	put	VERB
ap-658	32	11	forward	forward	ADV
ap-658	32	12	in	in	ADP
ap-658	32	13	[	[	X
ap-658	32	14	14	14	NUM
ap-658	32	15	]	]	PUNCT
ap-658	32	16	that	that	PRON
ap-658	32	17	illustrate	illustrate	VERB
ap-658	32	18	the	the	DET
ap-658	32	19	well	well	ADV
ap-658	32	20	-	-	PUNCT
ap-658	32	21	known	know	VERB
ap-658	32	22	drawback	drawback	NOUN
ap-658	32	23	of	of	ADP
ap-658	32	24	the	the	DET
ap-658	32	25	so	so	ADV
ap-658	32	26	called	call	VERB
ap-658	32	27	“	"	PUNCT
ap-658	32	28	elastic	elastic	ADJ
ap-658	32	29	localization	localization	NOUN
ap-658	32	30	rule	rule	NOUN
ap-658	32	31	”	"	PUNCT
ap-658	32	32	for	for	ADP
ap-658	32	33	the	the	DET
ap-658	32	34	evaluation	evaluation	NOUN
ap-658	32	35	of	of	ADP
ap-658	32	36	local	local	ADJ
ap-658	32	37	stress	stress	NOUN
ap-658	32	38	and	and	CCONJ
ap-658	32	39	strain	strain	VERB
ap-658	32	40	averages	average	NOUN
ap-658	32	41	in	in	ADP
ap-658	32	42	a	a	DET
ap-658	32	43	two	two	NUM
ap-658	32	44	-	-	PUNCT
ap-658	32	45	phase	phase	NOUN
ap-658	32	46	medium	medium	NOUN
ap-658	32	47	.	.	PUNCT
ap-658	33	1	to	to	PART
ap-658	33	2	begin	begin	VERB
ap-658	33	3	with	with	ADP
ap-658	33	4	,	,	PUNCT
ap-658	33	5	consider	consider	VERB
ap-658	33	6	the	the	DET
ap-658	33	7	results	result	NOUN
ap-658	33	8	presented	present	VERB
ap-658	33	9	in	in	ADP
ap-658	33	10	fig	fig	NOUN
ap-658	33	11	.	.	PUNCT
ap-658	34	1	2	2	NUM
ap-658	34	2	featuring	feature	VERB
ap-658	34	3	macroscopic	macroscopic	ADJ
ap-658	34	4	stress	stress	NOUN
ap-658	34	5	-	-	PUNCT
ap-658	34	6	strain	strain	NOUN
ap-658	34	7	curves	curve	NOUN
ap-658	34	8	derived	derive	VERB
ap-658	34	9	for	for	ADP
ap-658	34	10	hexagonal	hexagonal	ADJ
ap-658	34	11	arrangement	arrangement	NOUN
ap-658	34	12	of	of	ADP
ap-658	34	13	fibers	fiber	NOUN
ap-658	34	14	under	under	ADP
ap-658	34	15	transverse	transverse	NOUN
ap-658	34	16	shear	shear	NOUN
ap-658	34	17	strain	strain	NOUN
ap-658	34	18	loading	loading	NOUN
ap-658	34	19	,	,	PUNCT
ap-658	34	20	see	see	VERB
ap-658	34	21	[	[	X
ap-658	34	22	14	14	NUM
ap-658	34	23	]	]	PUNCT
ap-658	34	24	for	for	ADP
ap-658	34	25	more	more	ADJ
ap-658	34	26	details	detail	NOUN
ap-658	34	27	.	.	PUNCT
ap-658	35	1	the	the	DET
ap-658	35	2	inability	inability	NOUN
ap-658	35	3	of	of	ADP
ap-658	35	4	the	the	DET
ap-658	35	5	hs	hs	PROPN
ap-658	35	6	principle	principle	PROPN
ap-658	35	7	,	,	PUNCT
ap-658	35	8	when	when	SCONJ
ap-658	35	9	used	use	VERB
ap-658	35	10	in	in	ADP
ap-658	35	11	its	its	PRON
ap-658	35	12	original	original	ADJ
ap-658	35	13	form	form	NOUN
ap-658	35	14	,	,	PUNCT
ap-658	35	15	to	to	PART
ap-658	35	16	correctly	correctly	ADV
ap-658	35	17	capture	capture	VERB
ap-658	35	18	the	the	DET
ap-658	35	19	stress	stress	NOUN
ap-658	35	20	redistribution	redistribution	NOUN
ap-658	35	21	is	be	AUX
ap-658	35	22	further	far	ADV
ap-658	35	23	revealed	reveal	VERB
ap-658	35	24	in	in	ADP
ap-658	35	25	fig	fig	NOUN
ap-658	35	26	.	.	PUNCT
ap-658	36	1	3	3	NUM
ap-658	36	2	,	,	PUNCT
ap-658	36	3	which	which	PRON
ap-658	36	4	shows	show	VERB
ap-658	36	5	plots	plot	NOUN
ap-658	36	6	of	of	ADP
ap-658	36	7	“	"	PUNCT
ap-658	36	8	localized	localized	ADJ
ap-658	36	9	”	"	PUNCT
ap-658	36	10	phase	phase	NOUN
ap-658	36	11	averages	average	NOUN
ap-658	36	12	.	.	PUNCT
ap-658	37	1	for	for	ADP
ap-658	37	2	the	the	DET
ap-658	37	3	present	present	ADJ
ap-658	37	4	material	material	NOUN
ap-658	37	5	system	system	NOUN
ap-658	37	6	(	(	PUNCT
ap-658	37	7	matrix	matrix	NOUN
ap-658	37	8	response	response	NOUN
ap-658	37	9	described	describe	VERB
ap-658	37	10	by	by	ADP
ap-658	37	11	the	the	DET
ap-658	37	12	generalized	generalized	ADJ
ap-658	37	13	leonov	leonov	NOUN
ap-658	37	14	model	model	NOUN
ap-658	37	15	)	)	PUNCT
ap-658	37	16	,	,	PUNCT
ap-658	37	17	the	the	DET
ap-658	37	18	deficiency	deficiency	NOUN
ap-658	37	19	of	of	ADP
ap-658	37	20	the	the	DET
ap-658	37	21	family	family	NOUN
ap-658	37	22	of	of	ADP
ap-658	37	23	elastic	elastic	ADJ
ap-658	37	24	localization	localization	NOUN
ap-658	37	25	rules	rule	NOUN
ap-658	37	26	can	can	AUX
ap-658	37	27	be	be	AUX
ap-658	37	28	attributed	attribute	VERB
ap-658	37	29	to	to	ADP
ap-658	37	30	the	the	DET
ap-658	37	31	fact	fact	NOUN
ap-658	37	32	that	that	SCONJ
ap-658	37	33	the	the	DET
ap-658	37	34	significant	significant	ADJ
ap-658	37	35	non	non	NOUN
ap-658	37	36	-	-	NOUN
ap-658	37	37	uniformity	uniformity	NOUN
ap-658	37	38	of	of	ADP
ap-658	37	39	local	local	ADJ
ap-658	37	40	fields	field	NOUN
ap-658	37	41	,	,	PUNCT
ap-658	37	42	which	which	PRON
ap-658	37	43	manifested	manifest	VERB
ap-658	37	44	itself	itself	PRON
ap-658	37	45	in	in	ADP
ap-658	37	46	an	an	DET
ap-658	37	47	evolution	evolution	NOUN
ap-658	37	48	of	of	ADP
ap-658	37	49	the	the	DET
ap-658	37	50	shear	shear	NOUN
ap-658	37	51	bands	band	NOUN
ap-658	37	52	as	as	SCONJ
ap-658	37	53	will	will	AUX
ap-658	37	54	be	be	AUX
ap-658	37	55	shown	show	VERB
ap-658	37	56	later	later	ADV
ap-658	37	57	in	in	ADP
ap-658	37	58	section	section	NOUN
ap-658	37	59	5	5	NUM
ap-658	37	60	,	,	PUNCT
ap-658	37	61	can	can	AUX
ap-658	37	62	not	not	PART
ap-658	37	63	be	be	AUX
ap-658	37	64	accurately	accurately	ADV
ap-658	37	65	represented	represent	VERB
ap-658	37	66	by	by	ADP
ap-658	37	67	the	the	DET
ap-658	37	68	piecewise	piecewise	NOUN
ap-658	37	69	uniform	uniform	NOUN
ap-658	37	70	variation	variation	NOUN
ap-658	37	71	of	of	ADP
ap-658	37	72	the	the	DET
ap-658	37	73	local	local	ADJ
ap-658	37	74	linearized	linearize	VERB
ap-658	37	75	modules	module	NOUN
ap-658	37	76	.	.	PUNCT
ap-658	38	1	to	to	PART
ap-658	38	2	further	far	ADV
ap-658	38	3	support	support	VERB
ap-658	38	4	this	this	DET
ap-658	38	5	statement	statement	NOUN
ap-658	38	6	,	,	PUNCT
ap-658	38	7	we	we	PRON
ap-658	38	8	consider	consider	VERB
ap-658	38	9	an	an	DET
ap-658	38	10	example	example	NOUN
ap-658	38	11	of	of	ADP
ap-658	38	12	a	a	DET
ap-658	38	13	two	two	NUM
ap-658	38	14	-	-	PUNCT
ap-658	38	15	phase	phase	NOUN
ap-658	38	16	laminate	laminate	NOUN
ap-658	38	17	having	have	VERB
ap-658	38	18	uniform	uniform	ADJ
ap-658	38	19	distribution	distribution	NOUN
ap-658	38	20	of	of	ADP
ap-658	38	21	local	local	ADJ
ap-658	38	22	fields	field	NOUN
ap-658	38	23	in	in	ADP
ap-658	38	24	individual	individual	ADJ
ap-658	38	25	phases	phase	NOUN
ap-658	38	26	,	,	PUNCT
ap-658	38	27	so	so	SCONJ
ap-658	38	28	that	that	SCONJ
ap-658	38	29	the	the	DET
ap-658	38	30	piecewise	piecewise	NOUN
ap-658	38	31	uniform	uniform	NOUN
ap-658	38	32	approximations	approximation	NOUN
ap-658	38	33	fit	fit	ADJ
ap-658	38	34	exactly	exactly	ADV
ap-658	38	35	,	,	PUNCT
ap-658	38	36	thus	thus	ADV
ap-658	38	37	suggesting	suggest	VERB
ap-658	38	38	a	a	DET
ap-658	38	39	perfect	perfect	ADJ
ap-658	38	40	match	match	NOUN
ap-658	38	41	with	with	ADP
ap-658	38	42	the	the	DET
ap-658	38	43	response	response	NOUN
ap-658	38	44	provided	provide	VERB
ap-658	38	45	by	by	ADP
ap-658	38	46	the	the	DET
ap-658	38	47	standard	standard	ADJ
ap-658	38	48	finite	finite	ADJ
ap-658	38	49	element	element	NOUN
ap-658	38	50	method	method	NOUN
ap-658	38	51	.	.	PUNCT
ap-658	39	1	fig	fig	NOUN
ap-658	39	2	.	.	PUNCT
ap-658	40	1	4	4	NUM
ap-658	40	2	shows	show	VERB
ap-658	40	3	a	a	DET
ap-658	40	4	variation	variation	NOUN
ap-658	40	5	of	of	ADP
ap-658	40	6	the	the	DET
ap-658	40	7	matrix	matrix	NOUN
ap-658	40	8	shear	shear	NOUN
ap-658	40	9	stress	stress	NOUN
ap-658	40	10	due	due	ADP
ap-658	40	11	to	to	ADP
ap-658	40	12	overall	overall	ADJ
ap-658	40	13	shear	shear	NOUN
ap-658	40	14	strain	strain	NOUN
ap-658	40	15	rate	rate	NOUN
ap-658	40	16	�	�	NOUN
ap-658	40	17	e12	e12	NOUN
ap-658	40	18	4	4	NUM
ap-658	40	19	110	110	NUM
ap-658	40	20	�	�	PROPN
ap-658	40	21	�	�	PROPN
ap-658	40	22	�	�	PROPN
ap-658	40	23	s	s	PART
ap-658	40	24	for	for	ADP
ap-658	40	25	several	several	ADJ
ap-658	40	26	values	value	NOUN
ap-658	40	27	of	of	ADP
ap-658	40	28	the	the	DET
ap-658	40	29	fiber	fiber	NOUN
ap-658	40	30	volume	volume	NOUN
ap-658	40	31	fractions	fraction	NOUN
ap-658	40	32	cf	cf	VERB
ap-658	40	33	.	.	PUNCT
ap-658	41	1	the	the	DET
ap-658	41	2	results	result	NOUN
ap-658	41	3	plotted	plot	VERB
ap-658	41	4	in	in	ADP
ap-658	41	5	fig	fig	NOUN
ap-658	41	6	.	.	PUNCT
ap-658	42	1	4	4	NUM
ap-658	42	2	indicate	indicate	VERB
ap-658	42	3	an	an	DET
ap-658	42	4	increase	increase	NOUN
ap-658	42	5	of	of	ADP
ap-658	42	6	the	the	DET
ap-658	42	7	matrix	matrix	NOUN
ap-658	42	8	strain	strain	NOUN
ap-658	42	9	rate	rate	NOUN
ap-658	42	10	for	for	ADP
ap-658	42	11	higher	high	ADJ
ap-658	42	12	values	value	NOUN
ap-658	42	13	of	of	ADP
ap-658	42	14	the	the	DET
ap-658	42	15	fiber	fiber	NOUN
ap-658	42	16	volume	volume	NOUN
ap-658	42	17	fraction	fraction	NOUN
ap-658	42	18	manifested	manifest	VERB
ap-658	42	19	here	here	ADV
ap-658	42	20	by	by	ADP
ap-658	42	21	higher	high	ADJ
ap-658	42	22	values	value	NOUN
ap-658	42	23	of	of	ADP
ap-658	42	24	the	the	DET
ap-658	42	25	plateau	plateau	NOUN
ap-658	42	26	stress	stress	NOUN
ap-658	42	27	.	.	PUNCT
ap-658	43	1	this	this	DET
ap-658	43	2	supposition	supposition	NOUN
ap-658	43	3	is	be	AUX
ap-658	43	4	confirmed	confirm	VERB
ap-658	43	5	in	in	ADP
ap-658	43	6	fig	fig	NOUN
ap-658	43	7	.	.	PUNCT
ap-658	44	1	5	5	NUM
ap-658	44	2	showing	show	VERB
ap-658	44	3	a	a	DET
ap-658	44	4	time	time	NOUN
ap-658	44	5	evolution	evolution	NOUN
ap-658	44	6	of	of	ADP
ap-658	44	7	the	the	DET
ap-658	44	8	matrix	matrix	NOUN
ap-658	44	9	shear	shear	NOUN
ap-658	44	10	strain	strain	NOUN
ap-658	44	11	.	.	PUNCT
ap-658	45	1	it	it	PRON
ap-658	45	2	is	be	AUX
ap-658	45	3	worth	worth	ADJ
ap-658	45	4	noting	note	VERB
ap-658	45	5	,	,	PUNCT
ap-658	45	6	however	however	ADV
ap-658	45	7	,	,	PUNCT
ap-658	45	8	that	that	SCONJ
ap-658	45	9	a	a	DET
ap-658	45	10	similar	similar	ADJ
ap-658	45	11	conclusion	conclusion	NOUN
ap-658	45	12	can	can	AUX
ap-658	45	13	not	not	PART
ap-658	45	14	be	be	AUX
ap-658	45	15	drawn	draw	VERB
ap-658	45	16	from	from	ADP
ap-658	45	17	fig	fig	NOUN
ap-658	45	18	.	.	PUNCT
ap-658	46	1	2	2	NUM
ap-658	46	2	,	,	PUNCT
ap-658	46	3	when	when	SCONJ
ap-658	46	4	the	the	DET
ap-658	46	5	fe	fe	NOUN
ap-658	46	6	method	method	NOUN
ap-658	46	7	is	be	AUX
ap-658	46	8	used	use	VERB
ap-658	46	9	to	to	PART
ap-658	46	10	derive	derive	VERB
ap-658	46	11	the	the	DET
ap-658	46	12	volume	volume	NOUN
ap-658	46	13	averages	average	NOUN
ap-658	46	14	of	of	ADP
ap-658	46	15	the	the	DET
ap-658	46	16	local	local	ADJ
ap-658	46	17	fields	field	NOUN
ap-658	46	18	.	.	PUNCT
ap-658	47	1	clearly	clearly	ADV
ap-658	47	2	,	,	PUNCT
ap-658	47	3	the	the	DET
ap-658	47	4	volume	volume	NOUN
ap-658	47	5	average	average	NOUN
ap-658	47	6	of	of	ADP
ap-658	47	7	the	the	DET
ap-658	47	8	matrix	matrix	NOUN
ap-658	47	9	phase	phase	NOUN
ap-658	47	10	for	for	ADP
ap-658	47	11	the	the	DET
ap-658	47	12	composite	composite	ADJ
ap-658	47	13	plots	plot	NOUN
ap-658	47	14	below	below	ADP
ap-658	47	15	the	the	DET
ap-658	47	16	curve	curve	NOUN
ap-658	47	17	is	be	AUX
ap-658	47	18	obtained	obtain	VERB
ap-658	47	19	for	for	ADP
ap-658	47	20	a	a	DET
ap-658	47	21	pure	pure	ADJ
ap-658	47	22	matrix	matrix	NOUN
ap-658	47	23	subjected	subject	VERB
ap-658	47	24	to	to	ADP
ap-658	47	25	the	the	DET
ap-658	47	26	same	same	ADJ
ap-658	47	27	loading	loading	NOUN
ap-658	47	28	conditions	condition	NOUN
ap-658	47	29	.	.	PUNCT
ap-658	48	1	this	this	DET
ap-658	48	2	particular	particular	ADJ
ap-658	48	3	result	result	NOUN
ap-658	48	4	is	be	AUX
ap-658	48	5	in	in	ADP
ap-658	48	6	direct	direct	ADJ
ap-658	48	7	contradiction	contradiction	NOUN
ap-658	48	8	with	with	ADP
ap-658	48	9	the	the	DET
ap-658	48	10	observations	observation	NOUN
ap-658	48	11	gained	gain	VERB
ap-658	48	12	from	from	ADP
ap-658	48	13	figs	fig	NOUN
ap-658	48	14	.	.	PUNCT
ap-658	49	1	4–5	4–5	X
ap-658	49	2	.	.	PUNCT
ap-658	50	1	a	a	DET
ap-658	50	2	sound	sound	ADJ
ap-658	50	3	explanation	explanation	NOUN
ap-658	50	4	of	of	ADP
ap-658	50	5	this	this	DET
ap-658	50	6	behavior	behavior	NOUN
ap-658	50	7	is	be	AUX
ap-658	50	8	therefore	therefore	ADV
ap-658	50	9	needed	need	VERB
ap-658	50	10	.	.	PUNCT
ap-658	51	1	similar	similar	ADJ
ap-658	51	2	experiments	experiment	NOUN
ap-658	51	3	were	be	AUX
ap-658	51	4	examined	examine	VERB
ap-658	51	5	in	in	ADP
ap-658	51	6	[	[	X
ap-658	51	7	14	14	NUM
ap-658	51	8	]	]	PUNCT
ap-658	51	9	with	with	ADP
ap-658	51	10	reference	reference	NOUN
ap-658	51	11	to	to	ADP
ap-658	51	12	the	the	DET
ap-658	51	13	primary	primary	ADJ
ap-658	51	14	hs	hs	PROPN
ap-658	51	15	principle	principle	NOUN
ap-658	51	16	in	in	ADP
ap-658	51	17	the	the	DET
ap-658	51	18	framework	framework	NOUN
ap-658	51	19	of	of	ADP
ap-658	51	20	the	the	DET
ap-658	51	21	two	two	NUM
ap-658	51	22	-	-	PUNCT
ap-658	51	23	point	point	NOUN
ap-658	51	24	integration	integration	NOUN
ap-658	51	25	scheme	scheme	NOUN
ap-658	51	26	augmented	augment	VERB
ap-658	51	27	with	with	ADP
ap-658	51	28	a	a	DET
ap-658	51	29	special	special	ADJ
ap-658	51	30	choice	choice	NOUN
ap-658	51	31	of	of	ADP
ap-658	51	32	©	©	PROPN
ap-658	51	33	czech	czech	PROPN
ap-658	51	34	technical	technical	PROPN
ap-658	51	35	university	university	PROPN
ap-658	51	36	publishing	publishing	NOUN
ap-658	51	37	house	house	NOUN
ap-658	51	38	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	51	39	201	201	NUM
ap-658	51	40	acta	acta	PROPN
ap-658	51	41	polytechnica	polytechnica	PROPN
ap-658	51	42	vol	vol	NOUN
ap-658	51	43	.	.	PROPN
ap-658	52	1	44	44	NUM
ap-658	52	2	no.5–6/2004	no.5–6/2004	PROPN
ap-658	52	3	fig	fig	NOUN
ap-658	52	4	.	.	PUNCT
ap-658	53	1	2	2	NUM
ap-658	53	2	:	:	PUNCT
ap-658	53	3	motivation	motivation	NOUN
ap-658	53	4	:	:	PUNCT
ap-658	53	5	macroscopic	macroscopic	ADJ
ap-658	53	6	response	response	NOUN
ap-658	53	7	for	for	ADP
ap-658	53	8	�	�	NOUN
ap-658	53	9	e12	e12	NOUN
ap-658	53	10	4	4	NUM
ap-658	53	11	110	110	NUM
ap-658	53	12	�	�	PROPN
ap-658	53	13	�	�	PROPN
ap-658	53	14	�	�	PROPN
ap-658	53	15	s	s	PART
ap-658	53	16	–	–	PUNCT
ap-658	53	17	hexagonal	hexagonal	ADJ
ap-658	53	18	packing	packing	NOUN
ap-658	53	19	fig	fig	NOUN
ap-658	53	20	.	.	PUNCT
ap-658	54	1	3	3	NUM
ap-658	54	2	:	:	PUNCT
ap-658	54	3	motivation	motivation	NOUN
ap-658	54	4	:	:	PUNCT
ap-658	54	5	localized	localized	ADJ
ap-658	54	6	response	response	NOUN
ap-658	54	7	for	for	ADP
ap-658	54	8	�	�	NOUN
ap-658	54	9	e12	e12	NOUN
ap-658	54	10	4	4	NUM
ap-658	54	11	110	110	NUM
ap-658	54	12	�	�	PROPN
ap-658	54	13	�	�	PROPN
ap-658	54	14	�	�	PROPN
ap-658	54	15	s	s	PART
ap-658	54	16	–	–	PUNCT
ap-658	54	17	hexagonal	hexagonal	ADJ
ap-658	54	18	packing	packing	NOUN
ap-658	54	19	fig	fig	NOUN
ap-658	54	20	.	.	PUNCT
ap-658	55	1	4	4	NUM
ap-658	55	2	:	:	PUNCT
ap-658	55	3	motivation	motivation	NOUN
ap-658	55	4	:	:	PUNCT
ap-658	55	5	laminate	laminate	ADJ
ap-658	55	6	response	response	NOUN
ap-658	55	7	for	for	ADP
ap-658	55	8	strain	strain	NOUN
ap-658	55	9	rate	rate	NOUN
ap-658	55	10	�	�	NOUN
ap-658	55	11	e12	e12	NOUN
ap-658	55	12	4	4	NUM
ap-658	55	13	110	110	NUM
ap-658	55	14	�	�	PROPN
ap-658	55	15	�	�	PROPN
ap-658	55	16	�	�	PROPN
ap-658	55	17	s	s	PART
ap-658	55	18	the	the	DET
ap-658	55	19	reference	reference	NOUN
ap-658	55	20	medium	medium	NOUN
ap-658	55	21	.	.	PUNCT
ap-658	56	1	the	the	DET
ap-658	56	2	results	result	NOUN
ap-658	56	3	summarized	summarize	VERB
ap-658	56	4	in	in	ADP
ap-658	56	5	fig	fig	NOUN
ap-658	56	6	.	.	PUNCT
ap-658	57	1	6	6	NUM
ap-658	57	2	provide	provide	VERB
ap-658	57	3	comparisons	comparison	NOUN
ap-658	57	4	of	of	ADP
ap-658	57	5	stress	stress	NOUN
ap-658	57	6	-	-	PUNCT
ap-658	57	7	strain	strain	NOUN
ap-658	57	8	curves	curve	NOUN
ap-658	57	9	obtained	obtain	VERB
ap-658	57	10	for	for	ADP
ap-658	57	11	this	this	DET
ap-658	57	12	formulation	formulation	NOUN
ap-658	57	13	.	.	PUNCT
ap-658	58	1	clearly	clearly	ADV
ap-658	58	2	,	,	PUNCT
ap-658	58	3	for	for	ADP
ap-658	58	4	material	material	NOUN
ap-658	58	5	systems	system	NOUN
ap-658	58	6	with	with	ADP
ap-658	58	7	uniform	uniform	ADJ
ap-658	58	8	fields	field	VERB
ap-658	58	9	the	the	DET
ap-658	58	10	modified	modify	VERB
ap-658	58	11	incremental	incremental	ADJ
ap-658	58	12	elastic	elastic	ADJ
ap-658	58	13	localization	localization	NOUN
ap-658	58	14	rule	rule	NOUN
ap-658	58	15	is	be	AUX
ap-658	58	16	sufficient	sufficient	ADJ
ap-658	58	17	for	for	ADP
ap-658	58	18	all	all	DET
ap-658	58	19	values	value	NOUN
ap-658	58	20	of	of	ADP
ap-658	58	21	fiber	fiber	NOUN
ap-658	58	22	volume	volume	NOUN
ap-658	58	23	fraction	fraction	NOUN
ap-658	58	24	cf	cf	NOUN
ap-658	58	25	.	.	PUNCT
ap-658	59	1	this	this	DET
ap-658	59	2	result	result	NOUN
ap-658	59	3	just	just	ADV
ap-658	59	4	demonstrates	demonstrate	VERB
ap-658	59	5	that	that	SCONJ
ap-658	59	6	the	the	DET
ap-658	59	7	resulting	result	VERB
ap-658	59	8	mismatch	mismatch	NOUN
ap-658	59	9	between	between	ADP
ap-658	59	10	the	the	DET
ap-658	59	11	hs	hs	PROPN
ap-658	59	12	principles	principle	NOUN
ap-658	59	13	and	and	CCONJ
ap-658	59	14	the	the	DET
ap-658	59	15	finite	finite	ADJ
ap-658	59	16	element	element	NOUN
ap-658	59	17	simulations	simulation	NOUN
ap-658	59	18	,	,	PUNCT
ap-658	59	19	fig	fig	NOUN
ap-658	59	20	.	.	PUNCT
ap-658	59	21	2	2	NUM
ap-658	59	22	,	,	PUNCT
ap-658	59	23	is	be	AUX
ap-658	59	24	a	a	DET
ap-658	59	25	consequence	consequence	NOUN
ap-658	59	26	of	of	ADP
ap-658	59	27	non	non	ADJ
ap-658	59	28	uniformity	uniformity	NOUN
ap-658	59	29	of	of	ADP
ap-658	59	30	the	the	DET
ap-658	59	31	involved	involved	ADJ
ap-658	59	32	fields	field	NOUN
ap-658	59	33	appearing	appear	VERB
ap-658	59	34	in	in	ADP
ap-658	59	35	a	a	DET
ap-658	59	36	composite	composite	NOUN
ap-658	59	37	.	.	PUNCT
ap-658	60	1	this	this	DET
ap-658	60	2	phenomenon	phenomenon	NOUN
ap-658	60	3	is	be	AUX
ap-658	60	4	examined	examine	VERB
ap-658	60	5	below	below	ADP
ap-658	60	6	particularly	particularly	ADV
ap-658	60	7	with	with	ADP
ap-658	60	8	reference	reference	NOUN
ap-658	60	9	to	to	ADP
ap-658	60	10	geometrically	geometrically	ADV
ap-658	60	11	more	more	ADV
ap-658	60	12	complex	complex	ADJ
ap-658	60	13	microstructures	microstructure	NOUN
ap-658	60	14	,	,	PUNCT
ap-658	60	15	fig	fig	NOUN
ap-658	60	16	.	.	PUNCT
ap-658	61	1	1	1	X
ap-658	61	2	.	.	X
ap-658	61	3	in	in	ADP
ap-658	61	4	achieving	achieve	VERB
ap-658	61	5	this	this	DET
ap-658	61	6	goal	goal	NOUN
ap-658	61	7	the	the	DET
ap-658	61	8	behavior	behavior	NOUN
ap-658	61	9	of	of	ADP
ap-658	61	10	so	so	ADV
ap-658	61	11	-	-	PUNCT
ap-658	61	12	called	call	VERB
ap-658	61	13	statistically	statistically	ADV
ap-658	61	14	equivalent	equivalent	ADJ
ap-658	61	15	unit	unit	NOUN
ap-658	61	16	cells	cell	NOUN
ap-658	61	17	is	be	AUX
ap-658	61	18	studied	study	VERB
ap-658	61	19	.	.	PUNCT
ap-658	62	1	the	the	DET
ap-658	62	2	derivation	derivation	NOUN
ap-658	62	3	of	of	ADP
ap-658	62	4	such	such	DET
ap-658	62	5	a	a	DET
ap-658	62	6	unit	unit	NOUN
ap-658	62	7	cell	cell	NOUN
ap-658	62	8	is	be	AUX
ap-658	62	9	reviewed	review	VERB
ap-658	62	10	in	in	ADP
ap-658	62	11	section	section	NOUN
ap-658	62	12	2	2	NUM
ap-658	62	13	.	.	PUNCT
ap-658	63	1	the	the	DET
ap-658	63	2	first	first	ADJ
ap-658	63	3	order	order	NOUN
ap-658	63	4	homogenization	homogenization	NOUN
ap-658	63	5	scheme	scheme	NOUN
ap-658	63	6	is	be	AUX
ap-658	63	7	then	then	ADV
ap-658	63	8	addressed	address	VERB
ap-658	63	9	in	in	ADP
ap-658	63	10	section	section	NOUN
ap-658	63	11	3	3	NUM
ap-658	63	12	in	in	ADP
ap-658	63	13	the	the	DET
ap-658	63	14	framework	framework	NOUN
ap-658	63	15	of	of	ADP
ap-658	63	16	the	the	DET
ap-658	63	17	finite	finite	ADJ
ap-658	63	18	element	element	NOUN
ap-658	63	19	method	method	NOUN
ap-658	63	20	.	.	PUNCT
ap-658	64	1	the	the	DET
ap-658	64	2	basic	basic	ADJ
ap-658	64	3	ingredients	ingredient	NOUN
ap-658	64	4	of	of	ADP
ap-658	64	5	the	the	DET
ap-658	64	6	used	use	VERB
ap-658	64	7	constitutive	constitutive	ADJ
ap-658	64	8	model	model	NOUN
ap-658	64	9	are	be	AUX
ap-658	64	10	presented	present	VERB
ap-658	64	11	in	in	ADP
ap-658	64	12	section	section	NOUN
ap-658	64	13	4	4	NUM
ap-658	64	14	.	.	PUNCT
ap-658	65	1	the	the	DET
ap-658	65	2	paper	paper	NOUN
ap-658	65	3	concludes	conclude	VERB
ap-658	65	4	with	with	ADP
ap-658	65	5	a	a	DET
ap-658	65	6	detailed	detailed	ADJ
ap-658	65	7	discussion	discussion	NOUN
ap-658	65	8	of	of	ADP
ap-658	65	9	the	the	DET
ap-658	65	10	studied	study	VERB
ap-658	65	11	phenomena	phenomenon	NOUN
ap-658	65	12	presented	present	VERB
ap-658	65	13	in	in	ADP
ap-658	65	14	section	section	NOUN
ap-658	65	15	6	6	NUM
ap-658	65	16	.	.	PUNCT
ap-658	66	1	in	in	ADP
ap-658	66	2	the	the	DET
ap-658	66	3	following	follow	VERB
ap-658	66	4	text	text	NOUN
ap-658	66	5	,	,	PUNCT
ap-658	66	6	lowercase	lowercase	PROPN
ap-658	66	7	boldface	boldface	NOUN
ap-658	66	8	letters	letter	NOUN
ap-658	66	9	,	,	PUNCT
ap-658	66	10	e.g.	e.g.	ADV
ap-658	66	11	,	,	PUNCT
ap-658	66	12	a	a	PRON
ap-658	66	13	are	be	AUX
ap-658	66	14	used	use	VERB
ap-658	66	15	for	for	ADP
ap-658	66	16	column	column	NOUN
ap-658	66	17	vectors	vector	NOUN
ap-658	66	18	while	while	SCONJ
ap-658	66	19	capital	capital	NOUN
ap-658	66	20	boldface	boldface	NOUN
ap-658	66	21	letters	letter	NOUN
ap-658	66	22	,	,	PUNCT
ap-658	66	23	e.g.	e.g.	ADV
ap-658	66	24	a	a	PRON
ap-658	66	25	will	will	AUX
ap-658	66	26	be	be	AUX
ap-658	66	27	used	use	VERB
ap-658	66	28	to	to	PART
ap-658	66	29	denote	denote	VERB
ap-658	66	30	a	a	DET
ap-658	66	31	matrix	matrix	NOUN
ap-658	66	32	.	.	PUNCT
ap-658	67	1	lightface	lightface	PROPN
ap-658	67	2	letters	letter	NOUN
ap-658	67	3	are	be	AUX
ap-658	67	4	used	use	VERB
ap-658	67	5	for	for	ADP
ap-658	67	6	scalar	scalar	ADJ
ap-658	67	7	quantities	quantity	NOUN
ap-658	67	8	,	,	PUNCT
ap-658	67	9	e.g.	e.g.	ADV
ap-658	67	10	,	,	PUNCT
ap-658	67	11	a.	a.	NOUN
ap-658	67	12	specific	specific	ADJ
ap-658	67	13	dimensions	dimension	NOUN
ap-658	67	14	of	of	ADP
ap-658	67	15	individual	individual	ADJ
ap-658	67	16	quantities	quantity	NOUN
ap-658	67	17	follow	follow	VERB
ap-658	67	18	from	from	ADP
ap-658	67	19	the	the	DET
ap-658	67	20	context	context	NOUN
ap-658	67	21	.	.	PUNCT
ap-658	68	1	the	the	DET
ap-658	68	2	inverse	inverse	NOUN
ap-658	68	3	of	of	ADP
ap-658	68	4	a	a	DET
ap-658	68	5	non	non	ADJ
ap-658	68	6	-	-	ADJ
ap-658	68	7	singular	singular	ADJ
ap-658	68	8	matrix	matrix	NOUN
ap-658	68	9	is	be	AUX
ap-658	68	10	denoted	denote	VERB
ap-658	68	11	as	as	ADP
ap-658	68	12	a	a	DET
ap-658	68	13	�	�	NOUN
ap-658	68	14	1	1	NUM
ap-658	68	15	while	while	SCONJ
ap-658	68	16	the	the	DET
ap-658	68	17	superscript	superscript	PROPN
ap-658	68	18	t	t	PROPN
ap-658	68	19	indicates	indicate	VERB
ap-658	68	20	the	the	DET
ap-658	68	21	transpose	transpose	NOUN
ap-658	68	22	of	of	ADP
ap-658	68	23	a	a	DET
ap-658	68	24	matrix	matrix	NOUN
ap-658	68	25	.	.	PUNCT
ap-658	69	1	finally	finally	ADV
ap-658	69	2	,	,	PUNCT
ap-658	69	3	only	only	ADV
ap-658	69	4	the	the	DET
ap-658	69	5	loading	loading	NOUN
ap-658	69	6	due	due	ADJ
ap-658	69	7	to	to	ADP
ap-658	69	8	constant	constant	ADJ
ap-658	69	9	overall	overall	ADJ
ap-658	69	10	strain	strain	NOUN
ap-658	69	11	rate	rate	NOUN
ap-658	69	12	is	be	AUX
ap-658	69	13	considered	consider	VERB
ap-658	69	14	and	and	CCONJ
ap-658	69	15	the	the	DET
ap-658	69	16	analysis	analysis	NOUN
ap-658	69	17	is	be	AUX
ap-658	69	18	carried	carry	VERB
ap-658	69	19	out	out	ADP
ap-658	69	20	under	under	ADP
ap-658	69	21	the	the	DET
ap-658	69	22	generalized	generalized	ADJ
ap-658	69	23	plane	plane	NOUN
ap-658	69	24	strain	strain	NOUN
ap-658	69	25	conditions	condition	NOUN
ap-658	69	26	[	[	X
ap-658	69	27	24	24	NUM
ap-658	69	28	,	,	PUNCT
ap-658	69	29	appendix	appendix	VERB
ap-658	69	30	b	b	NOUN
ap-658	69	31	]	]	PUNCT
ap-658	69	32	with	with	ADP
ap-658	69	33	x3	x3	ADJ
ap-658	69	34	being	be	AUX
ap-658	69	35	the	the	DET
ap-658	69	36	axis	axis	NOUN
ap-658	69	37	of	of	ADP
ap-658	69	38	the	the	DET
ap-658	69	39	fibers	fiber	NOUN
ap-658	69	40	.	.	PUNCT
ap-658	70	1	2	2	NUM
ap-658	70	2	geometrical	geometrical	ADJ
ap-658	70	3	modeling	modeling	NOUN
ap-658	70	4	:	:	PUNCT
ap-658	70	5	construction	construction	NOUN
ap-658	70	6	of	of	ADP
ap-658	70	7	statistically	statistically	ADV
ap-658	70	8	optimized	optimize	VERB
ap-658	70	9	unit	unit	NOUN
ap-658	70	10	cells	cell	NOUN
ap-658	70	11	this	this	DET
ap-658	70	12	section	section	NOUN
ap-658	70	13	offers	offer	VERB
ap-658	70	14	a	a	DET
ap-658	70	15	certain	certain	ADJ
ap-658	70	16	statistically	statistically	ADV
ap-658	70	17	optimized	optimize	VERB
ap-658	70	18	periodic	periodic	ADJ
ap-658	70	19	unit	unit	NOUN
ap-658	70	20	cell	cell	NOUN
ap-658	70	21	(	(	PUNCT
ap-658	70	22	puc	puc	PROPN
ap-658	70	23	)	)	PUNCT
ap-658	70	24	consisting	consist	VERB
ap-658	70	25	of	of	ADP
ap-658	70	26	only	only	ADV
ap-658	70	27	a	a	DET
ap-658	70	28	small	small	ADJ
ap-658	70	29	number	number	NOUN
ap-658	70	30	of	of	ADP
ap-658	70	31	particles	particle	NOUN
ap-658	70	32	as	as	ADP
ap-658	70	33	a	a	DET
ap-658	70	34	suitable	suitable	ADJ
ap-658	70	35	representative	representative	NOUN
ap-658	70	36	of	of	ADP
ap-658	70	37	a	a	DET
ap-658	70	38	real	real	ADJ
ap-658	70	39	microstructure	microstructure	NOUN
ap-658	70	40	.	.	PUNCT
ap-658	71	1	such	such	DET
ap-658	71	2	a	a	DET
ap-658	71	3	unit	unit	NOUN
ap-658	71	4	cell	cell	NOUN
ap-658	71	5	is	be	AUX
ap-658	71	6	found	find	VERB
ap-658	71	7	through	through	ADP
ap-658	71	8	a	a	DET
ap-658	71	9	minimization	minimization	NOUN
ap-658	71	10	procedure	procedure	NOUN
ap-658	71	11	formulated	formulate	VERB
ap-658	71	12	in	in	ADP
ap-658	71	13	terms	term	NOUN
ap-658	71	14	of	of	ADP
ap-658	71	15	certain	certain	ADJ
ap-658	71	16	statistical	statistical	ADJ
ap-658	71	17	descriptors	descriptor	NOUN
ap-658	71	18	characterizing	characterize	VERB
ap-658	71	19	the	the	DET
ap-658	71	20	geometrical	geometrical	ADJ
ap-658	71	21	configuration	configuration	NOUN
