id	sid	tid	token	lemma	pos
ap-614	1	1	ap04-bittnar1.vp	ap04-bittnar1.vp	PROPN
ap-614	1	2	1	1	NUM
ap-614	1	3	introduction	introduction	NOUN
ap-614	1	4	a	a	DET
ap-614	1	5	variety	variety	NOUN
ap-614	1	6	of	of	ADP
ap-614	1	7	computational	computational	ADJ
ap-614	1	8	techniques	technique	NOUN
ap-614	1	9	exist	exist	VERB
ap-614	1	10	to	to	PART
ap-614	1	11	describe	describe	VERB
ap-614	1	12	the	the	DET
ap-614	1	13	fracture	fracture	ADJ
ap-614	1	14	behaviour	behaviour	NOUN
ap-614	1	15	of	of	ADP
ap-614	1	16	quasi	quasi	ADJ
ap-614	1	17	-	-	ADJ
ap-614	1	18	brittle	brittle	ADJ
ap-614	1	19	materials	material	NOUN
ap-614	1	20	.	.	PUNCT
ap-614	2	1	these	these	DET
ap-614	2	2	models	model	NOUN
ap-614	2	3	can	can	AUX
ap-614	2	4	be	be	AUX
ap-614	2	5	classified	classify	VERB
ap-614	2	6	into	into	ADP
ap-614	2	7	two	two	NUM
ap-614	2	8	main	main	ADJ
ap-614	2	9	groups	group	NOUN
ap-614	2	10	:	:	PUNCT
ap-614	2	11	continuous	continuous	ADJ
ap-614	2	12	and	and	CCONJ
ap-614	2	13	discontinuous	discontinuous	ADJ
ap-614	2	14	models	model	NOUN
ap-614	2	15	.	.	PUNCT
ap-614	3	1	in	in	ADP
ap-614	3	2	a	a	DET
ap-614	3	3	continuous	continuous	ADJ
ap-614	3	4	model	model	NOUN
ap-614	3	5	,	,	PUNCT
ap-614	3	6	the	the	DET
ap-614	3	7	displacement	displacement	NOUN
ap-614	3	8	and	and	CCONJ
ap-614	3	9	strain	strain	NOUN
ap-614	3	10	fields	field	NOUN
ap-614	3	11	remain	remain	VERB
ap-614	3	12	continuous	continuous	ADJ
ap-614	3	13	,	,	PUNCT
ap-614	3	14	even	even	ADV
ap-614	3	15	after	after	ADP
ap-614	3	16	a	a	DET
ap-614	3	17	strong	strong	ADJ
ap-614	3	18	localization	localization	NOUN
ap-614	3	19	of	of	ADP
ap-614	3	20	the	the	DET
ap-614	3	21	deformations	deformation	NOUN
ap-614	3	22	.	.	PUNCT
ap-614	4	1	localization	localization	NOUN
ap-614	4	2	of	of	ADP
ap-614	4	3	deformation	deformation	NOUN
ap-614	4	4	can	can	AUX
ap-614	4	5	be	be	AUX
ap-614	4	6	triggered	trigger	VERB
ap-614	4	7	by	by	ADP
ap-614	4	8	strain	strain	NOUN
ap-614	4	9	softening	soften	VERB
ap-614	4	10	.	.	PUNCT
ap-614	5	1	a	a	DET
ap-614	5	2	major	major	ADJ
ap-614	5	3	problem	problem	NOUN
ap-614	5	4	with	with	ADP
ap-614	5	5	classical	classical	ADJ
ap-614	5	6	continuum	continuum	ADJ
ap-614	5	7	models	model	NOUN
ap-614	5	8	is	be	AUX
ap-614	5	9	that	that	SCONJ
ap-614	5	10	the	the	DET
ap-614	5	11	governing	govern	VERB
ap-614	5	12	equations	equation	NOUN
ap-614	5	13	lose	lose	VERB
ap-614	5	14	ellipticity	ellipticity	NOUN
ap-614	5	15	for	for	ADP
ap-614	5	16	quasi	quasi	ADJ
ap-614	5	17	-	-	ADJ
ap-614	5	18	static	static	ADJ
ap-614	5	19	problems	problem	NOUN
ap-614	5	20	and	and	CCONJ
ap-614	5	21	hyperbolicity	hyperbolicity	NOUN
ap-614	5	22	for	for	ADP
ap-614	5	23	dynamic	dynamic	ADJ
ap-614	5	24	problems	problem	NOUN
ap-614	5	25	if	if	SCONJ
ap-614	5	26	strain	strain	ADJ
ap-614	5	27	softening	soften	VERB
ap-614	5	28	is	be	AUX
ap-614	5	29	introduced	introduce	VERB
ap-614	5	30	.	.	PUNCT
ap-614	6	1	when	when	SCONJ
ap-614	6	2	using	use	VERB
ap-614	6	3	finite	finite	ADJ
ap-614	6	4	elements	element	NOUN
ap-614	6	5	,	,	PUNCT
ap-614	6	6	this	this	PRON
ap-614	6	7	results	result	VERB
ap-614	6	8	in	in	ADP
ap-614	6	9	a	a	DET
ap-614	6	10	strong	strong	ADJ
ap-614	6	11	sensitivity	sensitivity	NOUN
ap-614	6	12	to	to	ADP
ap-614	6	13	the	the	DET
ap-614	6	14	mesh	mesh	NOUN
ap-614	6	15	.	.	PUNCT
ap-614	7	1	upon	upon	SCONJ
ap-614	7	2	mesh	mesh	NOUN
ap-614	7	3	refinement	refinement	NOUN
ap-614	7	4	,	,	PUNCT
ap-614	7	5	deformations	deformation	NOUN
ap-614	7	6	localize	localize	VERB
ap-614	7	7	into	into	ADP
ap-614	7	8	a	a	DET
ap-614	7	9	band	band	NOUN
ap-614	7	10	of	of	ADP
ap-614	7	11	zero	zero	NUM
ap-614	7	12	thickness	thickness	NOUN
ap-614	7	13	and	and	CCONJ
ap-614	7	14	complete	complete	ADJ
ap-614	7	15	structural	structural	ADJ
ap-614	7	16	failure	failure	NOUN
ap-614	7	17	can	can	AUX
ap-614	7	18	occur	occur	VERB
ap-614	7	19	without	without	ADP
ap-614	7	20	dissipation	dissipation	NOUN
ap-614	7	21	of	of	ADP
ap-614	7	22	energy	energy	NOUN
ap-614	7	23	.	.	PUNCT
ap-614	8	1	to	to	PART
ap-614	8	2	regularize	regularize	VERB
ap-614	8	3	the	the	DET
ap-614	8	4	governing	govern	VERB
ap-614	8	5	differential	differential	ADJ
ap-614	8	6	equations	equation	NOUN
ap-614	8	7	,	,	PUNCT
ap-614	8	8	non	non	ADJ
ap-614	8	9	-	-	ADJ
ap-614	8	10	locality	locality	ADJ
ap-614	8	11	or	or	CCONJ
ap-614	8	12	rate	rate	NOUN
ap-614	8	13	dependency	dependency	NOUN
ap-614	8	14	can	can	AUX
ap-614	8	15	be	be	AUX
ap-614	8	16	introduced	introduce	VERB
ap-614	8	17	in	in	ADP
ap-614	8	18	the	the	DET
ap-614	8	19	constitutive	constitutive	ADJ
ap-614	8	20	model	model	NOUN
ap-614	8	21	.	.	PUNCT
ap-614	9	1	this	this	PRON
ap-614	9	2	controls	control	VERB
ap-614	9	3	the	the	DET
ap-614	9	4	zone	zone	NOUN
ap-614	9	5	in	in	ADP
ap-614	9	6	which	which	PRON
ap-614	9	7	the	the	DET
ap-614	9	8	deformations	deformation	NOUN
ap-614	9	9	tend	tend	VERB
ap-614	9	10	to	to	PART
ap-614	9	11	localize	localize	VERB
ap-614	9	12	.	.	PUNCT
ap-614	10	1	examples	example	NOUN
ap-614	10	2	of	of	ADP
ap-614	10	3	regularized	regularize	VERB
ap-614	10	4	continuum	continuum	ADJ
ap-614	10	5	models	model	NOUN
ap-614	10	6	are	be	AUX
ap-614	10	7	non	non	ADJ
ap-614	10	8	-	-	ADJ
ap-614	10	9	local	local	ADJ
ap-614	10	10	damage	damage	NOUN
ap-614	10	11	models	model	NOUN
ap-614	10	12	[	[	X
ap-614	10	13	1	1	NUM
ap-614	10	14	]	]	PUNCT
ap-614	10	15	,	,	PUNCT
ap-614	10	16	gradient	gradient	ADJ
ap-614	10	17	damage	damage	NOUN
ap-614	10	18	models	model	NOUN
ap-614	10	19	[	[	X
ap-614	10	20	2	2	NUM
ap-614	10	21	]	]	PUNCT
ap-614	10	22	,	,	PUNCT
ap-614	10	23	cosserat	cosserat	ADJ
ap-614	10	24	continuum	continuum	ADJ
ap-614	10	25	models	model	NOUN
ap-614	10	26	[	[	X
ap-614	10	27	3	3	X
ap-614	10	28	]	]	PUNCT
ap-614	10	29	or	or	CCONJ
ap-614	10	30	viscous	viscous	ADJ
ap-614	10	31	models	model	NOUN
ap-614	10	32	[	[	X
ap-614	10	33	4	4	NUM
ap-614	10	34	,	,	PUNCT
ap-614	10	35	5	5	NUM
ap-614	10	36	]	]	PUNCT
ap-614	10	37	.	.	PUNCT
ap-614	11	1	discontinuous	discontinuous	ADJ
ap-614	11	2	models	model	NOUN
ap-614	11	3	represent	represent	VERB
ap-614	11	4	cracks	crack	NOUN
ap-614	11	5	as	as	ADP
ap-614	11	6	displacement	displacement	ADJ
ap-614	11	7	discontinuities	discontinuity	NOUN
ap-614	11	8	.	.	PUNCT
ap-614	12	1	a	a	DET
ap-614	12	2	discontinuous	discontinuous	ADJ
ap-614	12	3	term	term	NOUN
ap-614	12	4	can	can	AUX
ap-614	12	5	be	be	AUX
ap-614	12	6	incorporated	incorporate	VERB
ap-614	12	7	into	into	ADP
ap-614	12	8	the	the	DET
ap-614	12	9	strain	strain	NOUN
ap-614	12	10	field	field	NOUN
ap-614	12	11	(	(	PUNCT
ap-614	12	12	weak	weak	ADJ
ap-614	12	13	discontinuity	discontinuity	NOUN
ap-614	12	14	)	)	PUNCT
ap-614	13	1	[	[	X
ap-614	13	2	6–8	6–8	X
ap-614	13	3	]	]	X
ap-614	13	4	or	or	CCONJ
ap-614	13	5	into	into	ADP
ap-614	13	6	the	the	DET
ap-614	13	7	displacement	displacement	ADJ
ap-614	13	8	field	field	NOUN
ap-614	13	9	(	(	PUNCT
ap-614	13	10	strong	strong	ADJ
ap-614	13	11	discontinuity	discontinuity	NOUN
ap-614	13	12	)	)	PUNCT
ap-614	14	1	[	[	X
ap-614	14	2	9–18	9–18	NOUN
ap-614	14	3	]	]	PUNCT
ap-614	14	4	.	.	PUNCT
ap-614	15	1	in	in	ADP
ap-614	15	2	this	this	DET
ap-614	15	3	paper	paper	NOUN
ap-614	15	4	,	,	PUNCT
ap-614	15	5	a	a	DET