ap-658	71	22	of	of	ADP
ap-658	71	23	a	a	DET
ap-658	71	24	random	random	ADJ
ap-658	71	25	medium	medium	NOUN
ap-658	71	26	.	.	PUNCT
ap-658	72	1	it	it	PRON
ap-658	72	2	is	be	AUX
ap-658	72	3	believed	believe	VERB
ap-658	72	4	that	that	SCONJ
ap-658	72	5	if	if	SCONJ
ap-658	72	6	the	the	DET
ap-658	72	7	two	two	NUM
ap-658	72	8	systems	system	NOUN
ap-658	72	9	,	,	PUNCT
ap-658	72	10	the	the	DET
ap-658	72	11	real	real	ADJ
ap-658	72	12	microstructure	microstructure	NOUN
ap-658	72	13	and	and	CCONJ
ap-658	72	14	the	the	DET
ap-658	72	15	corresponding	corresponding	ADJ
ap-658	72	16	unit	unit	NOUN
ap-658	72	17	cell	cell	NOUN
ap-658	72	18	,	,	PUNCT
ap-658	72	19	are	be	AUX
ap-658	72	20	the	the	DET
ap-658	72	21	same	same	ADJ
ap-658	72	22	in	in	ADP
ap-658	72	23	the	the	DET
ap-658	72	24	statistical	statistical	ADJ
ap-658	72	25	sense	sense	NOUN
ap-658	72	26	then	then	ADV
ap-658	72	27	the	the	DET
ap-658	72	28	mechanical	mechanical	ADJ
ap-658	72	29	response	response	NOUN
ap-658	72	30	of	of	ADP
ap-658	72	31	both	both	DET
ap-658	72	32	systems	system	NOUN
ap-658	72	33	will	will	AUX
ap-658	72	34	also	also	ADV
ap-658	72	35	be	be	AUX
ap-658	72	36	the	the	DET
ap-658	72	37	same	same	ADJ
ap-658	72	38	.	.	PUNCT
ap-658	73	1	this	this	DET
ap-658	73	2	idea	idea	NOUN
ap-658	73	3	has	have	AUX
ap-658	73	4	been	be	AUX
ap-658	73	5	successfully	successfully	ADV
ap-658	73	6	exploited	exploit	VERB
ap-658	73	7	in	in	ADP
ap-658	73	8	a	a	DET
ap-658	73	9	number	number	NOUN
ap-658	73	10	of	of	ADP
ap-658	73	11	the	the	DET
ap-658	73	12	authors	author	NOUN
ap-658	73	13	’	’	PART
ap-658	73	14	previous	previous	ADJ
ap-658	73	15	works	work	NOUN
ap-658	73	16	[	[	X
ap-658	73	17	15–19	15–19	NOUN
ap-658	73	18	]	]	PUNCT
ap-658	73	19	.	.	PUNCT
ap-658	74	1	see	see	VERB
ap-658	74	2	also	also	ADV
ap-658	74	3	[	[	X
ap-658	74	4	20	20	NUM
ap-658	74	5	]	]	PUNCT
ap-658	74	6	for	for	SCONJ
ap-658	74	7	other	other	ADJ
ap-658	74	8	routes	route	NOUN
ap-658	74	9	to	to	PART
ap-658	74	10	tackle	tackle	VERB
ap-658	74	11	disordered	disordered	ADJ
ap-658	74	12	microstructures	microstructure	NOUN
ap-658	74	13	.	.	PUNCT
ap-658	75	1	it	it	PRON
ap-658	75	2	has	have	AUX
ap-658	75	3	been	be	AUX
ap-658	75	4	shown	show	VERB
ap-658	75	5	that	that	SCONJ
ap-658	75	6	successful	successful	ADJ
ap-658	75	7	completion	completion	NOUN
ap-658	75	8	of	of	ADP
ap-658	75	9	this	this	DET
ap-658	75	10	step	step	NOUN
ap-658	75	11	requires	require	VERB
ap-658	75	12	some	some	DET
ap-658	75	13	measures	measure	NOUN
ap-658	75	14	for	for	ADP
ap-658	75	15	a	a	DET
ap-658	75	16	reliable	reliable	ADJ
ap-658	75	17	quantification	quantification	NOUN
ap-658	75	18	of	of	ADP
ap-658	75	19	the	the	DET
ap-658	75	20	random	random	ADJ
ap-658	75	21	microstructure	microstructure	NOUN
ap-658	75	22	.	.	PUNCT
ap-658	76	1	to	to	PART
ap-658	76	2	do	do	VERB
ap-658	76	3	so	so	ADV
ap-658	76	4	it	it	PRON
ap-658	76	5	is	be	AUX
ap-658	76	6	convenient	convenient	ADJ
ap-658	76	7	to	to	PART
ap-658	76	8	introduce	introduce	VERB
ap-658	76	9	the	the	DET
ap-658	76	10	concept	concept	NOUN
ap-658	76	11	of	of	ADP
ap-658	76	12	an	an	DET
ap-658	76	13	ensemble	ensemble	ADJ
ap-658	76	14	–	–	PUNCT
ap-658	76	15	a	a	DET
ap-658	76	16	collection	collection	NOUN
ap-658	76	17	of	of	ADP
ap-658	76	18	a	a	DET
ap-658	76	19	large	large	ADJ
ap-658	76	20	number	number	NOUN
ap-658	76	21	of	of	ADP
ap-658	76	22	systems	system	NOUN
ap-658	76	23	,	,	PUNCT
ap-658	76	24	which	which	PRON
ap-658	76	25	are	be	AUX
ap-658	76	26	identical	identical	ADJ
ap-658	76	27	from	from	ADP
ap-658	76	28	the	the	DET
ap-658	76	29	macroscopic	macroscopic	ADJ
ap-658	76	30	point	point	NOUN
ap-658	76	31	of	of	ADP
ap-658	76	32	view	view	NOUN
ap-658	76	33	and	and	CCONJ
ap-658	76	34	different	different	ADJ
ap-658	76	35	in	in	ADP
ap-658	76	36	their	their	PRON
ap-658	76	37	microscopical	microscopical	ADJ
ap-658	76	38	details	detail	NOUN
ap-658	76	39	.	.	PUNCT
ap-658	77	1	the	the	DET
ap-658	77	2	morphology	morphology	NOUN
ap-658	77	3	of	of	ADP
ap-658	77	4	such	such	DET
ap-658	77	5	a	a	DET
ap-658	77	6	composite	composite	ADJ
ap-658	77	7	system	system	NOUN
ap-658	77	8	is	be	AUX
ap-658	77	9	fully	fully	ADV
ap-658	77	10	characterized	characterize	VERB
ap-658	77	11	by	by	ADP
ap-658	77	12	a	a	DET
ap-658	77	13	random	random	ADJ
ap-658	77	14	function	function	NOUN
ap-658	77	15	�	�	PROPN
ap-658	77	16	�	�	PROPN
ap-658	77	17	r	r	PROPN
ap-658	77	18	(	(	PUNCT
ap-658	77	19	,	,	PUNCT
ap-658	77	20	)	)	PUNCT
ap-658	77	21	x	x	SYM
ap-658	77	22	,	,	PUNCT
ap-658	77	23	which	which	PRON
ap-658	77	24	is	be	AUX
ap-658	77	25	equal	equal	ADJ
ap-658	77	26	to	to	ADP
ap-658	77	27	one	one	NUM
ap-658	77	28	when	when	SCONJ
ap-658	77	29	a	a	DET
ap-658	77	30	point	point	NOUN
ap-658	77	31	x	x	PUNCT
ap-658	77	32	lies	lie	VERB
ap-658	77	33	in	in	ADP
ap-658	77	34	the	the	DET
ap-658	77	35	phase	phase	NOUN
ap-658	77	36	r	r	NOUN
ap-658	77	37	within	within	ADP
ap-658	77	38	the	the	DET
ap-658	77	39	sample	sample	NOUN
ap-658	77	40	�	�	PROPN
ap-658	77	41	�	�	PROPN
ap-658	77	42	and	and	CCONJ
ap-658	77	43	equal	equal	ADJ
ap-658	77	44	to	to	ADP
ap-658	77	45	zero	zero	NUM
ap-658	77	46	otherwise	otherwise	ADV
ap-658	77	47	.	.	PUNCT
ap-658	78	1	with	with	ADP
ap-658	78	2	the	the	DET
ap-658	78	3	aid	aid	NOUN
ap-658	78	4	of	of	ADP
ap-658	78	5	function	function	NOUN
ap-658	78	6	�	�	PROPN
ap-658	78	7	r	r	NOUN
ap-658	78	8	,	,	PUNCT
ap-658	78	9	the	the	DET
ap-658	78	10	n	n	CCONJ
ap-658	78	11	-	-	PUNCT
ap-658	78	12	point	point	NOUN
ap-658	78	13	probability	probability	NOUN
ap-658	78	14	function	function	NOUN
ap-658	78	15	sr1	sr1	PROPN
ap-658	78	16	,	,	PUNCT
ap-658	78	17	…	…	PUNCT
ap-658	78	18	,	,	PUNCT
ap-658	78	19	rn	rn	PROPN
ap-658	78	20	can	can	AUX
ap-658	78	21	be	be	AUX
ap-658	78	22	defined	define	VERB
ap-658	78	23	as	as	ADP
ap-658	78	24	[	[	X
ap-658	78	25	21	21	NUM
ap-658	78	26	,	,	PUNCT
ap-658	78	27	22	22	NUM
ap-658	78	28	]	]	PUNCT
ap-658	78	29	sr	sr	PROPN
ap-658	78	30	rn	rn	PROPN
ap-658	78	31	n	n	PROPN
ap-658	78	32	r	r	PROPN
ap-658	78	33	rn	rn	PROPN
ap-658	78	34	n1	n1	PROPN
ap-658	78	35	1	1	NUM
ap-658	78	36	1	1	NUM
ap-658	78	37	1	1	NUM
ap-658	78	38	,	,	PUNCT
ap-658	78	39	,	,	PUNCT
ap-658	78	40	(	(	PUNCT
ap-658	78	41	,	,	PUNCT
ap-658	78	42	,	,	PUNCT
ap-658	78	43	)	)	PUNCT
ap-658	78	44	(	(	PUNCT
ap-658	78	45	,	,	PUNCT
ap-658	78	46	)	)	PUNCT
ap-658	78	47	(	(	PUNCT
ap-658	78	48	,	,	PUNCT
ap-658	78	49	)	)	PUNCT
ap-658	78	50	,	,	PUNCT
ap-658	78	51	�	�	PROPN
ap-658	78	52	�	�	PROPN
ap-658	78	53	�	�	PROPN
ap-658	78	54	x	x	X
ap-658	78	55	x	x	SYM
ap-658	78	56	x	x	SYM
ap-658	78	57	x	x	PRON
ap-658	78	58	�	�	PROPN
ap-658	78	59	�	�	PROPN
ap-658	78	60	�	�	PROPN
ap-658	78	61	�	�	PROPN
ap-658	78	62	�	�	PROPN
ap-658	78	63	(	(	PUNCT
ap-658	78	64	1	1	NUM
ap-658	78	65	)	)	PUNCT
ap-658	78	66	where	where	SCONJ
ap-658	78	67	�	�	PROPN
ap-658	78	68	denotes	denote	VERB
ap-658	78	69	the	the	DET
ap-658	78	70	ensemble	ensemble	ADJ
ap-658	78	71	average	average	NOUN
ap-658	78	72	.	.	PUNCT
ap-658	79	1	thus	thus	ADV
ap-658	79	2	,	,	PUNCT
ap-658	79	3	sr1	sr1	PROPN
ap-658	79	4	,	,	PUNCT
ap-658	79	5	…	…	PUNCT
ap-658	79	6	,	,	PUNCT
ap-658	79	7	rn	rn	PROPN
ap-658	79	8	gives	give	VERB
ap-658	79	9	the	the	DET
ap-658	79	10	probability	probability	NOUN
ap-658	79	11	of	of	ADP
ap-658	79	12	finding	find	VERB
ap-658	79	13	n	n	PRON
ap-658	79	14	points	point	NOUN
ap-658	79	15	(	(	PUNCT
ap-658	79	16	,	,	PUNCT
ap-658	79	17	,	,	PUNCT
ap-658	79	18	)	)	PUNCT
ap-658	79	19	x	x	SYM
ap-658	79	20	x1	x1	PROPN
ap-658	79	21	�	�	PROPN
ap-658	79	22	n	n	PRON
ap-658	79	23	randomly	randomly	ADV
ap-658	79	24	thrown	throw	VERB
ap-658	79	25	into	into	ADP
ap-658	79	26	a	a	DET
ap-658	79	27	medium	medium	NOUN
ap-658	79	28	located	locate	VERB
ap-658	79	29	in	in	ADP
ap-658	79	30	the	the	DET
ap-658	79	31	phases	phase	NOUN
ap-658	79	32	r1	r1	PROPN
ap-658	79	33	,	,	PUNCT
ap-658	79	34	…	…	NUM
ap-658	79	35	,	,	PUNCT
ap-658	79	36	rn	rn	PROPN
ap-658	79	37	.	.	PROPN
ap-658	80	1	in	in	ADP
ap-658	80	2	the	the	DET
ap-658	80	3	following	following	NOUN
ap-658	80	4	,	,	PUNCT
ap-658	80	5	we	we	PRON
ap-658	80	6	limit	limit	VERB
ap-658	80	7	our	our	PRON
ap-658	80	8	attention	attention	NOUN
ap-658	80	9	to	to	ADP
ap-658	80	10	functions	function	NOUN
ap-658	80	11	of	of	ADP
ap-658	80	12	the	the	DET
ap-658	80	13	order	order	NOUN
ap-658	80	14	of	of	ADP
ap-658	80	15	one	one	NUM
ap-658	80	16	and	and	CCONJ
ap-658	80	17	two	two	NUM
ap-658	80	18	.	.	PUNCT
ap-658	81	1	analysis	analysis	NOUN
ap-658	81	2	of	of	ADP
ap-658	81	3	random	random	ADJ
ap-658	81	4	composites	composite	NOUN
ap-658	81	5	usually	usually	ADV
ap-658	81	6	relies	rely	VERB
ap-658	81	7	on	on	ADP
ap-658	81	8	various	various	ADJ
ap-658	81	9	hypotheses	hypothesis	NOUN
ap-658	81	10	,	,	PUNCT
ap-658	81	11	which	which	PRON
ap-658	81	12	simplify	simplify	VERB
ap-658	81	13	the	the	DET
ap-658	81	14	computational	computational	ADJ
ap-658	81	15	effort	effort	NOUN
ap-658	81	16	to	to	ADP
ap-658	81	17	a	a	DET
ap-658	81	18	great	great	ADJ
ap-658	81	19	extent	extent	NOUN
ap-658	81	20	.	.	PUNCT
ap-658	82	1	in	in	ADP
ap-658	82	2	particular	particular	ADJ
ap-658	82	3	,	,	PUNCT
ap-658	82	4	under	under	ADP
ap-658	82	5	the	the	DET
ap-658	82	6	ergodic	ergodic	ADJ
ap-658	82	7	hypothesis	hypothesis	NOUN
ap-658	82	8	[	[	X
ap-658	82	9	21	21	NUM
ap-658	82	10	]	]	PUNCT
ap-658	82	11	the	the	DET
ap-658	82	12	volume	volume	NOUN
ap-658	82	13	average	average	NOUN
ap-658	82	14	of	of	ADP
ap-658	82	15	function	function	PROPN
ap-658	82	16	�	�	PROPN
ap-658	82	17	�	�	PROPN
ap-658	82	18	r	r	PROPN
ap-658	82	19	(	(	PUNCT
ap-658	82	20	,	,	PUNCT
ap-658	82	21	)	)	PUNCT
ap-658	82	22	x	x	PUNCT
ap-658	82	23	given	give	VERB
ap-658	82	24	by	by	ADP
ap-658	82	25	�	�	PROPN
ap-658	82	26	�	�	PROPN
ap-658	82	27	�	�	PROPN
ap-658	82	28	r	r	NOUN
ap-658	82	29	v	v	NOUN
ap-658	82	30	r	r	NOUN
ap-658	82	31	v	v	NOUN
ap-658	82	32	v	v	NOUN
ap-658	82	33	(	(	PUNCT
ap-658	82	34	,	,	PUNCT
ap-658	82	35	)	)	PUNCT
ap-658	82	36	lim	lim	PROPN
ap-658	82	37	(	(	PUNCT
ap-658	82	38	)	)	PUNCT
ap-658	82	39	x	x	SYM
ap-658	82	40	x	x	SYM
ap-658	82	41	y	y	PROPN
ap-658	82	42	y	y	PROPN
ap-658	82	43	�	�	PROPN
ap-658	82	44	�	�	PROPN
ap-658	82	45	�	�	PROPN
ap-658	82	46	�	�	PROPN
ap-658	82	47	�	�	PROPN
ap-658	82	48	1	1	NUM
ap-658	82	49	d	d	NOUN
ap-658	82	50	,	,	PUNCT
ap-658	82	51	(	(	PUNCT
ap-658	82	52	2	2	X
ap-658	82	53	)	)	PUNCT
ap-658	82	54	is	be	AUX
ap-658	82	55	independent	independent	ADJ
ap-658	82	56	of	of	ADP
ap-658	82	57	�	�	PROPN
ap-658	82	58	and	and	CCONJ
ap-658	82	59	identical	identical	ADJ
ap-658	82	60	to	to	ADP
ap-658	82	61	the	the	DET
ap-658	82	62	ensemble	ensemble	ADJ
ap-658	82	63	average	average	ADJ
ap-658	82	64	�	�	PROPN
ap-658	82	65	�	�	PROPN
ap-658	82	66	r	r	NOUN
ap-658	82	67	r	r	NOUN
ap-658	82	68	r	r	NOUN
ap-658	82	69	rs	rs	NOUN
ap-658	82	70	c	c	NOUN
ap-658	82	71	(	(	PUNCT
ap-658	82	72	)	)	PUNCT
ap-658	82	73	(	(	PUNCT
ap-658	82	74	)	)	PUNCT
ap-658	82	75	(	(	PUNCT
ap-658	82	76	)	)	PUNCT
ap-658	82	77	x	x	SYM
ap-658	82	78	x	x	SYM
ap-658	82	79	x	x	X
ap-658	82	80	�	�	PROPN
ap-658	82	81	�	�	PROPN
ap-658	82	82	�	�	PROPN
ap-658	82	83	,	,	PUNCT
ap-658	82	84	(	(	PUNCT
ap-658	82	85	3	3	X
ap-658	82	86	)	)	PUNCT
ap-658	82	87	where	where	SCONJ
ap-658	82	88	cr	cr	PROPN
ap-658	82	89	is	be	AUX
ap-658	82	90	the	the	DET
ap-658	82	91	volume	volume	NOUN
ap-658	82	92	fraction	fraction	NOUN
ap-658	82	93	of	of	ADP
ap-658	82	94	the	the	DET
ap-658	82	95	rth	rth	NOUN
ap-658	82	96	phase	phase	NOUN
ap-658	82	97	.	.	PUNCT
ap-658	83	1	the	the	DET
ap-658	83	2	statistical	statistical	ADJ
ap-658	83	3	homogeneity	homogeneity	NOUN
ap-658	83	4	assumption	assumption	NOUN
ap-658	83	5	means	mean	VERB
ap-658	83	6	that	that	SCONJ
ap-658	83	7	the	the	DET
ap-658	83	8	value	value	NOUN
ap-658	83	9	of	of	ADP
ap-658	83	10	the	the	DET
ap-658	83	11	ensemble	ensemble	ADJ
ap-658	83	12	average	average	NOUN
ap-658	83	13	is	be	AUX
ap-658	83	14	translation	translation	NOUN
ap-658	83	15	invariant	invariant	ADJ
ap-658	83	16	.	.	PUNCT
ap-658	84	1	then	then	ADV
ap-658	84	2	,	,	PUNCT
ap-658	84	3	for	for	ADP
ap-658	84	4	example	example	NOUN
ap-658	84	5	,	,	PUNCT
ap-658	84	6	the	the	DET
ap-658	84	7	two	two	NUM
ap-658	84	8	-	-	PUNCT
ap-658	84	9	point	point	NOUN
ap-658	84	10	matrix	matrix	NOUN
ap-658	84	11	probability	probability	NOUN
ap-658	84	12	function	function	NOUN
ap-658	84	13	reads	read	VERB
ap-658	84	14	s	s	PRON
ap-658	84	15	smm	smm	ADJ
ap-658	84	16	mm	mm	PROPN
ap-658	84	17	(	(	PUNCT
ap-658	84	18	,	,	PUNCT
ap-658	84	19	)	)	PUNCT
ap-658	84	20	(	(	PUNCT
ap-658	84	21	)	)	PUNCT
ap-658	84	22	x	x	X
ap-658	84	23	x	x	SYM
ap-658	84	24	x1	x1	ADJ
ap-658	84	25	2	2	NUM
ap-658	84	26	12	12	NUM
ap-658	84	27	�	�	PROPN
ap-658	84	28	,	,	PUNCT
ap-658	84	29	(	(	PUNCT
ap-658	84	30	4	4	X
ap-658	84	31	)	)	PUNCT
ap-658	84	32	where	where	SCONJ
ap-658	84	33	x	x	X
ap-658	84	34	x	x	VERB
ap-658	84	35	xij	xij	PROPN
ap-658	84	36	j	j	PROPN
ap-658	84	37	i	i	PROPN
ap-658	84	38	�	�	PROPN
ap-658	84	39	�	�	PROPN
ap-658	84	40	.	.	PUNCT
ap-658	85	1	note	note	VERB
ap-658	85	2	that	that	SCONJ
ap-658	85	3	for	for	ADP
ap-658	85	4	an	an	DET
ap-658	85	5	ergodic	ergodic	ADJ
ap-658	85	6	and	and	CCONJ
ap-658	85	7	periodic	periodic	ADJ
ap-658	85	8	microstructure	microstructure	NOUN
ap-658	85	9	,	,	PUNCT
ap-658	85	10	the	the	DET
ap-658	85	11	two	two	NUM
ap-658	85	12	-	-	PUNCT
ap-658	85	13	point	point	NOUN
ap-658	85	14	probability	probability	NOUN
ap-658	85	15	function	function	NOUN
ap-658	85	16	srs	srs	PROPN
ap-658	85	17	has	have	VERB
ap-658	85	18	the	the	DET
ap-658	85	19	following	follow	VERB
ap-658	85	20	form	form	NOUN
ap-658	85	21	srs	srs	PROPN
ap-658	85	22	r	r	PROPN
ap-658	85	23	s	s	PROPN
ap-658	85	24	(	(	PUNCT
ap-658	85	25	)	)	PUNCT
ap-658	85	26	(	(	PUNCT
ap-658	85	27	)	)	PUNCT
ap-658	85	28	(	(	PUNCT
ap-658	85	29	)	)	PUNCT
ap-658	85	30	x	x	SYM
ap-658	85	31	x	x	PUNCT
ap-658	85	32	x	x	SYM
ap-658	85	33	y	y	PROPN
ap-658	85	34	y	y	PROPN
ap-658	85	35	�	�	PROPN
ap-658	85	36	�	�	PROPN
ap-658	85	37	�	�	PROPN
ap-658	85	38	1	1	NUM
ap-658	85	39	�	�	PROPN
ap-658	85	40	�	�	PROPN
ap-658	85	41	�	�	PROPN
ap-658	85	42	�	�	PROPN
ap-658	85	43	d	d	PROPN
ap-658	85	44	,	,	PUNCT
ap-658	85	45	(	(	PUNCT
ap-658	85	46	5	5	NUM
ap-658	85	47	)	)	PUNCT
ap-658	85	48	202	202	NUM
ap-658	85	49	©	©	PROPN
ap-658	85	50	czech	czech	PROPN
ap-658	85	51	technical	technical	PROPN
ap-658	85	52	university	university	PROPN
ap-658	85	53	publishing	publishing	NOUN
ap-658	85	54	house	house	NOUN
ap-658	85	55	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	85	56	acta	acta	PROPN
ap-658	85	57	polytechnica	polytechnica	PROPN
ap-658	85	58	vol	vol	NOUN
ap-658	85	59	.	.	PROPN
ap-658	86	1	44	44	NUM
ap-658	86	2	no.5–6/2004	no.5–6/2004	PROPN
ap-658	86	3	fig	fig	NOUN
ap-658	86	4	.	.	PUNCT
ap-658	87	1	5	5	NUM
ap-658	87	2	:	:	PUNCT
ap-658	87	3	motivation	motivation	NOUN
ap-658	87	4	:	:	PUNCT
ap-658	87	5	laminate	laminate	ADJ
ap-658	87	6	response	response	NOUN
ap-658	87	7	for	for	ADP
ap-658	87	8	strain	strain	NOUN
ap-658	87	9	rate	rate	NOUN
ap-658	87	10	�	�	NOUN
ap-658	87	11	e12	e12	NOUN
ap-658	87	12	4	4	NUM
ap-658	87	13	110	110	NUM
ap-658	87	14	�	�	PROPN
ap-658	87	15	�	�	PROPN
ap-658	87	16	�	�	PROPN
ap-658	87	17	s	s	PART
ap-658	87	18	–	–	PUNCT
ap-658	87	19	evolution	evolution	NOUN
ap-658	87	20	of	of	ADP
ap-658	87	21	the	the	DET
ap-658	87	22	matrix	matrix	NOUN
ap-658	87	23	strain	strain	NOUN
ap-658	87	24	rate	rate	NOUN
ap-658	87	25	as	as	ADP
ap-658	87	26	a	a	DET
ap-658	87	27	function	function	NOUN
ap-658	87	28	of	of	ADP
ap-658	87	29	the	the	DET
ap-658	87	30	volume	volume	NOUN
ap-658	87	31	fractions	fraction	NOUN
ap-658	87	32	fig	fig	NOUN
ap-658	87	33	.	.	PUNCT
ap-658	88	1	6	6	NUM
ap-658	88	2	:	:	PUNCT
ap-658	88	3	motivation	motivation	NOUN
ap-658	88	4	:	:	PUNCT
ap-658	88	5	comparison	comparison	NOUN
ap-658	88	6	of	of	ADP
ap-658	88	7	fem	fem	NOUN
ap-658	88	8	and	and	CCONJ
ap-658	88	9	hs	h	NOUN
ap-658	88	10	-	-	PUNCT
ap-658	88	11	based	base	VERB
ap-658	88	12	estimates	estimate	NOUN
ap-658	88	13	for	for	ADP
ap-658	88	14	strain	strain	NOUN
ap-658	88	15	rate	rate	NOUN
ap-658	88	16	�	�	NOUN
ap-658	88	17	e12	e12	NOUN
ap-658	88	18	4	4	NUM
ap-658	88	19	110	110	NUM
ap-658	88	20	�	�	PROPN
ap-658	88	21	�	�	PROPN
ap-658	88	22	�	�	PROPN
ap-658	88	23	s	s	PART
ap-658	88	24	where	where	SCONJ
ap-658	88	25	�	�	PROPN
ap-658	88	26	represents	represent	VERB
ap-658	88	27	the	the	DET
ap-658	88	28	size	size	NOUN
ap-658	88	29	of	of	ADP
ap-658	88	30	the	the	DET
ap-658	88	31	analyzed	analyze	VERB
ap-658	88	32	domain	domain	NOUN
ap-658	88	33	.	.	PUNCT
ap-658	89	1	the	the	DET
ap-658	89	2	fourier	fourier	NOUN
ap-658	89	3	transform	transform	NOUN
ap-658	89	4	of	of	ADP
ap-658	89	5	function	function	NOUN
ap-658	89	6	srs	srs	PROPN
ap-658	89	7	is	be	AUX
ap-658	89	8	given	give	VERB
ap-658	89	9	by	by	ADP
ap-658	89	10	f	f	PROPN
ap-658	89	11	f	f	PROPN
ap-658	89	12	fsrs	fsr	VERB
ap-658	89	13	r	r	PROPN
ap-658	89	14	s	s	PROPN
ap-658	89	15	(	(	PUNCT
ap-658	89	16	)	)	PUNCT
ap-658	89	17	(	(	PUNCT
ap-658	89	18	)	)	PUNCT
ap-658	89	19	(	(	PUNCT
ap-658	89	20	)	)	PUNCT
ap-658	89	21	�	�	PROPN
ap-658	89	22	�	�	PROPN
ap-658	89	23	�	�	PROPN
ap-658	89	24	�	�	PROPN
ap-658	89	25	�	�	PROPN
ap-658	89	26	�	�	PROPN
ap-658	89	27	1	1	NUM
ap-658	89	28	�	�	PROPN
ap-658	89	29	,	,	PUNCT
ap-658	89	30	(	(	PUNCT
ap-658	89	31	6	6	NUM
ap-658	89	32	)	)	PUNCT
ap-658	89	33	where	where	SCONJ
ap-658	89	34	�	�	PROPN
ap-658	89	35	now	now	ADV
ap-658	89	36	denotes	denote	VERB
ap-658	89	37	the	the	DET
ap-658	89	38	complex	complex	ADJ
ap-658	89	39	conjugate	conjugate	NOUN
ap-658	89	40	.	.	PUNCT
ap-658	90	1	when	when	SCONJ
ap-658	90	2	introducing	introduce	VERB
ap-658	90	3	a	a	DET
ap-658	90	4	binary	binary	ADJ
ap-658	90	5	image	image	NOUN
ap-658	90	6	of	of	ADP
ap-658	90	7	the	the	DET
ap-658	90	8	actual	actual	ADJ
ap-658	90	9	microstructure	microstructure	NOUN
ap-658	90	10	and	and	CCONJ
ap-658	90	11	taking	take	VERB
ap-658	90	12	into	into	ADP
ap-658	90	13	account	account	NOUN
ap-658	90	14	the	the	DET
ap-658	90	15	periodicity	periodicity	NOUN
ap-658	90	16	of	of	ADP
ap-658	90	17	the	the	DET
ap-658	90	18	rve	rve	PROPN
ap-658	90	19	we	we	PRON
ap-658	90	20	may	may	AUX
ap-658	90	21	approximate	approximate	VERB
ap-658	90	22	eq	eq	ADP
ap-658	90	23	.	.	PUNCT
ap-658	91	1	(	(	PUNCT
ap-658	91	2	6	6	NUM
ap-658	91	3	)	)	PUNCT
ap-658	91	4	by	by	ADP
ap-658	91	5	the	the	DET
ap-658	91	6	discrete	discrete	ADJ
ap-658	91	7	fourier	fourier	NOUN
ap-658	91	8	transform	transform	NOUN
ap-658	91	9	:	:	PUNCT
ap-658	91	10	�	�	PROPN
ap-658	91	11	�	�	PROPN
ap-658	91	12	s	s	PART
ap-658	91	13	n	n	PRON
ap-658	91	14	nmm	nmm	PROPN
ap-658	91	15	x	x	SYM
ap-658	91	16	y	y	PROPN
ap-658	91	17	m	m	PROPN
ap-658	91	18	m	m	VERB
ap-658	91	19	�	�	PROPN
ap-658	91	20	1	1	NUM
ap-658	91	21	idft	idft	PROPN
ap-658	91	22	dft	dft	PROPN
ap-658	91	23	dft	dft	PROPN
ap-658	91	24	(	(	PUNCT
ap-658	91	25	)	)	PUNCT
ap-658	91	26	(	(	PUNCT
ap-658	91	27	)	)	PUNCT
ap-658	91	28	�	�	PROPN
ap-658	91	29	�	�	PROPN
ap-658	91	30	,	,	PUNCT
ap-658	91	31	(	(	PUNCT
ap-658	91	32	7	7	X
ap-658	91	33	)	)	PUNCT
ap-658	91	34	where	where	SCONJ
ap-658	91	35	nx	nx	PROPN
ap-658	91	36	and	and	CCONJ
ap-658	91	37	ny	ny	PROPN
ap-658	91	38	are	be	AUX
ap-658	91	39	the	the	DET
ap-658	91	40	horizontal	horizontal	ADJ
ap-658	91	41	and	and	CCONJ
ap-658	91	42	the	the	DET
ap-658	91	43	vertical	vertical	ADJ
ap-658	91	44	resolution	resolution	NOUN
ap-658	91	45	of	of	ADP
ap-658	91	46	the	the	DET
ap-658	91	47	bitmap	bitmap	NOUN
ap-658	91	48	.	.	PUNCT
ap-658	92	1	note	note	VERB
ap-658	92	2	that	that	SCONJ
ap-658	92	3	this	this	DET
ap-658	92	4	approach	approach	NOUN
ap-658	92	5	requires	require	VERB
ap-658	92	6	only	only	ADV
ap-658	92	7	o(nxny	o(nxny	NOUN
ap-658	92	8	)	)	PUNCT
ap-658	92	9	log(nxny	log(nxny	NOUN
ap-658	92	10	)	)	PUNCT
ap-658	92	11	operations	operation	NOUN
ap-658	92	12	,	,	PUNCT
ap-658	92	13	instead	instead	ADV
ap-658	92	14	of	of	ADP
ap-658	92	15	o(n	o(n	NUM
ap-658	92	16	nx	nx	NOUN
ap-658	92	17	y	y	PROPN
ap-658	92	18	2	2	NUM
ap-658	92	19	2	2	NUM
ap-658	92	20	)	)	PUNCT
ap-658	92	21	operations	operation	NOUN
ap-658	92	22	needed	need	VERB
ap-658	92	23	by	by	ADP
ap-658	92	24	the	the	DET
ap-658	92	25	direct	direct	ADJ
ap-658	92	26	method	method	NOUN
ap-658	92	27	.	.	PUNCT
ap-658	93	1	moreover	moreover	ADV
ap-658	93	2	,	,	PUNCT
ap-658	93	3	the	the	DET
ap-658	93	4	possibility	possibility	NOUN
ap-658	93	5	of	of	ADP
ap-658	93	6	using	use	VERB
ap-658	93	7	highly	highly	ADV
ap-658	93	8	optimized	optimize	VERB
ap-658	93	9	public	public	ADJ
ap-658	93	10	software	software	NOUN
ap-658	93	11	packages	package	NOUN
ap-658	93	12	makes	make	VERB
ap-658	93	13	the	the	DET
ap-658	93	14	dft	dft	NOUN
ap-658	93	15	-	-	PUNCT
ap-658	93	16	based	base	VERB
ap-658	93	17	approach	approach	NOUN
ap-658	93	18	very	very	ADV
ap-658	93	19	efficient	efficient	ADJ
ap-658	93	20	.	.	PUNCT
ap-658	94	1	see	see	VERB
ap-658	94	2	,	,	PUNCT
ap-658	94	3	e.g.	e.g.	ADV
ap-658	94	4	,	,	PUNCT
ap-658	94	5	[	[	X
ap-658	94	6	16	16	NUM
ap-658	94	7	]	]	PUNCT
ap-658	94	8	for	for	ADP
ap-658	94	9	detailed	detailed	ADJ
ap-658	94	10	discussion	discussion	NOUN
ap-658	94	11	and	and	CCONJ
ap-658	94	12	numerical	numerical	ADJ
ap-658	94	13	experiments	experiment	NOUN
ap-658	94	14	.	.	PUNCT
ap-658	95	1	having	have	VERB
ap-658	95	2	the	the	DET
ap-658	95	3	original	original	ADJ
ap-658	95	4	microstructure	microstructure	NOUN
ap-658	95	5	characterized	characterize	VERB
ap-658	95	6	in	in	ADP
ap-658	95	7	an	an	DET
ap-658	95	8	appropriate	appropriate	ADJ
ap-658	95	9	sense	sense	NOUN
ap-658	95	10	,	,	PUNCT
ap-658	95	11	the	the	DET
ap-658	95	12	construction	construction	NOUN
ap-658	95	13	of	of	ADP
ap-658	95	14	an	an	DET
ap-658	95	15	equivalent	equivalent	ADJ
ap-658	95	16	puc	puc	NOUN
ap-658	95	17	is	be	AUX
ap-658	95	18	relatively	relatively	ADV
ap-658	95	19	straightforward	straightforward	ADJ
ap-658	95	20	.	.	PUNCT
ap-658	96	1	in	in	ADP
ap-658	96	2	particular	particular	ADJ
ap-658	96	3	,	,	PUNCT
ap-658	96	4	the	the	DET
ap-658	96	5	puc	puc	NOUN
ap-658	96	6	is	be	AUX
ap-658	96	7	derived	derive	VERB
ap-658	96	8	by	by	ADP
ap-658	96	9	matching	match	VERB
ap-658	96	10	a	a	DET
ap-658	96	11	selected	select	VERB
ap-658	96	12	microstructure	microstructure	NOUN
ap-658	96	13	describing	describe	VERB
ap-658	96	14	function	function	NOUN
ap-658	96	15	of	of	ADP
ap-658	96	16	the	the	DET
ap-658	96	17	real	real	ADJ
ap-658	96	18	microstructure	microstructure	NOUN
ap-658	96	19	and	and	CCONJ
ap-658	96	20	the	the	DET
ap-658	96	21	puc	puc	NOUN
ap-658	96	22	.	.	PUNCT
ap-658	97	1	to	to	PART
ap-658	97	2	be	be	AUX
ap-658	97	3	more	more	ADV
ap-658	97	4	concrete	concrete	ADJ
ap-658	97	5	,	,	PUNCT
ap-658	97	6	consider	consider	VERB
ap-658	97	7	a	a	DET
ap-658	97	8	periodic	periodic	ADJ
ap-658	97	9	unit	unit	NOUN
ap-658	97	10	cell	cell	NOUN
ap-658	97	11	consisting	consist	VERB
ap-658	97	12	of	of	ADP
ap-658	97	13	n	n	DET
ap-658	97	14	particles	particle	NOUN
ap-658	97	15	.	.	PUNCT
ap-658	98	1	dimensions	dimension	NOUN
ap-658	98	2	h1	h1	PROPN
ap-658	98	3	and	and	CCONJ
ap-658	98	4	h2	h2	PROPN
ap-658	98	5	and	and	CCONJ
ap-658	98	6	the	the	DET
ap-658	98	7	x	x	X
ap-658	98	8	and	and	CCONJ
ap-658	98	9	y	y	PROPN
ap-658	98	10	coordinates	coordinate	NOUN
ap-658	98	11	of	of	ADP
ap-658	98	12	all	all	DET
ap-658	98	13	particle	particle	NOUN
ap-658	98	14	centers	center	NOUN
ap-658	98	15	determine	determine	VERB
ap-658	98	16	the	the	DET
ap-658	98	17	geometry	geometry	NOUN
ap-658	98	18	of	of	ADP
ap-658	98	19	such	such	DET
ap-658	98	20	a	a	DET
ap-658	98	21	unit	unit	NOUN
ap-658	98	22	cell	cell	NOUN
ap-658	98	23	.	.	PUNCT
ap-658	99	1	the	the	DET
ap-658	99	2	particle	particle	NOUN
ap-658	99	3	locations	location	NOUN
ap-658	99	4	together	together	ADV
ap-658	99	5	with	with	ADP
ap-658	99	6	an	an	DET
ap-658	99	7	optimal	optimal	ADJ
ap-658	99	8	ratio	ratio	NOUN
ap-658	99	9	of	of	ADP
ap-658	99	10	cell	cell	NOUN
ap-658	99	11	dimensions	dimension	NOUN
ap-658	99	12	h1	h1	PROPN
ap-658	99	13	/	/	SYM
ap-658	99	14	h2	h2	PROPN
ap-658	99	15	are	be	AUX
ap-658	99	16	found	find	VERB
ap-658	99	17	by	by	ADP
ap-658	99	18	minimizing	minimize	VERB
ap-658	99	19	an	an	DET
ap-658	99	20	objective	objective	ADJ
ap-658	99	21	function	function	NOUN
ap-658	99	22	involving	involve	VERB
ap-658	100	1	two	two	NUM
ap-658	100	2	-	-	PUNCT
ap-658	100	3	point	point	NOUN
ap-658	100	4	probability	probability	NOUN
ap-658	100	5	function	function	NOUN
ap-658	100	6	f	f	PROPN
ap-658	100	7	h	h	NOUN
ap-658	100	8	h	h	NOUN
ap-658	100	9	s	s	VERB
ap-658	101	1	r	r	NOUN
ap-658	101	2	s	s	PROPN
ap-658	101	3	s	s	NOUN
ap-658	101	4	r	r	NOUN
ap-658	101	5	sn	sn	NOUN
ap-658	102	1	i	i	PRON
ap-658	102	2	i	i	PRON
ap-658	103	1	i	i	PRON
ap-658	103	2	i	i	PRON
ap-658	104	1	i	i	PRON
ap-658	104	2	nm	nm	VERB
ap-658	104	3	(	(	PUNCT
ap-658	104	4	,	,	PUNCT
ap-658	104	5	,	,	PUNCT
ap-658	104	6	)	)	PUNCT
ap-658	104	7	(	(	PUNCT
ap-658	104	8	(	(	PUNCT
ap-658	104	9	,	,	PUNCT
ap-658	104	10	)	)	PUNCT
ap-658	104	11	(	(	PUNCT
ap-658	104	12	,	,	PUNCT
ap-658	104	13	)	)	PUNCT
ap-658	104	14	)	)	PUNCT
ap-658	104	15	x	x	SYM
ap-658	104	16	1	1	NUM
ap-658	104	17	2	2	NUM
ap-658	104	18	0	0	NUM
ap-658	104	19	2	2	NUM
ap-658	104	20	1	1	NUM
ap-658	104	21	�	�	PROPN
ap-658	104	22	�	�	PROPN
ap-658	104	23	�	�	PROPN
ap-658	104	24	(	(	PUNCT
ap-658	104	25	8)	8)	NUM
ap-658	104	26	where	where	SCONJ
ap-658	104	27	�	�	PROPN
ap-658	104	28	�	�	PROPN
ap-658	104	29	xn	xn	PROPN
ap-658	104	30	n	n	NUM
ap-658	104	31	nx	nx	NOUN
ap-658	104	32	y	y	PROPN
ap-658	104	33	x	x	PROPN