ap-614	15	6	displacement	displacement	ADJ
ap-614	15	7	discontinuity	discontinuity	NOUN
ap-614	15	8	is	be	AUX
ap-614	15	9	introduced	introduce	VERB
ap-614	15	10	using	use	VERB
ap-614	15	11	a	a	DET
ap-614	15	12	specific	specific	ADJ
ap-614	15	13	property	property	NOUN
ap-614	15	14	of	of	ADP
ap-614	15	15	finite	finite	ADJ
ap-614	15	16	element	element	NOUN
ap-614	15	17	shape	shape	NOUN
ap-614	15	18	functions	function	NOUN
ap-614	15	19	.	.	PUNCT
ap-614	16	1	these	these	PRON
ap-614	16	2	form	form	VERB
ap-614	16	3	a	a	DET
ap-614	16	4	partition	partition	NOUN
ap-614	16	5	of	of	ADP
ap-614	16	6	unity	unity	NOUN
ap-614	16	7	,	,	PUNCT
ap-614	16	8	which	which	PRON
ap-614	16	9	allows	allow	VERB
ap-614	16	10	enhancing	enhance	VERB
ap-614	16	11	nodes	node	NOUN
ap-614	16	12	with	with	ADP
ap-614	16	13	additional	additional	ADJ
ap-614	16	14	degrees	degree	NOUN
ap-614	16	15	of	of	ADP
ap-614	16	16	freedom	freedom	NOUN
ap-614	16	17	.	.	PUNCT
ap-614	17	1	the	the	DET
ap-614	17	2	first	first	ADJ
ap-614	17	3	section	section	NOUN
ap-614	17	4	covers	cover	VERB
ap-614	17	5	the	the	DET
ap-614	17	6	kinematics	kinematic	NOUN
ap-614	17	7	of	of	ADP
ap-614	17	8	a	a	DET
ap-614	17	9	body	body	NOUN
ap-614	17	10	crossed	cross	VERB
ap-614	17	11	by	by	ADP
ap-614	17	12	a	a	DET
ap-614	17	13	discontinuity	discontinuity	NOUN
ap-614	17	14	.	.	PUNCT
ap-614	18	1	then	then	ADV
ap-614	18	2	,	,	PUNCT
ap-614	18	3	the	the	DET
ap-614	18	4	governing	govern	VERB
ap-614	18	5	equations	equation	NOUN
ap-614	18	6	are	be	AUX
ap-614	18	7	derived	derive	VERB
ap-614	18	8	.	.	PUNCT
ap-614	19	1	in	in	ADP
ap-614	19	2	the	the	DET
ap-614	19	3	third	third	ADJ
ap-614	19	4	section	section	NOUN
ap-614	19	5	,	,	PUNCT
ap-614	19	6	implementation	implementation	NOUN
ap-614	19	7	aspects	aspect	NOUN
ap-614	19	8	are	be	AUX
ap-614	19	9	discussed	discuss	VERB
ap-614	19	10	and	and	CCONJ
ap-614	19	11	finally	finally	ADV
ap-614	19	12	an	an	DET
ap-614	19	13	example	example	NOUN
ap-614	19	14	is	be	AUX
ap-614	19	15	treated	treat	VERB
ap-614	19	16	.	.	PUNCT
ap-614	20	1	2	2	NUM
ap-614	20	2	cohesive	cohesive	ADJ
ap-614	20	3	zone	zone	NOUN
ap-614	20	4	model	model	NOUN
ap-614	20	5	based	base	VERB
ap-614	20	6	on	on	ADP
ap-614	20	7	partitions	partition	NOUN
ap-614	20	8	of	of	ADP
ap-614	20	9	unity	unity	NOUN
ap-614	20	10	2.1	2.1	NUM
ap-614	20	11	kinematics	kinematic	NOUN
ap-614	20	12	of	of	ADP
ap-614	20	13	a	a	DET
ap-614	20	14	displacement	displacement	NOUN
ap-614	20	15	jump	jump	NOUN
ap-614	20	16	consider	consider	VERB
ap-614	20	17	a	a	DET
ap-614	20	18	body	body	NOUN
ap-614	20	19	�	�	NOUN
ap-614	20	20	crossed	cross	VERB
ap-614	20	21	by	by	ADP
ap-614	20	22	2	2	NUM
ap-614	20	23	non	non	ADJ
ap-614	20	24	-	-	ADJ
ap-614	20	25	intersecting	intersecting	ADJ
ap-614	20	26	discontinuities	discontinuity	NOUN
ap-614	20	27	,	,	PUNCT
ap-614	20	28	�	�	PROPN
ap-614	20	29	1	1	NUM
ap-614	20	30	and	and	CCONJ
ap-614	20	31	�	�	NOUN
ap-614	20	32	2	2	NUM
ap-614	20	33	,	,	PUNCT
ap-614	20	34	as	as	SCONJ
ap-614	20	35	shown	show	VERB
ap-614	20	36	in	in	ADP
ap-614	20	37	fig	fig	NOUN
ap-614	20	38	.	.	PUNCT
ap-614	21	1	1	1	X
ap-614	21	2	.	.	X
ap-614	21	3	the	the	DET
ap-614	21	4	displacement	displacement	ADJ
ap-614	21	5	field	field	NOUN
ap-614	21	6	is	be	AUX
ap-614	21	7	given	give	VERB
ap-614	21	8	by	by	ADP
ap-614	21	9	:	:	PUNCT
ap-614	21	10	u	u	NOUN
ap-614	21	11	u	u	NOUN
ap-614	21	12	u	u	PRON
ap-614	21	13	�	�	PROPN
ap-614	21	14	�	�	PROPN
ap-614	21	15	�	�	PROPN
ap-614	21	16	�	�	PROPN
ap-614	21	17	�	�	PROPN
ap-614	21	18	~h	~h	PROPN
ap-614	21	19	�	�	PROPN
ap-614	21	20	i	i	PRON
ap-614	22	1	i	i	PRON
ap-614	22	2	i	i	PRON
ap-614	22	3	m	m	VERB
ap-614	22	4	1	1	NUM
ap-614	22	5	,	,	PUNCT
ap-614	22	6	(	(	PUNCT
ap-614	22	7	1	1	X
ap-614	22	8	)	)	PUNCT
ap-614	22	9	where	where	SCONJ
ap-614	22	10	u	u	NOUN
ap-614	22	11	is	be	AUX
ap-614	22	12	the	the	DET
ap-614	22	13	displacement	displacement	ADJ
ap-614	22	14	field	field	NOUN
ap-614	22	15	of	of	ADP
ap-614	22	16	the	the	DET
ap-614	22	17	body	body	NOUN
ap-614	22	18	�	�	PROPN
ap-614	22	19	,	,	PUNCT
ap-614	22	20	�	�	NOUN
ap-614	22	21	u	u	NOUN
ap-614	22	22	and	and	CCONJ
ap-614	22	23	~u	~u	NUM
ap-614	22	24	i	i	PRON
ap-614	22	25	are	be	AUX
ap-614	22	26	continuous	continuous	ADJ
ap-614	22	27	fields	field	NOUN
ap-614	22	28	and	and	CCONJ
ap-614	22	29	h	h	NOUN
ap-614	22	30	�	�	PROPN
ap-614	22	31	i	i	PRON
ap-614	22	32	is	be	AUX
ap-614	22	33	the	the	DET
ap-614	22	34	heaviside	heaviside	ADJ
ap-614	22	35	step	step	NOUN
ap-614	22	36	function	function	NOUN
ap-614	22	37	defined	define	VERB
ap-614	22	38	as	as	ADP
ap-614	22	39	:	:	PUNCT
ap-614	22	40	h	h	PROPN
ap-614	22	41	�	�	PROPN
ap-614	22	42	�	�	PROPN
ap-614	22	43	�	�	PROPN
ap-614	22	44	i	i	PRON
ap-614	23	1	i	i	PRON
ap-614	23	2	i	i	PRON
ap-614	23	3	�	�	PROPN
ap-614	23	4	�	�	PROPN
ap-614	23	5	�	�	PROPN
ap-614	23	6	�	�	PROPN
ap-614	23	7	�	�	PROPN
ap-614	23	8	�	�	PROPN
ap-614	23	9	�	�	PROPN
ap-614	23	10	�	�	PROPN
ap-614	23	11	1	1	NUM
ap-614	23	12	0	0	NUM
ap-614	23	13	x	x	SYM
ap-614	23	14	x	x	X
ap-614	23	15	(	(	PUNCT
ap-614	23	16	2	2	NUM
ap-614	23	17	)	)	PUNCT
ap-614	23	18	where	where	SCONJ
ap-614	23	19	�	�	PROPN
ap-614	23	20	i	i	PRON
ap-614	23	21	�	�	PROPN
ap-614	23	22	and	and	CCONJ
ap-614	23	23	�	�	PROPN
ap-614	23	24	i	i	PRON
ap-614	23	25	are	be	AUX
ap-614	23	26	subvolumes	subvolume	NOUN
ap-614	23	27	of	of	ADP
ap-614	23	28	�	�	PROPN
ap-614	23	29	such	such	ADJ
ap-614	23	30	that	that	PRON
ap-614	23	31	w	w	NOUN
ap-614	23	32	i	i	PRON
ap-614	23	33	i	i	PROPN
ap-614	23	34	�	�	PROPN
ap-614	23	35	�	�	PROPN
ap-614	23	36	�	�	PROPN
ap-614	23	37	�	�	PROPN
ap-614	23	38	�	�	PROPN
ap-614	23	39	and	and	CCONJ
ap-614	23	40	the	the	DET
ap-614	23	41	discontinuity	discontinuity	NOUN
ap-614	23	42	�	�	NOUN
ap-614	23	43	i	i	PRON
ap-614	23	44	is	be	AUX
ap-614	23	45	the	the	DET
ap-614	23	46	border	border	NOUN
ap-614	23	47	between	between	ADP
ap-614	23	48	the	the	DET
ap-614	23	49	two	two	NUM
ap-614	23	50	subvolumes	subvolume	NOUN
ap-614	23	51	.	.	PUNCT
ap-614	24	1	the	the	DET
ap-614	24	2	normal	normal	ADJ
ap-614	24	3	ni	ni	PROPN
ap-614	24	4	to	to	ADP
ap-614	24	5	the	the	DET
ap-614	24	6	discontinuity	discontinuity	NOUN
ap-614	24	7	is	be	AUX
ap-614	24	8	pointed	point	VERB
ap-614	24	9	towards	towards	ADP
ap-614	24	10	�	�	PROPN
ap-614	24	11	i	i	PRON
ap-614	24	12	�	�	PROPN
ap-614	24	13	.	.	PUNCT
ap-614	25	1	taking	take	VERB
ap-614	25	2	the	the	DET
ap-614	25	3	symmetric	symmetric	ADJ
ap-614	25	4	gradient	gradient	NOUN
ap-614	25	5	of	of	ADP
ap-614	25	6	the	the	DET
ap-614	25	7	displacement	displacement	ADJ
ap-614	25	8	field	field	NOUN
ap-614	25	9	(	(	PUNCT
ap-614	25	10	1	1	X
ap-614	25	11	)	)	PUNCT
ap-614	25	12	results	result	NOUN
ap-614	25	13	in	in	ADP
ap-614	25	14	the	the	DET
ap-614	25	15	infinitesimal	infinitesimal	ADJ
ap-614	25	16	strain	strain	NOUN
ap-614	25	17	field	field	NOUN
ap-614	25	18	:	:	PUNCT
ap-614	25	19	�	�	PROPN
ap-614	25	20	�	�	PROPN
ap-614	25	21	�	�	PROPN
ap-614	25	22	�	�	PROPN
ap-614	25	23	�	�	PROPN
ap-614	25	24	�	�	PROPN
ap-614	25	25	�	�	PROPN
ap-614	25	26	�	�	PROPN
ap-614	25	27	s	s	PART
ap-614	25	28	s	s	X
ap-614	25	29	i	i	PRON
ap-614	25	30	i=	i=	VERB
ap-614	25	31	m	m	VERB
ap-614	26	1	i	i	INTJ
ap-614	27	1	i	i	PRON