ap-658	104	34	y	y	PROPN
ap-658	104	35	�	�	PROPN
ap-658	104	36	1	1	NUM
ap-658	104	37	1	1	NUM
ap-658	104	38	,	,	PUNCT
ap-658	104	39	,	,	PUNCT
ap-658	104	40	,	,	PUNCT
ap-658	104	41	,	,	PUNCT
ap-658	104	42	�	�	PROPN
ap-658	104	43	stores	store	VERB
ap-658	104	44	the	the	DET
ap-658	104	45	positions	position	NOUN
ap-658	104	46	of	of	ADP
ap-658	104	47	the	the	DET
ap-658	104	48	particle	particle	NOUN
ap-658	104	49	centers	center	NOUN
ap-658	104	50	,	,	PUNCT
ap-658	104	51	s	s	PART
ap-658	104	52	r	r	NOUN
ap-658	104	53	si	si	X
ap-658	104	54	i0	i0	PROPN
ap-658	104	55	(	(	PUNCT
ap-658	104	56	,	,	PUNCT
ap-658	104	57	)	)	PUNCT
ap-658	104	58	is	be	AUX
ap-658	104	59	the	the	DET
ap-658	104	60	value	value	NOUN
ap-658	104	61	of	of	ADP
ap-658	104	62	a	a	DET
ap-658	104	63	two	two	NUM
ap-658	104	64	-	-	PUNCT
ap-658	104	65	point	point	NOUN
ap-658	104	66	(	(	PUNCT
ap-658	104	67	matrix	matrix	NOUN
ap-658	104	68	)	)	PUNCT
ap-658	104	69	probability	probability	NOUN
ap-658	104	70	function	function	NOUN
ap-658	104	71	corresponding	correspond	VERB
ap-658	104	72	to	to	ADP
ap-658	104	73	the	the	DET
ap-658	104	74	original	original	ADJ
ap-658	104	75	medium	medium	NOUN
ap-658	104	76	evaluated	evaluate	VERB
ap-658	104	77	at	at	ADP
ap-658	104	78	a	a	DET
ap-658	104	79	point	point	NOUN
ap-658	104	80	(	(	PUNCT
ap-658	104	81	,	,	PUNCT
ap-658	104	82	)	)	PUNCT
ap-658	104	83	r	r	NOUN
ap-658	104	84	si	si	NOUN
ap-658	104	85	i	i	PRON
ap-658	104	86	,	,	PUNCT
ap-658	104	87	and	and	CCONJ
ap-658	104	88	nm	nm	ADV
ap-658	104	89	is	be	AUX
ap-658	104	90	the	the	DET
ap-658	104	91	number	number	NOUN
ap-658	104	92	of	of	ADP
ap-658	104	93	points	point	NOUN
ap-658	104	94	in	in	ADP
ap-658	104	95	which	which	PRON
ap-658	104	96	both	both	DET
ap-658	104	97	functions	function	NOUN
ap-658	104	98	are	be	AUX
ap-658	104	99	matched	match	VERB
ap-658	104	100	.	.	PUNCT
ap-658	105	1	a	a	DET
ap-658	105	2	closer	close	ADJ
ap-658	105	3	inspection	inspection	NOUN
ap-658	105	4	of	of	ADP
ap-658	105	5	the	the	DET
ap-658	105	6	objective	objective	ADJ
ap-658	105	7	function	function	NOUN
ap-658	105	8	(	(	PUNCT
ap-658	105	9	8)	8)	NUM
ap-658	105	10	reveals	reveal	VERB
ap-658	105	11	that	that	SCONJ
ap-658	105	12	it	it	PRON
ap-658	105	13	is	be	AUX
ap-658	105	14	discontinuous	discontinuous	ADJ
ap-658	105	15	and	and	CCONJ
ap-658	105	16	multimodal	multimodal	NOUN
ap-658	105	17	with	with	ADP
ap-658	105	18	a	a	DET
ap-658	105	19	large	large	ADJ
ap-658	105	20	number	number	NOUN
ap-658	105	21	of	of	ADP
ap-658	105	22	local	local	ADJ
ap-658	105	23	plateaus	plateaus	NOUN
ap-658	105	24	.	.	PUNCT
ap-658	106	1	this	this	PRON
ap-658	106	2	is	be	AUX
ap-658	106	3	a	a	DET
ap-658	106	4	direct	direct	ADJ
ap-658	106	5	consequence	consequence	NOUN
ap-658	106	6	of	of	ADP
ap-658	106	7	using	use	VERB
ap-658	106	8	bitmap	bitmap	NOUN
ap-658	106	9	images	image	NOUN
ap-658	106	10	,	,	PUNCT
ap-658	106	11	where	where	SCONJ
ap-658	106	12	individual	individual	ADJ
ap-658	106	13	entries	entry	NOUN
ap-658	106	14	of	of	ADP
ap-658	106	15	the	the	DET
ap-658	106	16	searched	search	VERB
ap-658	106	17	vector	vector	NOUN
ap-658	106	18	are	be	AUX
ap-658	106	19	integer	integer	NOUN
ap-658	106	20	variables	variable	NOUN
ap-658	106	21	.	.	PUNCT
ap-658	107	1	based	base	VERB
ap-658	107	2	on	on	ADP
ap-658	107	3	our	our	PRON
ap-658	107	4	previous	previous	ADJ
ap-658	107	5	experience	experience	NOUN
ap-658	107	6	with	with	ADP
ap-658	107	7	optimization	optimization	NOUN
ap-658	107	8	of	of	ADP
ap-658	107	9	these	these	DET
ap-658	107	10	functions	function	NOUN
ap-658	107	11	[	[	X
ap-658	107	12	17	17	NUM
ap-658	107	13	]	]	PUNCT
ap-658	107	14	,	,	PUNCT
ap-658	107	15	the	the	DET
ap-658	107	16	augmented	augment	VERB
ap-658	107	17	simulated	simulate	VERB
ap-658	107	18	annealing	annealing	NOUN
ap-658	107	19	method	method	NOUN
ap-658	107	20	[	[	X
ap-658	107	21	19	19	NUM
ap-658	107	22	]	]	PUNCT
ap-658	107	23	is	be	AUX
ap-658	107	24	implemented	implement	VERB
ap-658	107	25	to	to	PART
ap-658	107	26	solve	solve	VERB
ap-658	107	27	the	the	DET
ap-658	107	28	optimization	optimization	NOUN
ap-658	107	29	problem	problem	NOUN
ap-658	107	30	.	.	PUNCT
ap-658	108	1	examples	example	NOUN
ap-658	108	2	of	of	ADP
ap-658	108	3	the	the	DET
ap-658	108	4	resulting	result	VERB
ap-658	108	5	5and	5and	NUM
ap-658	108	6	10	10	NUM
ap-658	108	7	-	-	PUNCT
ap-658	108	8	particle	particle	NOUN
ap-658	108	9	pucs	pucs	NOUN
ap-658	108	10	are	be	AUX
ap-658	108	11	displayed	display	VERB
ap-658	108	12	in	in	ADP
ap-658	108	13	fig	fig	NOUN
ap-658	108	14	.	.	PUNCT
ap-658	109	1	7	7	X
ap-658	109	2	.	.	X
ap-658	109	3	the	the	DET
ap-658	109	4	hexagonal	hexagonal	ADJ
ap-658	109	5	unit	unit	NOUN
ap-658	109	6	cell	cell	NOUN
ap-658	109	7	with	with	ADP
ap-658	109	8	the	the	DET
ap-658	109	9	same	same	ADJ
ap-658	109	10	volume	volume	NOUN
ap-658	109	11	fraction	fraction	NOUN
ap-658	109	12	is	be	AUX
ap-658	109	13	shown	show	VERB
ap-658	109	14	for	for	ADP
ap-658	109	15	comparison	comparison	NOUN
ap-658	109	16	.	.	PUNCT
ap-658	110	1	3	3	NUM
ap-658	110	2	numerical	numerical	ADJ
ap-658	110	3	modeling	modeling	NOUN
ap-658	110	4	:	:	PUNCT
ap-658	110	5	finite	finite	PROPN
ap-658	110	6	element	element	NOUN
ap-658	110	7	discretization	discretization	NOUN
ap-658	110	8	in	in	ADP
ap-658	110	9	this	this	DET
ap-658	110	10	section	section	NOUN
ap-658	110	11	,	,	PUNCT
ap-658	110	12	the	the	DET
ap-658	110	13	numerical	numerical	ADJ
ap-658	110	14	analysis	analysis	NOUN
ap-658	110	15	is	be	AUX
ap-658	110	16	performed	perform	VERB
ap-658	110	17	in	in	ADP
ap-658	110	18	the	the	DET
ap-658	110	19	spirit	spirit	NOUN
ap-658	110	20	of	of	ADP
ap-658	110	21	the	the	DET
ap-658	110	22	first	first	ADJ
ap-658	110	23	order	order	NOUN
ap-658	110	24	homogenization	homogenization	NOUN
ap-658	110	25	of	of	ADP
ap-658	110	26	periodic	periodic	ADJ
ap-658	110	27	fields	field	NOUN
ap-658	110	28	[	[	X
ap-658	110	29	1	1	NUM
ap-658	110	30	-	-	SYM
ap-658	110	31	2	2	NUM
ap-658	110	32	,	,	PUNCT
ap-658	110	33	23	23	NUM
ap-658	110	34	]	]	PUNCT
ap-658	110	35	.	.	PUNCT
ap-658	111	1	to	to	ADP
ap-658	111	2	that	that	DET
ap-658	111	3	end	end	NOUN
ap-658	111	4	,	,	PUNCT
ap-658	111	5	consider	consider	VERB
ap-658	111	6	a	a	DET
ap-658	111	7	representative	representative	ADJ
ap-658	111	8	volume	volume	NOUN
ap-658	111	9	element	element	NOUN
ap-658	111	10	y	y	PROPN
ap-658	111	11	in	in	ADP
ap-658	111	12	terms	term	NOUN
ap-658	111	13	of	of	ADP
ap-658	111	14	one	one	NUM
ap-658	111	15	of	of	ADP
ap-658	111	16	the	the	DET
ap-658	111	17	statistically	statistically	ADV
ap-658	111	18	optimized	optimize	VERB
ap-658	111	19	unit	unit	NOUN
ap-658	111	20	cells	cell	NOUN
ap-658	111	21	derived	derive	VERB
ap-658	111	22	in	in	ADP
ap-658	111	23	the	the	DET
ap-658	111	24	previous	previous	ADJ
ap-658	111	25	section	section	NOUN
ap-658	111	26	.	.	PUNCT
ap-658	112	1	next	next	ADV
ap-658	112	2	,	,	PUNCT
ap-658	112	3	let	let	VERB
ap-658	112	4	the	the	DET
ap-658	112	5	applied	apply	VERB
ap-658	112	6	loading	loading	NOUN
ap-658	112	7	conditions	condition	NOUN
ap-658	112	8	produce	produce	VERB
ap-658	112	9	a	a	DET
ap-658	112	10	uniform	uniform	ADJ
ap-658	112	11	distribution	distribution	NOUN
ap-658	112	12	of	of	ADP
ap-658	112	13	macroscopic	macroscopic	ADJ
ap-658	112	14	strain	strain	NOUN
ap-658	112	15	e	e	NOUN
ap-658	112	16	or	or	CCONJ
ap-658	112	17	the	the	DET
ap-658	112	18	macroscopic	macroscopic	ADJ
ap-658	112	19	stress	stress	NOUN
ap-658	112	20	�	�	PROPN
ap-658	112	21	fields	field	NOUN
ap-658	112	22	.	.	PUNCT
ap-658	113	1	when	when	SCONJ
ap-658	113	2	further	far	ADV
ap-658	113	3	assuming	assume	VERB
ap-658	113	4	a	a	DET
ap-658	113	5	periodicity	periodicity	NOUN
ap-658	113	6	of	of	ADP
ap-658	113	7	microstructure	microstructure	NOUN
ap-658	113	8	,	,	PUNCT
ap-658	113	9	the	the	DET
ap-658	113	10	local	local	ADJ
ap-658	113	11	displacement	displacement	ADJ
ap-658	113	12	field	field	NOUN
ap-658	113	13	u(x	u(x	NOUN
ap-658	113	14	)	)	PUNCT
ap-658	113	15	and	and	CCONJ
ap-658	113	16	strain	strain	VERB
ap-658	113	17	field	field	NOUN
ap-658	113	18	�	�	PROPN
ap-658	113	19	(	(	PUNCT
ap-658	113	20	x	x	NOUN
ap-658	113	21	)	)	PUNCT
ap-658	113	22	admit	admit	VERB
ap-658	113	23	the	the	DET
ap-658	113	24	following	follow	VERB
ap-658	113	25	decomposition	decomposition	NOUN
ap-658	113	26	u	u	NOUN
ap-658	113	27	x	x	X
ap-658	113	28	e	e	NOUN
ap-658	113	29	x	x	X
ap-658	113	30	u	u	NOUN
ap-658	113	31	x	x	X
ap-658	113	32	x	x	X
ap-658	113	33	e	e	NOUN
ap-658	113	34	x	x	X
ap-658	113	35	(	(	PUNCT
ap-658	113	36	)	)	PUNCT
ap-658	113	37	(	(	PUNCT
ap-658	113	38	)	)	PUNCT
ap-658	113	39	,	,	PUNCT
ap-658	113	40	(	(	PUNCT
ap-658	113	41	)	)	PUNCT
ap-658	113	42	(	(	PUNCT
ap-658	113	43	)	)	PUNCT
ap-658	113	44	*	*	PUNCT
ap-658	113	45	*	*	PUNCT
ap-658	113	46	�	�	PROPN
ap-658	113	47	�	�	PROPN
ap-658	113	48	�	�	PROPN
ap-658	113	49	�	�	PROPN
ap-658	113	50	�	�	PROPN
ap-658	113	51	�	�	PROPN
ap-658	113	52	,	,	PUNCT
ap-658	113	53	(	(	PUNCT
ap-658	113	54	9	9	X
ap-658	113	55	)	)	PUNCT
ap-658	113	56	where	where	SCONJ
ap-658	113	57	u*(x	u*(x	NOUN
ap-658	113	58	)	)	PUNCT
ap-658	113	59	and	and	CCONJ
ap-658	113	60	�	�	PROPN
ap-658	113	61	*	*	PUNCT
ap-658	113	62	(	(	PUNCT
ap-658	113	63	)	)	PUNCT
ap-658	113	64	x	x	PROPN
ap-658	113	65	represent	represent	VERB
ap-658	113	66	fluctuations	fluctuation	NOUN
ap-658	113	67	of	of	ADP
ap-658	113	68	the	the	DET
ap-658	113	69	local	local	ADJ
ap-658	113	70	fields	field	NOUN
ap-658	113	71	due	due	ADP
ap-658	113	72	to	to	ADP
ap-658	113	73	the	the	DET
ap-658	113	74	presence	presence	NOUN
ap-658	113	75	of	of	ADP
ap-658	113	76	heterogeneities	heterogeneity	NOUN
ap-658	113	77	[	[	X
ap-658	113	78	21	21	NUM
ap-658	113	79	,	,	PUNCT
ap-658	113	80	23	23	NUM
ap-658	113	81	]	]	PUNCT
ap-658	113	82	.	.	PUNCT
ap-658	114	1	the	the	DET
ap-658	114	2	local	local	ADJ
ap-658	114	3	stresses	stress	NOUN
ap-658	114	4	are	be	AUX
ap-658	114	5	related	relate	VERB
ap-658	114	6	to	to	ADP
ap-658	114	7	the	the	DET
ap-658	114	8	strains	strain	NOUN
ap-658	114	9	by	by	ADP
ap-658	114	10	the	the	DET
ap-658	114	11	constitutive	constitutive	ADJ
ap-658	114	12	equation	equation	NOUN
ap-658	114	13	�	�	PROPN
ap-658	114	14	�	�	PROPN
ap-658	114	15	(	(	PUNCT
ap-658	114	16	)	)	PUNCT
ap-658	114	17	(	(	PUNCT
ap-658	114	18	)	)	PUNCT
ap-658	114	19	(	(	PUNCT
ap-658	114	20	)	)	PUNCT
ap-658	114	21	(	(	PUNCT
ap-658	114	22	)	)	PUNCT
ap-658	114	23	x	x	SYM
ap-658	114	24	x	x	PUNCT
ap-658	114	25	x	x	SYM
ap-658	114	26	x	x	X
ap-658	114	27	�	�	PROPN
ap-658	114	28	�	�	PROPN
ap-658	114	29	l	l	PROPN
ap-658	114	30	�	�	PROPN
ap-658	114	31	,	,	PUNCT
ap-658	114	32	(	(	PUNCT
ap-658	114	33	10	10	NUM
ap-658	114	34	)	)	PUNCT
ap-658	114	35	where	where	SCONJ
ap-658	114	36	l(x	l(x	PROPN
ap-658	114	37	)	)	PUNCT
ap-658	114	38	is	be	AUX
ap-658	114	39	the	the	DET
ap-658	114	40	material	material	ADJ
ap-658	114	41	stiffness	stiffness	NOUN
ap-658	114	42	matrix	matrix	NOUN
ap-658	114	43	and	and	CCONJ
ap-658	114	44	�	�	PROPN
ap-658	114	45	(	(	PUNCT
ap-658	114	46	x	x	NOUN
ap-658	114	47	)	)	PUNCT
ap-658	114	48	is	be	AUX
ap-658	114	49	the	the	DET
ap-658	114	50	vector	vector	NOUN
ap-658	114	51	of	of	ADP
ap-658	114	52	eigenstresses	eigenstresse	NOUN
ap-658	114	53	(	(	PUNCT
ap-658	114	54	strain	strain	NOUN
ap-658	114	55	-	-	PUNCT
ap-658	114	56	free	free	ADJ
ap-658	114	57	stresses	stress	NOUN
ap-658	114	58	)	)	PUNCT
ap-658	114	59	.	.	PUNCT
ap-658	115	1	note	note	VERB
ap-658	115	2	that	that	SCONJ
ap-658	115	3	�	�	PROPN
ap-658	115	4	(	(	PUNCT
ap-658	115	5	x	x	NOUN
ap-658	115	6	)	)	PUNCT
ap-658	115	7	can	can	AUX
ap-658	115	8	present	present	VERB
ap-658	115	9	a	a	DET
ap-658	115	10	variety	variety	NOUN
ap-658	115	11	of	of	ADP
ap-658	115	12	physical	physical	ADJ
ap-658	115	13	phenomena	phenomenon	NOUN
ap-658	115	14	like	like	ADP
ap-658	115	15	temperature	temperature	NOUN
ap-658	115	16	or	or	CCONJ
ap-658	115	17	moisture	moisture	NOUN
ap-658	115	18	effects	effect	NOUN
ap-658	115	19	,	,	PUNCT
ap-658	115	20	creep	creep	PROPN
ap-658	115	21	stresses	stress	NOUN
ap-658	115	22	,	,	PUNCT
ap-658	115	23	etc	etc	X
ap-658	115	24	.	.	X
ap-658	115	25	employing	employ	VERB
ap-658	115	26	the	the	DET
ap-658	115	27	principle	principle	NOUN
ap-658	115	28	of	of	ADP
ap-658	115	29	virtual	virtual	ADJ
ap-658	115	30	work	work	NOUN
ap-658	115	31	(	(	PUNCT
ap-658	115	32	the	the	DET
ap-658	115	33	hill	hill	NOUN
ap-658	115	34	lemma	lemma	PROPN
ap-658	115	35	)	)	PUNCT
ap-658	115	36	in	in	ADP
ap-658	115	37	the	the	DET
ap-658	115	38	form	form	NOUN
ap-658	115	39	�	�	PROPN
ap-658	115	40	�	�	PROPN
ap-658	115	41	�	�	PROPN
ap-658	115	42	�	�	PROPN
ap-658	115	43	�	�	PROPN
ap-658	115	44	�	�	PROPN
ap-658	115	45	�	�	PROPN
ap-658	115	46	�	�	PROPN
ap-658	115	47	�	�	PROPN
ap-658	115	48	t	t	PROPN
ap-658	115	49	*	*	PROPN
ap-658	115	50	t	t	PROPN
ap-658	115	51	t	t	PROPN
ap-658	115	52	t	t	PROPN
ap-658	115	53	(	(	PUNCT
ap-658	115	54	)	)	PUNCT
ap-658	115	55	(	(	PUNCT
ap-658	115	56	)	)	PUNCT
ap-658	115	57	(	(	PUNCT
ap-658	115	58	(	(	PUNCT
ap-658	115	59	)	)	PUNCT
ap-658	115	60	)	)	PUNCT
ap-658	115	61	(	(	PUNCT
ap-658	115	62	(	(	PUNCT
ap-658	115	63	)	)	PUNCT
ap-658	115	64	(	(	PUNCT
ap-658	115	65	)	)	PUNCT
ap-658	115	66	(	(	PUNCT
ap-658	115	67	)	)	PUNCT
ap-658	115	68	,	,	PUNCT
ap-658	115	69	x	x	PUNCT
ap-658	115	70	x	x	PUNCT
ap-658	115	71	x	x	PUNCT
ap-658	115	72	e	e	NOUN
ap-658	115	73	x	x	SYM
ap-658	115	74	x	x	SYM
ap-658	115	75	x	x	SYM
ap-658	115	76	e	e	X
ap-658	115	77	�	�	PROPN
ap-658	115	78	�	�	PROPN
ap-658	115	79	�	�	PROPN
ap-658	115	80	�	�	PROPN
ap-658	115	81	�	�	PROPN
ap-658	115	82	l	l	PROPN
ap-658	115	83	(	(	PUNCT
ap-658	115	84	11	11	NUM
ap-658	115	85	)	)	PUNCT
ap-658	115	86	and	and	CCONJ
ap-658	115	87	introducing	introduce	VERB
ap-658	115	88	the	the	DET
ap-658	115	89	standard	standard	ADJ
ap-658	115	90	finite	finite	ADJ
ap-658	115	91	element	element	NOUN
ap-658	115	92	approximation	approximation	NOUN
ap-658	115	93	u	u	NOUN
ap-658	115	94	x	x	X
ap-658	115	95	x	x	PUNCT
ap-658	115	96	r	r	NOUN
ap-658	115	97	x	x	X
ap-658	115	98	x	x	SYM
ap-658	115	99	r	r	X
ap-658	115	100	*	*	PUNCT
ap-658	115	101	*	*	PUNCT
ap-658	115	102	(	(	PUNCT
ap-658	115	103	)	)	PUNCT
ap-658	115	104	(	(	PUNCT
ap-658	115	105	)	)	PUNCT
ap-658	115	106	,	,	PUNCT
ap-658	115	107	(	(	PUNCT
ap-658	115	108	)	)	PUNCT
ap-658	115	109	(	(	PUNCT
ap-658	115	110	)	)	PUNCT
ap-658	115	111	�	�	PROPN
ap-658	115	112	�	�	PROPN
ap-658	115	113	n	n	CCONJ
ap-658	115	114	b	b	PROPN
ap-658	115	115	�	�	PROPN
ap-658	116	1	[	[	X
ap-658	116	2	24	24	NUM
ap-658	116	3	]	]	PUNCT
ap-658	116	4	,	,	PUNCT
ap-658	116	5	we	we	PRON
ap-658	116	6	finally	finally	ADV
ap-658	116	7	obtain	obtain	VERB
ap-658	116	8	the	the	DET
ap-658	116	9	discretized	discretized	ADJ
ap-658	116	10	equilibrium	equilibrium	NOUN
ap-658	116	11	equations	equation	NOUN
ap-658	116	12	l	l	PROPN
ap-658	116	13	l	l	PROPN
ap-658	116	14	b	b	X
ap-658	116	15	b	b	PROPN
ap-658	116	16	l	l	NOUN
ap-658	116	17	b	b	PROPN
ap-658	116	18	l	l	NOUN
ap-658	116	19	b	b	PROPN
ap-658	116	20	(	(	PUNCT
ap-658	116	21	)	)	PUNCT
ap-658	116	22	(	(	PUNCT
ap-658	116	23	)	)	PUNCT
ap-658	116	24	(	(	PUNCT
ap-658	116	25	)	)	PUNCT
ap-658	116	26	(	(	PUNCT
ap-658	116	27	)	)	PUNCT
ap-658	116	28	(	(	PUNCT
ap-658	116	29	)	)	PUNCT
ap-658	116	30	(	(	PUNCT
ap-658	116	31	)	)	PUNCT
ap-658	116	32	(	(	PUNCT
ap-658	116	33	)	)	PUNCT
ap-658	116	34	(	(	PUNCT
ap-658	116	35	)	)	PUNCT
ap-658	116	36	x	x	PUNCT
ap-658	117	1	x	x	PUNCT
ap-658	117	2	x	x	PUNCT
ap-658	117	3	x	x	PUNCT
ap-658	117	4	x	x	PUNCT
ap-658	117	5	x	x	PUNCT
ap-658	117	6	x	x	PUNCT
ap-658	117	7	x	x	PUNCT
ap-658	117	8	x	x	PUNCT
ap-658	117	9	x	x	PUNCT
ap-658	117	10	x	x	PUNCT
ap-658	117	11	x	x	PUNCT
ap-658	117	12	d	d	PUNCT
ap-658	117	13	d	d	X
ap-658	117	14	d	d	X
ap-658	117	15	dt	dt	X
ap-658	117	16	t	t	PROPN
ap-658	117	17	y	y	PROPN
ap-658	117	18	y	y	PROPN
ap-658	117	19	y	y	PROPN
ap-658	117	20	y	y	PROPN
ap-658	117	21	�	�	PROPN
ap-658	117	22	�	�	PROPN
ap-658	117	23	�	�	PROPN
ap-658	117	24	�	�	PROPN
ap-658	117	25	�	�	PROPN
ap-658	117	26	�	�	PROPN
ap-658	117	27	�	�	PROPN
ap-658	117	28	�	�	PROPN
ap-658	117	29	�	�	PROPN
ap-658	117	30	�	�	PROPN
ap-658	117	31	�	�	PROPN
ap-658	117	32	�	�	PROPN
ap-658	117	33	�	�	PROPN
ap-658	117	34	�	�	PROPN
ap-658	117	35	�	�	PROPN
ap-658	117	36	�	�	PROPN
ap-658	117	37	�	�	PROPN
ap-658	117	38	�	�	PROPN
ap-658	117	39	�	�	PROPN
ap-658	117	40	�	�	PROPN
ap-658	117	41	�	�	PROPN
ap-658	117	42	�	�	PROPN
ap-658	117	43	�	�	PROPN
ap-658	117	44	�	�	PROPN
ap-658	117	45	�	�	PROPN
ap-658	117	46	�	�	PROPN
ap-658	117	47	�	�	PROPN
ap-658	117	48	�	�	PROPN
ap-658	117	49	�	�	PROPN
ap-658	117	50	�	�	PROPN
ap-658	117	51	�	�	PROPN
ap-658	117	52	e	e	NOUN
ap-658	117	53	r	r	NOUN
ap-658	117	54	x	x	PUNCT
ap-658	117	55	x	x	PUNCT
ap-658	117	56	x	x	SYM
ap-658	117	57	x	x	SYM
ap-658	117	58	x	x	SYM
ap-658	117	59	�	�	PROPN
ap-658	117	60	�	�	PROPN
ap-658	117	61	�	�	PROPN
ap-658	117	62	�	�	PROPN
ap-658	117	63	(	(	PUNCT
ap-658	117	64	)	)	PUNCT
ap-658	117	65	(	(	PUNCT
ap-658	117	66	)	)	PUNCT
ap-658	117	67	(	(	PUNCT
ap-658	117	68	)	)	PUNCT
ap-658	118	1	d	d	X
ap-658	118	2	dt	dt	X
ap-658	118	3	y	y	PROPN
ap-658	118	4	y	y	PROPN
ap-658	118	5	b	b	PROPN
ap-658	118	6	�	�	PROPN
ap-658	118	7	�	�	PROPN
ap-658	118	8	�	�	PROPN
ap-658	118	9	�	�	PROPN
ap-658	118	10	�	�	PROPN
ap-658	118	11	�	�	PROPN
ap-658	118	12	�	�	PROPN
ap-658	118	13	�	�	PROPN
ap-658	118	14	�	�	PROPN
ap-658	118	15	�	�	PROPN
ap-658	118	16	�	�	PROPN
ap-658	118	17	.	.	PUNCT
ap-658	119	1	(	(	PUNCT
ap-658	119	2	12	12	NUM
ap-658	119	3	)	)	PUNCT
ap-658	119	4	©	©	PROPN
ap-658	119	5	czech	czech	PROPN
ap-658	119	6	technical	technical	PROPN
ap-658	119	7	university	university	PROPN
ap-658	119	8	publishing	publishing	NOUN
ap-658	119	9	house	house	NOUN
ap-658	119	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	119	11	203	203	NUM
ap-658	119	12	acta	acta	PROPN
ap-658	119	13	polytechnica	polytechnica	PROPN
ap-658	119	14	vol	vol	NOUN
ap-658	119	15	.	.	PROPN
ap-658	120	1	44	44	NUM
ap-658	120	2	no.5–6/2004	no.5–6/2004	PROPN
ap-658	120	3	fig	fig	NOUN
ap-658	120	4	.	.	PUNCT
ap-658	121	1	7	7	NUM
ap-658	121	2	:	:	PUNCT
ap-658	121	3	examples	example	NOUN
ap-658	121	4	of	of	ADP
ap-658	121	5	statistically	statistically	ADV
ap-658	121	6	optimized	optimize	VERB
ap-658	121	7	periodic	periodic	ADJ
ap-658	121	8	unit	unit	NOUN
ap-658	121	9	cells	cell	NOUN
ap-658	121	10	denoting	denote	VERB
ap-658	121	11	kij	kij	PROPN
ap-658	121	12	individual	individual	ADJ
ap-658	121	13	blocks	block	NOUN
ap-658	121	14	of	of	ADP
ap-658	121	15	the	the	DET
ap-658	121	16	left	left	ADJ
ap-658	121	17	-	-	PUNCT
ap-658	121	18	hand	hand	NOUN
ap-658	121	19	side	side	NOUN
ap-658	121	20	of	of	ADP
ap-658	121	21	eq	eq	PROPN
ap-658	121	22	.	.	PUNCT
ap-658	122	1	(	(	PUNCT
ap-658	122	2	12	12	NUM
ap-658	122	3	)	)	PUNCT
ap-658	122	4	,	,	PUNCT
ap-658	122	5	we	we	PRON
ap-658	122	6	can	can	AUX
ap-658	122	7	formally	formally	ADV
ap-658	122	8	eliminate	eliminate	VERB
ap-658	122	9	the	the	DET
ap-658	122	10	unknown	unknown	ADJ
ap-658	122	11	vector	vector	NOUN
ap-658	122	12	r	r	NOUN
ap-658	122	13	from	from	ADP
ap-658	122	14	(	(	PUNCT
ap-658	122	15	12	12	NUM
ap-658	122	16	)	)	PUNCT
ap-658	122	17	and	and	CCONJ
ap-658	122	18	obtain	obtain	VERB
ap-658	122	19	the	the	DET
ap-658	122	20	resulting	result	VERB
ap-658	122	21	macroscopic	macroscopic	ADJ
ap-658	122	22	homogenized	homogenize	VERB
ap-658	122	23	constitutive	constitutive	ADJ
ap-658	122	24	law	law	NOUN
ap-658	122	25	�	�	PROPN
ap-658	122	26	�	�	PROPN
ap-658	122	27	�	�	PROPN
ap-658	122	28	�	�	PROPN
ap-658	122	29	lfe	lfe	PROPN
ap-658	122	30	fee	fee	NOUN
ap-658	122	31	(	(	PUNCT
ap-658	122	32	13	13	NUM
ap-658	122	33	)	)	PUNCT
ap-658	122	34	where	where	SCONJ
ap-658	122	35	l	l	NOUN
ap-658	122	36	k	k	PROPN
ap-658	122	37	k	k	PROPN
ap-658	122	38	k	k	PROPN
ap-658	122	39	k	k	PROPN
ap-658	122	40	k	k	PROPN
ap-658	122	41	k	k	PROPN
ap-658	122	42	b	b	PROPN
ap-658	122	43	fe	fe	X
ap-658	122	44	t	t	X
ap-658	122	45	fe	fe	X
ap-658	122	46	td	td	PROPN
ap-658	122	47	�	�	PROPN
ap-658	122	48	�	�	PROPN
ap-658	122	49	�	�	PROPN
ap-658	122	50	�	�	PROPN
ap-658	122	51	�	�	PROPN
ap-658	122	52	�	�	PROPN
ap-658	122	53	�	�	PROPN
ap-658	122	54	1	1	NUM
ap-658	122	55	1	1	NUM
ap-658	122	56	11	11	NUM
ap-658	122	57	12	12	NUM
ap-658	122	58	22	22	NUM
ap-658	122	59	1	1	NUM
ap-658	122	60	12	12	NUM
ap-658	122	61	12	12	NUM
ap-658	122	62	22	22	NUM
ap-658	122	63	1	1	NUM
ap-658	122	64	y	y	PROPN
ap-658	122	65	y	y	PROPN
ap-658	122	66	y	y	PROPN
ap-658	122	67	(	(	PUNCT
ap-658	122	68	)	)	PUNCT
ap-658	122	69	,	,	PUNCT
ap-658	122	70	(	(	PUNCT
ap-658	122	71	)	)	PUNCT
ap-658	122	72	�	�	PROPN
ap-658	122	73	�	�	PROPN
ap-658	122	74	x	x	PUNCT
ap-658	122	75	x	x	SYM
ap-658	122	76	(	(	PUNCT
ap-658	122	77	)	)	PUNCT
ap-658	122	78	(	(	PUNCT
ap-658	122	79	)	)	PUNCT
ap-658	122	80	.x	.x	NOUN
ap-658	123	1	x	x	PUNCT
ap-658	123	2	x	x	X
ap-658	123	3	�	�	PROPN
ap-658	123	4	d	d	PROPN
ap-658	123	5	y	y	PROPN
ap-658	123	6	�	�	PROPN
ap-658	123	7	�	�	PROPN
ap-658	123	8	�	�	PROPN
ap-658	123	9	�	�	PROPN
ap-658	123	10	�	�	PROPN
ap-658	123	11	�	�	PROPN
ap-658	123	12	!	!	PUNCT
ap-658	123	13	"	"	PUNCT
ap-658	124	1	"	"	PUNCT
ap-658	124	2	"	"	PUNCT
ap-658	124	3	(	(	PUNCT
ap-658	124	4	14	14	NUM
ap-658	124	5	)	)	PUNCT
ap-658	124	6	when	when	SCONJ
ap-658	124	7	analyzing	analyze	VERB
ap-658	124	8	the	the	DET
ap-658	124	9	non	non	ADJ
ap-658	124	10	-	-	ADJ
ap-658	124	11	linear	linear	ADJ
ap-658	124	12	material	material	NOUN
ap-658	124	13	system	system	NOUN
ap-658	124	14	,	,	PUNCT
ap-658	124	15	eq	eq	NOUN
ap-658	124	16	.	.	PUNCT
ap-658	124	17	(	(	PUNCT
ap-658	124	18	10	10	NUM
ap-658	124	19	)	)	PUNCT
ap-658	124	20	needs	need	VERB
ap-658	124	21	to	to	PART
ap-658	124	22	be	be	AUX
ap-658	124	23	replaced	replace	VERB
ap-658	124	24	by	by	ADP
ap-658	124	25	an	an	DET
ap-658	124	26	appropriate	appropriate	ADJ
ap-658	124	27	linearized	linearize	VERB
ap-658	124	28	constitutive	constitutive	ADJ
ap-658	124	29	law	law	NOUN
ap-658	124	30	,	,	PUNCT
ap-658	124	31	and	and	CCONJ
ap-658	124	32	relations	relation	NOUN
ap-658	124	33	(	(	PUNCT
ap-658	124	34	13)–(14	13)–(14	NUM
ap-658	124	35	)	)	PUNCT
ap-658	124	36	are	be	AUX
ap-658	124	37	,	,	PUNCT
ap-658	124	38	rather	rather	ADV
ap-658	124	39	straightforwardly	straightforwardly	ADV
ap-658	124	40	,	,	PUNCT
ap-658	124	41	replaced	replace	VERB
ap-658	124	42	by	by	ADP
ap-658	124	43	an	an	DET
ap-658	124	44	incremental	incremental	ADJ
ap-658	124	45	counterpart	counterpart	NOUN
ap-658	124	46	.	.	PUNCT
ap-658	125	1	this	this	DET
ap-658	125	2	step	step	NOUN
ap-658	125	3	is	be	AUX
ap-658	125	4	discussed	discuss	VERB
ap-658	125	5	in	in	ADP
ap-658	125	6	the	the	DET
ap-658	125	7	next	next	ADJ
ap-658	125	8	section	section	NOUN
ap-658	125	9	.	.	PUNCT
ap-658	126	1	similar	similar	ADJ
ap-658	126	2	results	result	NOUN
ap-658	126	3	can	can	AUX
ap-658	126	4	also	also	ADV
ap-658	126	5	be	be	AUX
ap-658	126	6	derived	derive	VERB
ap-658	126	7	with	with	ADP
ap-658	126	8	help	help	NOUN
ap-658	126	9	of	of	ADP
ap-658	126	10	other	other	ADJ
ap-658	126	11	numerical	numerical	ADJ
ap-658	126	12	techniques	technique	NOUN
ap-658	126	13	such	such	ADJ
ap-658	126	14	as	as	ADP
ap-658	126	15	the	the	DET
ap-658	126	16	boundary	boundary	ADJ
ap-658	126	17	element	element	NOUN
ap-658	126	18	method	method	NOUN
ap-658	126	19	[	[	X
ap-658	126	20	25	25	NUM
ap-658	126	21	]	]	PUNCT
ap-658	126	22	.	.	PUNCT
ap-658	127	1	4	4	NUM
ap-658	127	2	constitutive	constitutive	ADJ
ap-658	127	3	modeling	modeling	NOUN
ap-658	127	4	:	:	PUNCT
ap-658	127	5	generalized	generalize	VERB
ap-658	127	6	leonov	leonov	NOUN
ap-658	127	7	model	model	NOUN
ap-658	127	8	as	as	SCONJ
ap-658	127	9	suggested	suggest	VERB
ap-658	127	10	in	in	ADP
ap-658	127	11	the	the	DET
ap-658	127	12	introductory	introductory	ADJ
ap-658	127	13	part	part	NOUN
ap-658	127	14	,	,	PUNCT
ap-658	127	15	a	a	DET
ap-658	127	16	graphite	graphite	NOUN
ap-658	127	17	/	/	SYM
ap-658	127	18	epoxy	epoxy	NOUN
ap-658	127	19	material	material	NOUN
ap-658	127	20	system	system	NOUN
ap-658	127	21	is	be	AUX
ap-658	127	22	selected	select	VERB
ap-658	127	23	as	as	ADP
ap-658	127	24	a	a	DET
ap-658	127	25	particular	particular	ADJ
ap-658	127	26	example	example	NOUN
ap-658	127	27	in	in	ADP
ap-658	127	28	this	this	DET
ap-658	127	29	study	study	NOUN
ap-658	127	30	.	.	PUNCT
ap-658	128	1	note	note	VERB
ap-658	128	2	that	that	SCONJ
ap-658	128	3	the	the	DET
ap-658	128	4	fiber	fiber	NOUN
ap-658	128	5	is	be	AUX
ap-658	128	6	assumed	assume	VERB
ap-658	128	7	to	to	PART
ap-658	128	8	remain	remain	VERB
ap-658	128	9	elastic	elastic	ADJ
ap-658	128	10	during	during	ADP
ap-658	128	11	deformation	deformation	NOUN
ap-658	128	12	so	so	SCONJ
ap-658	128	13	that	that	SCONJ
ap-658	128	14	the	the	DET
ap-658	128	15	inelastic	inelastic	ADJ
ap-658	128	16	effects	effect	NOUN
ap-658	128	17	are	be	AUX
ap-658	128	18	limited	limit	VERB
ap-658	128	19	to	to	ADP
ap-658	128	20	the	the	DET
ap-658	128	21	matrix	matrix	NOUN
ap-658	128	22	phase	phase	NOUN
ap-658	128	23	.	.	PUNCT
ap-658	129	1	for	for	ADP
ap-658	129	2	the	the	DET
ap-658	129	3	composite	composite	ADJ
ap-658	129	4	structure	structure	NOUN
ap-658	129	5	plotted	plot	VERB
ap-658	129	6	in	in	ADP
ap-658	129	7	fig	fig	NOUN
ap-658	129	8	.	.	PUNCT
ap-658	130	1	1	1	NUM
ap-658	130	2	,	,	PUNCT
ap-658	130	3	pr100/2+em100e	pr100/2+em100e	NOUN
ap-658	130	4	epoxy	epoxy	NOUN
ap-658	130	5	is	be	AUX
ap-658	130	6	used	use	VERB
ap-658	130	7	as	as	ADP
ap-658	130	8	a	a	DET
ap-658	130	9	bonding	bonding	NOUN
ap-658	130	10	agent	agent	NOUN
ap-658	130	11	.	.	PUNCT
ap-658	131	1	an	an	DET