ap-614	27	2	s	s	VERB
ap-614	27	3	i=	i=	NOUN
ap-614	28	1	m	m	VERB
ap-614	29	1	i	i	PRON
ap-614	29	2	i	i	PRON
ap-614	29	3	�	�	X
ap-614	29	4	~	~	PUNCT
ap-614	29	5	(	(	PUNCT
ap-614	29	6	~	~	PUNCT
ap-614	29	7	)	)	PUNCT
ap-614	29	8	u	u	NOUN
ap-614	29	9	u	u	PROPN
ap-614	29	10	u	u	PROPN
ap-614	29	11	nh	nh	PROPN
ap-614	29	12	�	�	PROPN
ap-614	29	13	�	�	PROPN
ap-614	29	14	1	1	NUM
ap-614	29	15	1	1	NUM
ap-614	29	16	�	�	PROPN
ap-614	29	17	(	(	PUNCT
ap-614	29	18	3	3	NUM
ap-614	29	19	)	)	PUNCT
ap-614	29	20	where	where	SCONJ
ap-614	29	21	�	�	PROPN
ap-614	29	22	�	�	PROPN
ap-614	29	23	i	i	PRON
ap-614	29	24	is	be	AUX
ap-614	29	25	the	the	DET
ap-614	29	26	dirac	dirac	NOUN
ap-614	29	27	delta	delta	NOUN
ap-614	29	28	distribution	distribution	NOUN
ap-614	29	29	centred	centre	VERB
ap-614	29	30	on	on	ADP
ap-614	29	31	the	the	DET
ap-614	29	32	discontinuity	discontinuity	NOUN
ap-614	29	33	.	.	PUNCT
ap-614	30	1	2.2	2.2	NUM
ap-614	30	2	partition	partition	NOUN
ap-614	30	3	of	of	ADP
ap-614	30	4	unity	unity	NOUN
ap-614	30	5	concept	concept	NOUN
ap-614	30	6	a	a	DET
ap-614	30	7	partition	partition	NOUN
ap-614	30	8	of	of	ADP
ap-614	30	9	unity	unity	NOUN
ap-614	30	10	is	be	AUX
ap-614	30	11	a	a	DET
ap-614	30	12	set	set	NOUN
ap-614	30	13	of	of	ADP
ap-614	30	14	functions	function	NOUN
ap-614	30	15	ni	ni	PROPN
ap-614	30	16	,	,	PUNCT
ap-614	30	17	such	such	ADJ
ap-614	30	18	that	that	SCONJ
ap-614	30	19	:	:	PUNCT
ap-614	30	20	ni	ni	PROPN
ap-614	30	21	i	i	PROPN
ap-614	30	22	n	n	PROPN
ap-614	30	23	(	(	PUNCT
ap-614	30	24	)	)	PUNCT
ap-614	30	25	x	x	PROPN
ap-614	30	26	�	�	PROPN
ap-614	30	27	�	�	PROPN
ap-614	30	28	�	�	PROPN
ap-614	30	29	1	1	NUM
ap-614	30	30	1	1	NUM
ap-614	30	31	(	(	PUNCT
ap-614	30	32	4	4	NUM
ap-614	30	33	)	)	PUNCT
ap-614	30	34	42	42	NUM
ap-614	30	35	©	©	PROPN
ap-614	30	36	czech	czech	PROPN
ap-614	30	37	technical	technical	PROPN
ap-614	30	38	university	university	PROPN
ap-614	30	39	publishing	publishing	NOUN
ap-614	30	40	house	house	NOUN
ap-614	30	41	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	30	42	acta	acta	PROPN
ap-614	30	43	polytechnica	polytechnica	PROPN
ap-614	30	44	vol	vol	NOUN
ap-614	30	45	.	.	PROPN
ap-614	31	1	44	44	NUM
ap-614	31	2	no	no	NOUN
ap-614	31	3	.	.	PUNCT
ap-614	32	1	5–6/2004	5–6/2004	NUM
ap-614	32	2	a	a	DET
ap-614	32	3	discontinuous	discontinuous	ADJ
ap-614	32	4	model	model	NOUN
ap-614	32	5	to	to	PART
ap-614	32	6	study	study	VERB
ap-614	32	7	fracture	fracture	NOUN
ap-614	32	8	of	of	ADP
ap-614	32	9	brittle	brittle	ADJ
ap-614	32	10	materials	material	NOUN
ap-614	32	11	k.	k.	PROPN
ap-614	32	12	de	de	PROPN
ap-614	32	13	proft	proft	PROPN
ap-614	32	14	,	,	PUNCT
ap-614	32	15	w.	w.	PROPN
ap-614	32	16	p.	p.	PROPN
ap-614	32	17	de	de	PROPN
ap-614	32	18	wilde	wilde	PROPN
ap-614	32	19	in	in	ADP
ap-614	32	20	this	this	DET
ap-614	32	21	paper	paper	NOUN
ap-614	32	22	,	,	PUNCT
ap-614	32	23	the	the	DET
ap-614	32	24	partition	partition	NOUN
ap-614	32	25	of	of	ADP
ap-614	32	26	the	the	DET
ap-614	32	27	unity	unity	NOUN
ap-614	32	28	property	property	NOUN
ap-614	32	29	of	of	ADP
ap-614	32	30	finite	finite	ADJ
ap-614	32	31	element	element	NOUN
ap-614	32	32	shape	shape	NOUN
ap-614	32	33	functions	function	NOUN
ap-614	32	34	is	be	AUX
ap-614	32	35	used	use	VERB
ap-614	32	36	to	to	PART
ap-614	32	37	introduce	introduce	VERB
ap-614	32	38	displacement	displacement	ADJ
ap-614	32	39	discontinuities	discontinuity	NOUN
ap-614	32	40	into	into	ADP
ap-614	32	41	finite	finite	ADJ
ap-614	32	42	elements	element	NOUN
ap-614	32	43	.	.	PUNCT
ap-614	33	1	the	the	DET
ap-614	33	2	discontinuous	discontinuous	ADJ
ap-614	33	3	character	character	NOUN
ap-614	33	4	of	of	ADP
ap-614	33	5	the	the	DET
ap-614	33	6	displacement	displacement	ADJ
ap-614	33	7	field	field	NOUN
ap-614	33	8	is	be	AUX
ap-614	33	9	captured	capture	VERB
ap-614	33	10	with	with	ADP
ap-614	33	11	the	the	DET
ap-614	33	12	heaviside	heaviside	ADJ
ap-614	33	13	step	step	NOUN
ap-614	33	14	function	function	NOUN
ap-614	33	15	.	.	PUNCT
ap-614	34	1	using	use	VERB
ap-614	34	2	the	the	DET
ap-614	34	3	partition	partition	NOUN
ap-614	34	4	of	of	ADP
ap-614	34	5	unity	unity	NOUN
ap-614	34	6	concept	concept	NOUN
ap-614	34	7	,	,	PUNCT
ap-614	34	8	the	the	DET
ap-614	34	9	governing	govern	VERB
ap-614	34	10	equation	equation	NOUN
ap-614	34	11	of	of	ADP
ap-614	34	12	the	the	DET
ap-614	34	13	continuum	continuum	NOUN
ap-614	34	14	and	and	CCONJ
ap-614	34	15	the	the	DET
ap-614	34	16	discontinuity	discontinuity	NOUN
ap-614	34	17	are	be	AUX
ap-614	34	18	separated	separate	VERB
ap-614	34	19	and	and	CCONJ
ap-614	34	20	are	be	AUX
ap-614	34	21	consequently	consequently	ADV
ap-614	34	22	described	describe	VERB
ap-614	34	23	by	by	ADP
ap-614	34	24	different	different	ADJ
ap-614	34	25	constitutive	constitutive	ADJ
ap-614	34	26	laws	law	NOUN
ap-614	34	27	.	.	PUNCT
ap-614	35	1	inside	inside	ADP
ap-614	35	2	the	the	DET
ap-614	35	3	discontinuity	discontinuity	NOUN
ap-614	35	4	,	,	PUNCT
ap-614	35	5	a	a	DET
ap-614	35	6	plasticity	plasticity	NOUN
ap-614	35	7	based	base	VERB
ap-614	35	8	constitutive	constitutive	ADJ
ap-614	35	9	law	law	NOUN
ap-614	35	10	is	be	AUX
ap-614	35	11	used	use	VERB
ap-614	35	12	to	to	PART
ap-614	35	13	describe	describe	VERB
ap-614	35	14	the	the	DET
ap-614	35	15	decrease	decrease	NOUN
ap-614	35	16	of	of	ADP
ap-614	35	17	tractions	traction	NOUN
ap-614	35	18	in	in	ADP
ap-614	35	19	function	function	NOUN
ap-614	35	20	of	of	ADP
ap-614	35	21	the	the	DET
ap-614	35	22	crack	crack	NOUN
ap-614	35	23	opening	opening	NOUN
ap-614	35	24	while	while	SCONJ
ap-614	35	25	the	the	DET
ap-614	35	26	continuum	continuum	NOUN
ap-614	35	27	is	be	AUX
ap-614	35	28	assumed	assume	VERB
ap-614	35	29	to	to	PART
ap-614	35	30	remain	remain	VERB
ap-614	35	31	elastic	elastic	ADJ
ap-614	35	32	.	.	PUNCT
ap-614	36	1	the	the	DET
ap-614	36	2	methodology	methodology	NOUN
ap-614	36	3	will	will	AUX
ap-614	36	4	be	be	AUX
ap-614	36	5	described	describe	VERB
ap-614	36	6	and	and	CCONJ
ap-614	36	7	validated	validate	VERB
ap-614	36	8	with	with	ADP
ap-614	36	9	a	a	DET
ap-614	36	10	comparison	comparison	NOUN
ap-614	36	11	between	between	ADP
ap-614	36	12	numerical	numerical	ADJ
ap-614	36	13	simulations	simulation	NOUN
ap-614	36	14	and	and	CCONJ
ap-614	36	15	experimental	experimental	ADJ
ap-614	36	16	results	result	NOUN
ap-614	36	17	.	.	PUNCT
ap-614	37	1	this	this	DET
ap-614	37	2	paper	paper	NOUN
ap-614	37	3	is	be	AUX
ap-614	37	4	dedicated	dedicate	VERB
ap-614	37	5	to	to	ADP
ap-614	37	6	j.	j.	PROPN
ap-614	37	7	sejnoha	sejnoha	PROPN
ap-614	37	8	,	,	PUNCT
ap-614	37	9	tu	tu	PROPN
ap-614	37	10	prague	prague	PROPN
ap-614	37	11	,	,	PUNCT
ap-614	37	12	with	with	ADP
ap-614	37	13	respect	respect	NOUN
ap-614	37	14	and	and	CCONJ
ap-614	37	15	admiration	admiration	NOUN
ap-614	37	16	for	for	ADP
ap-614	37	17	his	his	PRON
ap-614	37	18	scientific	scientific	ADJ
ap-614	37	19	achievement	achievement	NOUN
ap-614	37	20	.	.	PUNCT
ap-614	38	1	1	1	NUM
ap-614	38	2	2	2	NUM
ap-614	38	3	n1	n1	NOUN
ap-614	38	4	n2	n2	NOUN
ap-614	38	5	se	se	PROPN
ap-614	38	6	t	t	PROPN
ap-614	38	7	�	�	PROPN
ap-614	38	8	1	1	NUM
ap-614	38	9	�	�	PROPN
ap-614	38	10	2	2	NUM
ap-614	38	11	n1	n1	PROPN
ap-614	38	12	n2	n2	NOUN