ap-658	131	2	experimental	experimental	ADJ
ap-658	131	3	program	program	NOUN
ap-658	131	4	carried	carry	VERB
ap-658	131	5	out	out	ADP
ap-658	131	6	on	on	ADP
ap-658	131	7	this	this	DET
ap-658	131	8	type	type	NOUN
ap-658	131	9	of	of	ADP
ap-658	131	10	material	material	NOUN
ap-658	131	11	[	[	X
ap-658	131	12	27	27	NUM
ap-658	131	13	,	,	PUNCT
ap-658	131	14	29	29	NUM
ap-658	131	15	]	]	PUNCT
ap-658	131	16	demonstrates	demonstrate	VERB
ap-658	131	17	that	that	SCONJ
ap-658	131	18	the	the	DET
ap-658	131	19	relevant	relevant	ADJ
ap-658	131	20	rate	rate	NOUN
ap-658	131	21	dependent	dependent	ADJ
ap-658	131	22	response	response	NOUN
ap-658	131	23	of	of	ADP
ap-658	131	24	the	the	DET
ap-658	131	25	epoxy	epoxy	NOUN
ap-658	131	26	as	as	ADV
ap-658	131	27	well	well	ADV
ap-658	131	28	described	describe	VERB
ap-658	131	29	by	by	ADP
ap-658	131	30	the	the	DET
ap-658	131	31	generalized	generalize	VERB
ap-658	131	32	leonov	leonov	NOUN
ap-658	131	33	model	model	NOUN
ap-658	131	34	.	.	PUNCT
ap-658	132	1	combining	combine	VERB
ap-658	132	2	the	the	DET
ap-658	132	3	eyring	eyring	NOUN
ap-658	132	4	flow	flow	NOUN
ap-658	132	5	model	model	NOUN
ap-658	132	6	for	for	ADP
ap-658	132	7	the	the	DET
ap-658	132	8	plastic	plastic	ADJ
ap-658	132	9	component	component	NOUN
ap-658	132	10	of	of	ADP
ap-658	132	11	the	the	DET
ap-658	132	12	shear	shear	NOUN
ap-658	132	13	strain	strain	NOUN
ap-658	132	14	rate	rate	NOUN
ap-658	132	15	d	d	PROPN
ap-658	132	16	d	d	X
ap-658	132	17	e	e	PROPN
ap-658	132	18	t	t	PROPN
ap-658	132	19	a	a	DET
ap-658	132	20	p	p	X
ap-658	132	21	�	�	PROPN
ap-658	132	22	1	1	NUM
ap-658	132	23	2	2	NUM
ap-658	132	24	0	0	NUM
ap-658	132	25	sinh	sinh	PROPN
ap-658	132	26	�	�	PROPN
ap-658	132	27	�	�	PROPN
ap-658	132	28	,	,	PUNCT
ap-658	132	29	(	(	PUNCT
ap-658	132	30	15	15	NUM
ap-658	132	31	)	)	PUNCT
ap-658	132	32	with	with	ADP
ap-658	132	33	the	the	DET
ap-658	132	34	elastic	elastic	ADJ
ap-658	132	35	shear	shear	NOUN
ap-658	132	36	strain	strain	NOUN
ap-658	132	37	rate	rate	NOUN
ap-658	132	38	dee	dee	PROPN
ap-658	132	39	/dt	/dt	PUNCT
ap-658	132	40	yields	yield	VERB
ap-658	132	41	the	the	DET
ap-658	132	42	one	one	NUM
ap-658	132	43	-	-	PUNCT
ap-658	132	44	dimensional	dimensional	ADJ
ap-658	132	45	leonov	leonov	NOUN
ap-658	132	46	model	model	NOUN
ap-658	133	1	[	[	X
ap-658	133	2	26	26	NUM
ap-658	133	3	]	]	X
ap-658	133	4	d	d	PROPN
ap-658	133	5	d	d	X
ap-658	133	6	d	d	PROPN
ap-658	133	7	d	d	PROPN
ap-658	133	8	d	d	PROPN
ap-658	133	9	d	d	PROPN
ap-658	133	10	d	d	PROPN
ap-658	133	11	d	d	PROPN
ap-658	133	12	d	d	X
ap-658	133	13	d	d	X
ap-658	133	14	e	e	X
ap-658	133	15	t	t	X
ap-658	133	16	e	e	PROPN
ap-658	133	17	t	t	PROPN
ap-658	133	18	e	e	PROPN
ap-658	133	19	t	t	PROPN
ap-658	133	20	e	e	PROPN
ap-658	133	21	t	t	PROPN
ap-658	133	22	e	e	X
ap-658	133	23	t	t	PROPN
ap-658	133	24	e	e	X
ap-658	133	25	p	p	PROPN
ap-658	133	26	e	e	PROPN
ap-658	133	27	p	p	PROPN
ap-658	133	28	�	�	PROPN
ap-658	133	29	�	�	PROPN
ap-658	133	30	�	�	PROPN
ap-658	133	31	�	�	PROPN
ap-658	133	32	�	�	PROPN
ap-658	133	33	2	2	NUM
ap-658	133	34	,	,	PUNCT
ap-658	133	35	(	(	PUNCT
ap-658	133	36	16a	16a	NOUN
ap-658	133	37	)	)	PUNCT
ap-658	133	38	�	�	PROPN
ap-658	133	39	�	�	PROPN
ap-658	133	40	�	�	PROPN
ap-658	133	41	�	�	PROPN
ap-658	133	42	�	�	PROPN
ap-658	133	43	�	�	PROPN
ap-658	133	44	d	d	PROPN
ap-658	133	45	d	d	PROPN
ap-658	133	46	(	(	PUNCT
ap-658	133	47	e	e	PROPN
ap-658	133	48	t	t	PROPN
ap-658	133	49	ap	ap	PROPN
ap-658	133	50	�	�	PROPN
ap-658	133	51	�	�	PROPN
ap-658	133	52	0	0	NUM
ap-658	133	53	0	0	NUM
ap-658	133	54	0	0	NUM
ap-658	133	55	0	0	NUM
ap-658	133	56	sinh	sinh	NOUN
ap-658	133	57	,	,	PUNCT
ap-658	133	58	(	(	PUNCT
ap-658	133	59	16b	16b	X
ap-658	133	60	)	)	PUNCT
ap-658	133	61	where	where	SCONJ
ap-658	133	62	is	be	AUX
ap-658	133	63	the	the	DET
ap-658	133	64	shear	shear	NOUN
ap-658	133	65	-	-	PUNCT
ap-658	133	66	dependent	dependent	ADJ
ap-658	133	67	viscosity	viscosity	NOUN
ap-658	133	68	.	.	PUNCT
ap-658	134	1	in	in	ADP
ap-658	134	2	eq	eq	ADP
ap-658	134	3	.	.	PUNCT
ap-658	135	1	(	(	PUNCT
ap-658	135	2	15	15	NUM
ap-658	135	3	)	)	PUNCT
ap-658	135	4	,	,	PUNCT
ap-658	135	5	a	a	DET
ap-658	135	6	and	and	CCONJ
ap-658	135	7	�	�	PROPN
ap-658	135	8	�	�	PROPN
ap-658	135	9	are	be	AUX
ap-658	135	10	material	material	NOUN
ap-658	135	11	parameters;	parameters;	X
ap-658	135	12	a	a	DET
ap-658	135	13	�	�	NOUN
ap-658	135	14	that	that	PRON
ap-658	135	15	appears	appear	VERB
ap-658	135	16	in	in	ADP
ap-658	135	17	eq	eq	ADP
ap-658	135	18	.	.	PUNCT
ap-658	136	1	(	(	PUNCT
ap-658	136	2	16b	16b	PROPN
ap-658	136	3	)	)	PUNCT
ap-658	136	4	is	be	AUX
ap-658	136	5	the	the	DET
ap-658	136	6	stress	stress	NOUN
ap-658	136	7	shift	shift	NOUN
ap-658	136	8	function	function	NOUN
ap-658	136	9	with	with	ADP
ap-658	136	10	respect	respect	NOUN
ap-658	136	11	to	to	ADP
ap-658	136	12	the	the	DET
ap-658	136	13	zero	zero	NUM
ap-658	136	14	shear	shear	NOUN
ap-658	136	15	viscosity	viscosity	NOUN
ap-658	136	16	0	0	NUM
ap-658	137	1	(	(	PUNCT
ap-658	137	2	viscosity	viscosity	NOUN
ap-658	137	3	corresponding	correspond	VERB
ap-658	137	4	to	to	ADP
ap-658	137	5	an	an	DET
ap-658	137	6	elastic	elastic	ADJ
ap-658	137	7	response	response	NOUN
ap-658	137	8	)	)	PUNCT
ap-658	137	9	.	.	PUNCT
ap-658	138	1	clearly	clearly	ADV
ap-658	138	2	,	,	PUNCT
ap-658	138	3	the	the	DET
ap-658	138	4	phenomenological	phenomenological	ADJ
ap-658	138	5	representation	representation	NOUN
ap-658	138	6	of	of	ADP
ap-658	138	7	eq	eq	PROPN
ap-658	138	8	.	.	PUNCT
ap-658	138	9	(	(	PUNCT
ap-658	138	10	16a	16a	NOUN
ap-658	138	11	)	)	PUNCT
ap-658	138	12	is	be	AUX
ap-658	138	13	the	the	DET
ap-658	138	14	maxwell	maxwell	PROPN
ap-658	138	15	model	model	NOUN
ap-658	138	16	with	with	ADP
ap-658	138	17	variable	variable	ADJ
ap-658	138	18	viscosity	viscosity	NOUN
ap-658	138	19	.	.	PUNCT
ap-658	139	1	note	note	VERB
ap-658	139	2	that	that	SCONJ
ap-658	139	3	a	a	DET
ap-658	139	4	single	single	ADJ
ap-658	139	5	leonov	leonov	NOUN
ap-658	139	6	mode	mode	NOUN
ap-658	139	7	is	be	AUX
ap-658	139	8	not	not	PART
ap-658	139	9	able	able	ADJ
ap-658	139	10	to	to	PART
ap-658	139	11	describe	describe	VERB
ap-658	139	12	a	a	DET
ap-658	139	13	realistic	realistic	ADJ
ap-658	139	14	response	response	NOUN
ap-658	139	15	of	of	ADP
ap-658	139	16	real	real	ADJ
ap-658	139	17	polymers	polymer	NOUN
ap-658	139	18	,	,	PUNCT
ap-658	139	19	as	as	SCONJ
ap-658	139	20	it	it	PRON
ap-658	139	21	only	only	ADV
ap-658	139	22	accounts	account	VERB
ap-658	139	23	correctly	correctly	ADV
ap-658	139	24	for	for	ADP
ap-658	139	25	the	the	DET
ap-658	139	26	initial	initial	ADJ
ap-658	139	27	stiffness	stiffness	NOUN
ap-658	139	28	and	and	CCONJ
ap-658	139	29	the	the	DET
ap-658	139	30	strain	strain	NOUN
ap-658	139	31	rate	rate	NOUN
ap-658	139	32	dependent	dependent	ADJ
ap-658	139	33	yield	yield	NOUN
ap-658	139	34	stress	stress	NOUN
ap-658	139	35	.	.	PUNCT
ap-658	140	1	to	to	PART
ap-658	140	2	describe	describe	VERB
ap-658	140	3	the	the	DET
ap-658	140	4	multi	multi	ADJ
ap-658	140	5	-	-	ADJ
ap-658	140	6	dimensional	dimensional	ADJ
ap-658	140	7	behavior	behavior	NOUN
ap-658	140	8	of	of	ADP
ap-658	140	9	the	the	DET
ap-658	140	10	material	material	NOUN
ap-658	140	11	,	,	PUNCT
ap-658	140	12	the	the	DET
ap-658	140	13	generalized	generalized	ADJ
ap-658	140	14	compressible	compressible	ADJ
ap-658	140	15	leonov	leonov	NOUN
ap-658	140	16	model	model	NOUN
ap-658	140	17	,	,	PUNCT
ap-658	140	18	equivalent	equivalent	ADJ
ap-658	140	19	to	to	ADP
ap-658	140	20	the	the	DET
ap-658	140	21	generalized	generalized	ADJ
ap-658	140	22	maxwell	maxwell	PROPN
ap-658	140	23	chain	chain	NOUN
ap-658	140	24	model	model	NOUN
ap-658	140	25	,	,	PUNCT
ap-658	140	26	can	can	AUX
ap-658	140	27	be	be	AUX
ap-658	140	28	used	use	VERB
ap-658	140	29	.	.	PUNCT
ap-658	141	1	the	the	DET
ap-658	141	2	viscosity	viscosity	NOUN
ap-658	141	3	term	term	NOUN
ap-658	141	4	corresponding	correspond	VERB
ap-658	141	5	to	to	ADP
ap-658	141	6	the	the	DET
ap-658	141	7	μ	μ	PROPN
ap-658	141	8	-	-	PUNCT
ap-658	141	9	th	th	VERB
ap-658	141	10	unit	unit	NOUN
ap-658	141	11	receives	receive	VERB
ap-658	141	12	the	the	DET
ap-658	141	13	form	form	NOUN
ap-658	141	14	�	�	PROPN
ap-658	141	15	�	�	PROPN
ap-658	141	16	�	�	PROPN
ap-658	141	17	�	�	PROPN
ap-658	141	18	�	�	PROPN
ap-658	141	19	�	�	PROPN
ap-658	141	20	�	�	PROPN
ap-658	141	21	0	0	NUM
ap-658	141	22	1	1	NUM
ap-658	141	23	2	2	NUM
ap-658	141	24	,	,	PUNCT
ap-658	141	25	(	(	PUNCT
ap-658	141	26	)	)	PUNCT
ap-658	141	27	,	,	PUNCT
ap-658	141	28	a	a	DET
ap-658	141	29	eq	eq	NOUN
ap-658	141	30	eq	eq	PROPN
ap-658	141	31	ij	ij	PROPN
ap-658	141	32	ijs	ijs	PROPN
ap-658	141	33	s	s	PROPN
ap-658	141	34	,	,	PUNCT
ap-658	141	35	(	(	PUNCT
ap-658	141	36	17	17	NUM
ap-658	141	37	)	)	PUNCT
ap-658	141	38	where	where	SCONJ
ap-658	141	39	�	�	PROPN
ap-658	141	40	eq	eq	PROPN
ap-658	141	41	is	be	AUX
ap-658	141	42	the	the	DET
ap-658	141	43	equivalent	equivalent	ADJ
ap-658	141	44	shear	shear	NOUN
ap-658	141	45	stress	stress	NOUN
ap-658	141	46	and	and	CCONJ
ap-658	141	47	sij	sij	PROPN
ap-658	141	48	is	be	AUX
ap-658	141	49	the	the	DET
ap-658	141	50	stress	stress	NOUN
ap-658	141	51	deviator	deviator	NOUN
ap-658	141	52	tensor	tensor	NOUN
ap-658	141	53	.	.	PUNCT
ap-658	142	1	admitting	admit	VERB
ap-658	142	2	only	only	ADJ
ap-658	142	3	small	small	ADJ
ap-658	142	4	strains	strain	NOUN
ap-658	142	5	and	and	CCONJ
ap-658	142	6	isotropic	isotropic	ADJ
ap-658	142	7	materials	material	NOUN
ap-658	142	8	,	,	PUNCT
ap-658	142	9	a	a	DET
ap-658	142	10	set	set	NOUN
ap-658	142	11	of	of	ADP
ap-658	142	12	constitutive	constitutive	ADJ
ap-658	142	13	equations	equation	NOUN
ap-658	142	14	defining	define	VERB
ap-658	142	15	the	the	DET
ap-658	142	16	generalized	generalized	ADJ
ap-658	142	17	compressible	compressible	ADJ
ap-658	142	18	leonov	leonov	NOUN
ap-658	142	19	model	model	NOUN
ap-658	142	20	can	can	AUX
ap-658	142	21	be	be	AUX
ap-658	142	22	written	write	VERB
ap-658	142	23	as	as	ADP
ap-658	142	24	�	�	PROPN
ap-658	142	25	�	�	PROPN
ap-658	142	26	m	m	PROPN
ap-658	142	27	k	k	NOUN
ap-658	142	28	�	�	PROPN
ap-658	142	29	,	,	PUNCT
ap-658	142	30	(	(	PUNCT
ap-658	142	31	18	18	NUM
ap-658	142	32	)	)	PUNCT
ap-658	142	33	�	�	PROPN
ap-658	142	34	(	(	PUNCT
ap-658	142	35	�	�	PROPN
ap-658	142	36	�	�	PROPN
ap-658	142	37	)	)	PUNCT
ap-658	142	38	,	,	PUNCT
ap-658	142	39	,	,	PUNCT
ap-658	142	40	sij	sij	PROPN
ap-658	143	1	ij	ij	INTJ
ap-658	143	2	ij	ij	INTJ
ap-658	143	3	pg	pg	X
ap-658	144	1	e	e	PROPN
ap-658	144	2	e	e	PROPN
ap-658	144	3	�	�	PROPN
ap-658	144	4	�	�	PROPN
ap-658	144	5	�	�	PROPN
ap-658	144	6	�	�	PROPN
ap-658	144	7	�	�	PROPN
ap-658	144	8	2	2	NUM
ap-658	144	9	,	,	PUNCT
ap-658	144	10	(	(	PUNCT
ap-658	144	11	19	19	NUM
ap-658	144	12	)	)	PUNCT
ap-658	144	13	�	�	PROPN
ap-658	144	14	(	(	PUNCT
ap-658	144	15	)	)	PUNCT
ap-658	144	16	(	(	PUNCT
ap-658	144	17	)	)	PUNCT
ap-658	144	18	,	,	PUNCT
ap-658	144	19	,	,	PUNCT
ap-658	144	20	,	,	PUNCT
ap-658	144	21	,	,	PUNCT
ap-658	144	22	e	e	X
ap-658	144	23	s	s	NOUN
ap-658	144	24	s	s	X
ap-658	144	25	ij	ij	NOUN
ap-658	144	26	p	p	X
ap-658	144	27	ij	ij	NOUN
ap-658	144	28	eq	eq	ADP
ap-658	144	29	ij	ij	PROPN
ap-658	144	30	eqa	eqa	PROPN
ap-658	144	31	�	�	PROPN
ap-658	144	32	�	�	PROPN
ap-658	144	33	�	�	PROPN
ap-658	144	34	�	�	PROPN
ap-658	144	35	�	�	PROPN
ap-658	144	36	�	�	PROPN
ap-658	144	37	�	�	PROPN
ap-658	144	38	�	�	PROPN
ap-658	144	39	�	�	PROPN
ap-658	144	40	�	�	PROPN
ap-658	144	41	1	1	NUM
ap-658	144	42	2	2	NUM
ap-658	144	43	1	1	NUM
ap-658	144	44	2	2	NUM
ap-658	144	45	0	0	NUM
ap-658	144	46	,	,	PUNCT
ap-658	144	47	(	(	PUNCT
ap-658	144	48	20	20	NUM
ap-658	144	49	)	)	PUNCT
ap-658	144	50	�	�	PROPN
ap-658	144	51	�	�	PROPN
ap-658	144	52	�	�	PROPN
ap-658	144	53	�	�	PROPN
ap-658	144	54	�	�	PROPN
ap-658	144	55	ij	ij	NOUN
ap-658	144	56	m	m	PROPN
ap-658	144	57	ij	ij	INTJ
ap-658	144	58	ij	ij	INTJ
ap-658	144	59	ij	ij	INTJ
ap-658	144	60	ij	ij	INTJ
ap-658	144	61	m	m	PROPN
ap-658	144	62	�	�	PROPN
ap-658	144	63	�	�	PROPN
ap-658	144	64	�	�	PROPN
ap-658	144	65	�	�	PROPN
ap-658	144	66	s	s	PART
ap-658	144	67	s	s	NOUN
ap-658	144	68	s	s	NOUN
ap-658	144	69	,	,	PUNCT
ap-658	144	70	,	,	PUNCT
ap-658	144	71	1	1	NUM
ap-658	144	72	,	,	PUNCT
ap-658	144	73	(	(	PUNCT
ap-658	144	74	21	21	NUM
ap-658	144	75	)	)	PUNCT
ap-658	144	76	where	where	SCONJ
ap-658	144	77	�	�	NOUN
ap-658	144	78	m	m	PROPN
ap-658	144	79	is	be	AUX
ap-658	144	80	the	the	DET
ap-658	144	81	mean	mean	ADJ
ap-658	144	82	stress	stress	NOUN
ap-658	144	83	,	,	PUNCT
ap-658	144	84	�	�	PROPN
ap-658	144	85	is	be	AUX
ap-658	144	86	the	the	DET
ap-658	144	87	volumetric	volumetric	NOUN
ap-658	144	88	strain	strain	NOUN
ap-658	144	89	,	,	PUNCT
ap-658	144	90	k	k	PROPN
ap-658	144	91	is	be	AUX
ap-658	144	92	the	the	DET
ap-658	144	93	bulk	bulk	ADJ
ap-658	144	94	modulus	modulus	NOUN
ap-658	144	95	,	,	PUNCT
ap-658	144	96	g	g	PROPN
ap-658	144	97	�	�	PROPN
ap-658	144	98	is	be	AUX
ap-658	144	99	the	the	DET
ap-658	144	100	shear	shear	NOUN
ap-658	144	101	modulus	modulus	NOUN
ap-658	144	102	of	of	ADP
ap-658	144	103	the	the	DET
ap-658	144	104	�	�	PROPN
ap-658	144	105	-th	-th	NOUN
ap-658	144	106	unit	unit	NOUN
ap-658	144	107	and	and	CCONJ
ap-658	144	108	�	�	PROPN
ap-658	144	109	ij	ij	NOUN
ap-658	144	110	is	be	AUX
ap-658	144	111	the	the	DET
ap-658	144	112	kronecker	kronecker	NOUN
ap-658	144	113	delta	delta	NOUN
ap-658	144	114	.	.	PUNCT
ap-658	145	1	the	the	DET
ap-658	145	2	material	material	NOUN
ap-658	145	3	parameters	parameter	NOUN
ap-658	145	4	required	require	VERB
ap-658	145	5	by	by	ADP
ap-658	145	6	the	the	DET
ap-658	145	7	generalized	generalized	ADJ
ap-658	145	8	compressible	compressible	ADJ
ap-658	145	9	leonov	leonov	NOUN
ap-658	145	10	model	model	NOUN
ap-658	145	11	are	be	AUX
ap-658	145	12	parameters	parameter	NOUN
ap-658	145	13	a	a	PRON
ap-658	145	14	,	,	PUNCT
ap-658	145	15	�	�	PROPN
ap-658	145	16	0	0	NUM
ap-658	145	17	and	and	CCONJ
ap-658	145	18	g	g	PROPN
ap-658	145	19	�	�	PROPN
ap-658	145	20	(	(	PUNCT
ap-658	145	21	0	0	NUM
ap-658	145	22	�	�	NOUN
ap-658	145	23	)	)	PUNCT
ap-658	145	24	.	.	PUNCT
ap-658	146	1	the	the	DET
ap-658	146	2	material	material	NOUN
ap-658	146	3	parameters	parameter	NOUN
ap-658	146	4	a	a	DET
ap-658	146	5	and	and	CCONJ
ap-658	146	6	�	�	NOUN
ap-658	146	7	0	0	NUM
ap-658	146	8	describe	describe	VERB
ap-658	146	9	the	the	DET
ap-658	146	10	stress	stress	NOUN
ap-658	146	11	dependency	dependency	NOUN
ap-658	146	12	of	of	ADP
ap-658	146	13	the	the	DET
ap-658	146	14	model	model	NOUN
ap-658	146	15	and	and	CCONJ
ap-658	146	16	can	can	AUX
ap-658	146	17	be	be	AUX
ap-658	146	18	derived	derive	VERB
ap-658	146	19	from	from	ADP
ap-658	146	20	the	the	DET
ap-658	146	21	eyring	eyring	NOUN
ap-658	146	22	plot	plot	NOUN
ap-658	146	23	,	,	PUNCT
ap-658	146	24	fig	fig	NOUN
ap-658	146	25	.	.	PUNCT
ap-658	147	1	8(b	8(b	NUM
ap-658	147	2	)	)	PUNCT
ap-658	148	1	,	,	PUNCT
ap-658	148	2	assuming	assume	VERB
ap-658	148	3	that	that	SCONJ
ap-658	148	4	at	at	ADP
ap-658	148	5	yielding	yield	VERB
ap-658	148	6	the	the	DET
ap-658	148	7	overall	overall	ADJ
ap-658	148	8	deformation	deformation	NOUN
ap-658	148	9	as	as	ADP
ap-658	148	10	204	204	NUM
ap-658	148	11	©	©	PROPN
ap-658	148	12	czech	czech	PROPN
ap-658	148	13	technical	technical	PROPN
ap-658	148	14	university	university	PROPN
ap-658	148	15	publishing	publishing	NOUN
ap-658	148	16	house	house	NOUN
ap-658	148	17	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	148	18	acta	acta	PROPN
ap-658	148	19	polytechnica	polytechnica	PROPN
ap-658	148	20	vol	vol	NOUN
ap-658	148	21	.	.	PROPN
ap-658	148	22	44	44	NUM
ap-658	148	23	no.5–6/2004	no.5–6/2004	PROPN
ap-658	148	24	fig	fig	NOUN
ap-658	148	25	.	.	PUNCT
ap-658	149	1	8	8	NUM
ap-658	149	2	:	:	PUNCT
ap-658	149	3	(	(	PUNCT
ap-658	149	4	a	a	X
ap-658	149	5	)	)	PUNCT
ap-658	149	6	uniaxial	uniaxial	ADJ
ap-658	149	7	tensile	tensile	NOUN
ap-658	149	8	experiments	experiment	NOUN
ap-658	149	9	,	,	PUNCT
ap-658	149	10	(	(	PUNCT
ap-658	149	11	b	b	X
ap-658	149	12	)	)	PUNCT
ap-658	149	13	the	the	DET
ap-658	149	14	eyring	eyring	NOUN
ap-658	149	15	plot	plot	NOUN
ap-658	149	16	equal	equal	ADJ
ap-658	149	17	to	to	ADP
ap-658	149	18	the	the	DET
ap-658	149	19	plastic	plastic	ADJ
ap-658	149	20	deformation	deformation	NOUN
ap-658	149	21	.	.	PUNCT
ap-658	150	1	experimental	experimental	ADJ
ap-658	150	2	measurements	measurement	NOUN
ap-658	150	3	needed	need	VERB
ap-658	150	4	to	to	PART
ap-658	150	5	calibrate	calibrate	VERB
ap-658	150	6	the	the	DET
ap-658	150	7	eyring	eyring	NOUN
ap-658	150	8	flow	flow	NOUN
ap-658	150	9	model	model	NOUN
ap-658	150	10	appear	appear	VERB
ap-658	150	11	in	in	ADP
ap-658	150	12	fig	fig	NOUN
ap-658	150	13	.	.	PUNCT
ap-658	151	1	8(a	8(a	NUM
ap-658	151	2	)	)	PUNCT
ap-658	151	3	.	.	PUNCT
ap-658	152	1	the	the	DET
ap-658	152	2	shear	shear	NOUN
ap-658	152	3	modules	module	NOUN
ap-658	152	4	g	g	PROPN
ap-658	152	5	�	�	NUM
ap-658	152	6	related	relate	VERB
ap-658	152	7	to	to	ADP
ap-658	152	8	relaxation	relaxation	NOUN
ap-658	152	9	times	times	PROPN
ap-658	152	10	�	�	PROPN
ap-658	152	11	�	�	PROPN
ap-658	152	12	�	�	PROPN
ap-658	152	13	�	�	PROPN
ap-658	152	14	�	�	PROPN
ap-658	152	15	�	�	PROPN
ap-658	152	16	�	�	PROPN
ap-658	152	17	0	0	NUM
ap-658	152	18	�	�	PROPN
ap-658	152	19	#	#	SYM
ap-658	152	20	g	g	NOUN
ap-658	152	21	)	)	PUNCT
ap-658	152	22	then	then	ADV
ap-658	152	23	provide	provide	VERB
ap-658	152	24	the	the	DET
ap-658	152	25	time	time	NOUN
ap-658	152	26	dependency	dependency	NOUN
ap-658	152	27	of	of	ADP
ap-658	152	28	the	the	DET
ap-658	152	29	model	model	NOUN
ap-658	152	30	.	.	PUNCT
ap-658	153	1	they	they	PRON
ap-658	153	2	are	be	AUX
ap-658	153	3	usually	usually	ADV
ap-658	153	4	found	find	VERB
ap-658	153	5	by	by	ADP
ap-658	153	6	transforming	transform	VERB
ap-658	153	7	the	the	DET
ap-658	153	8	experimentally	experimentally	ADV
ap-658	153	9	derived	derive	VERB
ap-658	153	10	creep	creep	NOUN
ap-658	153	11	function	function	NOUN
ap-658	153	12	into	into	ADP
ap-658	153	13	the	the	DET
ap-658	153	14	relaxation	relaxation	NOUN
ap-658	153	15	function	function	NOUN
ap-658	153	16	using	use	VERB
ap-658	153	17	the	the	DET
ap-658	153	18	laplace	laplace	NOUN
ap-658	153	19	transform	transform	NOUN
ap-658	153	20	combined	combine	VERB
ap-658	153	21	with	with	ADP
ap-658	153	22	the	the	DET
ap-658	153	23	method	method	NOUN
ap-658	153	24	of	of	ADP
ap-658	153	25	partial	partial	ADJ
ap-658	153	26	fractions	fraction	NOUN
ap-658	153	27	[	[	X
ap-658	153	28	27	27	NUM
ap-658	153	29	]	]	PUNCT
ap-658	153	30	.	.	PUNCT
ap-658	154	1	coefficients	coefficient	NOUN
ap-658	154	2	of	of	ADP
ap-658	154	3	the	the	DET
ap-658	154	4	creep	creep	PROPN
ap-658	154	5	function	function	NOUN
ap-658	154	6	were	be	AUX
ap-658	154	7	determined	determine	VERB
ap-658	154	8	from	from	ADP
ap-658	154	9	a	a	DET
ap-658	154	10	set	set	NOUN
ap-658	154	11	of	of	ADP
ap-658	154	12	creep	creep	PROPN
ap-658	154	13	experiments	experiment	NOUN
ap-658	154	14	performed	perform	VERB
ap-658	154	15	at	at	ADP
ap-658	154	16	various	various	ADJ
ap-658	154	17	stress	stress	NOUN
ap-658	154	18	levels	level	NOUN
ap-658	154	19	.	.	PUNCT
ap-658	155	1	thirteen	thirteen	NUM
ap-658	155	2	elements	element	NOUN
ap-658	155	3	of	of	ADP
ap-658	155	4	the	the	DET
ap-658	155	5	generalized	generalize	VERB
ap-658	155	6	kelvin	kelvin	PROPN
ap-658	155	7	-	-	PUNCT
ap-658	155	8	voight	voight	PROPN
ap-658	155	9	chain	chain	NOUN
ap-658	155	10	model	model	NOUN
ap-658	155	11	were	be	AUX
ap-658	155	12	used	use	VERB
ap-658	155	13	to	to	PART
ap-658	155	14	obtain	obtain	VERB
ap-658	155	15	an	an	DET
ap-658	155	16	accurate	accurate	ADJ
ap-658	155	17	description	description	NOUN
ap-658	155	18	of	of	ADP
ap-658	155	19	the	the	DET
ap-658	155	20	linear	linear	PROPN
ap-658	155	21	compliance	compliance	NOUN
ap-658	155	22	function	function	NOUN
ap-658	155	23	.	.	PUNCT
ap-658	156	1	the	the	DET
ap-658	156	2	resulting	result	VERB
ap-658	156	3	coefficients	coefficient	NOUN
ap-658	156	4	for	for	ADP
ap-658	156	5	the	the	DET
ap-658	156	6	pr100/2+em100e	pr100/2+em100e	NOUN
ap-658	156	7	epoxy	epoxy	NOUN
ap-658	156	8	needed	need	VERB
ap-658	156	9	in	in	ADP
ap-658	156	10	the	the	DET
ap-658	156	11	generalized	generalize	VERB
ap-658	156	12	leonov	leonov	NOUN
ap-658	156	13	model	model	NOUN
ap-658	156	14	are	be	AUX
ap-658	156	15	stored	store	VERB
ap-658	156	16	in	in	ADP
ap-658	156	17	table	table	NOUN
ap-658	156	18	1	1	NUM
ap-658	156	19	.	.	PUNCT
ap-658	157	1	modeling	model	VERB
ap-658	157	2	the	the	DET
ap-658	157	3	mechanical	mechanical	ADJ
ap-658	157	4	behavior	behavior	NOUN
ap-658	157	5	of	of	ADP
ap-658	157	6	a	a	DET
ap-658	157	7	bonding	bonding	NOUN
ap-658	157	8	agent	agent	NOUN
ap-658	157	9	in	in	ADP
ap-658	157	10	polymer	polymer	NOUN
ap-658	157	11	matrix	matrix	NOUN
ap-658	157	12	composites	composite	NOUN
ap-658	157	13	requires	require	VERB
ap-658	157	14	a	a	DET
ap-658	157	15	reliable	reliable	ADJ
ap-658	157	16	and	and	CCONJ
ap-658	157	17	stable	stable	ADJ
ap-658	157	18	procedure	procedure	NOUN
ap-658	157	19	for	for	ADP
ap-658	157	20	integration	integration	NOUN
ap-658	157	21	of	of	ADP
ap-658	157	22	the	the	DET
ap-658	157	23	set	set	NOUN
ap-658	157	24	of	of	ADP
ap-658	157	25	governing	govern	VERB
ap-658	157	26	equations	equation	NOUN
ap-658	157	27	(	(	PUNCT
ap-658	157	28	18)-(21	18)-(21	NUM
ap-658	157	29	)	)	PUNCT
ap-658	157	30	.	.	PUNCT
ap-658	158	1	to	to	PART
ap-658	158	2	avoid	avoid	VERB
ap-658	158	3	possible	possible	ADJ
ap-658	158	4	numerical	numerical	ADJ
ap-658	158	5	instabilities	instability	NOUN
ap-658	158	6	linked	link	VERB
ap-658	158	7	to	to	ADP
ap-658	158	8	explicit	explicit	ADJ
ap-658	158	9	integration	integration	NOUN
ap-658	158	10	schemes	scheme	NOUN
ap-658	158	11	a	a	DET
ap-658	158	12	fully	fully	ADV
ap-658	158	13	implicit	implicit	ADJ
ap-658	158	14	euler	euler	NOUN
ap-658	158	15	backward	backward	ADJ
ap-658	158	16	integration	integration	NOUN
ap-658	158	17	procedure	procedure	NOUN
ap-658	158	18	was	be	AUX
ap-658	158	19	developed	develop	VERB
ap-658	158	20	.	.	PUNCT
ap-658	159	1	providing	provide	VERB
ap-658	159	2	the	the	DET
ap-658	159	3	total	total	ADJ
ap-658	159	4	strain	strain	NOUN
ap-658	159	5	rate	rate	NOUN
ap-658	159	6	is	be	AUX
ap-658	159	7	constant	constant	ADJ
ap-658	159	8	during	during	ADP
ap-658	159	9	integration	integration	NOUN
ap-658	159	10	a	a	DET
ap-658	159	11	new	new	ADJ
ap-658	159	12	state	state	NOUN
ap-658	159	13	of	of	ADP
ap-658	159	14	stress	stress	NOUN
ap-658	159	15	in	in	ADP
ap-658	159	16	the	the	DET
ap-658	159	17	matrix	matrix	NOUN
ap-658	159	18	phase	phase	NOUN
ap-658	159	19	at	at	ADP
ap-658	159	20	the	the	DET
ap-658	159	21	end	end	NOUN
ap-658	159	22	of	of	ADP
ap-658	159	23	the	the	DET
ap-658	159	24	current	current	ADJ
ap-658	159	25	time	time	NOUN
ap-658	159	26	step	step	NOUN
ap-658	159	27	assumes	assume	VERB
ap-658	159	28	the	the	DET
ap-658	159	29	form	form	PROPN
ap-658	159	30	�	�	PROPN
ap-658	159	31	�	�	PROPN
ap-658	159	32	�	�	PROPN
ap-658	159	33	m	m	VERB
ap-658	159	34	i	i	PRON
ap-658	159	35	m	m	VERB
ap-658	159	36	it	it	PRON
ap-658	159	37	t	t	X
ap-658	159	38	k	k	X
ap-658	159	39	(	(	PUNCT
ap-658	159	40	)	)	PUNCT
ap-658	159	41	(	(	PUNCT
ap-658	159	42	)	)	PUNCT
ap-658	159	43	�	�	PROPN
ap-658	159	44	�	�	PROPN
ap-658	159	45	�	�	PROPN
ap-658	159	46	1	1	NUM
ap-658	159	47	�	�	PROPN
ap-658	159	48	,	,	PUNCT
ap-658	159	49	(	(	PUNCT
ap-658	159	50	22	22	NUM
ap-658	159	51	)	)	PUNCT
ap-658	159	52	s	s	PART
ap-658	159	53	s	s	X
ap-658	159	54	e	e	NOUN
ap-658	159	55	(	(	PUNCT
ap-658	159	56	)	)	PUNCT
ap-658	159	57	(	(	PUNCT
ap-658	159	58	)	)	PUNCT
ap-658	159	59	�	�	PROPN
ap-658	159	60	(	(	PUNCT
ap-658	159	61	)	)	PUNCT
ap-658	159	62	(	(	PUNCT
ap-658	159	63	)	)	PUNCT
ap-658	159	64	t	t	NOUN
ap-658	159	65	t	t	PROPN
ap-658	159	66	g	g	PROPN
ap-658	159	67	t	t	X
ap-658	159	68	ti	ti	VERB
ap-658	160	1	i	i	PRON
ap-658	160	2	i	i	PRON
ap-658	161	1	i	i	PROPN
ap-658	161	2	�	�	PROPN
ap-658	161	3	�	�	PROPN
ap-658	161	4	�	�	PROPN
ap-658	161	5	�	�	PROPN
ap-658	161	6	1	1	NUM
ap-658	161	7	2	2	NUM
ap-658	161	8	q	q	PROPN
ap-658	161	9	�	�	PROPN
ap-658	161	10	�	�	PROPN
ap-658	161	11	�	�	PROPN
ap-658	161	12	,	,	PUNCT
ap-658	161	13	(	(	PUNCT
ap-658	161	14	23	23	NUM
ap-658	161	15	)	)	PUNCT
ap-658	161	16	where	where	SCONJ
ap-658	161	17	ti	ti	PRON
ap-658	161	18	is	be	AUX
ap-658	161	19	the	the	DET
ap-658	161	20	current	current	ADJ
ap-658	161	21	time	time	NOUN
ap-658	161	22	at	at	ADP
ap-658	161	23	the	the	DET
ap-658	161	24	end	end	NOUN
ap-658	161	25	of	of	ADP
ap-658	161	26	the	the	DET
ap-658	161	27	i	i	PROPN
ap-658	161	28	-	-	PUNCT
ap-658	161	29	th	th	PROPN
ap-658	161	30	time	time	NOUN
ap-658	161	31	increment;	increment;	X
ap-658	161	32	�	�	PROPN
ap-658	161	33	m(ti	m(ti	NOUN
ap-658	161	34	)	)	PUNCT
ap-658	161	35	is	be	AUX
ap-658	161	36	the	the	DET
ap-658	161	37	elastic	elastic	ADJ
ap-658	161	38	mean	mean	NOUN
ap-658	161	39	stress	stress	NOUN
ap-658	161	40	,	,	PUNCT
ap-658	161	41	s(ti	s(ti	PROPN
ap-658	161	42	)	)	PUNCT
ap-658	161	43	stores	store	VERB
ap-658	161	44	the	the	DET
ap-658	161	45	deviatoric	deviatoric	ADJ
ap-658	161	46	part	part	NOUN
ap-658	161	47	of	of	ADP
ap-658	161	48	the	the	DET
ap-658	161	49	stress	stress	NOUN
ap-658	161	50	vector	vector	NOUN
ap-658	161	51	�	�	PROPN
ap-658	161	52	(	(	PUNCT
ap-658	161	53	ti	ti	NOUN
ap-658	161	54	)	)	PUNCT
ap-658	161	55	and	and	CCONJ
ap-658	161	56	�	�	PROPN
ap-658	161	57	e	e	NOUN
ap-658	161	58	is	be	AUX
ap-658	161	59	the	the	DET
ap-658	161	60	deviatoric	deviatoric	ADJ
ap-658	161	61	part	part	NOUN
ap-658	161	62	of	of	ADP
ap-658	161	63	the	the	DET
ap-658	161	64	total	total	ADJ
ap-658	161	65	strain	strain	NOUN
ap-658	161	66	increment	increment	NOUN
ap-658	161	67	.	.	PUNCT
ap-658	162	1	with	with	ADP
ap-658	162	2	reference	reference	NOUN
ap-658	162	3	to	to	ADP
ap-658	162	4	the	the	DET
ap-658	162	5	backward	backward	PROPN
ap-658	162	6	euler	euler	NOUN
ap-658	162	7	integration	integration	NOUN
ap-658	162	8	scheme	scheme	NOUN
ap-658	162	9	the	the	DET
ap-658	162	10	time	time	NOUN
ap-658	162	11	dependent	dependent	ADJ
ap-658	162	12	variables	variable	NOUN
ap-658	162	13	at	at	ADP
ap-658	162	14	time	time	NOUN
ap-658	162	15	ti	ti	PROPN
ap-658	162	16	receive	receive	VERB
ap-658	162	17	the	the	DET
ap-658	162	18	form	form	NOUN
ap-658	162	19	�	�	PROPN
ap-658	162	20	(	(	PUNCT
ap-658	162	21	)	)	PUNCT
ap-658	162	22	(	(	PUNCT
ap-658	162	23	)	)	PUNCT
ap-658	162	24	exp	exp	NOUN
ap-658	162	25	(	(	PUNCT
ap-658	162	26	)	)	PUNCT
ap-658	162	27	g	g	PROPN
ap-658	162	28	t	t	PROPN
ap-658	162	29	g	g	PROPN
ap-658	162	30	a	a	DET
ap-658	162	31	t	t	NOUN
ap-658	162	32	t	t	PROPN
ap-658	162	33	t	t	PROPN
ap-658	162	34	a	a	DET
ap-658	162	35	ti	ti	NOUN
ap-658	163	1	i	i	PRON
ap-658	163	2	i	i	PRON
ap-658	163	3	�	�	PROPN
ap-658	163	4	�	�	PROPN
ap-658	163	5	�	�	PROPN
ap-658	163	6	�	�	PROPN
ap-658	163	7	�	�	PROPN
ap-658	163	8	�	�	PROPN
ap-658	163	9	�	�	PROPN
ap-658	163	10	!	!	PUNCT
ap-658	163	11	"	"	PUNCT
ap-658	164	1	"	"	PUNCT
ap-658	164	2	�	�	PROPN
ap-658	164	3	�	�	PROPN
ap-658	164	4	�	�	PROPN
ap-658	164	5	�	�	PROPN
ap-658	164	6	�	�	PROPN
ap-658	164	7	�	�	PROPN
ap-658	164	8	�	�	PROPN
ap-658	164	9	�	�	PROPN
ap-658	164	10	�	�	PROPN
ap-658	164	11	�	�	PROPN
ap-658	164	12	�	�	PROPN
ap-658	164	13	�	�	PROPN
ap-658	164	14	�	�	PROPN
ap-658	164	15	�	�	PROPN
ap-658	164	16	�	�	PROPN
ap-658	164	17	�	�	PROPN
ap-658	164	18	1	1	NUM
ap-658	164	19	�	�	PROPN
ap-658	164	20	�	�	PROPN
ap-658	164	21	�	�	PROPN
ap-658	164	22	1	1	NUM
ap-658	164	23	m	m	NOUN
ap-658	164	24	,	,	PUNCT
ap-658	164	25	(	(	PUNCT
ap-658	164	26	24	24	NUM
ap-658	164	27	)	)	PUNCT
ap-658	164	28	�	�	PROPN
ap-658	164	29	�	�	PROPN
ap-658	164	30	�	�	PROPN
ap-658	164	31	(	(	PUNCT
ap-658	164	32	)	)	PUNCT
ap-658	164	33	exp	exp	NOUN
ap-658	164	34	(	(	PUNCT
ap-658	164	35	)	)	PUNCT
ap-658	164	36	(	(	PUNCT
ap-658	164	37	)	)	PUNCT
ap-658	164	38	t	t	NOUN
ap-658	164	39	t	t	PROPN
ap-658	164	40	a	a	DET
ap-658	164	41	t	t	NOUN
ap-658	164	42	ti	ti	X
ap-658	164	43	i	i	PRON
ap-658	164	44	i	i	PROPN
ap-658	164	45	�	�	PROPN
ap-658	164	46	�	�	PROPN
ap-658	164	47	�	�	PROPN
ap-658	164	48	�	�	PROPN
ap-658	164	49	�	�	PROPN
ap-658	164	50	�	�	PROPN
ap-658	164	51	�	�	PROPN
ap-658	164	52	�	�	PROPN
ap-658	164	53	!	!	PUNCT
ap-658	164	54	"	"	PUNCT
ap-658	164	55	"	"	PUNCT
ap-658	164	56	�	�	PROPN
ap-658	164	57	�	�	PROPN
ap-658	164	58	�	�	PROPN
ap-658	164	59	�	�	PROPN
ap-658	164	60	�	�	PROPN
ap-658	164	61	�	�	PROPN
ap-658	164	62	�	�	PROPN
ap-658	164	63	�	�	PROPN
ap-658	164	64	�	�	PROPN
ap-658	164	65	�	�	PROPN
ap-658	164	66	1	1	NUM
ap-658	164	67	1	1	NUM
ap-658	164	68	�	�	PROPN
ap-658	164	69	�	�	PROPN
ap-658	164	70	�	�	PROPN
ap-658	164	71	�	�	PROPN
ap-658	164	72	�	�	PROPN
ap-658	164	73	s	s	PART
ap-658	164	74	1	1	NUM
ap-658	164	75	m	m	NOUN
ap-658	164	76	,	,	PUNCT
ap-658	164	77	(	(	PUNCT
ap-658	164	78	25	25	NUM
ap-658	164	79	)	)	PUNCT
ap-658	164	80	where	where	SCONJ
ap-658	164	81	s	s	VERB
ap-658	164	82	�	�	NOUN
ap-658	164	83	(ti	(ti	NOUN
ap-658	164	84	)	)	PUNCT
ap-658	164	85	,	,	PUNCT
ap-658	164	86	�	�	PROPN
ap-658	164	87	�	�	PROPN
ap-658	164	88	1	1	NUM
ap-658	164	89	,	,	PUNCT
ap-658	164	90	2	2	NUM
ap-658	164	91	,	,	PUNCT
ap-658	164	92	…	…	PUNCT
ap-658	164	93	,	,	PUNCT
ap-658	164	94	m	m	VERB
ap-658	164	95	,	,	PUNCT
ap-658	164	96	is	be	AUX
ap-658	164	97	the	the	DET
ap-658	164	98	deviatoric	deviatoric	ADJ
ap-658	164	99	stress	stress	NOUN
ap-658	164	100	vector	vector	NOUN
ap-658	164	101	in	in	ADP
ap-658	164	102	individual	individual	ADJ
ap-658	164	103	units	unit	NOUN
ap-658	164	104	of	of	ADP
ap-658	164	105	the	the	DET
ap-658	164	106	maxwell	maxwell	PROPN
ap-658	164	107	chain	chain	NOUN
ap-658	164	108	model	model	NOUN
ap-658	164	109	evaluated	evaluate	VERB
ap-658	164	110	at	at	ADP
ap-658	164	111	the	the	DET
ap-658	164	112	beginning	beginning	NOUN
ap-658	164	113	of	of	ADP
ap-658	164	114	a	a	DET
ap-658	164	115	new	new	ADJ
ap-658	164	116	time	time	NOUN
ap-658	164	117	increment	increment	NOUN
ap-658	164	118	�	�	PROPN
ap-658	164	119	t	t	PROPN
ap-658	164	120	t	t	NOUN
ap-658	164	121	ti	ti	PROPN
ap-658	164	122	i	i	PROPN
ap-658	164	123	�	�	PROPN
ap-658	164	124	�	�	PROPN
ap-658	164	125	�	�	PROPN
ap-658	164	126	1	1	NUM
ap-658	164	127	,	,	PUNCT
ap-658	164	128	and	and	CCONJ
ap-658	164	129	m	m	PROPN
ap-658	164	130	is	be	AUX
ap-658	164	131	the	the	DET
ap-658	164	132	assumed	assumed	ADJ
ap-658	164	133	number	number	NOUN
ap-658	164	134	of	of	ADP
ap-658	164	135	mawell	mawell	PROPN
ap-658	164	136	units	unit	NOUN
ap-658	164	137	in	in	ADP
ap-658	164	138	the	the	DET
ap-658	164	139	chain	chain	NOUN
ap-658	164	140	model	model	NOUN
ap-658	164	141	.	.	PUNCT
ap-658	165	1	the	the	DET
ap-658	165	2	stress	stress	NOUN
ap-658	165	3	shift	shift	NOUN
ap-658	165	4	factor	factor	NOUN
ap-658	165	5	is	be	AUX
ap-658	165	6	given	give	VERB
ap-658	165	7	by	by	ADP
ap-658	165	8	a	a	DET
ap-658	165	9	t	t	NOUN
ap-658	165	10	t	t	X
ap-658	165	11	ti	ti	X
ap-658	165	12	eq	eq	NOUN
ap-658	166	1	i	i	PRON
ap-658	166	2	eq	eq	NOUN
ap-658	167	1	i	i	PRON
ap-658	167	2	�	�	PROPN
ap-658	167	3	�	�	PROPN
ap-658	167	4	�	�	PROPN
ap-658	167	5	�	�	PROPN
ap-658	167	6	�	�	PROPN
ap-658	167	7	(	(	PUNCT
ap-658	167	8	)	)	PUNCT
ap-658	167	9	(	(	PUNCT
ap-658	167	10	)	)	PUNCT
ap-658	167	11	sinh	sinh	PROPN
ap-658	167	12	(	(	PUNCT
ap-658	167	13	)	)	PUNCT
ap-658	167	14	�	�	PROPN
ap-658	167	15	�	�	PROPN
ap-658	167	16	�	�	PROPN
ap-658	167	17	�	�	PROPN
ap-658	167	18	�	�	PROPN
ap-658	167	19	!	!	PUNCT
ap-658	168	1	"	"	PUNCT
ap-658	168	2	"	"	PUNCT
ap-658	168	3	0	0	NUM
ap-658	168	4	0	0	NUM
ap-658	168	5	,	,	PUNCT
ap-658	168	6	(	(	PUNCT
ap-658	168	7	26	26	NUM
ap-658	168	8	)	)	PUNCT
ap-658	168	9	where	where	SCONJ
ap-658	168	10	the	the	DET
ap-658	168	11	equivalent	equivalent	ADJ
ap-658	168	12	stress	stress	PROPN
ap-658	168	13	�	�	PROPN
ap-658	168	14	eq	eq	NOUN
ap-658	168	15	follows	follow	VERB
ap-658	168	16	from	from	ADP
ap-658	168	17	�	�	PROPN
ap-658	168	18	eq	eq	ADP
ap-658	169	1	i	i	PRON
ap-658	170	1	i	i	PRON
ap-658	170	2	it	it	PRON
ap-658	170	3	t	t	PROPN
ap-658	170	4	t	t	PROPN
ap-658	170	5	(	(	PUNCT
ap-658	170	6	)	)	PUNCT
ap-658	170	7	(	(	PUNCT
ap-658	170	8	)	)	PUNCT
ap-658	170	9	(	(	PUNCT
ap-658	170	10	)	)	PUNCT
ap-658	170	11	�	�	PROPN
ap-658	170	12	�	�	PROPN
ap-658	170	13	1	1	NUM
ap-658	170	14	2	2	NUM
ap-658	170	15	1s	1s	NUM
ap-658	170	16	st	st	PROPN
ap-658	170	17	q	q	X
ap-658	170	18	,	,	PUNCT
ap-658	170	19	(	(	PUNCT
ap-658	170	20	27	27	NUM
ap-658	170	21	)	)	PUNCT
ap-658	170	22	and	and	CCONJ
ap-658	170	23	q	q	PROPN
ap-658	170	24	�	�	PROPN
ap-658	170	25	�	�	PROPN
ap-658	170	26	�	�	PROPN
ap-658	170	27	�	�	PROPN
ap-658	170	28	�	�	PROPN
ap-658	170	29	�	�	PROPN
ap-658	170	30	�	�	PROPN
ap-658	170	31	diag	diag	NOUN
ap-658	171	1	1	1	NUM
ap-658	171	2	1	1	NUM
ap-658	171	3	1	1	NUM
ap-658	171	4	1	1	NUM
ap-658	171	5	2	2	NUM
ap-658	171	6	1	1	NUM
ap-658	171	7	2	2	NUM
ap-658	171	8	1	1	NUM
ap-658	171	9	2	2	NUM
ap-658	171	10	.	.	PUNCT
ap-658	172	1	(	(	PUNCT
ap-658	172	2	28	28	NUM
ap-658	172	3	)	)	PUNCT
ap-658	172	4	clearly	clearly	ADV
ap-658	172	5	,	,	PUNCT
ap-658	172	6	the	the	DET
ap-658	172	7	backward	backward	PROPN
ap-658	172	8	euler	euler	NOUN
ap-658	172	9	step	step	NOUN
ap-658	172	10	makes	make	VERB
ap-658	172	11	all	all	DET
ap-658	172	12	variables	variable	NOUN
ap-658	172	13	nonlinearly	nonlinearly	ADV
ap-658	172	14	dependent	dependent	ADJ
ap-658	172	15	on	on	ADP
ap-658	172	16	the	the	DET
ap-658	172	17	stress	stress	NOUN
ap-658	172	18	values	value	NOUN
ap-658	172	19	found	find	VERB
ap-658	172	20	at	at	ADP
ap-658	172	21	time	time	NOUN
ap-658	172	22	ti	ti	X
ap-658	172	23	.	.	PUNCT
ap-658	172	24	therefore	therefore	ADV
ap-658	172	25	,	,	PUNCT
ap-658	172	26	successful	successful	ADJ
ap-658	172	27	completion	completion	NOUN
ap-658	172	28	of	of	ADP
ap-658	172	29	a	a	DET
ap-658	172	30	given	give	VERB
ap-658	172	31	integration	integration	NOUN
ap-658	172	32	step	step	NOUN
ap-658	172	33	requires	require	VERB
ap-658	172	34	the	the	DET
ap-658	172	35	solution	solution	NOUN
ap-658	172	36	of	of	ADP
ap-658	172	37	a	a	DET
ap-658	172	38	system	system	NOUN
ap-658	172	39	of	of	ADP
ap-658	172	40	nonlinear	nonlinear	ADJ
ap-658	172	41	equations	equation	NOUN
ap-658	172	42	.	.	PUNCT
ap-658	173	1	here	here	ADV
ap-658	173	2	,	,	PUNCT
ap-658	173	3	the	the	DET
ap-658	173	4	solution	solution	NOUN
ap-658	173	5	is	be	AUX
ap-658	173	6	established	establish	VERB
ap-658	173	7	employing	employ	VERB
ap-658	173	8	the	the	DET
ap-658	173	9	newton	newton	PROPN
ap-658	173	10	-	-	PUNCT
ap-658	173	11	raphson	raphson	NOUN
ap-658	173	12	method	method	NOUN
ap-658	173	13	.	.	PUNCT
ap-658	174	1	to	to	ADP
ap-658	174	2	that	that	DET
ap-658	174	3	end	end	NOUN
ap-658	174	4	,	,	PUNCT
ap-658	174	5	define	define	VERB
ap-658	174	6	a	a	DET
ap-658	174	7	set	set	NOUN
ap-658	174	8	of	of	ADP
ap-658	174	9	residuals	residual	NOUN
ap-658	174	10	�	�	PROPN
ap-658	174	11	�	�	PROPN
ap-658	174	12	r	r	PROPN
ap-658	174	13	�	�	PROPN
ap-658	174	14	t	t	PROPN
ap-658	174	15	g	g	PROPN
ap-658	174	16	a	a	DET
ap-658	174	17	tas	tas	NOUN
ap-658	174	18	t	t	PROPN
ap-658	174	19	t	t	PROPN
ap-658	174	20	t	t	PROPN
ap-658	174	21	teq	teq	PROPN
ap-658	175	1	i	i	PRON
ap-658	175	2	i	i	PROPN
ap-658	176	1	i	i	PROPN
ap-658	176	2	�	�	PROPN
ap-658	176	3	�	�	PROPN
ap-658	176	4	�	�	PROPN
ap-658	176	5	�	�	PROPN
ap-658	176	6	(	(	PUNCT
ap-658	176	7	)	)	PUNCT
ap-658	176	8	(	(	PUNCT
ap-658	176	9	)	)	PUNCT
ap-658	176	10	(	(	PUNCT
ap-658	176	11	)	)	PUNCT
ap-658	176	12	1	1	NUM
ap-658	176	13	2	2	NUM
ap-658	176	14	1s	1s	NUM
ap-658	176	15	st	st	PROPN
ap-658	176	16	q	q	X
ap-658	176	17	,	,	PUNCT
ap-658	176	18	(	(	PUNCT
ap-658	176	19	29	29	NUM
ap-658	176	20	)	)	PUNCT
ap-658	176	21	g	g	NOUN
ap-658	176	22	g	g	PROPN
ap-658	176	23	t	t	PROPN
ap-658	176	24	g	g	PROPN
ap-658	176	25	a	a	DET
ap-658	176	26	t	t	NOUN
ap-658	176	27	t	t	PROPN
ap-658	176	28	t	t	PROPN
ap-658	176	29	a	a	DET
ap-658	176	30	ti	ti	NOUN
ap-658	177	1	i	i	PRON
ap-658	177	2	i	i	PRON
ap-658	177	3	�	�	PROPN
ap-658	177	4	�	�	PROPN
ap-658	177	5	�	�	PROPN
ap-658	177	6	�	�	PROPN
ap-658	177	7	�	�	PROPN
ap-658	177	8	�	�	PROPN
ap-658	177	9	�	�	PROPN
ap-658	177	10	�	�	PROPN
ap-658	177	11	!	!	PUNCT
ap-658	177	12	"	"	PUNCT
ap-658	178	1	"	"	PUNCT
ap-658	178	2	�	�	PROPN
ap-658	178	3	�	�	PROPN
ap-658	178	4	�	�	PROPN
ap-658	178	5	�	�	PROPN
ap-658	178	6	�	�	PROPN
ap-658	178	7	�	�	PROPN
ap-658	178	8	(	(	PUNCT
ap-658	178	9	)	)	PUNCT
ap-658	178	10	(	(	PUNCT
ap-658	178	11	)	)	PUNCT
ap-658	178	12	exp	exp	NOUN
ap-658	178	13	(	(	PUNCT
ap-658	178	14	)	)	PUNCT
ap-658	178	15	�	�	PROPN
ap-658	178	16	�	�	PROPN
ap-658	178	17	�	�	PROPN
ap-658	178	18	�	�	PROPN
ap-658	178	19	�	�	PROPN
ap-658	178	20	�	�	PROPN
ap-658	178	21	�	�	PROPN
ap-658	178	22	�	�	PROPN
ap-658	178	23	�	�	PROPN
ap-658	178	24	1	1	NUM
ap-658	178	25	�	�	PROPN
ap-658	178	26	�	�	PROPN
ap-658	178	27	�	�	PROPN
ap-658	178	28	�	�	PROPN
ap-658	178	29	�	�	PROPN
ap-658	178	30	1	1	NUM
ap-658	178	31	m	m	NOUN
ap-658	178	32	,	,	PUNCT
ap-658	178	33	(	(	PUNCT
ap-658	178	34	30	30	NUM
ap-658	178	35	)	)	PUNCT
ap-658	178	36	a	a	DET
ap-658	178	37	a	a	DET
ap-658	178	38	t	t	NOUN
ap-658	178	39	t	t	NOUN
ap-658	178	40	ti	ti	X
ap-658	178	41	eq	eq	NOUN
ap-658	179	1	i	i	PRON
ap-658	179	2	eq	eq	NOUN
ap-658	180	1	i	i	PRON
ap-658	180	2	�	�	PROPN
ap-658	180	3	�	�	PROPN
ap-658	180	4	�	�	PROPN
ap-658	180	5	�	�	PROPN
ap-658	180	6	�	�	PROPN
ap-658	180	7	�	�	PROPN
ap-658	180	8	!	!	PUNCT
ap-658	181	1	"	"	PUNCT
ap-658	181	2	"	"	PUNCT
ap-658	181	3	�	�	PROPN
ap-658	181	4	�	�	PROPN
ap-658	181	5	�	�	PROPN
ap-658	181	6	�	�	PROPN
ap-658	181	7	�	�	PROPN
ap-658	181	8	(	(	PUNCT
ap-658	181	9	)	)	PUNCT
ap-658	181	10	(	(	PUNCT
ap-658	181	11	)	)	PUNCT
ap-658	181	12	sinh	sinh	PROPN
ap-658	181	13	(	(	PUNCT
ap-658	181	14	)	)	PUNCT
ap-658	181	15	0	0	NUM
ap-658	181	16	0	0	NUM
ap-658	181	17	,	,	PUNCT
ap-658	181	18	(	(	PUNCT
ap-658	181	19	31	31	NUM
ap-658	181	20	)	)	PUNCT
ap-658	181	21	with	with	ADP
ap-658	181	22	the	the	DET
ap-658	181	23	primary	primary	ADJ
ap-658	181	24	variables	variable	NOUN
ap-658	181	25	�	�	PROPN
ap-658	181	26	�	�	PROPN
ap-658	181	27	a	a	DET
ap-658	181	28	�	�	PROPN
ap-658	181	29	�	�	PROPN
ap-658	181	30	�	�	PROPN
ap-658	181	31	eq	eq	NOUN
ap-658	181	32	i	i	PRON
ap-658	182	1	i	i	PRON
ap-658	182	2	it	it	PRON
ap-658	182	3	g	g	PROPN
ap-658	182	4	t	t	PROPN
ap-658	182	5	a	a	DET
ap-658	182	6	t	t	PROPN
ap-658	182	7	(	(	PUNCT
ap-658	182	8	)	)	PUNCT
ap-658	182	9	�	�	PROPN
ap-658	182	10	(	(	PUNCT
ap-658	182	11	)	)	PUNCT
ap-658	182	12	(	(	PUNCT
ap-658	182	13	)	)	PUNCT
ap-658	182	14	t	t	NOUN
ap-658	182	15	.	.	PUNCT
ap-658	183	1	(	(	PUNCT
ap-658	183	2	32	32	NUM
ap-658	183	3	)	)	PUNCT
ap-658	183	4	note	note	NOUN
ap-658	183	5	that	that	SCONJ
ap-658	183	6	the	the	DET
ap-658	183	7	current	current	ADJ
ap-658	183	8	increment	increment	NOUN
ap-658	183	9	of	of	ADP
ap-658	183	10	the	the	DET
ap-658	183	11	vector	vector	PROPN
ap-658	183	12	�	�	PROPN
ap-658	183	13	�	�	PROPN
ap-658	183	14	(	(	PUNCT
ap-658	183	15	ti	ti	NOUN
ap-658	183	16	)	)	PUNCT
ap-658	183	17	,	,	PUNCT
ap-658	183	18	which	which	PRON
ap-658	183	19	appears	appear	VERB
ap-658	183	20	in	in	ADP
ap-658	183	21	eq	eq	ADP
ap-658	183	22	.	.	PUNCT
ap-658	183	23	(	(	PUNCT
ap-658	183	24	23	23	NUM
ap-658	183	25	)	)	PUNCT
ap-658	183	26	,	,	PUNCT
ap-658	183	27	is	be	AUX
ap-658	183	28	considered	consider	VERB
ap-658	183	29	as	as	ADP
ap-658	183	30	a	a	DET
ap-658	183	31	secondary	secondary	ADJ
ap-658	183	32	variable	variable	NOUN
ap-658	183	33	.	.	PUNCT
ap-658	184	1	then	then	ADV
ap-658	184	2	,	,	PUNCT
ap-658	184	3	under	under	ADP
ap-658	184	4	the	the	DET
ap-658	184	5	condition	condition	NOUN
ap-658	184	6	that	that	SCONJ
ap-658	184	7	�	�	PROPN
ap-658	184	8	e	e	PROPN
ap-658	184	9	is	be	AUX
ap-658	184	10	constant	constant	ADJ
ap-658	184	11	,	,	PUNCT
ap-658	184	12	the	the	DET
ap-658	184	13	newton	newton	PROPN
ap-658	184	14	-	-	PUNCT
ap-658	184	15	raphson	raphson	PROPN
ap-658	184	16	iterative	iterative	NOUN
ap-658	184	17	scheme	scheme	NOUN
ap-658	184	18	reads	read	VERB
ap-658	184	19	a	a	DET
ap-658	184	20	a	a	DET
ap-658	184	21	rk	rk	NOUN
ap-658	185	1	i	i	NOUN
ap-658	185	2	k	k	PROPN
ap-658	186	1	i	i	PRON
ap-658	186	2	k	k	PROPN
ap-658	187	1	kt	kt	PROPN
ap-658	187	2	t	t	PROPN
ap-658	187	3	�	�	PROPN
ap-658	187	4	�	�	PROPN
ap-658	187	5	�	�	PROPN
ap-658	187	6	�	�	PROPN
ap-658	187	7	1	1	NUM
ap-658	187	8	1	1	NUM
ap-658	187	9	(	(	PUNCT
ap-658	187	10	)	)	PUNCT
ap-658	187	11	(	(	PUNCT
ap-658	187	12	)	)	PUNCT
ap-658	187	13	h	h	NOUN
ap-658	187	14	,	,	PUNCT
ap-658	187	15	(	(	PUNCT
ap-658	187	16	33	33	NUM
ap-658	187	17	)	)	PUNCT
ap-658	187	18	where	where	SCONJ
ap-658	187	19	jacobian	jacobian	ADJ
ap-658	187	20	matrix	matrix	NOUN
ap-658	187	21	h	h	NOUN
ap-658	187	22	is	be	AUX
ap-658	187	23	given	give	VERB
ap-658	187	24	by	by	ADP
ap-658	187	25	h	h	PROPN
ap-658	187	26	�	�	PROPN
ap-658	188	1	d	d	PROPN
ap-658	188	2	d	d	X
ap-658	188	3	r	r	NOUN
ap-658	188	4	a	a	PRON
ap-658	188	5	.	.	PUNCT
ap-658	189	1	(	(	PUNCT
ap-658	189	2	34	34	NUM
ap-658	189	3	)	)	PUNCT
ap-658	189	4	the	the	DET
ap-658	189	5	initial	initial	ADJ
ap-658	189	6	values	value	NOUN
ap-658	189	7	of	of	ADP
ap-658	189	8	primary	primary	ADJ
ap-658	189	9	variables	variable	NOUN
ap-658	189	10	at	at	ADP
ap-658	189	11	time	time	NOUN
ap-658	189	12	ti	ti	NOUN
ap-658	189	13	for	for	ADP
ap-658	189	14	k	k	PROPN
ap-658	189	15	�	�	PROPN
ap-658	189	16	0	0	NUM
ap-658	189	17	are	be	AUX
ap-658	189	18	set	set	VERB
ap-658	189	19	to	to	ADP
ap-658	189	20	forward	forward	NOUN
ap-658	189	21	euler	euler	PROPN
ap-658	189	22	estimates	estimate	NOUN
ap-658	189	23	.	.	PUNCT
ap-658	190	1	more	more	ADJ
ap-658	190	2	details	detail	NOUN
ap-658	190	3	about	about	ADP
ap-658	190	4	the	the	DET
ap-658	190	5	numerical	numerical	ADJ
ap-658	190	6	implementation	implementation	NOUN
ap-658	190	7	including	include	VERB
ap-658	190	8	comparison	comparison	NOUN
ap-658	190	9	of	of	ADP
ap-658	190	10	an	an	DET
ap-658	190	11	explicit	explicit	ADJ
ap-658	190	12	and	and	CCONJ
ap-658	190	13	implicit	implicit	ADJ
ap-658	190	14	integration	integration	NOUN
ap-658	190	15	scheme	scheme	NOUN
ap-658	190	16	can	can	AUX
ap-658	190	17	be	be	AUX
ap-658	190	18	found	find	VERB
ap-658	190	19	in	in	ADP
ap-658	190	20	[	[	X
ap-658	190	21	27,28	27,28	NOUN
ap-658	190	22	]	]	X
ap-658	190	23	.	.	PUNCT
ap-658	191	1	the	the	DET
ap-658	191	2	accuracy	accuracy	NOUN
ap-658	191	3	of	of	ADP
ap-658	191	4	the	the	DET
ap-658	191	5	proposed	propose	VERB
ap-658	191	6	numerical	numerical	ADJ
ap-658	191	7	procedure	procedure	NOUN
ap-658	191	8	is	be	AUX
ap-658	191	9	demonstrated	demonstrate	VERB
ap-658	191	10	in	in	ADP
ap-658	191	11	fig	fig	NOUN
ap-658	191	12	.	.	PUNCT
ap-658	192	1	9	9	NUM
ap-658	192	2	,	,	PUNCT
ap-658	192	3	which	which	PRON
ap-658	192	4	shows	show	VERB
ap-658	192	5	a	a	DET
ap-658	192	6	typical	typical	ADJ
ap-658	192	7	uniaxial	uniaxial	ADJ
ap-658	192	8	re	re	NOUN
ap-658	192	9	©	©	PROPN
ap-658	192	10	czech	czech	PROPN
ap-658	192	11	technical	technical	PROPN
ap-658	192	12	university	university	PROPN
ap-658	192	13	publishing	publishing	NOUN
ap-658	192	14	house	house	NOUN
ap-658	192	15	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	192	16	205	205	NUM
ap-658	192	17	acta	acta	PROPN
ap-658	192	18	polytechnica	polytechnica	PROPN
ap-658	192	19	vol	vol	NOUN
ap-658	192	20	.	.	PROPN
ap-658	193	1	44	44	NUM
ap-658	193	2	no.5–6/2004	no.5–6/2004	NOUN
ap-658	193	3	table	table	NOUN
ap-658	193	4	1	1	NUM
ap-658	193	5	:	:	PUNCT
ap-658	193	6	nonlinear	nonlinear	ADJ
ap-658	193	7	viscoelastic	viscoelastic	ADJ
ap-658	193	8	material	material	NOUN
ap-658	193	9	properties	property	NOUN
ap-658	193	10	of	of	ADP
ap-658	193	11	the	the	DET
ap-658	193	12	pr100/2+em100e	pr100/2+em100e	NOUN
ap-658	193	13	epoxy	epoxy	NOUN
ap-658	193	14	matrix	matrix	NOUN
ap-658	193	15	sponse	sponse	NOUN
ap-658	193	16	of	of	ADP
ap-658	193	17	the	the	DET
ap-658	193	18	pr100/2+em100e	pr100/2+em100e	NOUN
ap-658	193	19	epoxy	epoxy	NOUN
ap-658	193	20	resin	resin	NOUN
ap-658	193	21	for	for	ADP
ap-658	193	22	three	three	NUM
ap-658	193	23	different	different	ADJ
ap-658	193	24	constant	constant	ADJ
ap-658	193	25	strain	strain	NOUN
ap-658	193	26	rates	rate	NOUN
ap-658	193	27	,	,	PUNCT
ap-658	193	28	where	where	SCONJ
ap-658	193	29	the	the	DET
ap-658	193	30	solid	solid	ADJ
ap-658	193	31	lines	line	NOUN
ap-658	193	32	were	be	AUX
ap-658	193	33	obtained	obtain	VERB
ap-658	193	34	experimentally	experimentally	ADV
ap-658	193	35	,	,	PUNCT
ap-658	193	36	while	while	SCONJ
ap-658	193	37	the	the	DET
ap-658	193	38	others	other	NOUN
ap-658	193	39	follow	follow	VERB
ap-658	193	40	from	from	ADP
ap-658	193	41	the	the	DET
ap-658	193	42	numerical	numerical	ADJ
ap-658	193	43	analysis	analysis	NOUN
ap-658	193	44	.	.	PUNCT
ap-658	194	1	5	5	NUM
ap-658	194	2	inadequacy	inadequacy	NOUN
ap-658	194	3	of	of	ADP
ap-658	194	4	two	two	NUM
ap-658	194	5	-	-	PUNCT
ap-658	194	6	point	point	NOUN
ap-658	194	7	averaging	averaging	NOUN
ap-658	194	8	recall	recall	NOUN
ap-658	194	9	that	that	SCONJ
ap-658	194	10	,	,	PUNCT
ap-658	194	11	in	in	ADP
ap-658	194	12	section	section	NOUN
ap-658	194	13	2	2	NUM
ap-658	194	14	,	,	PUNCT
ap-658	194	15	rather	rather	ADV
ap-658	194	16	encouraging	encourage	VERB
ap-658	194	17	results	result	NOUN
ap-658	194	18	were	be	AUX
ap-658	194	19	obtained	obtain	VERB
ap-658	194	20	for	for	ADP
ap-658	194	21	(	(	PUNCT
ap-658	194	22	an	an	DET
ap-658	194	23	appropriately	appropriately	ADV
ap-658	194	24	modified	modify	VERB
ap-658	194	25	)	)	PUNCT
ap-658	194	26	two	two	NUM
ap-658	194	27	-	-	PUNCT
ap-658	194	28	point	point	NOUN
ap-658	194	29	averaging	averaging	NOUN
ap-658	194	30	scheme	scheme	NOUN
ap-658	194	31	for	for	ADP
ap-658	194	32	binary	binary	ADJ
ap-658	194	33	laminates	laminate	NOUN
ap-658	194	34	.	.	PUNCT
ap-658	195	1	this	this	DET
ap-658	195	2	scheme	scheme	NOUN
ap-658	195	3	,	,	PUNCT
ap-658	195	4	however	however	ADV
ap-658	195	5	,	,	PUNCT
ap-658	195	6	when	when	SCONJ
ap-658	195	7	applied	apply	VERB
ap-658	195	8	to	to	ADP
ap-658	195	9	more	more	ADJ
ap-658	195	10	complex	complex	ADJ
ap-658	195	11	microstructures	microstructure	NOUN
ap-658	195	12	such	such	ADJ
ap-658	195	13	as	as	ADP
ap-658	195	14	hexagonal	hexagonal	ADJ
ap-658	195	15	packing	packing	NOUN
ap-658	195	16	of	of	ADP
ap-658	195	17	fibers	fiber	NOUN
ap-658	195	18	delivers	deliver	VERB
ap-658	195	19	rather	rather	ADV
ap-658	195	20	inadequate	inadequate	ADJ
ap-658	195	21	results	result	NOUN
ap-658	195	22	,	,	PUNCT
ap-658	195	23	although	although	SCONJ
ap-658	195	24	having	have	VERB
ap-658	195	25	a	a	DET
ap-658	195	26	significantly	significantly	ADV
ap-658	195	27	softer	soft	ADJ
ap-658	195	28	prediction	prediction	NOUN
ap-658	195	29	of	of	ADP
ap-658	195	30	the	the	DET
ap-658	195	31	macroscopic	macroscopic	ADJ
ap-658	195	32	response	response	NOUN
ap-658	195	33	than	than	ADP
ap-658	195	34	the	the	DET
ap-658	195	35	classical	classical	ADJ
ap-658	195	36	one	one	NOUN
ap-658	195	37	,	,	PUNCT
ap-658	195	38	see	see	VERB
ap-658	195	39	fig	fig	NOUN
ap-658	195	40	.	.	PUNCT
ap-658	196	1	3	3	X
ap-658	196	2	.	.	X
ap-658	196	3	an	an	DET
ap-658	196	4	explanation	explanation	NOUN
ap-658	196	5	is	be	AUX
ap-658	196	6	offered	offer	VERB
ap-658	196	7	by	by	ADP
ap-658	196	8	examining	examine	VERB
ap-658	196	9	,	,	PUNCT
ap-658	196	10	among	among	ADP
ap-658	196	11	others	other	NOUN
ap-658	196	12	,	,	PUNCT
ap-658	196	13	also	also	ADV
ap-658	196	14	the	the	DET
ap-658	196	15	response	response	NOUN
ap-658	196	16	for	for	ADP
ap-658	196	17	a	a	DET
ap-658	196	18	pure	pure	ADJ
ap-658	196	19	matrix	matrix	NOUN
ap-658	196	20	subjected	subject	VERB
ap-658	196	21	to	to	ADP
ap-658	196	22	the	the	DET
ap-658	196	23	same	same	ADJ
ap-658	196	24	overall	overall	ADJ
ap-658	196	25	shear	shear	NOUN
ap-658	196	26	strain	strain	NOUN
ap-658	196	27	rate	rate	NOUN
ap-658	196	28	as	as	ADP
ap-658	196	29	the	the	DET
ap-658	196	30	composite	composite	NOUN
ap-658	196	31	.	.	PUNCT
ap-658	197	1	it	it	PRON
ap-658	197	2	is	be	AUX
ap-658	197	3	interesting	interesting	ADJ
ap-658	197	4	to	to	PART
ap-658	197	5	observe	observe	VERB
ap-658	197	6	,	,	PUNCT
ap-658	197	7	particularly	particularly	ADV
ap-658	197	8	in	in	ADP
ap-658	197	9	view	view	NOUN
ap-658	197	10	of	of	ADP
ap-658	197	11	the	the	DET
ap-658	197	12	results	result	NOUN
ap-658	197	13	presented	present	VERB
ap-658	197	14	in	in	ADP
ap-658	197	15	figs	fig	NOUN
ap-658	197	16	.	.	PUNCT
ap-658	198	1	4–6	4–6	X
ap-658	198	2	,	,	PUNCT
ap-658	198	3	that	that	SCONJ
ap-658	198	4	the	the	DET
ap-658	198	5	stress	stress	NOUN
ap-658	198	6	-	-	PUNCT
ap-658	198	7	strain	strain	NOUN
ap-658	198	8	curve	curve	NOUN
ap-658	198	9	for	for	ADP
ap-658	198	10	a	a	DET
ap-658	198	11	pure	pure	ADJ
ap-658	198	12	matrix	matrix	NOUN
ap-658	198	13	plots	plot	NOUN
ap-658	198	14	above	above	ADP
ap-658	198	15	the	the	DET
ap-658	198	16	finite	finite	ADJ
ap-658	198	17	element	element	NOUN
ap-658	198	18	estimates	estimate	NOUN
ap-658	198	19	of	of	ADP
ap-658	198	20	the	the	DET
ap-658	198	21	volume	volume	NOUN
ap-658	198	22	average	average	NOUN
ap-658	198	23	of	of	ADP
ap-658	198	24	matrix	matrix	NOUN
ap-658	198	25	stress	stress	NOUN
ap-658	198	26	derived	derive	VERB
ap-658	198	27	for	for	ADP
ap-658	198	28	the	the	DET
ap-658	198	29	composite	composite	NOUN
ap-658	198	30	.	.	PUNCT
ap-658	199	1	to	to	PART
ap-658	199	2	reconcile	reconcile	VERB
ap-658	199	3	this	this	DET
ap-658	199	4	“	"	PUNCT
ap-658	199	5	paradox	paradox	NOUN
ap-658	199	6	”	"	PUNCT
ap-658	199	7	,	,	PUNCT
ap-658	199	8	namely	namely	ADV
ap-658	199	9	the	the	DET
ap-658	199	10	fact	fact	NOUN
ap-658	199	11	that	that	SCONJ
ap-658	199	12	the	the	DET
ap-658	199	13	volume	volume	NOUN
ap-658	199	14	average	average	NOUN
ap-658	199	15	of	of	ADP
ap-658	199	16	the	the	DET
ap-658	199	17	matrix	matrix	NOUN
ap-658	199	18	yield	yield	NOUN
ap-658	199	19	stress	stress	NOUN
ap-658	199	20	decreases	decrease	VERB
ap-658	199	21	with	with	ADP
ap-658	199	22	an	an	DET
ap-658	199	23	increase	increase	NOUN
ap-658	199	24	in	in	ADP
ap-658	199	25	the	the	DET
ap-658	199	26	volume	volume	NOUN
ap-658	199	27	average	average	NOUN
ap-658	199	28	of	of	ADP
ap-658	199	29	the	the	DET
ap-658	199	30	matrix	matrix	NOUN
ap-658	199	31	strain	strain	NOUN
ap-658	199	32	rate	rate	NOUN
ap-658	199	33	,	,	PUNCT
ap-658	199	34	we	we	PRON
ap-658	199	35	can	can	AUX
ap-658	199	36	set	set	VERB
ap-658	199	37	up	up	ADP
ap-658	199	38	a	a	DET
ap-658	199	39	very	very	ADV
ap-658	199	40	simple	simple	ADJ
ap-658	199	41	geometrical	geometrical	ADJ
ap-658	199	42	model	model	NOUN
ap-658	199	43	with	with	ADP
ap-658	199	44	the	the	DET
ap-658	199	45	finite	finite	ADJ
ap-658	199	46	element	element	NOUN
ap-658	199	47	discretization	discretization	NOUN
ap-658	199	48	depicted	depict	VERB
ap-658	199	49	in	in	ADP
ap-658	199	50	fig	fig	NOUN
ap-658	199	51	.	.	PUNCT
ap-658	200	1	10	10	NUM
ap-658	200	2	.	.	PUNCT
ap-658	201	1	elements	element	NOUN
ap-658	201	2	that	that	PRON
ap-658	201	3	exhibit	exhibit	VERB
ap-658	201	4	the	the	DET
ap-658	201	5	same	same	ADJ
ap-658	201	6	stress	stress	NOUN
ap-658	201	7	response	response	NOUN
ap-658	201	8	were	be	AUX
ap-658	201	9	marked	mark	VERB
ap-658	201	10	with	with	ADP
ap-658	201	11	the	the	DET