ap-614	38	13	se	se	PROPN
ap-614	38	14	t	t	PROPN
ap-614	38	15	�	�	PROPN
ap-614	38	16	�	�	PROPN
ap-614	38	17	2	2	NUM
ap-614	38	18	�	�	PROPN
ap-614	38	19	�	�	PROPN
ap-614	38	20	2	2	NUM
ap-614	38	21	�	�	PROPN
ap-614	38	22	�	�	PROPN
ap-614	38	23	1	1	NUM
ap-614	38	24	�	�	PROPN
ap-614	38	25	�	�	PROPN
ap-614	38	26	1	1	NUM
ap-614	38	27	fig	fig	NOUN
ap-614	38	28	.	.	PUNCT
ap-614	39	1	1	1	NUM
ap-614	39	2	:	:	PUNCT
ap-614	39	3	body	body	NOUN
ap-614	39	4	crossed	cross	VERB
ap-614	39	5	by	by	ADP
ap-614	39	6	2	2	NUM
ap-614	39	7	discontinuities	discontinuity	NOUN
ap-614	39	8	where	where	SCONJ
ap-614	39	9	n	n	X
ap-614	39	10	is	be	AUX
ap-614	39	11	the	the	DET
ap-614	39	12	number	number	NOUN
ap-614	39	13	of	of	ADP
ap-614	39	14	discrete	discrete	ADJ
ap-614	39	15	points	point	NOUN
ap-614	39	16	.	.	PUNCT
ap-614	40	1	since	since	SCONJ
ap-614	40	2	finite	finite	PROPN
ap-614	40	3	element	element	NOUN
ap-614	40	4	shape	shape	NOUN
ap-614	40	5	functions	function	NOUN
ap-614	40	6	must	must	AUX
ap-614	40	7	be	be	AUX
ap-614	40	8	able	able	ADJ
ap-614	40	9	to	to	PART
ap-614	40	10	describe	describe	VERB
ap-614	40	11	rigid	rigid	ADJ
ap-614	40	12	body	body	NOUN
ap-614	40	13	modes	mode	NOUN
ap-614	40	14	,	,	PUNCT
ap-614	40	15	they	they	PRON
ap-614	40	16	must	must	AUX
ap-614	40	17	fulfil	fulfil	VERB
ap-614	40	18	eq	eq	PROPN
ap-614	40	19	.	.	PUNCT
ap-614	41	1	(	(	PUNCT
ap-614	41	2	4	4	NUM
ap-614	41	3	)	)	PUNCT
ap-614	41	4	and	and	CCONJ
ap-614	41	5	consequently	consequently	ADV
ap-614	41	6	they	they	PRON
ap-614	41	7	form	form	VERB
ap-614	41	8	a	a	DET
ap-614	41	9	partition	partition	NOUN
ap-614	41	10	of	of	ADP
ap-614	41	11	unity	unity	NOUN
ap-614	41	12	.	.	PUNCT
ap-614	42	1	duarte	duarte	PROPN
ap-614	42	2	and	and	CCONJ
ap-614	42	3	oden	oden	PROPN
ap-614	43	1	[	[	X
ap-614	43	2	19	19	NUM
ap-614	43	3	]	]	PUNCT
ap-614	43	4	showed	show	VERB
ap-614	43	5	that	that	SCONJ
ap-614	43	6	a	a	DET
ap-614	43	7	field	field	NOUN
ap-614	43	8	such	such	ADJ
ap-614	43	9	as	as	ADP
ap-614	43	10	the	the	DET
ap-614	43	11	displacement	displacement	ADJ
ap-614	43	12	field	field	NOUN
ap-614	43	13	can	can	AUX
ap-614	43	14	be	be	AUX
ap-614	43	15	interpolated	interpolate	VERB
ap-614	43	16	making	make	VERB
ap-614	43	17	use	use	NOUN
ap-614	43	18	of	of	ADP
ap-614	43	19	these	these	DET
ap-614	43	20	partitions	partition	NOUN
ap-614	43	21	of	of	ADP
ap-614	43	22	unity	unity	NOUN
ap-614	43	23	,	,	PUNCT
ap-614	43	24	u	u	NOUN
ap-614	43	25	�	�	PROPN
ap-614	43	26	�	�	PROPN
ap-614	43	27	�	�	PROPN
ap-614	43	28	�	�	PROPN
ap-614	43	29	�	�	PROPN
ap-614	43	30	�	�	PROPN
ap-614	43	31	�	�	PROPN
ap-614	43	32	�	�	PROPN
ap-614	43	33	�	�	PROPN
ap-614	43	34	�	�	PROPN
ap-614	43	35	�	�	PROPN
ap-614	43	36	�	�	PROPN
ap-614	43	37	�	�	PROPN
ap-614	43	38	�	�	PROPN
ap-614	43	39	�	�	PROPN
ap-614	43	40	�	�	PROPN
ap-614	43	41	n	n	CCONJ
ap-614	43	42	a	a	DET
ap-614	43	43	bi	bi	NOUN
ap-614	44	1	i	i	PRON
ap-614	44	2	ij	ij	VERB
ap-614	44	3	j	j	PROPN
ap-614	45	1	j	j	PROPN
ap-614	45	2	k	k	PROPN
ap-614	46	1	i	i	PROPN
ap-614	46	2	n	n	PROPN
ap-614	46	3	�	�	PROPN
ap-614	46	4	11	11	NUM
ap-614	46	5	,	,	PUNCT
ap-614	46	6	(	(	PUNCT
ap-614	46	7	5	5	NUM
ap-614	46	8	)	)	PUNCT
ap-614	46	9	where	where	SCONJ
ap-614	46	10	ai	ai	NOUN
ap-614	46	11	are	be	AUX
ap-614	46	12	the	the	DET
ap-614	46	13	regular	regular	ADJ
ap-614	46	14	degrees	degree	NOUN
ap-614	46	15	of	of	ADP
ap-614	46	16	freedom	freedom	NOUN
ap-614	46	17	,	,	PUNCT
ap-614	46	18	bij	bij	NOUN
ap-614	46	19	are	be	AUX
ap-614	46	20	the	the	DET
ap-614	46	21	enhanced	enhance	VERB
ap-614	46	22	degrees	degree	NOUN
ap-614	46	23	of	of	ADP
ap-614	46	24	freedom	freedom	NOUN
ap-614	46	25	and	and	CCONJ
ap-614	46	26	�	�	PROPN
ap-614	46	27	j	j	PROPN
ap-614	46	28	is	be	AUX
ap-614	46	29	an	an	DET
ap-614	46	30	enhanced	enhanced	ADJ
ap-614	46	31	basis	basis	NOUN
ap-614	46	32	with	with	ADP
ap-614	46	33	k	k	PROPN
ap-614	46	34	basis	basis	NOUN
ap-614	46	35	terms	term	NOUN
ap-614	46	36	.	.	PUNCT
ap-614	47	1	as	as	SCONJ
ap-614	47	2	can	can	AUX
ap-614	47	3	be	be	AUX
ap-614	47	4	seen	see	VERB
ap-614	47	5	,	,	PUNCT
ap-614	47	6	the	the	DET
ap-614	47	7	classical	classical	ADJ
ap-614	47	8	degrees	degree	NOUN
ap-614	47	9	of	of	ADP
ap-614	47	10	freedom	freedom	NOUN
ap-614	47	11	are	be	AUX
ap-614	47	12	enriched	enrich	VERB
ap-614	47	13	with	with	ADP
ap-614	47	14	additional	additional	ADJ
ap-614	47	15	degrees	degree	NOUN
ap-614	47	16	of	of	ADP
ap-614	47	17	freedom	freedom	NOUN
ap-614	47	18	,	,	PUNCT
ap-614	47	19	when	when	SCONJ
ap-614	47	20	necessary	necessary	ADJ
ap-614	47	21	.	.	PUNCT
ap-614	48	1	this	this	DET
ap-614	48	2	enhancement	enhancement	NOUN
ap-614	48	3	can	can	AUX
ap-614	48	4	be	be	AUX
ap-614	48	5	done	do	VERB
ap-614	48	6	locally	locally	ADV
ap-614	48	7	.	.	PUNCT
ap-614	49	1	belytschko	belytschko	PROPN
ap-614	49	2	and	and	CCONJ
ap-614	49	3	black	black	ADJ
ap-614	49	4	[	[	X
ap-614	49	5	20	20	NUM
ap-614	49	6	]	]	PUNCT
ap-614	49	7	and	and	CCONJ
ap-614	49	8	moës	moës	VERB
ap-614	49	9	et	et	PROPN
ap-614	49	10	al	al	PROPN
ap-614	49	11	.	.	PUNCT
ap-614	50	1	[	[	X
ap-614	50	2	21	21	NUM
ap-614	50	3	]	]	PUNCT
ap-614	50	4	used	use	VERB
ap-614	50	5	the	the	DET
ap-614	50	6	partition	partition	NOUN
ap-614	50	7	of	of	ADP
ap-614	50	8	unity	unity	NOUN
ap-614	50	9	concept	concept	NOUN
ap-614	50	10	to	to	PART
ap-614	50	11	enrich	enrich	VERB
ap-614	50	12	standard	standard	ADJ
ap-614	50	13	approximations	approximation	NOUN
ap-614	50	14	with	with	ADP
ap-614	50	15	near	near	ADJ
ap-614	50	16	-	-	PUNCT
ap-614	50	17	tip	tip	NOUN
ap-614	50	18	asymptotic	asymptotic	ADJ
ap-614	50	19	fields	field	NOUN
ap-614	50	20	and	and	CCONJ
ap-614	50	21	a	a	DET
ap-614	50	22	discontinuous	discontinuous	ADJ
ap-614	50	23	function	function	NOUN
ap-614	50	24	for	for	ADP
ap-614	50	25	elastic	elastic	ADJ
ap-614	50	26	crack	crack	NOUN
ap-614	50	27	growth	growth	NOUN
ap-614	50	28	.	.	PUNCT
ap-614	51	1	wells	well	NOUN
ap-614	51	2	and	and	CCONJ
ap-614	51	3	sluys	sluys	PROPN
ap-614	51	4	[	[	X
ap-614	51	5	17	17	NUM
ap-614	51	6	]	]	PUNCT
ap-614	51	7	introduced	introduce	VERB
ap-614	51	8	the	the	DET
ap-614	51	9	partition	partition	NOUN
ap-614	51	10	of	of	ADP
ap-614	51	11	unity	unity	NOUN
ap-614	51	12	technique	technique	NOUN
ap-614	51	13	for	for	ADP
ap-614	51	14	describing	describe	VERB
ap-614	51	15	cohesive	cohesive	ADJ
ap-614	51	16	cracks	crack	NOUN
ap-614	51	17	in	in	ADP
ap-614	51	18	a	a	DET
ap-614	51	19	material	material	NOUN
ap-614	51	20	.	.	PUNCT
ap-614	52	1	when	when	SCONJ
ap-614	52	2	the	the	DET
ap-614	52	3	heaviside	heaviside	ADJ
ap-614	52	4	function	function	NOUN
ap-614	52	5	is	be	AUX
ap-614	52	6	chosen	choose	VERB
ap-614	52	7	as	as	ADP
ap-614	52	8	an	an	DET
ap-614	52	9	enhanced	enhanced	ADJ
ap-614	52	10	basis	basis	NOUN
ap-614	52	11	,	,	PUNCT
ap-614	52	12	the	the	DET
ap-614	52	13	displacement	displacement	ADJ
ap-614	52	14	field	field	NOUN
ap-614	52	15	can	can	AUX
ap-614	52	16	be	be	AUX
ap-614	52	17	interpolated	interpolate	VERB
ap-614	52	18	according	accord	VERB
ap-614	52	19	to	to	ADP
ap-614	52	20	equation	equation	NOUN
ap-614	52	21	(	(	PUNCT
ap-614	52	22	5	5	NUM
ap-614	52	23	):	):	PUNCT
ap-614	52	24	u	u	PROPN
ap-614	52	25	na	na	PROPN
ap-614	52	26	nb	nb	PROPN