ap-658	201	12	same	same	ADJ
ap-658	201	13	number	number	NOUN
ap-658	201	14	.	.	PUNCT
ap-658	202	1	note	note	VERB
ap-658	202	2	that	that	SCONJ
ap-658	202	3	6	6	NUM
ap-658	202	4	-	-	PUNCT
ap-658	202	5	noded	nod	VERB
ap-658	202	6	elements	element	NOUN
ap-658	202	7	with	with	ADP
ap-658	202	8	the	the	DET
ap-658	202	9	7	7	NUM
ap-658	202	10	-	-	PUNCT
ap-658	202	11	point	point	NOUN
ap-658	202	12	integration	integration	NOUN
ap-658	202	13	rule	rule	NOUN
ap-658	202	14	were	be	AUX
ap-658	202	15	used	use	VERB
ap-658	202	16	so	so	SCONJ
ap-658	202	17	that	that	SCONJ
ap-658	202	18	the	the	DET
ap-658	202	19	results	result	NOUN
ap-658	202	20	displayed	display	VERB
ap-658	202	21	in	in	ADP
ap-658	202	22	figs	fig	NOUN
ap-658	202	23	.	.	PUNCT
ap-658	203	1	11–12	11–12	NUM
ap-658	203	2	correspond	correspond	NOUN
ap-658	203	3	to	to	PART
ap-658	203	4	element	element	VERB
ap-658	203	5	averages	average	NOUN
ap-658	203	6	.	.	PUNCT
ap-658	204	1	fig	fig	NOUN
ap-658	204	2	.	.	PUNCT
ap-658	205	1	11	11	NUM
ap-658	205	2	indeed	indeed	ADV
ap-658	205	3	confirms	confirm	VERB
ap-658	205	4	large	large	ADJ
ap-658	205	5	non	non	ADJ
ap-658	205	6	-	-	NOUN
ap-658	205	7	homogeneity	homogeneity	NOUN
ap-658	205	8	in	in	ADP
ap-658	205	9	the	the	DET
ap-658	205	10	distribution	distribution	NOUN
ap-658	205	11	of	of	ADP
ap-658	205	12	local	local	ADJ
ap-658	205	13	fields	field	NOUN
ap-658	205	14	.	.	PUNCT
ap-658	206	1	it	it	PRON
ap-658	206	2	also	also	ADV
ap-658	206	3	shows	show	VERB
ap-658	206	4	an	an	DET
ap-658	206	5	increase	increase	NOUN
ap-658	206	6	in	in	ADP
ap-658	206	7	the	the	DET
ap-658	206	8	rate	rate	NOUN
ap-658	206	9	of	of	ADP
ap-658	206	10	deformation	deformation	NOUN
ap-658	206	11	of	of	ADP
ap-658	206	12	the	the	DET
ap-658	206	13	volume	volume	NOUN
ap-658	206	14	average	average	NOUN
ap-658	206	15	of	of	ADP
ap-658	206	16	matrix	matrix	NOUN
ap-658	206	17	shear	shear	NOUN
ap-658	206	18	strain	strain	NOUN
ap-658	206	19	in	in	ADP
ap-658	206	20	comparison	comparison	NOUN
ap-658	206	21	with	with	ADP
ap-658	206	22	the	the	DET
ap-658	206	23	response	response	NOUN
ap-658	206	24	of	of	ADP
ap-658	206	25	the	the	DET
ap-658	206	26	pure	pure	ADJ
ap-658	206	27	matrix	matrix	NOUN
ap-658	206	28	under	under	ADP
ap-658	206	29	the	the	DET
ap-658	206	30	same	same	ADJ
ap-658	206	31	loading	loading	NOUN
ap-658	206	32	conditions	condition	NOUN
ap-658	206	33	.	.	PUNCT
ap-658	207	1	this	this	PRON
ap-658	207	2	is	be	AUX
ap-658	207	3	clearly	clearly	ADV
ap-658	207	4	due	due	ADJ
ap-658	207	5	to	to	ADP
ap-658	207	6	the	the	DET
ap-658	207	7	heterogeneity	heterogeneity	NOUN
ap-658	207	8	of	of	ADP
ap-658	207	9	the	the	DET
ap-658	207	10	material	material	NOUN
ap-658	207	11	system	system	NOUN
ap-658	207	12	and	and	CCONJ
ap-658	207	13	is	be	AUX
ap-658	207	14	consequently	consequently	ADV
ap-658	207	15	due	due	ADJ
ap-658	207	16	to	to	ADP
ap-658	207	17	the	the	DET
ap-658	207	18	required	require	VERB
ap-658	207	19	compatibility	compatibility	NOUN
ap-658	207	20	of	of	ADP
ap-658	207	21	local	local	ADJ
ap-658	207	22	and	and	CCONJ
ap-658	207	23	overall	overall	ADJ
ap-658	207	24	fields	field	NOUN
ap-658	207	25	.	.	PUNCT
ap-658	208	1	this	this	DET
ap-658	208	2	condition	condition	NOUN
ap-658	208	3	inevitably	inevitably	ADV
ap-658	208	4	leads	lead	VERB
ap-658	208	5	to	to	ADP
ap-658	208	6	an	an	DET
ap-658	208	7	increase	increase	NOUN
ap-658	208	8	in	in	ADP
ap-658	208	9	reference	reference	NOUN
ap-658	208	10	yield	yield	NOUN
ap-658	208	11	stress	stress	NOUN
ap-658	208	12	of	of	ADP
ap-658	208	13	the	the	DET
ap-658	208	14	matrix	matrix	NOUN
ap-658	208	15	phase	phase	NOUN
ap-658	208	16	provided	provide	VERB
ap-658	208	17	by	by	ADP
ap-658	208	18	the	the	DET
ap-658	208	19	hs	hs	PROPN
ap-658	208	20	procedure	procedure	NOUN
ap-658	208	21	.	.	PUNCT
ap-658	209	1	recall	recall	VERB
ap-658	209	2	also	also	ADV
ap-658	209	3	the	the	DET
ap-658	209	4	laminate	laminate	ADJ
ap-658	209	5	response	response	NOUN
ap-658	209	6	studied	study	VERB
ap-658	209	7	in	in	ADP
ap-658	209	8	the	the	DET
ap-658	209	9	first	first	ADJ
ap-658	209	10	example	example	NOUN
ap-658	209	11	,	,	PUNCT
ap-658	209	12	figs	fig	NOUN
ap-658	209	13	.	.	PUNCT
ap-658	210	1	4–6	4–6	X
ap-658	210	2	.	.	PUNCT
ap-658	211	1	the	the	DET
ap-658	211	2	expected	expect	VERB
ap-658	211	3	increase	increase	NOUN
ap-658	211	4	in	in	ADP
ap-658	211	5	the	the	DET
ap-658	211	6	volume	volume	NOUN
ap-658	211	7	average	average	NOUN
ap-658	211	8	of	of	ADP
ap-658	211	9	the	the	DET
ap-658	211	10	matrix	matrix	NOUN
ap-658	211	11	yield	yield	NOUN
ap-658	211	12	stress	stress	NOUN
ap-658	211	13	,	,	PUNCT
ap-658	211	14	however	however	ADV
ap-658	211	15	,	,	PUNCT
ap-658	211	16	is	be	AUX
ap-658	211	17	not	not	PART
ap-658	211	18	observed	observe	VERB
ap-658	211	19	with	with	ADP
ap-658	211	20	the	the	DET
ap-658	211	21	finite	finite	PROPN
ap-658	211	22	element	element	NOUN
ap-658	211	23	calculations	calculation	NOUN
ap-658	211	24	even	even	ADV
ap-658	211	25	for	for	ADP
ap-658	211	26	such	such	DET
ap-658	211	27	a	a	DET
ap-658	211	28	simple	simple	ADJ
ap-658	211	29	geometry	geometry	NOUN
ap-658	211	30	.	.	PUNCT
ap-658	212	1	this	this	PRON
ap-658	212	2	can	can	AUX
ap-658	212	3	be	be	AUX
ap-658	212	4	attributed	attribute	VERB
ap-658	212	5	to	to	ADP
ap-658	212	6	the	the	DET
ap-658	212	7	highly	highly	ADV
ap-658	212	8	nonlinear	nonlinear	ADJ
ap-658	212	9	dependency	dependency	NOUN
ap-658	212	10	of	of	ADP
ap-658	212	11	the	the	DET
ap-658	212	12	yield	yield	NOUN
ap-658	212	13	stress	stress	NOUN
ap-658	212	14	on	on	ADP
ap-658	212	15	the	the	DET
ap-658	212	16	applied	apply	VERB
ap-658	212	17	rate	rate	NOUN
ap-658	212	18	of	of	ADP
ap-658	212	19	deformation	deformation	NOUN
ap-658	212	20	provided	provide	VERB
ap-658	212	21	by	by	ADP
ap-658	212	22	the	the	DET
ap-658	212	23	leonov	leonov	NOUN
ap-658	212	24	model	model	NOUN
ap-658	212	25	.	.	PUNCT
ap-658	213	1	also	also	ADV
ap-658	213	2	note	note	VERB
ap-658	213	3	that	that	SCONJ
ap-658	213	4	the	the	DET
ap-658	213	5	elements	element	NOUN
ap-658	213	6	found	find	VERB
ap-658	213	7	in	in	ADP
ap-658	213	8	a	a	DET
ap-658	213	9	closer	close	ADJ
ap-658	213	10	206	206	NUM
ap-658	213	11	©	©	PROPN
ap-658	213	12	czech	czech	PROPN
ap-658	213	13	technical	technical	PROPN
ap-658	213	14	university	university	PROPN
ap-658	213	15	publishing	publishing	NOUN
ap-658	213	16	house	house	NOUN
ap-658	213	17	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	213	18	acta	acta	PROPN
ap-658	213	19	polytechnica	polytechnica	PROPN
ap-658	213	20	vol	vol	NOUN
ap-658	213	21	.	.	PROPN
ap-658	213	22	44	44	NUM
ap-658	213	23	no.5–6/2004	no.5–6/2004	PROPN
ap-658	213	24	fig	fig	NOUN
ap-658	213	25	9	9	NUM
ap-658	213	26	:	:	PUNCT
ap-658	213	27	experiments	experiment	NOUN
ap-658	213	28	vs.	vs.	ADP
ap-658	213	29	numerical	numerical	PROPN
ap-658	213	30	simulations	simulation	NOUN
ap-658	213	31	fig	fig	NOUN
ap-658	213	32	.	.	PUNCT
ap-658	214	1	10	10	NUM
ap-658	214	2	:	:	PUNCT
ap-658	214	3	a	a	DET
ap-658	214	4	simple	simple	ADJ
ap-658	214	5	finite	finite	ADJ
ap-658	214	6	element	element	NOUN
ap-658	214	7	mesh	mesh	NOUN
ap-658	214	8	with	with	ADP
ap-658	214	9	groups	group	NOUN
ap-658	214	10	of	of	ADP
ap-658	214	11	elements	element	NOUN
ap-658	214	12	fig	fig	NOUN
ap-658	214	13	.	.	PUNCT
ap-658	215	1	11	11	NUM
ap-658	215	2	:	:	PUNCT
ap-658	215	3	element	element	NOUN
ap-658	215	4	averages	average	NOUN
ap-658	215	5	of	of	ADP
ap-658	215	6	matrix	matrix	NOUN
ap-658	215	7	strains	strain	VERB
ap-658	215	8	for	for	ADP
ap-658	215	9	�	�	NOUN
ap-658	215	10	e12	e12	NOUN
ap-658	215	11	4	4	NUM
ap-658	215	12	110	110	NUM
ap-658	215	13	�	�	PROPN
ap-658	215	14	�	�	PROPN
ap-658	215	15	�	�	PROPN
ap-658	215	16	s	s	PART
ap-658	215	17	fig	fig	NOUN
ap-658	215	18	.	.	PUNCT
ap-658	216	1	12	12	NUM
ap-658	216	2	:	:	PUNCT
ap-658	216	3	element	element	NOUN
ap-658	216	4	averages	average	NOUN
ap-658	216	5	of	of	ADP
ap-658	216	6	matrix	matrix	NOUN
ap-658	216	7	stresses	stress	NOUN
ap-658	216	8	for	for	ADP
ap-658	216	9	�	�	NOUN
ap-658	216	10	e12	e12	NOUN
ap-658	216	11	4	4	NUM
ap-658	216	12	110	110	NUM
ap-658	216	13	�	�	PROPN
ap-658	216	14	�	�	PROPN
ap-658	216	15	�	�	PROPN
ap-658	216	16	s	s	PART
ap-658	216	17	vicinity	vicinity	NOUN
ap-658	216	18	of	of	ADP
ap-658	216	19	the	the	DET
ap-658	216	20	fiber	fiber	NOUN
ap-658	216	21	experience	experience	NOUN
ap-658	216	22	a	a	DET
ap-658	216	23	considerably	considerably	ADV
ap-658	216	24	slower	slow	ADJ
ap-658	216	25	response	response	NOUN
ap-658	216	26	that	that	SCONJ
ap-658	216	27	those	those	PRON
ap-658	216	28	located	locate	VERB
ap-658	216	29	away	away	ADV
ap-658	216	30	from	from	ADP
ap-658	216	31	the	the	DET
ap-658	216	32	fiber	fiber	NOUN
ap-658	216	33	phase	phase	NOUN
ap-658	216	34	.	.	PUNCT
ap-658	217	1	this	this	PRON
ap-658	217	2	eventually	eventually	ADV
ap-658	217	3	results	result	VERB
ap-658	217	4	in	in	ADP
ap-658	217	5	a	a	DET
ap-658	217	6	softer	soft	ADJ
ap-658	217	7	response	response	NOUN
ap-658	217	8	in	in	ADP
ap-658	217	9	comparison	comparison	NOUN
ap-658	217	10	with	with	ADP
ap-658	217	11	the	the	DET
ap-658	217	12	pure	pure	ADJ
ap-658	217	13	matrix	matrix	NOUN
ap-658	217	14	.	.	PUNCT
ap-658	218	1	clearly	clearly	ADV
ap-658	218	2	,	,	PUNCT
ap-658	218	3	such	such	DET
ap-658	218	4	a	a	DET
ap-658	218	5	behavior	behavior	NOUN
ap-658	218	6	can	can	AUX
ap-658	218	7	not	not	PART
ap-658	218	8	be	be	AUX
ap-658	218	9	represented	represent	VERB
ap-658	218	10	by	by	ADP
ap-658	218	11	any	any	PRON
ap-658	218	12	of	of	ADP
ap-658	218	13	the	the	DET
ap-658	218	14	existing	exist	VERB
ap-658	218	15	localization	localization	NOUN
ap-658	218	16	rules	rule	NOUN
ap-658	218	17	dealing	deal	VERB
ap-658	218	18	with	with	ADP
ap-658	218	19	two	two	NUM
ap-658	218	20	-	-	PUNCT
ap-658	218	21	phase	phase	NOUN
ap-658	218	22	material	material	NOUN
ap-658	218	23	systems	system	NOUN
ap-658	218	24	and	and	CCONJ
ap-658	218	25	piecewise	piecewise	NOUN
ap-658	218	26	uniform	uniform	ADJ
ap-658	218	27	variation	variation	NOUN
ap-658	218	28	of	of	ADP
ap-658	218	29	local	local	ADJ
ap-658	218	30	fields	field	NOUN
ap-658	218	31	,	,	PUNCT
ap-658	218	32	at	at	ADP
ap-658	218	33	least	least	ADJ
ap-658	218	34	for	for	ADP
ap-658	218	35	the	the	DET
ap-658	218	36	present	present	ADJ
ap-658	218	37	material	material	NOUN
ap-658	218	38	model	model	NOUN
ap-658	218	39	.	.	PUNCT
ap-658	219	1	the	the	DET
ap-658	219	2	conclusions	conclusion	NOUN
ap-658	219	3	of	of	ADP
ap-658	219	4	this	this	DET
ap-658	219	5	case	case	NOUN
ap-658	219	6	study	study	NOUN
ap-658	219	7	can	can	AUX
ap-658	219	8	,	,	PUNCT
ap-658	219	9	in	in	ADP
ap-658	219	10	principle	principle	NOUN
ap-658	219	11	be	be	AUX
ap-658	219	12	,	,	PUNCT
ap-658	219	13	extended	extend	VERB
ap-658	219	14	by	by	ADP
ap-658	219	15	analogy	analogy	NOUN
ap-658	219	16	to	to	ADP
ap-658	219	17	more	more	ADV
ap-658	219	18	complex	complex	ADJ
ap-658	219	19	periodic	periodic	ADJ
ap-658	219	20	unit	unit	NOUN
ap-658	219	21	cells	cell	NOUN
ap-658	219	22	such	such	ADJ
ap-658	219	23	as	as	ADP
ap-658	219	24	those	those	PRON
ap-658	219	25	displayed	display	VERB
ap-658	219	26	in	in	ADP
ap-658	219	27	fig	fig	NOUN
ap-658	219	28	.	.	PUNCT
ap-658	220	1	7	7	X
ap-658	220	2	.	.	PUNCT
ap-658	220	3	to	to	PART
ap-658	220	4	illustrate	illustrate	VERB
ap-658	220	5	the	the	DET
ap-658	220	6	governing	govern	VERB
ap-658	220	7	mechanism	mechanism	NOUN
ap-658	220	8	responsible	responsible	ADJ
ap-658	220	9	for	for	ADP
ap-658	220	10	this	this	DET
ap-658	220	11	fact	fact	NOUN
ap-658	220	12	,	,	PUNCT
ap-658	220	13	the	the	DET
ap-658	220	14	distribution	distribution	NOUN
ap-658	220	15	of	of	ADP
ap-658	220	16	local	local	ADJ
ap-658	220	17	equivalent	equivalent	ADJ
ap-658	220	18	strain	strain	NOUN
ap-658	220	19	in	in	ADP
ap-658	220	20	a	a	DET
ap-658	220	21	hexagonal	hexagonal	ADJ
ap-658	220	22	array	array	NOUN
ap-658	220	23	,	,	PUNCT
ap-658	220	24	5and	5and	NUM
ap-658	220	25	10	10	NUM
ap-658	220	26	-	-	PUNCT
ap-658	220	27	fiber	fiber	NOUN
ap-658	220	28	unit	unit	NOUN
ap-658	220	29	cells	cell	NOUN
ap-658	220	30	is	be	AUX
ap-658	220	31	shown	show	VERB
ap-658	220	32	in	in	ADP
ap-658	220	33	fig	fig	NOUN
ap-658	220	34	.	.	PUNCT
ap-658	221	1	13	13	NUM
ap-658	221	2	.	.	PUNCT
ap-658	222	1	each	each	DET
ap-658	222	2	microstructure	microstructure	NOUN
ap-658	222	3	was	be	AUX
ap-658	222	4	discretized	discretize	VERB
ap-658	222	5	with	with	ADP
ap-658	222	6	6	6	NUM
ap-658	222	7	-	-	PUNCT
ap-658	222	8	noded	nod	VERB
ap-658	222	9	triangular	triangular	NOUN
ap-658	222	10	elements	element	NOUN
ap-658	222	11	with	with	ADP
ap-658	222	12	7	7	NUM
ap-658	222	13	integration	integration	NOUN
ap-658	222	14	points	point	NOUN
ap-658	222	15	.	.	PUNCT
ap-658	223	1	in	in	ADP
ap-658	223	2	particular	particular	ADJ
ap-658	223	3	,	,	PUNCT
ap-658	223	4	the	the	DET
ap-658	223	5	plotted	plot	VERB
ap-658	223	6	local	local	ADJ
ap-658	223	7	fields	field	NOUN
ap-658	223	8	correspond	correspond	VERB
ap-658	223	9	to	to	ADP
ap-658	223	10	the	the	DET
ap-658	223	11	value	value	NOUN
ap-658	223	12	of	of	ADP
ap-658	223	13	overall	overall	ADJ
ap-658	223	14	deformation	deformation	NOUN
ap-658	223	15	e12	e12	NOUN
ap-658	223	16	�	�	PROPN
ap-658	223	17	0,1	0,1	NUM
ap-658	223	18	.	.	PUNCT
ap-658	224	1	for	for	ADP
ap-658	224	2	all	all	DET
ap-658	224	3	the	the	DET
ap-658	224	4	studied	study	VERB
ap-658	224	5	microstructures	microstructure	NOUN
ap-658	224	6	,	,	PUNCT
ap-658	224	7	the	the	DET
ap-658	224	8	final	final	ADJ
ap-658	224	9	deformation	deformation	NOUN
ap-658	224	10	pattern	pattern	NOUN
ap-658	224	11	has	have	VERB
ap-658	224	12	the	the	DET
ap-658	224	13	character	character	NOUN
ap-658	224	14	of	of	ADP
ap-658	224	15	a	a	DET
ap-658	224	16	localized	localize	VERB
ap-658	224	17	shear	shear	NOUN
ap-658	224	18	layer	layer	NOUN
ap-658	224	19	that	that	PRON
ap-658	224	20	is	be	AUX
ap-658	224	21	responsible	responsible	ADJ
ap-658	224	22	for	for	ADP
ap-658	224	23	the	the	DET
ap-658	224	24	plateau	plateau	NOUN
ap-658	224	25	regions	region	NOUN
ap-658	224	26	clearly	clearly	ADV
ap-658	224	27	visible	visible	ADJ
ap-658	224	28	in	in	ADP
ap-658	224	29	the	the	DET
ap-658	224	30	graphs	graph	NOUN
ap-658	224	31	depicted	depict	VERB
ap-658	224	32	in	in	ADP
ap-658	224	33	figs	fig	NOUN
ap-658	224	34	.	.	PUNCT
ap-658	225	1	3	3	NUM
ap-658	225	2	-	-	SYM
ap-658	225	3	4	4	NUM
ap-658	225	4	.	.	PUNCT
ap-658	226	1	this	this	DET
ap-658	226	2	behavior	behavior	NOUN
ap-658	226	3	simply	simply	ADV
ap-658	226	4	can	can	AUX
ap-658	226	5	not	not	PART
ap-658	226	6	be	be	AUX
ap-658	226	7	reliably	reliably	ADV
ap-658	226	8	captured	capture	VERB
ap-658	226	9	by	by	ADP
ap-658	226	10	a	a	DET
ap-658	226	11	two	two	NUM
ap-658	226	12	-	-	PUNCT
ap-658	226	13	point	point	NOUN
ap-658	226	14	averaging	averaging	NOUN
ap-658	226	15	scheme	scheme	NOUN
ap-658	226	16	and	and	CCONJ
ap-658	226	17	finally	finally	ADV
ap-658	226	18	leads	lead	VERB
ap-658	226	19	to	to	ADP
ap-658	226	20	erroneous	erroneous	ADJ
ap-658	226	21	response	response	NOUN
ap-658	226	22	of	of	ADP
ap-658	226	23	the	the	DET
ap-658	226	24	simplified	simplified	ADJ
ap-658	226	25	method	method	NOUN
ap-658	226	26	.	.	PUNCT
ap-658	227	1	note	note	VERB
ap-658	227	2	that	that	SCONJ
ap-658	227	3	a	a	DET
ap-658	227	4	quite	quite	ADV
ap-658	227	5	similar	similar	ADJ
ap-658	227	6	character	character	NOUN
ap-658	227	7	of	of	ADP
ap-658	227	8	the	the	DET
ap-658	227	9	overall	overall	ADJ
ap-658	227	10	response	response	NOUN
ap-658	227	11	appears	appear	VERB
ap-658	227	12	even	even	ADV
ap-658	227	13	for	for	ADP
ap-658	227	14	discretization	discretization	NOUN
ap-658	227	15	of	of	ADP
ap-658	227	16	the	the	DET
ap-658	227	17	structure	structure	NOUN
ap-658	227	18	with	with	ADP
ap-658	227	19	three	three	NUM
ap-658	227	20	-	-	PUNCT
ap-658	227	21	noded	nod	VERB
ap-658	227	22	constant	constant	ADJ
ap-658	227	23	strain	strain	NOUN
ap-658	227	24	triangular	triangular	NOUN
ap-658	227	25	elements	element	NOUN
ap-658	227	26	,	,	PUNCT
ap-658	227	27	see	see	VERB
ap-658	227	28	fig	fig	NOUN
ap-658	227	29	.	.	PUNCT
ap-658	228	1	4	4	X
ap-658	228	2	.	.	X
ap-658	228	3	in	in	ADP
ap-658	228	4	this	this	DET
ap-658	228	5	case	case	NOUN
ap-658	228	6	,	,	PUNCT
ap-658	228	7	however	however	ADV
ap-658	228	8	,	,	PUNCT
ap-658	228	9	the	the	DET
ap-658	228	10	approximation	approximation	NOUN
ap-658	228	11	is	be	AUX
ap-658	228	12	not	not	PART
ap-658	228	13	rich	rich	ADJ
ap-658	228	14	enough	enough	ADV
ap-658	228	15	to	to	PART
ap-658	228	16	correctly	correctly	ADV
ap-658	228	17	capture	capture	VERB
ap-658	228	18	the	the	DET
ap-658	228	19	fact	fact	NOUN
ap-658	228	20	that	that	SCONJ
ap-658	228	21	the	the	DET
ap-658	228	22	formed	form	VERB
ap-658	228	23	shear	shear	NOUN
ap-658	228	24	band	band	NOUN
ap-658	228	25	prohibits	prohibit	VERB
ap-658	228	26	interaction	interaction	NOUN
ap-658	228	27	of	of	ADP
ap-658	228	28	the	the	DET
ap-658	228	29	fibers	fiber	NOUN
ap-658	228	30	with	with	ADP
ap-658	228	31	the	the	DET
ap-658	228	32	matrix	matrix	NOUN
ap-658	228	33	phase	phase	NOUN
ap-658	228	34	,	,	PUNCT
ap-658	228	35	fig	fig	NOUN
ap-658	228	36	.	.	PUNCT
ap-658	229	1	15	15	NUM
ap-658	229	2	.	.	PUNCT
ap-658	230	1	an	an	DET
ap-658	230	2	additional	additional	ADJ
ap-658	230	3	explanation	explanation	NOUN
ap-658	230	4	comes	come	VERB
ap-658	230	5	from	from	ADP
ap-658	230	6	the	the	DET
ap-658	230	7	basic	basic	ADJ
ap-658	230	8	assumption	assumption	NOUN
ap-658	230	9	of	of	ADP
ap-658	230	10	the	the	DET
ap-658	230	11	selected	select	VERB
ap-658	230	12	material	material	NOUN
ap-658	230	13	model	model	NOUN
ap-658	230	14	.	.	PUNCT
ap-658	231	1	recall	recall	VERB
ap-658	231	2	that	that	SCONJ
ap-658	231	3	the	the	DET
ap-658	231	4	model	model	NOUN
ap-658	231	5	draws	draw	VERB
ap-658	231	6	on	on	ADP
ap-658	231	7	the	the	DET
ap-658	231	8	nonlinear	nonlinear	ADJ
ap-658	231	9	viscoelastic	viscoelastic	ADJ
ap-658	231	10	response	response	NOUN
ap-658	231	11	to	to	PART
ap-658	231	12	be	be	AUX
ap-658	231	13	limited	limit	VERB
ap-658	231	14	purely	purely	ADV
ap-658	231	15	to	to	ADP
ap-658	231	16	the	the	DET
ap-658	231	17	deviatoric	deviatoric	ADJ
ap-658	231	18	part	part	NOUN
ap-658	231	19	of	of	ADP
ap-658	231	20	©	©	PROPN
ap-658	231	21	czech	czech	PROPN
ap-658	231	22	technical	technical	PROPN
ap-658	231	23	university	university	PROPN
ap-658	231	24	publishing	publishing	NOUN
ap-658	231	25	house	house	NOUN
ap-658	231	26	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	231	27	207	207	NUM
ap-658	231	28	acta	acta	PROPN
ap-658	231	29	polytechnica	polytechnica	PROPN
ap-658	231	30	vol	vol	NOUN
ap-658	231	31	.	.	PROPN
ap-658	232	1	44	44	NUM
ap-658	232	2	no.5–6/2004	no.5–6/2004	PROPN
ap-658	232	3	fig	fig	NOUN
ap-658	232	4	.	.	PUNCT
ap-658	233	1	13	13	NUM
ap-658	233	2	:	:	PUNCT
ap-658	233	3	distribution	distribution	NOUN
ap-658	233	4	of	of	ADP
ap-658	233	5	local	local	ADJ
ap-658	233	6	equivalent	equivalent	ADJ
ap-658	233	7	strain	strain	NOUN
ap-658	233	8	fields	field	NOUN
ap-658	233	9	for	for	ADP
ap-658	233	10	discretization	discretization	NOUN
ap-658	233	11	with	with	ADP
ap-658	233	12	6	6	NUM
ap-658	233	13	-	-	PUNCT
ap-658	233	14	noded	nod	VERB
ap-658	233	15	elements	element	NOUN
ap-658	233	16	:	:	PUNCT
ap-658	233	17	(	(	PUNCT
ap-658	233	18	a	a	X
ap-658	233	19	)	)	PUNCT
ap-658	233	20	hexagonal	hexagonal	ADJ
ap-658	233	21	array	array	NOUN
ap-658	233	22	,	,	PUNCT
ap-658	233	23	(	(	PUNCT
ap-658	233	24	b	b	X
ap-658	233	25	)	)	PUNCT
ap-658	233	26	5	5	NUM
ap-658	233	27	-	-	PUNCT
ap-658	233	28	fiber	fiber	NOUN
ap-658	233	29	puc	puc	NOUN
ap-658	233	30	,	,	PUNCT
ap-658	233	31	(	(	PUNCT
ap-658	233	32	c	c	NOUN
ap-658	233	33	)	)	PUNCT
ap-658	233	34	10	10	NUM
ap-658	233	35	-	-	PUNCT
ap-658	233	36	fiber	fiber	NOUN
ap-658	233	37	puc	puc	NOUN
ap-658	233	38	fig	fig	NOUN
ap-658	233	39	.	.	PUNCT
ap-658	234	1	14	14	NUM
ap-658	234	2	:	:	PUNCT
ap-658	234	3	distribution	distribution	NOUN
ap-658	234	4	of	of	ADP
ap-658	234	5	local	local	ADJ
ap-658	234	6	equivalent	equivalent	ADJ
ap-658	234	7	strain	strain	NOUN
ap-658	234	8	fields	field	NOUN
ap-658	234	9	for	for	ADP
ap-658	234	10	discretization	discretization	NOUN
ap-658	234	11	with	with	ADP
ap-658	234	12	3	3	NUM
ap-658	234	13	-	-	PUNCT
ap-658	234	14	noded	nod	VERB
ap-658	234	15	elements	element	NOUN
ap-658	234	16	:	:	PUNCT
ap-658	234	17	(	(	PUNCT
ap-658	234	18	a	a	X
ap-658	234	19	)	)	PUNCT
ap-658	234	20	hexagonal	hexagonal	ADJ
ap-658	234	21	array	array	NOUN
ap-658	234	22	,	,	PUNCT
ap-658	234	23	(	(	PUNCT
ap-658	234	24	b	b	X
ap-658	234	25	)	)	PUNCT
ap-658	234	26	5	5	NUM
ap-658	234	27	-	-	PUNCT
ap-658	234	28	fiber	fiber	NOUN
ap-658	234	29	puc	puc	NOUN
ap-658	234	30	,	,	PUNCT
ap-658	234	31	(	(	PUNCT
ap-658	234	32	c	c	NOUN
ap-658	234	33	)	)	PUNCT
ap-658	234	34	10	10	NUM
ap-658	234	35	-	-	PUNCT
ap-658	234	36	fiber	fiber	NOUN
ap-658	234	37	puc	puc	NOUN
ap-658	234	38	fig	fig	NOUN
ap-658	234	39	.	.	PUNCT
ap-658	235	1	15	15	NUM
ap-658	235	2	:	:	PUNCT
ap-658	235	3	overall	overall	ADJ
ap-658	235	4	response	response	NOUN
ap-658	235	5	of	of	ADP
ap-658	235	6	optimized	optimize	VERB
ap-658	235	7	unit	unit	NOUN
ap-658	235	8	cells	cell	NOUN
ap-658	235	9	–	–	PUNCT
ap-658	235	10	effect	effect	NOUN
ap-658	235	11	of	of	ADP
ap-658	235	12	the	the	DET
ap-658	235	13	order	order	NOUN
ap-658	235	14	of	of	ADP
ap-658	235	15	discretization	discretization	NOUN
ap-658	235	16	the	the	DET
ap-658	235	17	stress	stress	NOUN
ap-658	235	18	-	-	PUNCT
ap-658	235	19	strain	strain	NOUN
ap-658	235	20	relationship	relationship	NOUN
ap-658	235	21	,	,	PUNCT
ap-658	235	22	while	while	SCONJ
ap-658	235	23	the	the	DET
ap-658	235	24	volumetric	volumetric	ADJ
ap-658	235	25	response	response	NOUN
ap-658	235	26	remains	remain	VERB
ap-658	235	27	elastic	elastic	ADJ
ap-658	235	28	.	.	PUNCT
ap-658	236	1	as	as	ADV
ap-658	236	2	often	often	ADV
ap-658	236	3	observed	observe	VERB
ap-658	236	4	with	with	ADP
ap-658	236	5	j2	j2	PROPN
ap-658	236	6	plasticity	plasticity	NOUN
ap-658	236	7	,	,	PUNCT
ap-658	236	8	this	this	PRON
ap-658	236	9	may	may	AUX
ap-658	236	10	eventually	eventually	ADV
ap-658	236	11	lead	lead	VERB
ap-658	236	12	to	to	ADP
ap-658	236	13	what	what	PRON
ap-658	236	14	we	we	PRON
ap-658	236	15	call	call	VERB
ap-658	236	16	volumetric	volumetric	NOUN
ap-658	236	17	locking	locking	NOUN
ap-658	236	18	and	and	CCONJ
ap-658	236	19	consequently	consequently	ADV
ap-658	236	20	to	to	PART
ap-658	236	21	substantially	substantially	ADV
ap-658	236	22	stiffer	stiffer	VERB
ap-658	236	23	response	response	NOUN
ap-658	236	24	when	when	SCONJ
ap-658	236	25	compared	compare	VERB
ap-658	236	26	to	to	ADP
ap-658	236	27	reality	reality	NOUN
ap-658	236	28	.	.	PUNCT
ap-658	237	1	this	this	PRON
ap-658	237	2	,	,	PUNCT
ap-658	237	3	in	in	ADP
ap-658	237	4	particular	particular	ADJ
ap-658	237	5	,	,	PUNCT
ap-658	237	6	suggests	suggest	VERB
ap-658	237	7	that	that	SCONJ
ap-658	237	8	even	even	ADV
ap-658	237	9	when	when	SCONJ
ap-658	237	10	using	use	VERB
ap-658	237	11	a	a	DET
ap-658	237	12	refined	refined	ADJ
ap-658	237	13	variant	variant	NOUN
ap-658	237	14	of	of	ADP
ap-658	237	15	the	the	DET
ap-658	237	16	tfa	tfa	NOUN
ap-658	237	17	method	method	NOUN
ap-658	237	18	–	–	PUNCT
ap-658	237	19	“	"	PUNCT
ap-658	237	20	multi	multi	ADJ
ap-658	237	21	-	-	ADJ
ap-658	237	22	point	point	ADJ
ap-658	237	23	incremental	incremental	ADJ
ap-658	237	24	homogenization	homogenization	NOUN
ap-658	237	25	”	"	PUNCT
ap-658	238	1	[	[	X
ap-658	238	2	10	10	NUM
ap-658	238	3	]	]	PUNCT
ap-658	238	4	–	–	PUNCT
ap-658	238	5	the	the	DET
ap-658	238	6	global	global	ADJ
ap-658	238	7	response	response	NOUN
ap-658	238	8	will	will	AUX
ap-658	238	9	probably	probably	ADV
ap-658	238	10	not	not	PART
ap-658	238	11	be	be	AUX
ap-658	238	12	captured	capture	VERB
ap-658	238	13	properly	properly	ADV
ap-658	238	14	.	.	PUNCT
ap-658	239	1	6	6	NUM
ap-658	239	2	conclusions	conclusion	NOUN
ap-658	239	3	the	the	DET
ap-658	239	4	paper	paper	NOUN
ap-658	239	5	reviewed	review	VERB
ap-658	239	6	essential	essential	ADJ
ap-658	239	7	steps	step	NOUN
ap-658	239	8	of	of	ADP
ap-658	239	9	first	first	ADJ
ap-658	239	10	order	order	NOUN
ap-658	239	11	homogenization	homogenization	NOUN
ap-658	239	12	procedure	procedure	NOUN
ap-658	239	13	implemented	implement	VERB
ap-658	239	14	in	in	ADP
ap-658	239	15	the	the	DET
ap-658	239	16	framework	framework	NOUN
ap-658	239	17	of	of	ADP
ap-658	239	18	the	the	DET
ap-658	239	19	finite	finite	ADJ
ap-658	239	20	element	element	NOUN
ap-658	239	21	method	method	NOUN
ap-658	239	22	.	.	PUNCT
ap-658	240	1	a	a	DET
ap-658	240	2	family	family	NOUN
ap-658	240	3	of	of	ADP
ap-658	240	4	so	so	ADV
ap-658	240	5	-	-	PUNCT
ap-658	240	6	called	call	VERB
ap-658	240	7	statistical	statistical	ADJ
ap-658	240	8	equivalent	equivalent	ADJ
ap-658	240	9	unit	unit	NOUN
ap-658	240	10	cells	cell	NOUN
ap-658	240	11	was	be	AUX
ap-658	240	12	introduced	introduce	VERB
ap-658	240	13	to	to	PART
ap-658	240	14	deal	deal	VERB
ap-658	240	15	with	with	ADP
ap-658	240	16	random	random	ADJ
ap-658	240	17	microstructures	microstructure	NOUN
ap-658	240	18	.	.	PUNCT
ap-658	241	1	unlike	unlike	ADP
ap-658	241	2	the	the	DET
ap-658	241	3	elastic	elastic	ADJ
ap-658	241	4	analysis	analysis	NOUN
ap-658	241	5	,	,	PUNCT
ap-658	241	6	where	where	SCONJ
ap-658	241	7	a	a	DET
ap-658	241	8	5	5	NUM
ap-658	241	9	-	-	PUNCT
ap-658	241	10	fiber	fiber	NOUN
ap-658	241	11	unit	unit	NOUN
ap-658	241	12	cell	cell	NOUN
ap-658	241	13	was	be	AUX
ap-658	241	14	found	find	VERB
ap-658	241	15	sufficient	sufficient	ADJ
ap-658	241	16	to	to	PART
ap-658	241	17	arrive	arrive	VERB
ap-658	241	18	at	at	ADP
ap-658	241	19	reliable	reliable	ADJ
ap-658	241	20	estimates	estimate	NOUN
ap-658	241	21	of	of	ADP
ap-658	241	22	homogenized	homogenized	ADJ
ap-658	241	23	properties	property	NOUN
ap-658	241	24	[	[	X
ap-658	241	25	16	16	NUM
ap-658	241	26	,	,	PUNCT
ap-658	241	27	17	17	NUM
ap-658	241	28	]	]	PUNCT
ap-658	241	29	at	at	ADP
ap-658	241	30	least	least	ADJ
ap-658	241	31	a	a	DET
ap-658	241	32	10	10	NUM
ap-658	241	33	-	-	PUNCT
ap-658	241	34	fiber	fiber	NOUN
ap-658	241	35	unit	unit	NOUN
ap-658	241	36	cell	cell	NOUN
ap-658	241	37	is	be	AUX
ap-658	241	38	needed	need	VERB
ap-658	241	39	when	when	SCONJ
ap-658	241	40	highly	highly	ADV
ap-658	241	41	non	non	ADJ
ap-658	241	42	-	-	ADJ
ap-658	241	43	homogeneous	homogeneous	ADJ
ap-658	241	44	evolution	evolution	NOUN
ap-658	241	45	of	of	ADP
ap-658	241	46	local	local	ADJ
ap-658	241	47	fields	field	NOUN
ap-658	241	48	may	may	AUX
ap-658	241	49	occur	occur	VERB
ap-658	241	50	.	.	PUNCT
ap-658	242	1	recall	recall	VERB
ap-658	242	2	the	the	DET
ap-658	242	3	formation	formation	NOUN
ap-658	242	4	of	of	ADP
ap-658	242	5	shear	shear	NOUN
ap-658	242	6	bands	band	NOUN
ap-658	242	7	displayed	display	VERB
ap-658	242	8	in	in	ADP
ap-658	242	9	figs	fig	NOUN
ap-658	242	10	.	.	PUNCT
ap-658	243	1	13	13	NUM
ap-658	243	2	,	,	PUNCT
ap-658	243	3	14	14	NUM
ap-658	243	4	and	and	CCONJ
ap-658	243	5	corresponding	correspond	VERB
ap-658	243	6	overall	overall	ADJ
ap-658	243	7	response	response	NOUN
ap-658	243	8	plotted	plot	VERB
ap-658	243	9	in	in	ADP
ap-658	243	10	fig	fig	NOUN
ap-658	243	11	.	.	PUNCT
ap-658	244	1	15	15	NUM
ap-658	244	2	.	.	PUNCT
ap-658	245	1	the	the	DET
ap-658	245	2	existence	existence	NOUN
ap-658	245	3	of	of	ADP
ap-658	245	4	shear	shear	NOUN
ap-658	245	5	bands	band	NOUN
ap-658	245	6	,	,	PUNCT
ap-658	245	7	zones	zone	NOUN
ap-658	245	8	of	of	ADP
ap-658	245	9	highly	highly	ADV
ap-658	245	10	localized	localized	ADJ
ap-658	245	11	deformation	deformation	NOUN
ap-658	245	12	,	,	PUNCT
ap-658	245	13	on	on	ADP
ap-658	245	14	the	the	DET
ap-658	245	15	other	other	ADJ
ap-658	245	16	hand	hand	NOUN
ap-658	245	17	,	,	PUNCT
ap-658	245	18	may	may	AUX
ap-658	245	19	raise	raise	VERB
ap-658	245	20	a	a	DET
ap-658	245	21	question	question	NOUN
ap-658	245	22	about	about	ADP
ap-658	245	23	mesh	mesh	NOUN
ap-658	245	24	objectivity	objectivity	NOUN
ap-658	245	25	when	when	SCONJ
ap-658	245	26	local	local	ADJ
ap-658	245	27	formulation	formulation	NOUN
ap-658	245	28	is	be	AUX
ap-658	245	29	used	use	VERB
ap-658	245	30	.	.	PUNCT
ap-658	246	1	it	it	PRON
ap-658	246	2	is	be	AUX
ap-658	246	3	worth	worth	ADJ
ap-658	246	4	noting	note	VERB
ap-658	246	5	that	that	SCONJ
ap-658	246	6	in	in	ADP
ap-658	246	7	the	the	DET
ap-658	246	8	present	present	ADJ
ap-658	246	9	study	study	NOUN
ap-658	246	10	the	the	DET
ap-658	246	11	size	size	NOUN
ap-658	246	12	of	of	ADP
ap-658	246	13	the	the	DET
ap-658	246	14	shear	shear	NOUN
ap-658	246	15	band	band	NOUN
ap-658	246	16	is	be	AUX
ap-658	246	17	explicitly	explicitly	ADV
ap-658	246	18	given	give	VERB
ap-658	246	19	by	by	ADP
ap-658	246	20	the	the	DET
ap-658	246	21	underlying	underlie	VERB
ap-658	246	22	microstructure	microstructure	NOUN
ap-658	246	23	.	.	PUNCT
ap-658	247	1	clearly	clearly	ADV
ap-658	247	2	,	,	PUNCT
ap-658	247	3	when	when	SCONJ
ap-658	247	4	refining	refine	VERB
ap-658	247	5	the	the	DET
ap-658	247	6	finite	finite	PROPN
ap-658	247	7	element	element	NOUN
ap-658	247	8	mesh	mesh	NOUN
ap-658	247	9	such	such	DET
ap-658	247	10	a	a	DET
ap-658	247	11	shear	shear	NOUN
ap-658	247	12	band	band	NOUN
ap-658	247	13	will	will	AUX
ap-658	247	14	be	be	AUX
ap-658	247	15	captured	capture	VERB
ap-658	247	16	more	more	ADV
ap-658	247	17	accurately	accurately	ADV
ap-658	247	18	but	but	CCONJ
ap-658	247	19	will	will	AUX
ap-658	247	20	not	not	PART
ap-658	247	21	depend	depend	VERB
ap-658	247	22	on	on	ADP
ap-658	247	23	the	the	DET
ap-658	247	24	size	size	NOUN
ap-658	247	25	of	of	ADP
ap-658	247	26	the	the	DET
ap-658	247	27	elements	element	NOUN
ap-658	247	28	and	and	CCONJ
ap-658	247	29	will	will	AUX
ap-658	247	30	always	always	ADV
ap-658	247	31	attend	attend	VERB
ap-658	247	32	a	a	DET
ap-658	247	33	finite	finite	ADJ
ap-658	247	34	depth	depth	NOUN
ap-658	247	35	.	.	PUNCT
ap-658	248	1	regularization	regularization	NOUN
ap-658	248	2	from	from	ADP
ap-658	248	3	the	the	DET
ap-658	248	4	mathematical	mathematical	ADJ
ap-658	248	5	point	point	NOUN
ap-658	248	6	of	of	ADP
ap-658	248	7	view	view	NOUN
ap-658	248	8	is	be	AUX
ap-658	248	9	thus	thus	ADV
ap-658	248	10	not	not	PART
ap-658	248	11	needed	need	VERB
ap-658	248	12	.	.	PUNCT
ap-658	249	1	nevertheless	nevertheless	ADV
ap-658	249	2	,	,	PUNCT
ap-658	249	3	problems	problem	NOUN
ap-658	249	4	might	might	AUX
ap-658	249	5	be	be	AUX
ap-658	249	6	encountered	encounter	VERB
ap-658	249	7	for	for	ADP
ap-658	249	8	relatively	relatively	ADV
ap-658	249	9	coarse	coarse	ADJ
ap-658	249	10	meshes	mesh	NOUN
ap-658	249	11	or	or	CCONJ
ap-658	249	12	for	for	ADP
ap-658	249	13	microstructures	microstructure	NOUN
ap-658	249	14	with	with	ADP
ap-658	249	15	a	a	DET
ap-658	249	16	rather	rather	ADV
ap-658	249	17	low	low	ADJ
ap-658	249	18	value	value	NOUN
ap-658	249	19	of	of	ADP
ap-658	249	20	the	the	DET
ap-658	249	21	fiber	fiber	NOUN
ap-658	249	22	volume	volume	NOUN
ap-658	249	23	fraction	fraction	NOUN
ap-658	249	24	.	.	PUNCT
ap-658	250	1	in	in	ADP
ap-658	250	2	this	this	DET
ap-658	250	3	regard	regard	NOUN
ap-658	250	4	,	,	PUNCT
ap-658	250	5	owing	owe	VERB
ap-658	250	6	to	to	ADP
ap-658	250	7	the	the	DET
ap-658	250	8	material	material	NOUN
ap-658	250	9	model	model	NOUN
ap-658	250	10	used	use	VERB
ap-658	250	11	in	in	ADP
ap-658	250	12	this	this	DET
ap-658	250	13	study	study	NOUN
ap-658	250	14	a	a	DET
ap-658	250	15	phenomenon	phenomenon	NOUN
ap-658	250	16	known	know	VERB
ap-658	250	17	as	as	ADP
ap-658	250	18	volumetric	volumetric	NOUN
ap-658	250	19	locking	locking	NOUN
ap-658	250	20	occurred	occur	VERB
ap-658	250	21	for	for	ADP
ap-658	250	22	3	3	NUM
ap-658	250	23	-	-	PUNCT
ap-658	250	24	noded	nod	VERB
ap-658	250	25	triangular	triangular	NOUN
ap-658	250	26	elements	element	NOUN
ap-658	250	27	,	,	PUNCT
ap-658	250	28	recall	recall	VERB
ap-658	250	29	figs	fig	NOUN
ap-658	250	30	.	.	PUNCT
ap-658	251	1	14	14	NUM
ap-658	251	2	,	,	PUNCT
ap-658	251	3	15	15	NUM
ap-658	251	4	and	and	CCONJ
ap-658	251	5	the	the	DET
ap-658	251	6	discussion	discussion	NOUN
ap-658	251	7	in	in	ADP
ap-658	251	8	section	section	NOUN
ap-658	251	9	6	6	NUM
ap-658	251	10	.	.	PUNCT
ap-658	252	1	as	as	ADP
ap-658	252	2	for	for	ADP
ap-658	252	3	the	the	DET
ap-658	252	4	main	main	ADJ
ap-658	252	5	goal	goal	NOUN
ap-658	252	6	of	of	ADP
ap-658	252	7	this	this	DET
ap-658	252	8	paper	paper	NOUN
ap-658	252	9	,	,	PUNCT
ap-658	252	10	the	the	DET
ap-658	252	11	analysis	analysis	NOUN
ap-658	252	12	clearly	clearly	ADV
ap-658	252	13	uncovered	uncover	VERB
ap-658	252	14	major	major	ADJ
ap-658	252	15	drawbacks	drawback	NOUN
ap-658	252	16	of	of	ADP
ap-658	252	17	two	two	NUM
ap-658	252	18	point	point	NOUN
ap-658	252	19	averaging	average	VERB
ap-658	252	20	schemes	scheme	NOUN
ap-658	252	21	when	when	SCONJ
ap-658	252	22	applied	apply	VERB
ap-658	252	23	to	to	ADP
ap-658	252	24	random	random	ADJ
ap-658	252	25	microstructures	microstructure	NOUN
ap-658	252	26	with	with	ADP
ap-658	252	27	possibly	possibly	ADV
ap-658	252	28	inelastic	inelastic	ADJ
ap-658	252	29	phases	phase	NOUN
ap-658	252	30	.	.	PUNCT
ap-658	253	1	as	as	SCONJ
ap-658	253	2	already	already	ADV
ap-658	253	3	suggested	suggest	VERB
ap-658	253	4	,	,	PUNCT
ap-658	253	5	the	the	DET
ap-658	253	6	existence	existence	NOUN
ap-658	253	7	of	of	ADP
ap-658	253	8	regions	region	NOUN
ap-658	253	9	of	of	ADP
ap-658	253	10	highly	highly	ADV
ap-658	253	11	localized	localized	ADJ
ap-658	253	12	deformation	deformation	NOUN
ap-658	253	13	attributed	attribute	VERB
ap-658	253	14	heterogeneity	heterogeneity	NOUN
ap-658	253	15	of	of	ADP
ap-658	253	16	a	a	DET
ap-658	253	17	microstructure	microstructure	NOUN
ap-658	253	18	may	may	AUX
ap-658	253	19	considerably	considerably	ADV
ap-658	253	20	influence	influence	VERB
ap-658	253	21	the	the	DET
ap-658	253	22	overall	overall	ADJ
ap-658	253	23	response	response	NOUN
ap-658	253	24	(	(	PUNCT
ap-658	253	25	this	this	DET
ap-658	253	26	phenomenon	phenomenon	NOUN
ap-658	253	27	can	can	AUX
ap-658	253	28	be	be	AUX
ap-658	253	29	further	far	ADV
ap-658	253	30	magnified	magnify	VERB
ap-658	253	31	if	if	SCONJ
ap-658	253	32	one	one	NUM
ap-658	253	33	of	of	ADP
ap-658	253	34	the	the	DET
ap-658	253	35	phases	phase	NOUN
ap-658	253	36	is	be	AUX
ap-658	253	37	elastic	elastic	ADJ
ap-658	253	38	while	while	SCONJ
ap-658	253	39	the	the	DET
ap-658	253	40	other	other	ADJ
ap-658	253	41	experiences	experience	VERB
ap-658	253	42	an	an	DET
ap-658	253	43	inelastic	inelastic	ADJ
ap-658	253	44	response	response	NOUN
ap-658	253	45	)	)	PUNCT
ap-658	253	46	.	.	PUNCT
ap-658	254	1	here	here	ADV
ap-658	254	2	we	we	PRON
ap-658	254	3	refer	refer	VERB
ap-658	254	4	to	to	ADP
ap-658	254	5	the	the	DET
ap-658	254	6	results	result	NOUN
ap-658	254	7	presented	present	VERB
ap-658	254	8	in	in	ADP
ap-658	254	9	figs	fig	NOUN
ap-658	254	10	.	.	PUNCT
ap-658	255	1	11	11	NUM
ap-658	255	2	,	,	PUNCT
ap-658	255	3	12	12	NUM
ap-658	255	4	identifying	identify	VERB
ap-658	255	5	the	the	DET
ap-658	255	6	mechanism	mechanism	NOUN
ap-658	255	7	of	of	ADP
ap-658	255	8	the	the	DET
ap-658	255	9	actual	actual	ADJ
ap-658	255	10	localization	localization	NOUN
ap-658	255	11	rule	rule	NOUN
ap-658	255	12	and	and	CCONJ
ap-658	255	13	clearly	clearly	ADV
ap-658	255	14	suggesting	suggest	VERB
ap-658	255	15	an	an	DET
ap-658	255	16	inadequacy	inadequacy	NOUN
ap-658	255	17	of	of	ADP
ap-658	255	18	the	the	DET
ap-658	255	19	“	"	PUNCT
ap-658	255	20	total	total	ADJ
ap-658	255	21	elastic	elastic	ADJ
ap-658	255	22	”	"	PUNCT
ap-658	255	23	localization	localization	NOUN
ap-658	255	24	rule	rule	NOUN
ap-658	255	25	used	use	VERB
ap-658	255	26	with	with	ADP
ap-658	255	27	the	the	DET
ap-658	255	28	present	present	ADJ
ap-658	255	29	form	form	NOUN
ap-658	255	30	of	of	ADP
ap-658	255	31	the	the	DET
ap-658	255	32	hs	hs	PROPN
ap-658	255	33	principles	principle	NOUN
ap-658	255	34	.	.	PUNCT
ap-658	256	1	the	the	DET
ap-658	256	2	two	two	NUM
ap-658	256	3	-	-	PUNCT
ap-658	256	4	point	point	NOUN
ap-658	256	5	averaging	average	VERB
ap-658	256	6	schemes	scheme	NOUN
ap-658	256	7	,	,	PUNCT
ap-658	256	8	if	if	SCONJ
ap-658	256	9	at	at	ADP
ap-658	256	10	hand	hand	NOUN
ap-658	256	11	,	,	PUNCT
ap-658	256	12	should	should	AUX
ap-658	256	13	therefore	therefore	ADV
ap-658	256	14	be	be	AUX
ap-658	256	15	used	use	VERB
ap-658	256	16	with	with	ADP
ap-658	256	17	caution	caution	NOUN
ap-658	256	18	.	.	PUNCT
ap-658	257	1	nevertheless	nevertheless	ADV
ap-658	257	2	,	,	PUNCT
ap-658	257	3	if	if	SCONJ
ap-658	257	4	the	the	DET
ap-658	257	5	“	"	PUNCT
ap-658	257	6	exact	exact	ADJ
ap-658	257	7	”	"	PUNCT
ap-658	257	8	local	local	ADJ
ap-658	257	9	response	response	NOUN
ap-658	257	10	is	be	AUX
ap-658	257	11	not	not	PART
ap-658	257	12	of	of	ADP
ap-658	257	13	the	the	DET
ap-658	257	14	main	main	ADJ
ap-658	257	15	interest	interest	NOUN
ap-658	257	16	the	the	DET
ap-658	257	17	parameters	parameter	NOUN
ap-658	257	18	of	of	ADP
ap-658	257	19	a	a	DET
ap-658	257	20	given	give	VERB
ap-658	257	21	material	material	NOUN
ap-658	257	22	model	model	NOUN
ap-658	257	23	can	can	AUX
ap-658	257	24	be	be	AUX
ap-658	257	25	adjusted	adjust	VERB
ap-658	257	26	to	to	PART
ap-658	257	27	meet	meet	VERB
ap-658	257	28	the	the	DET
ap-658	257	29	desired	desire	VERB
ap-658	257	30	overall	overall	ADJ
ap-658	257	31	response	response	NOUN
ap-658	257	32	.	.	PUNCT
ap-658	258	1	in	in	ADP
ap-658	258	2	such	such	DET
ap-658	258	3	a	a	DET
ap-658	258	4	case	case	NOUN
ap-658	258	5	,	,	PUNCT
ap-658	258	6	numerical	numerical	ADJ
ap-658	258	7	experiments	experiment	NOUN
ap-658	258	8	on	on	ADP
ap-658	258	9	refined	refined	ADJ
ap-658	258	10	geometry	geometry	NOUN
ap-658	258	11	are	be	AUX
ap-658	258	12	usually	usually	ADV
ap-658	258	13	used	use	VERB
ap-658	258	14	in	in	ADP
ap-658	258	15	place	place	NOUN
ap-658	258	16	of	of	ADP
ap-658	258	17	laboratory	laboratory	NOUN
ap-658	258	18	measurements	measurement	NOUN
ap-658	258	19	.	.	PUNCT
ap-658	259	1	an	an	DET
ap-658	259	2	example	example	NOUN
ap-658	259	3	of	of	ADP
ap-658	259	4	combining	combine	VERB
ap-658	259	5	such	such	DET
ap-658	259	6	an	an	DET
ap-658	259	7	approach	approach	NOUN
ap-658	259	8	with	with	ADP
ap-658	259	9	a	a	DET
ap-658	259	10	two	two	NUM
ap-658	259	11	-	-	PUNCT
ap-658	259	12	point	point	NOUN
ap-658	259	13	averaging	averaging	NOUN
ap-658	259	14	scheme	scheme	NOUN
ap-658	259	15	has	have	AUX
ap-658	259	16	been	be	AUX
ap-658	259	17	presented	present	VERB
ap-658	259	18	in	in	ADP
ap-658	259	19	[	[	X
ap-658	259	20	14	14	NUM
ap-658	259	21	]	]	PUNCT
ap-658	259	22	.	.	PUNCT
ap-658	260	1	acknowledgments	acknowledgment	NOUN
ap-658	260	2	financial	financial	ADJ
ap-658	260	3	support	support	NOUN
ap-658	260	4	for	for	ADP
ap-658	260	5	this	this	DET
ap-658	260	6	work	work	NOUN
ap-658	260	7	was	be	AUX
ap-658	260	8	provided	provide	VERB
ap-658	260	9	by	by	ADP
ap-658	260	10	ga	ga	PROPN
ap-658	260	11	r	r	NOUN
ap-658	260	12	grant	grant	NOUN
ap-658	260	13	no	no	NOUN
ap-658	260	14	.	.	PUNCT
ap-658	261	1	103/01	103/01	NUM
ap-658	261	2	/	/	SYM
ap-658	261	3	d052	d052	PROPN
ap-658	261	4	.	.	PUNCT
ap-658	262	1	references	reference	NOUN
ap-658	262	2	[	[	X
ap-658	262	3	1	1	NUM
ap-658	262	4	]	]	PUNCT
ap-658	262	5	fish	fish	NOUN
ap-658	262	6	j.	j.	PROPN
ap-658	262	7	,	,	PUNCT
ap-658	262	8	shek	shek	PROPN
ap-658	262	9	k.	k.	PROPN
ap-658	262	10	,	,	PUNCT
ap-658	262	11	pandheeradi	pandheeradi	NOUN
ap-658	262	12	m.	m.	NOUN
ap-658	262	13	,	,	PUNCT
ap-658	262	14	shephard	shephard	NOUN
ap-658	262	15	m.	m.	PROPN
ap-658	262	16	s.	s.	PROPN
ap-658	262	17	:	:	PUNCT
ap-658	262	18	“	"	PUNCT
ap-658	262	19	computational	computational	ADJ
ap-658	262	20	plasticity	plasticity	NOUN
ap-658	262	21	for	for	ADP
ap-658	262	22	composite	composite	ADJ
ap-658	262	23	structures	structure	NOUN
ap-658	262	24	based	base	VERB
ap-658	262	25	on	on	ADP
ap-658	262	26	mathematical	mathematical	ADJ
ap-658	262	27	homogenization	homogenization	NOUN
ap-658	262	28	:	:	PUNCT
ap-658	262	29	theory	theory	NOUN
ap-658	262	30	and	and	CCONJ
ap-658	262	31	practice	practice	NOUN
ap-658	262	32	.	.	PUNCT
ap-658	262	33	”	"	PUNCT
ap-658	263	1	computer	computer	NOUN
ap-658	263	2	methods	method	NOUN
ap-658	263	3	in	in	ADP
ap-658	263	4	applied	applied	ADJ
ap-658	263	5	mechanics	mechanic	NOUN
ap-658	263	6	and	and	CCONJ
ap-658	263	7	engineering	engineering	NOUN
ap-658	263	8	,	,	PUNCT
ap-658	263	9	vol	vol	NOUN
ap-658	263	10	.	.	NOUN
ap-658	263	11	148	148	NUM
ap-658	263	12	(	(	PUNCT
ap-658	263	13	1997	1997	NUM
ap-658	263	14	)	)	PUNCT
ap-658	264	1	no	no	INTJ
ap-658	264	2	.	.	PUNCT
ap-658	265	1	1–2	1–2	NUM
ap-658	265	2	,	,	PUNCT
ap-658	265	3	p.	p.	NOUN
ap-658	265	4	53–73	53–73	NUM
ap-658	265	5	.	.	PUNCT
ap-658	266	1	[	[	X
ap-658	266	2	2	2	X
ap-658	266	3	]	]	PUNCT
ap-658	266	4	fish	fish	NOUN
ap-658	266	5	j.	j.	PROPN
ap-658	266	6	,	,	PUNCT
ap-658	266	7	shek	shek	PROPN
ap-658	266	8	k.	k.	PROPN
ap-658	266	9	:	:	PUNCT
ap-658	266	10	“	"	PUNCT
ap-658	266	11	multiscale	multiscale	ADJ
ap-658	266	12	analysis	analysis	NOUN
ap-658	266	13	of	of	ADP
ap-658	266	14	large	large	ADJ
ap-658	266	15	-	-	PUNCT
ap-658	266	16	scale	scale	NOUN
ap-658	266	17	nonlinear	nonlinear	ADJ
ap-658	266	18	structures	structure	NOUN
ap-658	266	19	and	and	CCONJ
ap-658	266	20	materials	material	NOUN
ap-658	266	21	.	.	PUNCT
ap-658	266	22	”	"	PUNCT
ap-658	266	23	international	international	ADJ
ap-658	266	24	journal	journal	NOUN
ap-658	266	25	for	for	ADP
ap-658	266	26	computational	computational	ADJ
ap-658	266	27	civil	civil	ADJ
ap-658	266	28	and	and	CCONJ
ap-658	266	29	structural	structural	ADJ
ap-658	266	30	engineering	engineering	NOUN
ap-658	266	31	,	,	PUNCT
ap-658	266	32	vol	vol	NOUN
ap-658	266	33	.	.	PROPN
ap-658	266	34	1	1	NUM
ap-658	266	35	(	(	PUNCT
ap-658	266	36	2000	2000	NUM
ap-658	266	37	)	)	PUNCT
ap-658	266	38	,	,	PUNCT
ap-658	266	39	no	no	INTJ
ap-658	266	40	.	.	NOUN
ap-658	266	41	1	1	NUM
ap-658	266	42	,	,	PUNCT
ap-658	266	43	p.	p.	NOUN
ap-658	266	44	79–90	79–90	NUM
ap-658	266	45	.	.	PUNCT
ap-658	267	1	[	[	X
ap-658	267	2	3	3	X
ap-658	267	3	]	]	PUNCT
ap-658	267	4	kouznetsova	kouznetsova	X
ap-658	267	5	v.g	v.g	PROPN
ap-658	267	6	.	.	PROPN
ap-658	267	7	,	,	PUNCT
ap-658	267	8	geers	geer	NOUN
ap-658	267	9	m.g.d	m.g.d	NOUN
ap-658	267	10	.	.	PUNCT
ap-658	267	11	,	,	PUNCT
ap-658	267	12	brekelmans	brekelman	NOUN
ap-658	267	13	w.a.m	w.a.m	PROPN
ap-658	267	14	.	.	PUNCT
ap-658	267	15	:	:	PUNCT
ap-658	267	16	“	"	PUNCT
ap-658	267	17	multi	multi	ADJ
ap-658	267	18	-	-	ADJ
ap-658	267	19	scale	scale	ADJ
ap-658	267	20	second	second	ADJ
ap-658	267	21	-	-	PUNCT
ap-658	267	22	order	order	NOUN
ap-658	267	23	computational	computational	ADJ
ap-658	267	24	homogenization	homogenization	NOUN
ap-658	267	25	of	of	ADP
ap-658	267	26	multi	multi	ADJ
ap-658	267	27	-	-	ADJ
ap-658	267	28	phase	phase	NOUN
ap-658	267	29	materials	material	NOUN
ap-658	267	30	:	:	PUNCT
ap-658	267	31	a	a	DET
ap-658	267	32	nested	nested	ADJ
ap-658	267	33	finite	finite	ADJ
ap-658	267	34	element	element	NOUN
ap-658	267	35	solution	solution	NOUN
ap-658	267	36	strategy	strategy	NOUN
ap-658	267	37	.	.	PUNCT
ap-658	267	38	”	"	PUNCT
ap-658	268	1	computer	computer	NOUN
ap-658	268	2	methods	method	NOUN
ap-658	268	3	in	in	ADP
ap-658	268	4	applied	applied	ADJ
ap-658	268	5	mechanics	mechanic	NOUN
ap-658	268	6	and	and	CCONJ
ap-658	268	7	engineering	engineering	NOUN
ap-658	268	8	,	,	PUNCT
ap-658	268	9	(	(	PUNCT
ap-658	268	10	2004	2004	NUM
ap-658	268	11	)	)	PUNCT
ap-658	268	12	,	,	PUNCT
ap-658	268	13	accepted	accept	VERB
ap-658	268	14	for	for	ADP
ap-658	268	15	publication	publication	NOUN
ap-658	268	16	.	.	PUNCT
ap-658	269	1	[	[	X
ap-658	269	2	4	4	X
ap-658	269	3	]	]	X
ap-658	269	4	massart	massart	PROPN
ap-658	269	5	t.	t.	PROPN
ap-658	269	6	j.	j.	PROPN
ap-658	269	7	:	:	PUNCT
ap-658	269	8	“	"	PUNCT
ap-658	269	9	multi	multi	ADJ
ap-658	269	10	-	-	NOUN
ap-658	269	11	scale	scale	ADJ
ap-658	269	12	modeling	modeling	NOUN
ap-658	269	13	of	of	ADP
ap-658	269	14	damage	damage	NOUN
ap-658	269	15	in	in	ADP
ap-658	269	16	masonry	masonry	NOUN
ap-658	269	17	structures	structure	NOUN
ap-658	269	18	”	"	PUNCT
ap-658	269	19	,	,	PUNCT
ap-658	269	20	ph.d	ph.d	PROPN
ap-658	269	21	.	.	PUNCT
ap-658	270	1	thesis	thesis	PROPN
ap-658	270	2	,	,	PUNCT
ap-658	270	3	technische	technische	PROPN
ap-658	270	4	universiteit	universiteit	PROPN
ap-658	270	5	eindhoven	eindhoven	PROPN
ap-658	270	6	,	,	PUNCT
ap-658	270	7	2003	2003	NUM
ap-658	270	8	.	.	PUNCT
ap-658	271	1	[	[	X
ap-658	271	2	5	5	X
ap-658	271	3	]	]	PUNCT
ap-658	271	4	kabele	kabele	PROPN
ap-658	271	5	p.	p.	NOUN
ap-658	271	6	:	:	PUNCT
ap-658	271	7	“	"	PUNCT
ap-658	271	8	assesment	assesment	NOUN
ap-658	271	9	of	of	ADP
ap-658	271	10	structural	structural	ADJ
ap-658	271	11	performance	performance	NOUN
ap-658	271	12	of	of	ADP
ap-658	271	13	engineered	engineer	VERB
ap-658	271	14	cementitious	cementitious	ADJ
ap-658	271	15	composites	composite	NOUN
ap-658	271	16	by	by	ADP
ap-658	271	17	computer	computer	NOUN
ap-658	271	18	simulation	simulation	NOUN
ap-658	271	19	.	.	PUNCT
ap-658	271	20	”	"	PUNCT
ap-658	272	1	ctu	ctu	NOUN
ap-658	272	2	reports	report	NOUN
ap-658	272	3	,	,	PUNCT
ap-658	272	4	vol	vol	NOUN
ap-658	272	5	.	.	PROPN
ap-658	272	6	5	5	NUM
ap-658	272	7	(	(	PUNCT
ap-658	272	8	2001	2001	NUM
ap-658	272	9	)	)	PUNCT
ap-658	272	10	,	,	PUNCT
ap-658	272	11	no	no	INTJ
ap-658	272	12	.	.	NOUN
ap-658	273	1	4	4	X
ap-658	273	2	.	.	PUNCT
ap-658	274	1	[	[	X
ap-658	274	2	6	6	NUM
ap-658	274	3	]	]	PUNCT
ap-658	274	4	hashin	hashin	PROPN
ap-658	274	5	z.	z.	PROPN
ap-658	274	6	,	,	PUNCT
ap-658	274	7	shtrikman	shtrikman	PROPN
ap-658	274	8	s.	s.	PROPN
ap-658	274	9	:	:	PUNCT
ap-658	274	10	“	"	PUNCT
ap-658	274	11	on	on	ADP
ap-658	274	12	some	some	DET
ap-658	274	13	variational	variational	ADJ
ap-658	274	14	principles	principle	NOUN
ap-658	274	15	in	in	ADP
ap-658	274	16	anisotropic	anisotropic	NOUN
ap-658	274	17	and	and	CCONJ
ap-658	274	18	nonhomogeneous	nonhomogeneous	ADJ
ap-658	274	19	elasticity	elasticity	NOUN
ap-658	274	20	.	.	PUNCT
ap-658	274	21	”	"	PUNCT
ap-658	274	22	journal	journal	NOUN
ap-658	274	23	of	of	ADP
ap-658	274	24	the	the	DET
ap-658	274	25	mechanics	mechanic	NOUN
ap-658	274	26	ans	ans	PROPN
ap-658	274	27	physics	physics	PROPN
ap-658	274	28	of	of	ADP
ap-658	274	29	solids	solid	NOUN
ap-658	274	30	,	,	PUNCT
ap-658	274	31	vol	vol	NOUN
ap-658	274	32	.	.	PROPN
ap-658	274	33	10	10	NUM
ap-658	274	34	(	(	PUNCT
ap-658	274	35	1962	1962	NUM
ap-658	274	36	)	)	PUNCT
ap-658	274	37	,	,	PUNCT
ap-658	274	38	p.	p.	NOUN
ap-658	274	39	335–342	335–342	NUM
ap-658	274	40	.	.	PUNCT
ap-658	275	1	[	[	X
ap-658	275	2	7	7	X
ap-658	275	3	]	]	X
ap-658	275	4	willis	willis	PROPN
ap-658	275	5	j.	j.	PROPN
ap-658	275	6	r.	r.	PROPN
ap-658	275	7	:	:	PUNCT
ap-658	275	8	“	"	PUNCT
ap-658	275	9	variational	variational	ADJ
ap-658	275	10	and	and	CCONJ
ap-658	275	11	related	related	ADJ
ap-658	275	12	methods	method	NOUN
ap-658	275	13	for	for	ADP
ap-658	275	14	the	the	DET
ap-658	275	15	overall	overall	ADJ
ap-658	275	16	properties	property	NOUN
ap-658	275	17	of	of	ADP
ap-658	275	18	composites	composite	NOUN
ap-658	275	19	.	.	PUNCT
ap-658	275	20	”	"	PUNCT
ap-658	276	1	advances	advance	NOUN
ap-658	276	2	in	in	ADP
ap-658	276	3	applied	apply	VERB
ap-658	276	4	mechanics	mechanic	NOUN
ap-658	276	5	,	,	PUNCT
ap-658	276	6	vol	vol	NOUN
ap-658	276	7	.	.	PROPN
ap-658	276	8	21	21	NUM
ap-658	276	9	(	(	PUNCT
ap-658	276	10	1981	1981	NUM
ap-658	276	11	)	)	PUNCT
ap-658	276	12	,	,	PUNCT
ap-658	276	13	p.	p.	NOUN
ap-658	276	14	2–4	2–4	NUM
ap-658	276	15	.	.	PUNCT
ap-658	277	1	[	[	X
ap-658	277	2	8	8	NUM
ap-658	277	3	]	]	X
ap-658	277	4	lagoudas	lagoudas	PROPN
ap-658	277	5	d.	d.	PROPN
ap-658	277	6	c.	c.	PROPN
ap-658	277	7	,	,	PUNCT
ap-658	277	8	gavazzi	gavazzi	PROPN
ap-658	277	9	a.	a.	PROPN
ap-658	277	10	c.	c.	PROPN
ap-658	277	11	,	,	PUNCT
ap-658	277	12	nigam	nigam	PROPN
ap-658	277	13	h.	h.	PROPN
ap-658	277	14	:	:	PUNCT
ap-658	277	15	“	"	PUNCT
ap-658	277	16	elastoplastic	elastoplastic	ADJ
ap-658	277	17	behavior	behavior	NOUN
ap-658	277	18	of	of	ADP
ap-658	277	19	metal	metal	NOUN
ap-658	277	20	matrix	matrix	NOUN
ap-658	277	21	composites	composite	NOUN
ap-658	277	22	based	base	VERB
ap-658	277	23	on	on	ADP
ap-658	277	24	incremental	incremental	ADJ
ap-658	277	25	plasticity	plasticity	NOUN
ap-658	277	26	and	and	CCONJ
ap-658	277	27	the	the	DET
ap-658	277	28	mori	mori	NOUN
ap-658	277	29	-	-	PUNCT
ap-658	277	30	tanaka	tanaka	PROPN
ap-658	277	31	averaging	average	VERB
ap-658	277	32	scheme	scheme	NOUN
ap-658	277	33	.	.	PUNCT
ap-658	277	34	”	"	PUNCT
ap-658	278	1	computational	computational	ADJ
ap-658	278	2	mechanics	mechanic	NOUN
ap-658	278	3	,	,	PUNCT
ap-658	278	4	vol	vol	NOUN
ap-658	278	5	.	.	NOUN
ap-658	278	6	8	8	NUM
ap-658	278	7	(	(	PUNCT
ap-658	278	8	1991	1991	NUM
ap-658	278	9	)	)	PUNCT
ap-658	278	10	,	,	PUNCT
ap-658	278	11	p.	p.	NOUN
ap-658	278	12	193–203	193–203	NUM
ap-658	278	13	.	.	PUNCT
ap-658	279	1	[	[	X
ap-658	279	2	9	9	NUM
ap-658	279	3	]	]	X
ap-658	279	4	dvorak	dvorak	PROPN
ap-658	279	5	g.	g.	PROPN
ap-658	279	6	j.	j.	PROPN
ap-658	279	7	:	:	PUNCT
ap-658	279	8	“	"	PUNCT
ap-658	279	9	transformation	transformation	NOUN
ap-658	279	10	field	field	NOUN
ap-658	279	11	analysis	analysis	NOUN
ap-658	279	12	of	of	ADP
ap-658	279	13	inelastic	inelastic	ADJ
ap-658	279	14	composite	composite	ADJ
ap-658	279	15	materials	material	NOUN
ap-658	279	16	.	.	PUNCT
ap-658	279	17	”	"	PUNCT
ap-658	280	1	proceedings	proceeding	NOUN
ap-658	280	2	of	of	ADP
ap-658	280	3	the	the	DET
ap-658	280	4	royal	royal	ADJ
ap-658	280	5	society	society	NOUN
ap-658	280	6	of	of	ADP
ap-658	280	7	london	london	PROPN
ap-658	280	8	series	series	PROPN
ap-658	280	9	a	a	DET
ap-658	280	10	mathematical	mathematical	ADJ
ap-658	280	11	,	,	PUNCT
ap-658	280	12	physical	physical	ADJ
ap-658	280	13	and	and	CCONJ
ap-658	280	14	engineering	engineering	NOUN
ap-658	280	15	sciences	science	NOUN
ap-658	280	16	,	,	PUNCT
ap-658	280	17	vol	vol	NOUN
ap-658	280	18	.	.	PROPN
ap-658	281	1	437	437	NUM
ap-658	281	2	(	(	PUNCT
ap-658	281	3	1992	1992	NUM
ap-658	281	4	)	)	PUNCT
ap-658	281	5	,	,	PUNCT
ap-658	281	6	p.	p.	NOUN
ap-658	281	7	311–327	311–327	NUM
ap-658	281	8	.	.	PUNCT
ap-658	282	1	[	[	X
ap-658	282	2	10	10	NUM
ap-658	282	3	]	]	X
ap-658	282	4	dvorak	dvorak	PROPN
ap-658	282	5	g.	g.	PROPN
ap-658	282	6	j.	j.	PROPN
ap-658	282	7	,	,	PUNCT
ap-658	282	8	bahei	bahei	PROPN
ap-658	282	9	-	-	PUNCT
ap-658	282	10	el	el	PROPN
ap-658	282	11	-	-	PUNCT
ap-658	282	12	din	din	PROPN
ap-658	282	13	y.	y.	PROPN
ap-658	282	14	a.	a.	PROPN
ap-658	282	15	,	,	PUNCT
ap-658	282	16	wafa	wafa	PROPN
ap-658	282	17	a.	a.	NOUN
ap-658	282	18	m.	m.	PROPN
ap-658	282	19	:	:	PUNCT
ap-658	282	20	“	"	PUNCT
ap-658	282	21	implementation	implementation	NOUN
ap-658	282	22	of	of	ADP
ap-658	282	23	the	the	DET
ap-658	282	24	transformation	transformation	NOUN
ap-658	282	25	field	field	NOUN
ap-658	282	26	analysis	analysis	NOUN
ap-658	282	27	for	for	ADP
ap-658	282	28	inelastic	inelastic	ADJ
ap-658	282	29	composite	composite	ADJ
ap-658	282	30	-	-	PUNCT
ap-658	282	31	materials	material	NOUN
ap-658	282	32	.	.	PUNCT
ap-658	282	33	”	"	PUNCT
ap-658	283	1	computational	computational	ADJ
ap-658	283	2	mechanics	mechanic	NOUN