ap-614	52	27	�	�	PROPN
ap-614	52	28	�	�	PROPN
ap-614	52	29	�	�	PROPN
ap-614	52	30	�	�	PROPN
ap-614	52	31	h	h	PROPN
ap-614	52	32	�	�	PROPN
ap-614	52	33	i	i	PRON
ap-614	53	1	i	i	PRON
ap-614	53	2	i	i	PRON
ap-614	53	3	m	m	VERB
ap-614	53	4	1	1	NUM
ap-614	53	5	(	(	PUNCT
ap-614	53	6	6	6	NUM
ap-614	53	7	)	)	PUNCT
ap-614	53	8	where	where	SCONJ
ap-614	53	9	n	n	PRON
ap-614	53	10	is	be	AUX
ap-614	53	11	a	a	DET
ap-614	53	12	matrix	matrix	NOUN
ap-614	53	13	containing	contain	VERB
ap-614	53	14	the	the	DET
ap-614	53	15	finite	finite	ADJ
ap-614	53	16	element	element	NOUN
ap-614	53	17	shape	shape	NOUN
ap-614	53	18	functions	function	NOUN
ap-614	53	19	,	,	PUNCT
ap-614	53	20	a	a	PRON
ap-614	53	21	are	be	AUX
ap-614	53	22	the	the	DET
ap-614	53	23	regular	regular	ADJ
ap-614	53	24	degrees	degree	NOUN
ap-614	53	25	of	of	ADP
ap-614	53	26	freedom	freedom	NOUN
ap-614	53	27	and	and	CCONJ
ap-614	53	28	bi	bi	NOUN
ap-614	53	29	are	be	AUX
ap-614	53	30	the	the	DET
ap-614	53	31	enhanced	enhance	VERB
ap-614	53	32	degrees	degree	NOUN
ap-614	53	33	of	of	ADP
ap-614	53	34	freedom	freedom	NOUN
ap-614	53	35	related	relate	VERB
ap-614	53	36	to	to	ADP
ap-614	53	37	discontinuity	discontinuity	NOUN
ap-614	53	38	i.	i.	NOUN
ap-614	53	39	for	for	ADP
ap-614	53	40	each	each	DET
ap-614	53	41	crack	crack	NOUN
ap-614	53	42	,	,	PUNCT
ap-614	53	43	a	a	DET
ap-614	53	44	basis	basis	NOUN
ap-614	53	45	term	term	NOUN
ap-614	53	46	and	and	CCONJ
ap-614	53	47	an	an	DET
ap-614	53	48	additional	additional	ADJ
ap-614	53	49	set	set	NOUN
ap-614	53	50	of	of	ADP
ap-614	53	51	degrees	degree	NOUN
ap-614	53	52	of	of	ADP
ap-614	53	53	freedom	freedom	NOUN
ap-614	53	54	is	be	AUX
ap-614	53	55	added	add	VERB
ap-614	53	56	.	.	PUNCT
ap-614	54	1	2.3	2.3	NUM
ap-614	54	2	governing	govern	VERB
ap-614	54	3	finite	finite	PROPN
ap-614	54	4	element	element	NOUN
ap-614	54	5	equations	equation	NOUN
ap-614	54	6	the	the	DET
ap-614	54	7	weak	weak	ADJ
ap-614	54	8	form	form	NOUN
ap-614	54	9	of	of	ADP
ap-614	54	10	the	the	DET
ap-614	54	11	virtual	virtual	ADJ
ap-614	54	12	work	work	NOUN
ap-614	54	13	equation	equation	NOUN
ap-614	54	14	without	without	ADP
ap-614	54	15	body	body	NOUN
ap-614	54	16	forces	force	NOUN
ap-614	54	17	reads	read	VERB
ap-614	54	18	:	:	PUNCT
ap-614	54	19	�	�	PROPN
ap-614	54	20	�	�	PROPN
ap-614	54	21	�	�	PROPN
ap-614	54	22	�	�	PROPN
ap-614	54	23	�	�	PROPN
ap-614	54	24	s	s	PART
ap-614	54	25	s	s	NOUN
ap-614	54	26	s	s	X
ap-614	54	27	e	e	X
ap-614	54	28	�	�	PROPN
ap-614	54	29	�	�	PROPN
ap-614	54	30	�	�	PROPN
ap-614	54	31	:	:	PUNCT
ap-614	54	32	d	d	X
ap-614	54	33	d	d	X
ap-614	54	34	e	e	X
ap-614	54	35	�	�	PROPN
ap-614	54	36	�	�	PROPN
ap-614	54	37	t	t	PROPN
ap-614	54	38	(	(	PUNCT
ap-614	54	39	7	7	NUM
ap-614	54	40	)	)	PUNCT
ap-614	54	41	where	where	SCONJ
ap-614	54	42	�	�	PROPN
ap-614	54	43	is	be	AUX
ap-614	54	44	taken	take	VERB
ap-614	54	45	from	from	ADP
ap-614	54	46	the	the	DET
ap-614	54	47	set	set	NOUN
ap-614	54	48	of	of	ADP
ap-614	54	49	admissible	admissible	ADJ
ap-614	54	50	displacement	displacement	ADJ
ap-614	54	51	variations	variation	NOUN
ap-614	54	52	and	and	CCONJ
ap-614	54	53	se	se	X
ap-614	54	54	is	be	AUX
ap-614	54	55	the	the	DET
ap-614	54	56	outer	outer	ADJ
ap-614	54	57	surface	surface	NOUN
ap-614	54	58	where	where	SCONJ
ap-614	54	59	external	external	ADJ
ap-614	54	60	tractions	traction	NOUN
ap-614	54	61	t	t	NOUN
ap-614	54	62	are	be	AUX
ap-614	54	63	applied	apply	VERB
ap-614	54	64	.	.	PUNCT
ap-614	55	1	using	use	VERB
ap-614	55	2	a	a	DET
ap-614	55	3	galerkin	galerkin	ADJ
ap-614	55	4	approach	approach	NOUN
ap-614	55	5	,	,	PUNCT
ap-614	55	6	the	the	DET
ap-614	55	7	admissible	admissible	ADJ
ap-614	55	8	displacement	displacement	ADJ
ap-614	55	9	variations	variation	NOUN
ap-614	55	10	can	can	AUX
ap-614	55	11	be	be	AUX
ap-614	55	12	decomposed	decompose	VERB
ap-614	55	13	in	in	ADP
ap-614	55	14	the	the	DET
ap-614	55	15	same	same	ADJ
ap-614	55	16	manner	manner	NOUN
ap-614	55	17	as	as	ADP
ap-614	55	18	the	the	DET
ap-614	55	19	actual	actual	ADJ
ap-614	55	20	displacement	displacement	ADJ
ap-614	55	21	field	field	NOUN
ap-614	55	22	.	.	PUNCT
ap-614	56	1	inserting	insert	VERB
ap-614	56	2	the	the	DET
ap-614	56	3	kinematical	kinematical	ADJ
ap-614	56	4	expressions	expression	NOUN
ap-614	56	5	for	for	ADP
ap-614	56	6	multiple	multiple	ADJ
ap-614	56	7	(	(	PUNCT
ap-614	56	8	in	in	ADP
ap-614	56	9	this	this	DET
ap-614	56	10	case	case	NOUN
ap-614	56	11	m	m	NOUN
ap-614	56	12	)	)	PUNCT
ap-614	56	13	non	non	ADJ
ap-614	56	14	-	-	ADJ
ap-614	56	15	intersecting	intersecting	ADJ
ap-614	56	16	discontinuities	discontinuity	NOUN
ap-614	56	17	,	,	PUNCT
ap-614	56	18	the	the	DET
ap-614	56	19	virtual	virtual	ADJ
ap-614	56	20	work	work	NOUN
ap-614	56	21	equation	equation	NOUN
ap-614	56	22	can	can	AUX
ap-614	56	23	be	be	AUX
ap-614	56	24	rewritten	rewrite	VERB
ap-614	56	25	as	as	ADP
ap-614	56	26	:	:	PUNCT
ap-614	56	27	�	�	PROPN
ap-614	56	28	�	�	PROPN
ap-614	56	29	�	�	PROPN
ap-614	56	30	�	�	PROPN
ap-614	56	31	�	�	PROPN
ap-614	56	32	�	�	PROPN
ap-614	56	33	�	�	PROPN
ap-614	56	34	�	�	PROPN
ap-614	56	35	�	�	PROPN
ap-614	56	36	�	�	PROPN
ap-614	56	37	s	s	PART
ap-614	56	38	s	s	X
ap-614	56	39	i	i	PRON
ap-614	57	1	i	i	PRON
ap-614	58	1	m	m	VERB
ap-614	59	1	i	i	INTJ
ap-614	60	1	i	i	PRON
ap-614	60	2	s	s	VERB
ap-614	61	1	i	i	PRON
ap-614	62	1	i	i	PROPN
ap-614	62	2	n	n	X
ap-614	62	3	�	�	PROPN
ap-614	62	4	:	:	PUNCT
ap-614	62	5	~	~	PUNCT
ap-614	62	6	:	:	PUNCT
ap-614	62	7	~	~	PUNCT
ap-614	62	8	)	)	PUNCT
ap-614	62	9	:	:	PUNCT
ap-614	62	10	�	�	PROPN
ap-614	62	11	�	�	PROPN
ap-614	62	12	�	�	PROPN
ap-614	62	13	�	�	PROPN
ap-614	62	14	�	�	PROPN
ap-614	62	15	�	�	PROPN
ap-614	62	16	�	�	PROPN
ap-614	62	17	d	d	PROPN
ap-614	62	18	d	d	PROPN
ap-614	62	19	d	d	X
ap-614	62	20	�	�	PROPN
ap-614	62	21	�	�	PROPN
ap-614	62	22	�	�	PROPN
ap-614	62	23	�	�	PROPN
ap-614	62	24	�	�	PROPN
ap-614	62	25	�	�	PROPN
ap-614	62	26	�	�	PROPN
ap-614	62	27	�	�	PROPN
ap-614	62	28	h	h	NOUN
ap-614	62	29	1	1	NUM
ap-614	62	30	�	�	PROPN
ap-614	62	31	i	i	PRON
ap-614	62	32	m	m	VERB
ap-614	62	33	s	s	VERB
ap-614	62	34	i	i	PRON
ap-614	62	35	si	si	PROPN
ap-614	63	1	m	m	PROPN
ap-614	63	2	s	s	PROPN
ap-614	63	3	s	s	PROPN
ap-614	63	4	�	�	PROPN
ap-614	63	5	�	�	PROPN
ap-614	63	6	�	�	PROPN
ap-614	63	7	�	�	PROPN
ap-614	63	8	�	�	PROPN
ap-614	63	9	�	�	PROPN
ap-614	63	10	�	�	PROPN
ap-614	63	11	�	�	PROPN
ap-614	63	12	�	�	PROPN
ap-614	63	13	�	�	PROPN
ap-614	63	14	�	�	PROPN
ap-614	63	15	1	1	NUM
ap-614	63	16	1	1	NUM
ap-614	63	17	�	�	PROPN
ap-614	63	18	~	~	PUNCT
ap-614	63	19	.	.	PUNCT
ap-614	63	20	�	�	PROPN
ap-614	63	21	�	�	PROPN
ap-614	63	22	t	t	PROPN
ap-614	63	23	td	td	NOUN
ap-614	63	24	de	de	X
ap-614	63	25	e	e	X
ap-614	63	26	e	e	X
ap-614	63	27	e	e	X
ap-614	63	28	(	(	PUNCT
ap-614	63	29	8)	8)	NUM
ap-614	63	30	taking	take	VERB
ap-614	63	31	first	first	ADJ
ap-614	63	32	variations	variation	NOUN
ap-614	63	33	of	of	ADP
ap-614	63	34	�	�	PROPN
ap-614	63	35	�	�	PROPN
ap-614	63	36	(	(	PUNCT
ap-614	63	37	~	~	NOUN
ap-614	63	38	�	�	PROPN
ap-614	63	39	i	i	PRON
ap-614	63	40	�	�	NOUN
ap-614	63	41	0	0	NUM
ap-614	63	42	)	)	PUNCT
ap-614	63	43	followed	follow	VERB
ap-614	63	44	by	by	ADP
ap-614	63	45	variations	variation	NOUN
ap-614	63	46	of	of	ADP
ap-614	63	47	~	~	PUNCT
ap-614	63	48	�	�	SYM
ap-614	63	49	i	i	PRON
ap-614	63	50	(	(	PUNCT
ap-614	63	51	�	�	PROPN
ap-614	63	52	�	�	PROPN
ap-614	63	53	�	�	PROPN
ap-614	63	54	0	0	NUM
ap-614	63	55	)	)	PUNCT
ap-614	63	56	,	,	PUNCT
ap-614	63	57	a	a	DET
ap-614	63	58	set	set	NOUN
ap-614	63	59	of	of	ADP
ap-614	63	60	m	m	PROPN
ap-614	63	61	�	�	PROPN
ap-614	63	62	1	1	NUM
ap-614	63	63	equations	equation	NOUN
ap-614	63	64	is	be	AUX
ap-614	63	65	obtained	obtain	VERB
ap-614	63	66	.	.	PUNCT
ap-614	64	1	�	�	PROPN
ap-614	64	2	�	�	PROPN
ap-614	64	3	�	�	PROPN
ap-614	64	4	�	�	PROPN
ap-614	64	5	�	�	PROPN
ap-614	64	6	s	s	PART
ap-614	64	7	s	s	NOUN
ap-614	64	8	s	s	PROPN
ap-614	64	9	�	�	PROPN
ap-614	64	10	:	:	PUNCT
ap-614	64	11	�	�	PROPN
ap-614	64	12	�	�	PROPN
ap-614	64	13	�	�	PROPN
ap-614	64	14	�	�	PROPN
ap-614	64	15	d	d	PROPN
ap-614	64	16	d	d	X
ap-614	64	17	e	e	X
ap-614	64	18	e	e	X
ap-614	64	19	�	�	PROPN
ap-614	64	20	�	�	PROPN
ap-614	64	21	t	t	PROPN
ap-614	64	22	(	(	PUNCT
ap-614	64	23	9	9	NUM
ap-614	64	24	)	)	PUNCT
ap-614	64	25	h	h	NOUN
ap-614	64	26	�	�	PROPN
ap-614	64	27	�	�	PROPN
ap-614	64	28	�	�	PROPN
ap-614	64	29	�	�	PROPN
ap-614	64	30	�	�	PROPN
ap-614	65	1	i	i	PRON
ap-614	65	2	i	i	PRON
ap-614	65	3	s	s	VERB
ap-614	65	4	i	i	PRON
ap-614	66	1	i	i	PRON
ap-614	66	2	i	i	PRON
ap-614	66	3	it	it	PRON
ap-614	66	4	�	�	PROPN
ap-614	66	5	�	�	PROPN
ap-614	66	6	�	�	PROPN
ap-614	66	7	�	�	PROPN
ap-614	66	8	�	�	PROPN
ap-614	66	9	�	�	PROPN
ap-614	66	10	~	~	PUNCT
ap-614	66	11	:	:	PUNCT
ap-614	66	12	~	~	PUNCT
ap-614	66	13	�	�	PROPN
ap-614	66	14	�	�	PROPN
ap-614	66	15	�	�	PROPN
ap-614	66	16	d	d	PROPN
ap-614	66	17	d	d	PROPN
ap-614	66	18	0	0	PUNCT
ap-614	66	19	(	(	PUNCT
ap-614	66	20	i	i	PRON
ap-614	66	21	�	�	PROPN
ap-614	66	22	1	1	NUM
ap-614	66	23	,	,	PUNCT
ap-614	66	24	…	…	PUNCT
ap-614	66	25	m	m	NOUN
ap-614	66	26	)	)	PUNCT
ap-614	66	27	,	,	PUNCT
ap-614	66	28	(	(	PUNCT
ap-614	66	29	10	10	NUM
ap-614	66	30	)	)	PUNCT
ap-614	66	31	where	where	SCONJ
ap-614	66	32	ti	ti	PRON
ap-614	66	33	are	be	AUX
ap-614	66	34	the	the	DET
ap-614	66	35	traction	traction	PROPN
ap-614	66	36	forces	force	NOUN
ap-614	66	37	working	work	VERB
ap-614	66	38	at	at	ADP
ap-614	66	39	the	the	DET
ap-614	66	40	discontinuity	discontinuity	NOUN
ap-614	66	41	�	�	PROPN
ap-614	66	42	i.	i.	PROPN
ap-614	66	43	to	to	PART
ap-614	66	44	obtain	obtain	VERB
ap-614	66	45	equation	equation	NOUN
ap-614	66	46	(	(	PUNCT
ap-614	66	47	9	9	NUM
ap-614	66	48	)	)	PUNCT
ap-614	66	49	,	,	PUNCT
ap-614	66	50	the	the	DET
ap-614	66	51	enhanced	enhanced	ADJ
ap-614	66	52	displacement	displacement	ADJ
ap-614	66	53	field	field	NOUN
ap-614	66	54	,	,	PUNCT
ap-614	66	55	~u	~u	NUM
ap-614	66	56	,	,	PUNCT
ap-614	66	57	is	be	AUX
ap-614	66	58	assumed	assume	VERB
ap-614	66	59	to	to	PART
ap-614	66	60	be	be	AUX
ap-614	66	61	zero	zero	NUM
ap-614	66	62	where	where	SCONJ
ap-614	66	63	essential	essential	ADJ
ap-614	66	64	boundary	boundary	ADJ
ap-614	66	65	conditions	condition	NOUN
ap-614	66	66	are	be	AUX
ap-614	66	67	imposed	impose	VERB
ap-614	66	68	.	.	PUNCT
ap-614	67	1	from	from	ADP
ap-614	67	2	equations	equation	NOUN
ap-614	67	3	(	(	PUNCT
ap-614	67	4	9	9	NUM
ap-614	67	5	,	,	PUNCT
ap-614	67	6	10	10	NUM
ap-614	67	7	)	)	PUNCT
ap-614	67	8	,	,	PUNCT
ap-614	67	9	the	the	DET
ap-614	67	10	set	set	NOUN
ap-614	67	11	of	of	ADP
ap-614	67	12	discretized	discretized	ADJ
ap-614	67	13	equations	equation	NOUN
ap-614	67	14	is	be	AUX
ap-614	67	15	obtained	obtain	VERB
ap-614	67	16	by	by	ADP
ap-614	67	17	introducing	introduce	VERB
ap-614	67	18	the	the	DET
ap-614	67	19	discretized	discretized	ADJ
ap-614	67	20	form	form	NOUN
ap-614	67	21	of	of	ADP
ap-614	67	22	the	the	DET
ap-614	67	23	displacement	displacement	NOUN
ap-614	67	24	and	and	CCONJ
ap-614	67	25	the	the	DET
ap-614	67	26	strain	strain	NOUN
ap-614	67	27	field	field	NOUN
ap-614	67	28	.	.	PUNCT
ap-614	68	1	b	b	X
ap-614	68	2	n	n	CCONJ
ap-614	68	3	tt	tt	PROPN
ap-614	68	4	t	t	NOUN
ap-614	68	5	s	s	PART
ap-614	68	6	s	s	PROPN
ap-614	68	7	e	e	X
ap-614	68	8	�	�	PROPN
ap-614	68	9	d	d	PROPN
ap-614	68	10	d	d	PROPN
ap-614	68	11	e	e	PROPN
ap-614	68	12	�	�	PROPN
ap-614	68	13	�	�	PROPN
ap-614	68	14	�	�	PROPN
ap-614	68	15	�	�	PROPN
ap-614	68	16	�	�	PROPN
ap-614	68	17	�	�	PROPN
ap-614	68	18	(	(	PUNCT
ap-614	68	19	11a	11a	NOUN
ap-614	68	20	)	)	PUNCT
ap-614	68	21	h	h	PROPN
ap-614	68	22	�	�	PROPN
ap-614	68	23	�	�	PROPN
ap-614	68	24	�	�	PROPN
ap-614	68	25	�	�	PROPN
ap-614	68	26	�	�	PROPN
ap-614	69	1	i	i	PRON
ap-614	69	2	i	i	PRON
ap-614	70	1	t	t	VERB
ap-614	70	2	t	t	X
ap-614	71	1	i	i	PRON
ap-614	71	2	itb	itb	PROPN
ap-614	71	3	n	n	CCONJ
ap-614	71	4	�	�	PROPN
ap-614	71	5	d	d	PROPN
ap-614	71	6	d	d	PROPN
ap-614	71	7	�	�	PROPN
ap-614	71	8	�	�	PROPN
ap-614	71	9	�	�	PROPN
ap-614	71	10	�	�	PROPN
ap-614	71	11	�	�	PROPN
ap-614	71	12	0	0	NUM
ap-614	71	13	(	(	PUNCT
ap-614	71	14	i	i	PRON
ap-614	71	15	�	�	PROPN
ap-614	71	16	1	1	NUM
ap-614	71	17	,	,	PUNCT
ap-614	71	18	…	…	PUNCT
ap-614	71	19	m	m	NOUN
ap-614	71	20	)	)	PUNCT
ap-614	71	21	.	.	PUNCT
ap-614	72	1	(	(	PUNCT
ap-614	72	2	11b	11b	NOUN
ap-614	72	3	)	)	PUNCT
ap-614	72	4	in	in	ADP
ap-614	72	5	these	these	DET
ap-614	72	6	equations	equation	NOUN
ap-614	72	7	,	,	PUNCT
ap-614	72	8	the	the	DET
ap-614	72	9	continuum	continuum	ADJ
ap-614	72	10	response	response	NOUN
ap-614	72	11	and	and	CCONJ
ap-614	72	12	the	the	DET
ap-614	72	13	discontinuity	discontinuity	NOUN
ap-614	72	14	response	response	NOUN
ap-614	72	15	are	be	AUX
ap-614	72	16	completely	completely	ADV
ap-614	72	17	split	split	VERB
ap-614	72	18	.	.	PUNCT
ap-614	73	1	the	the	DET
ap-614	73	2	continuum	continuum	PROPN
ap-614	73	3	is	be	AUX
ap-614	73	4	assumed	assume	VERB
ap-614	73	5	to	to	PART
ap-614	73	6	remain	remain	VERB
ap-614	73	7	elastic	elastic	ADJ
ap-614	73	8	during	during	ADP
ap-614	73	9	the	the	DET
ap-614	73	10	complete	complete	ADJ
ap-614	73	11	computation	computation	NOUN
ap-614	73	12	.	.	PUNCT
ap-614	74	1	the	the	DET
ap-614	74	2	stress	stress	NOUN
ap-614	74	3	rate	rate	NOUN
ap-614	74	4	in	in	ADP
ap-614	74	5	the	the	DET
ap-614	74	6	continuum	continuum	NOUN
ap-614	74	7	can	can	AUX
ap-614	74	8	be	be	AUX
ap-614	74	9	easily	easily	ADV
ap-614	74	10	obtained	obtain	VERB
ap-614	74	11	from	from	ADP
ap-614	74	12	the	the	DET
ap-614	74	13	expression	expression	NOUN
ap-614	74	14	of	of	ADP
ap-614	74	15	the	the	DET
ap-614	74	16	strain	strain	NOUN
ap-614	74	17	field	field	NOUN
ap-614	74	18	in	in	ADP
ap-614	74	19	the	the	DET
ap-614	74	20	bulk	bulk	NOUN
ap-614	74	21	,	,	PUNCT
ap-614	74	22	given	give	VERB
ap-614	74	23	by	by	ADP
ap-614	74	24	eq	eq	PROPN
ap-614	74	25	.	.	PUNCT
ap-614	75	1	(	(	PUNCT
ap-614	75	2	3	3	NUM
ap-614	75	3	):	):	PUNCT
ap-614	75	4	�	�	PROPN
ap-614	75	5	�	�	PROPN
ap-614	75	6	�	�	PROPN
ap-614	75	7	�	�	PROPN
ap-614	75	8	�	�	PROPN
ap-614	75	9	�	�	PROPN
ap-614	75	10	�	�	PROPN
ap-614	75	11	�	�	PROPN
ap-614	75	12	�	�	PROPN
ap-614	75	13	�	�	PROPN
ap-614	75	14	�	�	PROPN
ap-614	75	15	�	�	PROPN
ap-614	75	16	�	�	PROPN
ap-614	75	17	�	�	PROPN
ap-614	75	18	�	�	PROPN
ap-614	75	19	�	�	PROPN
ap-614	75	20	�	�	PROPN
ap-614	75	21	�	�	PROPN
ap-614	75	22	c	c	PROPN
ap-614	75	23	c	c	PROPN
ap-614	75	24	ba	ba	PROPN
ap-614	75	25	bbe	bbe	PROPN