ap-658	283	3	,	,	PUNCT
ap-658	283	4	vol	vol	NOUN
ap-658	283	5	.	.	PROPN
ap-658	283	6	14	14	NUM
ap-658	283	7	(	(	PUNCT
ap-658	283	8	1994	1994	NUM
ap-658	283	9	)	)	PUNCT
ap-658	283	10	,	,	PUNCT
ap-658	283	11	no	no	INTJ
ap-658	283	12	.	.	NOUN
ap-658	283	13	3	3	NUM
ap-658	283	14	,	,	PUNCT
ap-658	283	15	p.	p.	NOUN
ap-658	283	16	201–228	201–228	NUM
ap-658	283	17	.	.	PUNCT
ap-658	284	1	[	[	X
ap-658	284	2	11	11	NUM
ap-658	284	3	]	]	PUNCT
ap-658	284	4	castaneda	castaneda	PROPN
ap-658	284	5	p.	p.	PROPN
ap-658	284	6	p.	p.	PROPN
ap-658	284	7	,	,	PUNCT
ap-658	284	8	suquet	suquet	PROPN
ap-658	284	9	p.	p.	NOUN
ap-658	284	10	:	:	PUNCT
ap-658	284	11	”	"	PUNCT
ap-658	284	12	nonlinear	nonlinear	ADJ
ap-658	284	13	composites	composite	NOUN
ap-658	284	14	.	.	PUNCT
ap-658	284	15	”	"	PUNCT
ap-658	285	1	advances	advance	NOUN
ap-658	285	2	in	in	ADP
ap-658	285	3	applied	apply	VERB
ap-658	285	4	mechanics	mechanic	NOUN
ap-658	285	5	,	,	PUNCT
ap-658	285	6	vol	vol	NOUN
ap-658	285	7	.	.	PROPN
ap-658	286	1	34	34	NUM
ap-658	286	2	,	,	PUNCT
ap-658	286	3	no	no	INTJ
ap-658	286	4	.	.	NOUN
ap-658	286	5	998	998	NUM
ap-658	286	6	,	,	PUNCT
ap-658	286	7	p.	p.	NOUN
ap-658	286	8	171–302	171–302	NUM
ap-658	286	9	.	.	PUNCT
ap-658	287	1	[	[	X
ap-658	287	2	12	12	NUM
ap-658	287	3	]	]	X
ap-658	287	4	masson	masson	PROPN
ap-658	287	5	r.	r.	PROPN
ap-658	287	6	,	,	PUNCT
ap-658	287	7	bornert	bornert	ADJ
ap-658	287	8	m.	m.	NOUN
ap-658	287	9	,	,	PUNCT
ap-658	287	10	suquet	suquet	VERB
ap-658	287	11	p.	p.	NOUN
ap-658	287	12	,	,	PUNCT
ap-658	287	13	zaoui	zaoui	PROPN
ap-658	287	14	a.	a.	NOUN
ap-658	287	15	:	:	PUNCT
ap-658	287	16	“	"	PUNCT
ap-658	287	17	an	an	DET
ap-658	287	18	affine	affine	ADJ
ap-658	287	19	formulation	formulation	NOUN
ap-658	287	20	for	for	ADP
ap-658	287	21	the	the	DET
ap-658	287	22	prediction	prediction	NOUN
ap-658	287	23	of	of	ADP
ap-658	287	24	the	the	DET
ap-658	287	25	effective	effective	ADJ
ap-658	287	26	properties	property	NOUN
ap-658	287	27	of	of	ADP
ap-658	287	28	nonlinear	nonlinear	ADJ
ap-658	287	29	composites	composite	NOUN
ap-658	287	30	and	and	CCONJ
ap-658	287	31	polycrystals	polycrystal	NOUN
ap-658	287	32	.	.	PUNCT
ap-658	287	33	”	"	PUNCT
ap-658	288	1	journal	journal	NOUN
ap-658	288	2	of	of	ADP
ap-658	288	3	the	the	DET
ap-658	288	4	mechanics	mechanic	NOUN
ap-658	288	5	and	and	CCONJ
ap-658	288	6	physics	physic	NOUN
ap-658	288	7	of	of	ADP
ap-658	288	8	solids	solid	NOUN
ap-658	288	9	,	,	PUNCT
ap-658	288	10	vol	vol	NOUN
ap-658	288	11	.	.	PUNCT
ap-658	289	1	48	48	NUM
ap-658	289	2	(	(	PUNCT
ap-658	289	3	2000	2000	NUM
ap-658	289	4	)	)	PUNCT
ap-658	289	5	,	,	PUNCT
ap-658	290	1	p.	p.	NOUN
ap-658	290	2	1203–1227	1203–1227	NUM
ap-658	290	3	.	.	PUNCT
ap-658	291	1	[	[	X
ap-658	291	2	13	13	NUM
ap-658	291	3	]	]	PUNCT
ap-658	291	4	chaboche	chaboche	PROPN
ap-658	291	5	j.	j.	PROPN
ap-658	291	6	l.	l.	PROPN
ap-658	291	7	,	,	PUNCT
ap-658	291	8	kruch	kruch	PROPN
ap-658	291	9	s	s	PROPN
ap-658	291	10	,	,	PUNCT
ap-658	291	11	maire	maire	PROPN
ap-658	291	12	j.	j.	PROPN
ap-658	291	13	f.	f.	PROPN
ap-658	291	14	,	,	PUNCT
ap-658	291	15	pottier	pottier	PROPN
ap-658	291	16	t.	t.	PROPN
ap-658	291	17	:	:	PUNCT
ap-658	291	18	“	"	PUNCT
ap-658	291	19	towards	towards	ADP
ap-658	291	20	a	a	DET
ap-658	291	21	micromechanics	micromechanic	NOUN
ap-658	291	22	based	base	VERB
ap-658	291	23	inelastic	inelastic	ADJ
ap-658	291	24	and	and	CCONJ
ap-658	291	25	damage	damage	NOUN
ap-658	291	26	modeling	modeling	NOUN
ap-658	291	27	of	of	ADP
ap-658	291	28	composites	composite	NOUN
ap-658	291	29	.	.	PUNCT
ap-658	291	30	”	"	PUNCT
ap-658	292	1	international	international	ADJ
ap-658	292	2	journal	journal	NOUN
ap-658	292	3	of	of	ADP
ap-658	292	4	plasticity	plasticity	NOUN
ap-658	292	5	,	,	PUNCT
ap-658	292	6	vol	vol	NOUN
ap-658	292	7	.	.	PROPN
ap-658	292	8	17	17	NUM
ap-658	292	9	(	(	PUNCT
ap-658	292	10	2001	2001	NUM
ap-658	292	11	)	)	PUNCT
ap-658	292	12	,	,	PUNCT
ap-658	292	13	no	no	INTJ
ap-658	292	14	.	.	NOUN
ap-658	292	15	4	4	NUM
ap-658	292	16	,	,	PUNCT
ap-658	292	17	p.	p.	NOUN
ap-658	292	18	411–439	411–439	NUM
ap-658	292	19	.	.	PUNCT
ap-658	293	1	[	[	X
ap-658	293	2	14	14	NUM
ap-658	293	3	]	]	X
ap-658	293	4	šejnoha	šejnoha	X
ap-658	293	5	m.	m.	NOUN
ap-658	293	6	,	,	PUNCT
ap-658	293	7	valenta	valenta	PROPN
ap-658	293	8	r.	r.	PROPN
ap-658	293	9	,	,	PUNCT
ap-658	293	10	zeman	zeman	PROPN
ap-658	293	11	j.	j.	PROPN
ap-658	293	12	:	:	PUNCT
ap-658	293	13	“	"	PUNCT
ap-658	293	14	nonlinear	nonlinear	ADJ
ap-658	293	15	viscoelastic	viscoelastic	ADJ
ap-658	293	16	analysis	analysis	NOUN
ap-658	293	17	of	of	ADP
ap-658	293	18	statistically	statistically	ADV
ap-658	293	19	homogeneous	homogeneous	ADJ
ap-658	293	20	random	random	ADJ
ap-658	293	21	composites	composite	NOUN
ap-658	293	22	.	.	PUNCT
ap-658	293	23	”	"	PUNCT
ap-658	294	1	international	international	ADJ
ap-658	294	2	journal	journal	NOUN
ap-658	294	3	of	of	ADP
ap-658	294	4	multiscale	multiscale	ADJ
ap-658	294	5	computational	computational	ADJ
ap-658	294	6	engineering	engineering	NOUN
ap-658	294	7	,	,	PUNCT
ap-658	294	8	(	(	PUNCT
ap-658	294	9	2004	2004	NUM
ap-658	294	10	)	)	PUNCT
ap-658	294	11	,	,	PUNCT
ap-658	294	12	submitted	submit	VERB
ap-658	294	13	for	for	ADP
ap-658	294	14	publication	publication	NOUN
ap-658	294	15	.	.	PUNCT
ap-658	295	1	[	[	X
ap-658	295	2	15	15	NUM
ap-658	295	3	]	]	X
ap-658	295	4	šejnoha	šejnoha	X
ap-658	295	5	m.	m.	NOUN
ap-658	295	6	,	,	PUNCT
ap-658	295	7	zeman	zeman	PROPN
ap-658	295	8	j.	j.	PROPN
ap-658	295	9	:	:	PUNCT
ap-658	295	10	“	"	PUNCT
ap-658	295	11	overall	overall	ADJ
ap-658	295	12	viscoelastic	viscoelastic	ADJ
ap-658	295	13	response	response	NOUN
ap-658	295	14	of	of	ADP
ap-658	295	15	random	random	ADJ
ap-658	295	16	fibrous	fibrous	ADJ
ap-658	295	17	composites	composite	NOUN
ap-658	295	18	with	with	ADP
ap-658	295	19	statistically	statistically	ADV
ap-658	295	20	quasi	quasi	ADJ
ap-658	295	21	uniform	uniform	ADJ
ap-658	295	22	distribution	distribution	NOUN
ap-658	295	23	of	of	ADP
ap-658	295	24	reinforcements	reinforcement	NOUN
ap-658	295	25	.	.	PUNCT
ap-658	295	26	”	"	PUNCT
ap-658	296	1	computer	computer	NOUN
ap-658	296	2	methods	method	NOUN
ap-658	296	3	208	208	NUM
ap-658	296	4	©	©	PROPN
ap-658	296	5	czech	czech	PROPN
ap-658	296	6	technical	technical	PROPN
ap-658	296	7	university	university	PROPN
ap-658	296	8	publishing	publishing	NOUN
ap-658	296	9	house	house	NOUN
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ap-658	296	11	acta	acta	PROPN
ap-658	296	12	polytechnica	polytechnica	PROPN
ap-658	296	13	vol	vol	NOUN
ap-658	296	14	.	.	PROPN
ap-658	297	1	44	44	NUM
ap-658	297	2	no.5–6/2004	no.5–6/2004	NOUN
ap-658	297	3	in	in	ADP
ap-658	297	4	applied	apply	VERB
ap-658	297	5	mechanics	mechanic	NOUN
ap-658	297	6	and	and	CCONJ
ap-658	297	7	engineering	engineering	NOUN
ap-658	297	8	,	,	PUNCT
ap-658	297	9	vol	vol	NOUN
ap-658	297	10	.	.	PROPN
ap-658	297	11	191	191	NUM
ap-658	297	12	(	(	PUNCT
ap-658	297	13	2002	2002	NUM
ap-658	297	14	)	)	PUNCT
ap-658	297	15	,	,	PUNCT
ap-658	297	16	no	no	INTJ
ap-658	297	17	.	.	NOUN
ap-658	297	18	44	44	NUM
ap-658	297	19	,	,	PUNCT
ap-658	297	20	p.	p.	NOUN
ap-658	297	21	5027–5044	5027–5044	NUM
ap-658	297	22	.	.	PUNCT
ap-658	298	1	[	[	X
ap-658	298	2	16	16	NUM
ap-658	298	3	]	]	X
ap-658	298	4	šejnoha	šejnoha	X
ap-658	298	5	m.	m.	NOUN
ap-658	298	6	,	,	PUNCT
ap-658	298	7	zeman	zeman	PROPN
ap-658	298	8	j.	j.	PROPN
ap-658	298	9	:	:	PUNCT
ap-658	298	10	“	"	PUNCT
ap-658	298	11	micromechanical	micromechanical	ADJ
ap-658	298	12	analysis	analysis	NOUN
ap-658	298	13	of	of	ADP
ap-658	298	14	random	random	ADJ
ap-658	298	15	composites	composite	NOUN
ap-658	298	16	.	.	PUNCT
ap-658	298	17	”	"	PUNCT
ap-658	299	1	ctu	ctu	NOUN
ap-658	299	2	reports	report	NOUN
ap-658	299	3	,	,	PUNCT
ap-658	299	4	6	6	NUM
ap-658	299	5	(	(	PUNCT
ap-658	299	6	1	1	NUM
ap-658	299	7	)	)	PUNCT
ap-658	299	8	,	,	PUNCT
ap-658	299	9	czech	czech	PROPN
ap-658	299	10	technical	technical	PROPN
ap-658	299	11	university	university	PROPN
ap-658	299	12	in	in	ADP
ap-658	299	13	prague	prague	PROPN
ap-658	299	14	,	,	PUNCT
ap-658	299	15	2002	2002	NUM
ap-658	299	16	.	.	PUNCT
ap-658	300	1	[	[	X
ap-658	300	2	17	17	NUM
ap-658	300	3	]	]	X
ap-658	300	4	zeman	zeman	PROPN
ap-658	300	5	j.	j.	PROPN
ap-658	300	6	,	,	PUNCT
ap-658	300	7	šejnoha	šejnoha	PROPN
ap-658	300	8	m.	m.	NOUN
ap-658	300	9	:	:	PUNCT
ap-658	300	10	“	"	PUNCT
ap-658	300	11	numerical	numerical	ADJ
ap-658	300	12	evaluation	evaluation	NOUN
ap-658	300	13	of	of	ADP
ap-658	300	14	effective	effective	ADJ
ap-658	300	15	properties	property	NOUN
ap-658	300	16	of	of	ADP
ap-658	300	17	graphite	graphite	NOUN
ap-658	300	18	fiber	fiber	NOUN
ap-658	300	19	tow	tow	NOUN
ap-658	300	20	impregnated	impregnate	VERB
ap-658	300	21	by	by	ADP
ap-658	300	22	polymer	polymer	NOUN
ap-658	300	23	matrix	matrix	NOUN
ap-658	300	24	.	.	PUNCT
ap-658	300	25	”	"	PUNCT
ap-658	300	26	journal	journal	NOUN
ap-658	300	27	of	of	ADP
ap-658	300	28	the	the	DET
ap-658	300	29	mechanics	mechanic	NOUN
ap-658	300	30	and	and	CCONJ
ap-658	300	31	physics	physic	NOUN
ap-658	300	32	of	of	ADP
ap-658	300	33	solids	solid	NOUN
ap-658	300	34	,	,	PUNCT
ap-658	300	35	vol	vol	NOUN
ap-658	300	36	.	.	PROPN
ap-658	300	37	49	49	NUM
ap-658	300	38	(	(	PUNCT
ap-658	300	39	2001	2001	NUM
ap-658	300	40	)	)	PUNCT
ap-658	300	41	,	,	PUNCT
ap-658	300	42	no	no	INTJ
ap-658	300	43	.	.	NOUN
ap-658	300	44	1	1	NUM
ap-658	300	45	,	,	PUNCT
ap-658	300	46	p.	p.	NOUN
ap-658	300	47	69–90	69–90	PROPN
ap-658	300	48	.	.	PUNCT
ap-658	301	1	[	[	X
ap-658	301	2	18	18	NUM
ap-658	301	3	]	]	X
ap-658	301	4	zeman	zeman	PROPN
ap-658	301	5	j.	j.	PROPN
ap-658	301	6	,	,	PUNCT
ap-658	301	7	šejnoha	šejnoha	PROPN
ap-658	301	8	m.	m.	NOUN
ap-658	301	9	:	:	PUNCT
ap-658	301	10	“	"	PUNCT
ap-658	301	11	homogenization	homogenization	NOUN
ap-658	301	12	of	of	ADP
ap-658	301	13	plain	plain	ADJ
ap-658	301	14	weave	weave	NOUN
ap-658	301	15	composites	composite	NOUN
ap-658	301	16	with	with	ADP
ap-658	301	17	imperfect	imperfect	ADJ
ap-658	301	18	microstructure	microstructure	NOUN
ap-658	301	19	:	:	PUNCT
ap-658	301	20	part	part	NOUN
ap-658	301	21	i	i	PRON
ap-658	301	22	theoretical	theoretical	ADJ
ap-658	301	23	formulation	formulation	NOUN
ap-658	301	24	.	.	PUNCT
ap-658	301	25	”	"	PUNCT
ap-658	301	26	international	international	ADJ
ap-658	301	27	journal	journal	NOUN
ap-658	301	28	of	of	ADP
ap-658	301	29	solids	solid	NOUN
ap-658	301	30	and	and	CCONJ
ap-658	301	31	structures	structure	NOUN
ap-658	301	32	,	,	PUNCT
ap-658	301	33	(	(	PUNCT
ap-658	301	34	2004	2004	NUM
ap-658	301	35	)	)	PUNCT
ap-658	301	36	,	,	PUNCT
ap-658	301	37	in	in	ADP
ap-658	301	38	print	print	NOUN
ap-658	301	39	.	.	PUNCT
ap-658	302	1	[	[	X
ap-658	302	2	19	19	NUM
ap-658	302	3	]	]	PUNCT
ap-658	302	4	matouš	matouš	PROPN
ap-658	302	5	k.	k.	PROPN
ap-658	302	6	,	,	PUNCT
ap-658	302	7	lepš	lepš	NOUN
ap-658	302	8	m.	m.	NOUN
ap-658	302	9	,	,	PUNCT
ap-658	302	10	zeman	zeman	PROPN
ap-658	302	11	j.	j.	PROPN
ap-658	302	12	šejnoha	šejnoha	PROPN
ap-658	302	13	m.	m.	NOUN
ap-658	302	14	:	:	PUNCT
ap-658	302	15	“	"	PUNCT
ap-658	302	16	applying	apply	VERB
ap-658	302	17	genetic	genetic	ADJ
ap-658	302	18	algorithms	algorithm	NOUN
ap-658	302	19	to	to	ADP
ap-658	302	20	selected	select	VERB
ap-658	302	21	topics	topic	NOUN
ap-658	302	22	commonly	commonly	ADV
ap-658	302	23	encountered	encounter	VERB
ap-658	302	24	in	in	ADP
ap-658	302	25	engineering	engineering	NOUN
ap-658	302	26	practice	practice	NOUN
ap-658	302	27	.	.	PUNCT
ap-658	302	28	”	"	PUNCT
ap-658	303	1	computer	computer	NOUN
ap-658	303	2	methods	method	NOUN
ap-658	303	3	in	in	ADP
ap-658	303	4	applied	applied	ADJ
ap-658	303	5	mechanics	mechanic	NOUN
ap-658	303	6	and	and	CCONJ
ap-658	303	7	engineering	engineering	NOUN
ap-658	303	8	,	,	PUNCT
ap-658	303	9	vol	vol	NOUN
ap-658	303	10	.	.	PROPN
ap-658	303	11	190	190	NUM
ap-658	303	12	(	(	PUNCT
ap-658	303	13	2000	2000	NUM
ap-658	303	14	)	)	PUNCT
ap-658	303	15	,	,	PUNCT
ap-658	303	16	no	no	INTJ
ap-658	303	17	.	.	NOUN
ap-658	304	1	13–14	13–14	NUM
ap-658	304	2	,	,	PUNCT
ap-658	304	3	p.	p.	NOUN
ap-658	304	4	1629–1650	1629–1650	NUM
ap-658	304	5	.	.	PUNCT
ap-658	305	1	[	[	X
ap-658	305	2	20	20	NUM
ap-658	305	3	]	]	X
ap-658	305	4	shan	shan	PROPN
ap-658	305	5	z.	z.	PROPN
ap-658	305	6	,	,	PUNCT
ap-658	305	7	gokhale	gokhale	NOUN
ap-658	305	8	a.	a.	NOUN
ap-658	305	9	m.	m.	NOUN
ap-658	305	10	:	:	PUNCT
ap-658	305	11	“	"	PUNCT
ap-658	305	12	representative	representative	ADJ
ap-658	305	13	volume	volume	NOUN
ap-658	305	14	element	element	NOUN
ap-658	305	15	for	for	ADP
ap-658	305	16	non	non	ADJ
ap-658	305	17	-	-	ADJ
ap-658	305	18	uniform	uniform	ADJ
ap-658	305	19	microstructures	microstructure	NOUN
ap-658	305	20	.	.	PUNCT
ap-658	305	21	”	"	PUNCT
ap-658	305	22	computational	computational	ADJ
ap-658	305	23	materials	material	NOUN
ap-658	305	24	science	science	NOUN
ap-658	305	25	,	,	PUNCT
ap-658	305	26	vol	vol	NOUN
ap-658	305	27	.	.	PROPN
ap-658	305	28	24	24	NUM
ap-658	305	29	(	(	PUNCT
ap-658	305	30	2002	2002	NUM
ap-658	305	31	)	)	PUNCT
ap-658	305	32	,	,	PUNCT
ap-658	305	33	p.	p.	NOUN
ap-658	305	34	361–379	361–379	NUM
ap-658	305	35	.	.	PUNCT
ap-658	306	1	[	[	X
ap-658	306	2	21	21	NUM
ap-658	306	3	]	]	PUNCT
ap-658	306	4	beran	beran	PROPN
ap-658	306	5	m.	m.	PROPN
ap-658	306	6	j.	j.	PROPN
ap-658	306	7	:	:	PUNCT
ap-658	306	8	“	"	PUNCT
ap-658	306	9	statistical	statistical	ADJ
ap-658	306	10	continuum	continuum	ADJ
ap-658	306	11	theories	theory	NOUN
ap-658	306	12	.	.	PUNCT
ap-658	306	13	”	"	PUNCT
ap-658	307	1	monographs	monograph	NOUN
ap-658	307	2	in	in	ADP
ap-658	307	3	statistical	statistical	ADJ
ap-658	307	4	physics	physics	NOUN
ap-658	307	5	,	,	PUNCT
ap-658	307	6	interscience	interscience	NOUN
ap-658	307	7	publishers	publisher	NOUN
ap-658	307	8	,	,	PUNCT
ap-658	307	9	1968	1968	NUM
ap-658	307	10	.	.	PUNCT
ap-658	308	1	[	[	X
ap-658	308	2	22	22	NUM
ap-658	308	3	]	]	PUNCT
ap-658	308	4	torquato	torquato	NOUN
ap-658	308	5	s.	s.	PROPN
ap-658	308	6	:	:	PUNCT
ap-658	308	7	“	"	PUNCT
ap-658	308	8	random	random	ADJ
ap-658	308	9	heterogeneous	heterogeneous	ADJ
ap-658	308	10	materials	material	NOUN
ap-658	308	11	:	:	PUNCT
ap-658	308	12	microstructure	microstructure	ADJ
ap-658	308	13	and	and	CCONJ
ap-658	308	14	macroscopic	macroscopic	ADJ
ap-658	308	15	properties	property	NOUN
ap-658	308	16	.	.	PUNCT
ap-658	308	17	”	"	PUNCT
ap-658	308	18	springer	springer	NOUN
ap-658	308	19	-	-	PUNCT
ap-658	308	20	verlag	verlag	PROPN
ap-658	308	21	,	,	PUNCT
ap-658	308	22	2002	2002	NUM
ap-658	308	23	.	.	PUNCT
ap-658	309	1	[	[	X
ap-658	309	2	23	23	NUM
ap-658	309	3	]	]	PUNCT
ap-658	309	4	michel	michel	PROPN
ap-658	309	5	j.	j.	PROPN
ap-658	309	6	c.	c.	PROPN
ap-658	309	7	,	,	PUNCT
ap-658	309	8	moulinec	moulinec	PROPN
ap-658	309	9	h.	h.	PROPN
ap-658	309	10	,	,	PUNCT
ap-658	309	11	suquet	suquet	VERB
ap-658	309	12	p.	p.	NOUN
ap-658	309	13	:	:	PUNCT
ap-658	309	14	“	"	PUNCT
ap-658	309	15	effective	effective	ADJ
ap-658	309	16	properties	property	NOUN
ap-658	309	17	of	of	ADP
ap-658	309	18	composite	composite	ADJ
ap-658	309	19	materials	material	NOUN
ap-658	309	20	with	with	ADP
ap-658	309	21	periodic	periodic	ADJ
ap-658	309	22	microstructure	microstructure	NOUN
ap-658	309	23	:	:	PUNCT
ap-658	309	24	a	a	DET
ap-658	309	25	computational	computational	ADJ
ap-658	309	26	approach	approach	NOUN
ap-658	309	27	.	.	PUNCT
ap-658	309	28	”	"	PUNCT
ap-658	310	1	computer	computer	NOUN
ap-658	310	2	methods	method	NOUN
ap-658	310	3	in	in	ADP
ap-658	310	4	applied	applied	ADJ
ap-658	310	5	mechanics	mechanic	NOUN
ap-658	310	6	and	and	CCONJ
ap-658	310	7	engineering	engineering	NOUN
ap-658	310	8	,	,	PUNCT
ap-658	310	9	vol	vol	NOUN
ap-658	310	10	.	.	PUNCT
ap-658	310	11	172	172	NUM
ap-658	310	12	(	(	PUNCT
ap-658	310	13	1999	1999	NUM
ap-658	310	14	)	)	PUNCT
ap-658	310	15	,	,	PUNCT
ap-658	310	16	p.	p.	NOUN
ap-658	310	17	109–143	109–143	NUM
ap-658	310	18	.	.	PUNCT
ap-658	311	1	[	[	X
ap-658	311	2	24	24	NUM
ap-658	311	3	]	]	PUNCT
ap-658	311	4	bittnar	bittnar	PROPN
ap-658	311	5	z.	z.	PROPN
ap-658	311	6	,	,	PUNCT
ap-658	311	7	šejnoha	šejnoha	PROPN
ap-658	311	8	j.	j.	PROPN
ap-658	311	9	:	:	PUNCT
ap-658	311	10	“	"	PUNCT
ap-658	311	11	numerical	numerical	ADJ
ap-658	311	12	methods	method	NOUN
ap-658	311	13	in	in	ADP
ap-658	311	14	structural	structural	ADJ
ap-658	311	15	engineering	engineering	NOUN
ap-658	311	16	.	.	PUNCT
ap-658	311	17	”	"	PUNCT
ap-658	312	1	asce	asce	PROPN
ap-658	312	2	press	press	PROPN
ap-658	312	3	,	,	PUNCT
ap-658	312	4	1996	1996	NUM
ap-658	312	5	.	.	PUNCT
ap-658	313	1	[	[	X
ap-658	313	2	25	25	NUM
ap-658	313	3	]	]	PUNCT
ap-658	313	4	procházka	procházka	PROPN
ap-658	313	5	p.	p.	PROPN
ap-658	313	6	,	,	PUNCT
ap-658	313	7	šejnoha	šejnoha	PROPN
ap-658	313	8	j.	j.	PROPN
ap-658	313	9	:	:	PUNCT
ap-658	313	10	“	"	PUNCT
ap-658	313	11	a	a	DET
ap-658	313	12	bem	bem	NOUN
ap-658	313	13	formulation	formulation	NOUN
ap-658	313	14	for	for	ADP
ap-658	313	15	homogenization	homogenization	NOUN
ap-658	313	16	of	of	ADP
ap-658	313	17	composites	composite	NOUN
ap-658	313	18	with	with	ADP
ap-658	313	19	randomly	randomly	ADV
ap-658	313	20	distributed	distribute	VERB
ap-658	313	21	fibers	fiber	NOUN
ap-658	313	22	.	.	PUNCT
ap-658	313	23	”	"	PUNCT
ap-658	314	1	engineering	engineer	VERB
ap-658	314	2	analysis	analysis	NOUN
ap-658	314	3	with	with	ADP
ap-658	314	4	boundary	boundary	ADJ
ap-658	314	5	elements	element	NOUN
ap-658	314	6	,	,	PUNCT
ap-658	314	7	vol	vol	NOUN
ap-658	314	8	.	.	PROPN
ap-658	314	9	27	27	NUM
ap-658	314	10	(	(	PUNCT
ap-658	314	11	2	2	NUM
ap-658	314	12	)	)	PUNCT
ap-658	314	13	(	(	PUNCT
ap-658	314	14	2003	2003	NUM
ap-658	314	15	)	)	PUNCT
ap-658	314	16	,	,	PUNCT
ap-658	315	1	p.	p.	NOUN
ap-658	315	2	137–144	137–144	NUM
ap-658	315	3	.	.	PUNCT
ap-658	316	1	[	[	X
ap-658	316	2	26	26	NUM
ap-658	316	3	]	]	X
ap-658	316	4	leonov	leonov	PROPN
ap-658	316	5	a.	a.	PROPN
ap-658	316	6	i.	i.	PROPN
ap-658	316	7	:	:	PUNCT
ap-658	316	8	“	"	PUNCT
ap-658	316	9	non	non	ADJ
ap-658	316	10	-	-	ADJ
ap-658	316	11	equilibrium	equilibrium	ADJ
ap-658	316	12	thermodynamics	thermodynamic	NOUN
ap-658	316	13	and	and	CCONJ
ap-658	316	14	rheology	rheology	NOUN
ap-658	316	15	of	of	ADP
ap-658	316	16	viscoelastic	viscoelastic	ADJ
ap-658	316	17	polymer	polymer	NOUN
ap-658	316	18	media	medium	NOUN
ap-658	316	19	.	.	PUNCT
ap-658	316	20	”	"	PUNCT
ap-658	317	1	rheologica	rheologica	PROPN
ap-658	317	2	acta	acta	PROPN
ap-658	317	3	,	,	PUNCT
ap-658	317	4	vol	vol	NOUN
ap-658	317	5	.	.	PROPN
ap-658	317	6	15	15	NUM
ap-658	317	7	,	,	PUNCT
ap-658	317	8	(	(	PUNCT
ap-658	317	9	1976	1976	NUM
ap-658	317	10	)	)	PUNCT
ap-658	317	11	,	,	PUNCT
ap-658	317	12	p.	p.	NOUN
ap-658	317	13	85–98	85–98	NUM
ap-658	317	14	.	.	PUNCT
ap-658	318	1	[	[	X
ap-658	318	2	27	27	NUM
ap-658	318	3	]	]	X
ap-658	318	4	valenta	valenta	PROPN
ap-658	318	5	r.	r.	PROPN
ap-658	318	6	:	:	PUNCT
ap-658	318	7	„	„	PUNCT
ap-658	318	8	numerické	numerické	ADJ
ap-658	318	9	modelování	modelování	NOUN
ap-658	318	10	polymerů	polymerů	NOUN
ap-658	318	11	“	"	PUNCT
ap-658	318	12	[	[	X
ap-658	318	13	numerical	numerical	ADJ
ap-658	318	14	modeling	modeling	NOUN
ap-658	318	15	of	of	ADP
ap-658	318	16	polymers	polymer	NOUN
ap-658	318	17	]	]	PUNCT
ap-658	318	18	,	,	PUNCT
ap-658	318	19	master	master	NOUN
ap-658	318	20	thesis	thesis	NOUN
ap-658	318	21	,	,	PUNCT
ap-658	318	22	czech	czech	PROPN
ap-658	318	23	technical	technical	PROPN
ap-658	318	24	university	university	PROPN
ap-658	318	25	in	in	ADP
ap-658	318	26	prague	prague	PROPN
ap-658	318	27	,	,	PUNCT
ap-658	318	28	(	(	PUNCT
ap-658	318	29	2003	2003	NUM
ap-658	318	30	)	)	PUNCT
ap-658	318	31	(	(	PUNCT
ap-658	318	32	in	in	ADP
ap-658	318	33	czech	czech	PROPN
ap-658	318	34	)	)	PUNCT
ap-658	318	35	.	.	PUNCT
ap-658	319	1	[	[	X
ap-658	319	2	28	28	NUM
ap-658	319	3	]	]	X
ap-658	319	4	valenta	valenta	PROPN
ap-658	319	5	r.	r.	PROPN
ap-658	319	6	:	:	PUNCT
ap-658	319	7	“	"	PUNCT
ap-658	319	8	numerical	numerical	ADJ
ap-658	319	9	implementation	implementation	NOUN
ap-658	319	10	of	of	ADP
ap-658	319	11	the	the	DET
ap-658	319	12	leonov	leonov	NOUN
ap-658	319	13	model	model	NOUN
ap-658	319	14	”	"	PUNCT
ap-658	319	15	,	,	PUNCT
ap-658	319	16	in	in	ADP
ap-658	319	17	engineering	engineering	NOUN
ap-658	319	18	mechanics	mechanic	NOUN
ap-658	319	19	2004	2004	NUM
ap-658	319	20	(	(	PUNCT
ap-658	319	21	i.	i.	PROPN
ap-658	319	22	zolotarev	zolotarev	PROPN
ap-658	319	23	–	–	PUNCT
ap-658	320	1	a.	a.	NOUN
ap-658	320	2	poživilová	poživilová	ADV
ap-658	320	3	,	,	PUNCT
ap-658	320	4	editors	editor	NOUN
ap-658	320	5	)	)	PUNCT
ap-658	320	6	,	,	PUNCT
ap-658	320	7	institute	institute	NOUN
ap-658	320	8	of	of	ADP
ap-658	320	9	thermomechanics	thermomechanic	NOUN
ap-658	320	10	,	,	PUNCT
ap-658	320	11	czech	czech	PROPN
ap-658	320	12	academy	academy	NOUN
ap-658	320	13	of	of	ADP
ap-658	320	14	science	science	PROPN
ap-658	320	15	,	,	PUNCT
ap-658	320	16	(	(	PUNCT
ap-658	320	17	2004	2004	NUM
ap-658	320	18	)	)	PUNCT
ap-658	320	19	,	,	PUNCT
ap-658	321	1	p.	p.	NOUN
ap-658	321	2	303–304	303–304	NUM
ap-658	321	3	.	.	PUNCT
ap-658	322	1	[	[	X
ap-658	322	2	29	29	NUM
ap-658	322	3	]	]	X
ap-658	322	4	valenta	valenta	PROPN
ap-658	322	5	r.	r.	PROPN
ap-658	322	6	,	,	PUNCT
ap-658	322	7	šejnoha	šejnoha	PROPN
ap-658	322	8	m.	m.	NOUN
ap-658	322	9	:	:	PUNCT
ap-658	322	10	”	"	PUNCT
ap-658	322	11	epoxy	epoxy	NOUN
ap-658	322	12	resin	resin	NOUN
ap-658	322	13	as	as	ADP
ap-658	322	14	a	a	DET
ap-658	322	15	bonding	bonding	NOUN
ap-658	322	16	agent	agent	NOUN
ap-658	322	17	in	in	ADP
ap-658	322	18	polymer	polymer	NOUN
ap-658	322	19	matrix	matrix	NOUN
ap-658	322	20	composites	composite	NOUN
ap-658	322	21	:	:	PUNCT
ap-658	322	22	material	material	NOUN
ap-658	322	23	properties	property	NOUN
ap-658	322	24	and	and	CCONJ
ap-658	322	25	numerical	numerical	ADJ
ap-658	322	26	implementation	implementation	NOUN
ap-658	322	27	.	.	PUNCT
ap-658	322	28	”	"	PUNCT
ap-658	323	1	to	to	PART
ap-658	323	2	be	be	AUX
ap-658	323	3	presented	present	VERB
ap-658	323	4	at	at	ADP
ap-658	323	5	icces’04	icces’04	PROPN
ap-658	323	6	madeira	madeira	PROPN
ap-658	323	7	,	,	PUNCT
ap-658	323	8	portugal	portugal	PROPN
ap-658	323	9	,	,	PUNCT
ap-658	323	10	july	july	PROPN
ap-658	323	11	26–29	26–29	NUM
ap-658	323	12	,	,	PUNCT
ap-658	323	13	2004	2004	NUM
ap-658	323	14	.	.	PUNCT
ap-658	324	1	ing	ing	PROPN
ap-658	324	2	.	.	PUNCT
ap-658	325	1	jan	jan	PROPN
ap-658	325	2	zeman	zeman	PROPN
ap-658	325	3	,	,	PUNCT
ap-658	325	4	ph.d	ph.d	PROPN
ap-658	325	5	.	.	PUNCT
ap-658	325	6	phone	phone	NOUN
ap-658	325	7	:	:	PUNCT
ap-658	325	8	+420	+420	PROPN
ap-658	325	9	224	224	NUM
ap-658	325	10	354	354	NUM
ap-658	325	11	482	482	NUM
ap-658	325	12	fax	fax	NOUN
ap-658	325	13	:	:	PUNCT
ap-658	325	14	+420	+420	PROPN
ap-658	325	15	224	224	NUM
ap-658	325	16	310	310	NUM
ap-658	325	17	775	775	NUM
ap-658	325	18	e	e	NOUN
ap-658	325	19	-	-	NOUN
ap-658	325	20	mail	mail	NOUN
ap-658	325	21	:	:	PUNCT
ap-658	325	22	zemanj@cml.fsv.cvut.cz	zemanj@cml.fsv.cvut.cz	NOUN
ap-658	325	23	ing	ing	PROPN
ap-658	325	24	.	.	PUNCT
ap-658	326	1	richard	richard	PROPN
ap-658	326	2	valenta	valenta	PROPN
ap-658	326	3	phone	phone	NOUN
ap-658	326	4	:	:	PUNCT
ap-658	326	5	+420	+420	PROPN
ap-658	326	6	224	224	NUM
ap-658	326	7	354	354	NUM
ap-658	326	8	472	472	NUM
ap-658	326	9	fax	fax	NOUN
ap-658	326	10	:	:	PUNCT
ap-658	326	11	+420	+420	PROPN
ap-658	326	12	224	224	NUM
ap-658	327	1	310	310	NUM
ap-658	327	2	775	775	NUM
ap-658	327	3	e	e	NOUN
ap-658	327	4	-	-	NOUN
ap-658	327	5	mail	mail	NOUN
ap-658	327	6	:	:	PUNCT
ap-658	327	7	richard.valenta@fsv.cvut.cz	richard.valenta@fsv.cvut.cz	NUM
ap-658	327	8	doc	doc	PROPN
ap-658	327	9	.	.	PROPN
ap-658	328	1	ing	ing	PROPN
ap-658	328	2	.	.	PUNCT
ap-658	329	1	michal	michal	PROPN
ap-658	329	2	šejnoha	šejnoha	PROPN
ap-658	329	3	,	,	PUNCT
ap-658	329	4	ph.d	ph.d	PROPN
ap-658	329	5	.	.	PUNCT
ap-658	329	6	phone	phone	NOUN
ap-658	329	7	:	:	PUNCT
ap-658	329	8	+420	+420	PROPN
ap-658	329	9	224	224	NUM
ap-658	329	10	354	354	NUM
ap-658	329	11	494	494	NUM
ap-658	329	12	fax	fax	NOUN
ap-658	329	13	:	:	PUNCT
ap-658	329	14	+420	+420	PROPN
ap-658	329	15	224	224	NUM
ap-658	329	16	310	310	NUM
ap-658	329	17	775	775	NUM
ap-658	329	18	e	e	NOUN
ap-658	329	19	-	-	NOUN
ap-658	329	20	mail	mail	NOUN
ap-658	329	21	:	:	PUNCT
ap-658	329	22	sejnom@fsv.cvut.cz	sejnom@fsv.cvut.cz	PROPN
ap-658	329	23	department	department	PROPN
ap-658	329	24	of	of	ADP
ap-658	329	25	structural	structural	ADJ
ap-658	329	26	mechanics	mechanic	NOUN
ap-658	329	27	czech	czech	PROPN
ap-658	329	28	technical	technical	PROPN
ap-658	329	29	university	university	PROPN
ap-658	329	30	in	in	ADP
ap-658	329	31	prague	prague	PROPN
ap-658	329	32	faculty	faculty	NOUN
ap-658	329	33	of	of	ADP
ap-658	329	34	civil	civil	ADJ
ap-658	329	35	engineering	engineering	NOUN
ap-658	329	36	thákurova	thákurova	VERB
ap-658	329	37	7	7	NUM
ap-658	329	38	166	166	NUM
ap-658	329	39	29	29	NUM
ap-658	329	40	prague	prague	NOUN
ap-658	329	41	6	6	NUM
ap-658	329	42	,	,	PUNCT
ap-658	329	43	czech	czech	PROPN
ap-658	329	44	republic	republic	NOUN
ap-658	329	45	©	©	PROPN
ap-658	329	46	czech	czech	PROPN
ap-658	329	47	technical	technical	PROPN
ap-658	329	48	university	university	PROPN
ap-658	329	49	publishing	publishing	NOUN
ap-658	329	50	house	house	NOUN
ap-658	329	51	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-658	329	52	209	209	NUM
ap-658	329	53	acta	acta	PROPN
ap-658	329	54	polytechnica	polytechnica	PROPN
ap-658	329	55	vol	vol	NOUN
ap-658	329	56	.	.	PROPN
ap-658	330	1	44	44	NUM
ap-658	330	2	no.5–6/2004	no.5–6/2004	NOUN