ap-614	75	26	e	e	PROPN
ap-614	75	27	�	�	PROPN
ap-614	75	28	h	h	PROPN
ap-614	75	29	�	�	PROPN
ap-614	75	30	i	i	PRON
ap-614	76	1	i	i	PRON
ap-614	76	2	i	i	PRON
ap-614	76	3	m	m	VERB
ap-614	76	4	1	1	NUM
ap-614	76	5	,	,	PUNCT
ap-614	76	6	(	(	PUNCT
ap-614	76	7	12	12	NUM
ap-614	76	8	)	)	PUNCT
ap-614	76	9	where	where	SCONJ
ap-614	76	10	ce	ce	PROPN
ap-614	76	11	is	be	AUX
ap-614	76	12	the	the	DET
ap-614	76	13	elastic	elastic	ADJ
ap-614	76	14	material	material	NOUN
ap-614	76	15	tensor	tensor	NOUN
ap-614	76	16	.	.	PUNCT
ap-614	77	1	the	the	DET
ap-614	77	2	behaviour	behaviour	NOUN
ap-614	77	3	at	at	ADP
ap-614	77	4	the	the	DET
ap-614	77	5	discontinuity	discontinuity	NOUN
ap-614	77	6	is	be	AUX
ap-614	77	7	stated	state	VERB
ap-614	77	8	in	in	ADP
ap-614	77	9	terms	term	NOUN
ap-614	77	10	of	of	ADP
ap-614	77	11	tractions	traction	NOUN
ap-614	77	12	and	and	CCONJ
ap-614	77	13	separations	separation	NOUN
ap-614	77	14	.	.	PUNCT
ap-614	78	1	the	the	DET
ap-614	78	2	separation	separation	NOUN
ap-614	78	3	of	of	ADP
ap-614	78	4	the	the	DET
ap-614	78	5	discontinuity	discontinuity	NOUN
ap-614	78	6	can	can	AUX
ap-614	78	7	be	be	AUX
ap-614	78	8	computed	compute	VERB
ap-614	78	9	as	as	ADP
ap-614	78	10	:	:	PUNCT
ap-614	78	11	�	�	PROPN
ap-614	78	12	�	�	PROPN
ap-614	78	13	�	�	PROPN
ap-614	78	14	�	�	PROPN
ap-614	78	15	�	�	PROPN
ap-614	78	16	�	�	PROPN
ap-614	78	17	�	�	PROPN
ap-614	78	18	u	u	NOUN
ap-614	78	19	u	u	PROPN
ap-614	78	20	u	u	NOUN
ap-614	78	21	u	u	X
ap-614	78	22	u	u	X
ap-614	78	23	u	u	PROPN
ap-614	78	24	nb	nb	PROPN
ap-614	78	25	�	�	PROPN
ap-614	78	26	~	~	PUNCT
ap-614	78	27	�	�	PROPN
ap-614	78	28	~	~	PUNCT
ap-614	78	29	.	.	PUNCT
ap-614	79	1	(	(	PUNCT
ap-614	79	2	13	13	NUM
ap-614	79	3	)	)	PUNCT
ap-614	79	4	eq	eq	NOUN
ap-614	79	5	.	.	PUNCT
ap-614	80	1	(	(	PUNCT
ap-614	80	2	13	13	NUM
ap-614	80	3	)	)	PUNCT
ap-614	80	4	shows	show	VERB
ap-614	80	5	that	that	SCONJ
ap-614	80	6	the	the	DET
ap-614	80	7	separation	separation	NOUN
ap-614	80	8	of	of	ADP
ap-614	80	9	the	the	DET
ap-614	80	10	discontinuity	discontinuity	NOUN
ap-614	80	11	is	be	AUX
ap-614	80	12	expressed	express	VERB
ap-614	80	13	as	as	ADP
ap-614	80	14	a	a	DET
ap-614	80	15	function	function	NOUN
ap-614	80	16	of	of	ADP
ap-614	80	17	the	the	DET
ap-614	80	18	enhanced	enhance	VERB
ap-614	80	19	degrees	degree	NOUN
ap-614	80	20	of	of	ADP
ap-614	80	21	freedom	freedom	NOUN
ap-614	80	22	.	.	PUNCT
ap-614	81	1	the	the	DET
ap-614	81	2	traction	traction	NOUN
ap-614	81	3	rate	rate	NOUN
ap-614	81	4	is	be	AUX
ap-614	81	5	defined	define	VERB
ap-614	81	6	as	as	ADP
ap-614	81	7	:	:	PUNCT
ap-614	81	8	�	�	PROPN
ap-614	81	9	�	�	PROPN
ap-614	81	10	t	t	PROPN
ap-614	81	11	dnbi	dnbi	NOUN
ap-614	81	12	i	i	PRON
ap-614	81	13	�	�	PROPN
ap-614	81	14	,	,	PUNCT
ap-614	81	15	(	(	PUNCT
ap-614	81	16	14	14	NUM
ap-614	81	17	)	)	PUNCT
ap-614	81	18	where	where	SCONJ
ap-614	81	19	d	d	NOUN
ap-614	81	20	is	be	AUX
ap-614	81	21	the	the	DET
ap-614	81	22	material	material	ADJ
ap-614	81	23	tangent	tangent	NOUN
ap-614	81	24	for	for	ADP
ap-614	81	25	the	the	DET
ap-614	81	26	discontinuity	discontinuity	NOUN
ap-614	81	27	.	.	PUNCT
ap-614	82	1	this	this	DET
ap-614	82	2	material	material	NOUN
ap-614	82	3	tangent	tangent	NOUN
ap-614	82	4	will	will	AUX
ap-614	82	5	be	be	AUX
ap-614	82	6	further	far	ADV
ap-614	82	7	elaborated	elaborate	VERB
ap-614	82	8	in	in	ADP
ap-614	82	9	the	the	DET
ap-614	82	10	next	next	ADJ
ap-614	82	11	paragraph	paragraph	NOUN
ap-614	82	12	.	.	PUNCT
ap-614	83	1	eq	eq	ADP
ap-614	83	2	.	.	PUNCT
ap-614	84	1	(	(	PUNCT
ap-614	84	2	11	11	NUM
ap-614	84	3	)	)	PUNCT
ap-614	84	4	is	be	AUX
ap-614	84	5	further	far	ADV
ap-614	84	6	linearized	linearize	VERB
ap-614	84	7	by	by	ADP
ap-614	84	8	inserting	insert	VERB
ap-614	84	9	eq	eq	ADP
ap-614	84	10	.	.	PUNCT
ap-614	85	1	(	(	PUNCT
ap-614	85	2	12	12	NUM
ap-614	85	3	)	)	PUNCT
ap-614	85	4	and	and	CCONJ
ap-614	85	5	eq	eq	NOUN
ap-614	85	6	.	.	PUNCT
ap-614	86	1	(	(	PUNCT
ap-614	86	2	14	14	NUM
ap-614	86	3	)	)	PUNCT
ap-614	86	4	.	.	PUNCT
ap-614	87	1	after	after	ADP
ap-614	87	2	some	some	DET
ap-614	87	3	mathematical	mathematical	ADJ
ap-614	87	4	manipulations	manipulation	NOUN
ap-614	87	5	,	,	PUNCT
ap-614	87	6	the	the	DET
ap-614	87	7	linearized	linearize	VERB
ap-614	87	8	set	set	NOUN
ap-614	87	9	of	of	ADP
ap-614	87	10	equations	equation	NOUN
ap-614	87	11	is	be	AUX
ap-614	87	12	given	give	VERB
ap-614	87	13	by	by	ADP
ap-614	87	14	k	k	PROPN
ap-614	87	15	k	k	PROPN
ap-614	88	1	k	k	PROPN
ap-614	89	1	k	k	PROPN
ap-614	90	1	k	k	PROPN
ap-614	91	1	k	k	PROPN
ap-614	92	1	k	k	PROPN
ap-614	92	2	k	k	PROPN
ap-614	93	1	k	k	PROPN
ap-614	93	2	aa	aa	PROPN
ap-614	93	3	ab	ab	PROPN
ap-614	93	4	ab	ab	PROPN
ap-614	93	5	b	b	PROPN
ap-614	93	6	a	a	DET
ap-614	93	7	b	b	PROPN
ap-614	93	8	b	b	PROPN
ap-614	93	9	b	b	PROPN
ap-614	93	10	b	b	PROPN
ap-614	93	11	b	b	PROPN
ap-614	93	12	a	a	PRON
ap-614	93	13	b	b	PROPN
ap-614	93	14	b	b	PROPN
ap-614	93	15	b	b	PROPN
ap-614	93	16	b	b	PROPN
ap-614	93	17	m	m	VERB
ap-614	93	18	m	m	VERB
ap-614	93	19	m	m	VERB
ap-614	93	20	m	m	VERB
ap-614	93	21	m	m	VERB
ap-614	93	22	m	m	VERB
ap-614	93	23	1	1	NUM
ap-614	93	24	1	1	NUM
ap-614	93	25	1	1	NUM
ap-614	93	26	1	1	NUM
ap-614	93	27	1	1	NUM
ap-614	93	28	1	1	NUM
ap-614	93	29	�	�	PROPN
ap-614	93	30	�	�	PROPN
ap-614	93	31	�	�	PROPN
ap-614	93	32	�	�	PROPN
ap-614	93	33	�	�	PROPN
ap-614	93	34	�	�	PROPN
ap-614	93	35	�	�	PROPN
ap-614	93	36	�	�	PROPN
ap-614	93	37	�	�	PROPN
ap-614	93	38	�	�	PROPN
ap-614	93	39	�	�	PROPN
ap-614	93	40	�	�	PROPN
ap-614	93	41	�	�	PROPN
ap-614	93	42	�	�	PROPN
ap-614	93	43	�	�	PROPN
ap-614	93	44	�	�	PROPN
ap-614	93	45	�	�	PROPN
ap-614	93	46	�	�	PROPN
ap-614	93	47	�	�	PROPN
ap-614	93	48	�	�	PROPN
ap-614	93	49	�	�	PROPN
ap-614	93	50	�	�	PROPN
ap-614	93	51	�	�	PROPN
ap-614	93	52	�	�	PROPN
ap-614	93	53	�	�	PROPN
ap-614	93	54	�	�	PROPN
ap-614	93	55	�	�	PROPN
ap-614	93	56	�	�	PROPN
ap-614	93	57	�	�	PROPN
ap-614	93	58	�	�	PROPN
ap-614	93	59	�	�	PROPN
ap-614	93	60	�	�	PROPN
ap-614	93	61	�	�	PROPN
ap-614	93	62	�	�	PROPN
ap-614	93	63	�	�	PROPN
ap-614	93	64	�	�	PROPN
ap-614	93	65	�	�	PROPN
ap-614	93	66	�	�	PROPN
ap-614	94	1	d	d	PROPN
ap-614	94	2	d	d	PROPN
ap-614	94	3	d	d	X
ap-614	94	4	ext	ext	PROPN
ap-614	94	5	da	da	PROPN
ap-614	94	6	b	b	PROPN
ap-614	94	7	b	b	PROPN
ap-614	94	8	f	f	PROPN
ap-614	94	9	1	1	NUM
ap-614	94	10	0	0	NUM
ap-614	94	11	0	0	NUM
ap-614	94	12	�	�	PROPN
ap-614	94	13	�	�	PROPN
ap-614	94	14	m	m	PROPN
ap-614	94	15	a	a	DET
ap-614	94	16	t	t	PROPN
ap-614	94	17	t	t	PROPN
ap-614	94	18	,	,	PUNCT
ap-614	94	19	�	�	PROPN
ap-614	94	20	�	�	PROPN
ap-614	94	21	�	�	PROPN
ap-614	94	22	�	�	PROPN
ap-614	94	23	�	�	PROPN
ap-614	94	24	�	�	PROPN
ap-614	94	25	�	�	PROPN
ap-614	94	26	�	�	PROPN
ap-614	94	27	�	�	PROPN
ap-614	94	28	�	�	PROPN
ap-614	94	29	�	�	PROPN
ap-614	94	30	�	�	PROPN
ap-614	94	31	�	�	PROPN
ap-614	94	32	�	�	PROPN
ap-614	94	33	�	�	PROPN
ap-614	94	34	�	�	PROPN
ap-614	94	35	�	�	PROPN
ap-614	94	36	�	�	PROPN
ap-614	94	37	�	�	PROPN
ap-614	94	38	�	�	PROPN
ap-614	94	39	�	�	PROPN
ap-614	95	1	f	f	PROPN
ap-614	95	2	f	f	PROPN
ap-614	96	1	f	f	PROPN
ap-614	97	1	a	a	DET
ap-614	97	2	t	t	PROPN
ap-614	97	3	b	b	PROPN
ap-614	97	4	t	t	PROPN
ap-614	97	5	b	b	PROPN
ap-614	97	6	t	t	PROPN
ap-614	97	7	m	m	NOUN
ap-614	97	8	int	int	NOUN
ap-614	97	9	,	,	PUNCT
ap-614	97	10	int	int	NOUN
ap-614	97	11	,	,	PUNCT
ap-614	97	12	int	int	NOUN
ap-614	97	13	,	,	PUNCT
ap-614	97	14	1	1	NUM
ap-614	97	15	�	�	PROPN
ap-614	97	16	�	�	PROPN
ap-614	97	17	(	(	PUNCT
ap-614	97	18	15	15	NUM
ap-614	97	19	)	)	PUNCT
ap-614	97	20	where	where	SCONJ
ap-614	97	21	k	k	PROPN
ap-614	97	22	b	b	PROPN
ap-614	97	23	c	c	PROPN
ap-614	97	24	baa	baa	PROPN
ap-614	97	25	t	t	PROPN
ap-614	97	26	�	�	PROPN
ap-614	97	27	�	�	PROPN
ap-614	97	28	e	e	PROPN
ap-614	97	29	d	d	PROPN
ap-614	97	30	�	�	PROPN
ap-614	97	31	�	�	PROPN
ap-614	97	32	(	(	PUNCT
ap-614	97	33	16a	16a	NOUN
ap-614	97	34	)	)	PUNCT
ap-614	98	1	k	k	PROPN
ap-614	98	2	b	b	PROPN
ap-614	98	3	c	c	PROPN
ap-614	98	4	bab	bab	PROPN
ap-614	98	5	t	t	PROPN
ap-614	98	6	j	j	PROPN
ap-614	98	7	j	j	PROPN
ap-614	98	8	�	�	PROPN
ap-614	98	9	�	�	PROPN
ap-614	98	10	h	h	PROPN
ap-614	98	11	�	�	PROPN
ap-614	98	12	�	�	PROPN
ap-614	98	13	�	�	PROPN
ap-614	98	14	e	e	PROPN
ap-614	98	15	d	d	X
ap-614	98	16	(	(	PUNCT
ap-614	98	17	16b	16b	X
ap-614	98	18	)	)	PUNCT
ap-614	98	19	k	k	PROPN
ap-614	99	1	b	b	X
ap-614	99	2	c	c	INTJ
ap-614	99	3	bb	bb	INTJ
ap-614	99	4	a	a	DET
ap-614	99	5	t	t	NOUN
ap-614	99	6	e	e	PROPN
ap-614	99	7	j	j	PROPN
ap-614	99	8	j	j	PROPN
ap-614	99	9	�	�	PROPN
ap-614	99	10	�	�	PROPN
ap-614	99	11	h	h	PROPN
ap-614	99	12	�	�	PROPN
ap-614	99	13	�	�	PROPN
ap-614	99	14	�	�	PROPN
ap-614	99	15	d	d	PROPN
ap-614	99	16	(	(	PUNCT
ap-614	99	17	16c	16c	NOUN
ap-614	99	18	)	)	PUNCT
ap-614	100	1	k	k	PROPN
ap-614	101	1	b	b	X
ap-614	101	2	c	c	NOUN
ap-614	101	3	bb	bb	INTJ
ap-614	101	4	b	b	PROPN
ap-614	101	5	t	t	PROPN
ap-614	101	6	e	e	X
ap-614	102	1	i	i	PRON
ap-614	102	2	j	j	VERB
ap-614	103	1	i	i	PRON
ap-614	103	2	j	j	PROPN
ap-614	103	3	�	�	PROPN
ap-614	103	4	�	�	PROPN
ap-614	103	5	h	h	PROPN
ap-614	103	6	h	h	PROPN
ap-614	103	7	�	�	PROPN
ap-614	103	8	�	�	PROPN
ap-614	103	9	�	�	PROPN
ap-614	103	10	�	�	PROPN
ap-614	103	11	d	d	PROPN
ap-614	103	12	(	(	PUNCT
ap-614	103	13	16d	16d	NOUN
ap-614	103	14	)	)	PUNCT
ap-614	103	15	k	k	PROPN
ap-614	103	16	b	b	PROPN
ap-614	103	17	c	c	PROPN
ap-614	103	18	b	b	PROPN
ap-614	103	19	n	n	CCONJ
ap-614	103	20	dnb	dnb	PROPN
ap-614	103	21	b	b	PROPN
ap-614	103	22	t	t	PROPN
ap-614	103	23	t	t	PROPN
ap-614	104	1	jj	jj	PROPN
ap-614	104	2	j	j	PROPN
ap-614	104	3	j	j	PROPN
ap-614	104	4	j	j	PROPN
ap-614	104	5	�	�	PROPN
ap-614	104	6	�	�	PROPN
ap-614	104	7	�	�	PROPN
ap-614	104	8	�	�	PROPN
ap-614	104	9	h	h	PROPN
ap-614	104	10	�	�	PROPN
ap-614	104	11	�	�	PROPN
ap-614	104	12	�	�	PROPN
ap-614	104	13	�	�	PROPN
ap-614	104	14	�	�	PROPN
ap-614	104	15	e	e	PROPN
ap-614	104	16	d	d	PROPN
ap-614	104	17	d	d	PROPN
ap-614	104	18	(	(	PUNCT
ap-614	104	19	16e	16e	NUM
ap-614	104	20	)	)	PUNCT
ap-614	104	21	©	©	PROPN
ap-614	104	22	czech	czech	PROPN
ap-614	104	23	technical	technical	PROPN
ap-614	104	24	university	university	PROPN
ap-614	104	25	publishing	publishing	NOUN
ap-614	104	26	house	house	NOUN
ap-614	104	27	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	104	28	43	43	NUM
ap-614	104	29	acta	acta	PROPN
ap-614	104	30	polytechnica	polytechnica	PROPN
ap-614	104	31	vol	vol	NOUN
ap-614	104	32	.	.	PROPN
ap-614	105	1	44	44	NUM
ap-614	105	2	no	no	NOUN
ap-614	105	3	.	.	PUNCT
ap-614	106	1	5–6/2004	5–6/2004	NUM
ap-614	106	2	it	it	PRON
ap-614	106	3	can	can	AUX
ap-614	106	4	be	be	AUX
ap-614	106	5	seen	see	VERB
ap-614	106	6	from	from	ADP
ap-614	106	7	previous	previous	ADJ
ap-614	106	8	equations	equation	NOUN
ap-614	106	9	that	that	SCONJ
ap-614	106	10	the	the	DET
ap-614	106	11	global	global	ADJ
ap-614	106	12	system	system	NOUN
ap-614	106	13	of	of	ADP
ap-614	106	14	equations	equation	NOUN
ap-614	106	15	(	(	PUNCT
ap-614	106	16	eq	eq	NOUN
ap-614	106	17	.	.	PUNCT
ap-614	107	1	(	(	PUNCT
ap-614	107	2	15	15	NUM
ap-614	107	3	)	)	PUNCT
ap-614	107	4	)	)	PUNCT
ap-614	107	5	remains	remain	VERB
ap-614	107	6	symmetric	symmetric	ADJ
ap-614	107	7	when	when	SCONJ
ap-614	107	8	ce	ce	PROPN
ap-614	107	9	and	and	CCONJ
ap-614	107	10	d	d	PROPN
ap-614	107	11	are	be	AUX
ap-614	107	12	symmetric	symmetric	ADJ
ap-614	107	13	.	.	PUNCT
ap-614	108	1	it	it	PRON
ap-614	108	2	should	should	AUX
ap-614	108	3	be	be	AUX
ap-614	108	4	noted	note	VERB
ap-614	108	5	that	that	SCONJ
ap-614	108	6	equations	equation	NOUN
ap-614	108	7	(	(	PUNCT
ap-614	108	8	16	16	NUM
ap-614	108	9	)	)	PUNCT
ap-614	108	10	are	be	AUX
ap-614	108	11	valid	valid	ADJ
ap-614	108	12	when	when	SCONJ
ap-614	108	13	only	only	ADV
ap-614	108	14	discontinuity	discontinuity	NOUN
ap-614	108	15	j	j	PROPN
ap-614	108	16	crosses	cross	VERB
ap-614	108	17	the	the	DET
ap-614	108	18	element	element	NOUN
ap-614	108	19	,	,	PUNCT
ap-614	108	20	but	but	CCONJ
ap-614	108	21	the	the	DET
ap-614	108	22	element	element	NOUN
ap-614	108	23	is	be	AUX
ap-614	108	24	also	also	ADV
ap-614	108	25	influenced	influence	VERB
ap-614	108	26	by	by	ADP
ap-614	108	27	discontinuity	discontinuity	NOUN
ap-614	108	28	i.	i.	NOUN
ap-614	108	29	note	note	VERB
ap-614	108	30	that	that	SCONJ
ap-614	108	31	all	all	DET
ap-614	108	32	stiffness	stiffness	ADJ
ap-614	108	33	contributions	contribution	NOUN
ap-614	108	34	in	in	ADP
ap-614	108	35	equations	equation	NOUN
ap-614	108	36	(	(	PUNCT
ap-614	108	37	16	16	NUM
ap-614	108	38	)	)	PUNCT
ap-614	108	39	are	be	AUX
ap-614	108	40	very	very	ADV
ap-614	108	41	similar	similar	ADJ
ap-614	108	42	.	.	PUNCT
ap-614	109	1	the	the	DET
ap-614	109	2	crucial	crucial	ADJ
ap-614	109	3	difference	difference	NOUN
ap-614	109	4	between	between	ADP
ap-614	109	5	the	the	DET
ap-614	109	6	terms	term	NOUN
ap-614	109	7	in	in	ADP
ap-614	109	8	equations	equation	NOUN
ap-614	109	9	(	(	PUNCT
ap-614	109	10	16	16	NUM
ap-614	109	11	)	)	PUNCT
ap-614	109	12	is	be	AUX
ap-614	109	13	the	the	DET
ap-614	109	14	presence	presence	NOUN
ap-614	109	15	of	of	ADP
ap-614	109	16	the	the	DET
ap-614	109	17	heaviside	heaviside	ADJ
ap-614	109	18	function	function	NOUN
ap-614	109	19	.	.	PUNCT
ap-614	110	1	this	this	PRON
ap-614	110	2	makes	make	VERB
ap-614	110	3	the	the	DET
ap-614	110	4	finite	finite	ADJ
ap-614	110	5	element	element	NOUN
ap-614	110	6	implementation	implementation	NOUN
ap-614	110	7	relatively	relatively	ADV
ap-614	110	8	simple	simple	ADJ
ap-614	110	9	.	.	PUNCT
ap-614	111	1	2.4	2.4	NUM
ap-614	111	2	numerical	numerical	ADJ
ap-614	111	3	implementation	implementation	NOUN
ap-614	111	4	aspects	aspect	VERB
ap-614	111	5	2.4.1	2.4.1	NUM
ap-614	111	6	integration	integration	NOUN
ap-614	111	7	of	of	ADP
ap-614	111	8	the	the	DET
ap-614	111	9	crossed	cross	VERB
ap-614	111	10	elements	element	NOUN
ap-614	111	11	from	from	ADP
ap-614	111	12	eq	eq	ADP
ap-614	111	13	.	.	PUNCT
ap-614	112	1	(	(	PUNCT
ap-614	112	2	16	16	NUM
ap-614	112	3	)	)	PUNCT
ap-614	112	4	it	it	PRON
ap-614	112	5	can	can	AUX
ap-614	112	6	be	be	AUX
ap-614	112	7	seen	see	VERB
ap-614	112	8	that	that	SCONJ
ap-614	112	9	the	the	DET
ap-614	112	10	heaviside	heaviside	ADJ
ap-614	112	11	step	step	NOUN
ap-614	112	12	functions	function	NOUN
ap-614	112	13	should	should	AUX
ap-614	112	14	be	be	AUX
ap-614	112	15	taken	take	VERB
ap-614	112	16	into	into	ADP
ap-614	112	17	account	account	NOUN
ap-614	112	18	for	for	ADP
ap-614	112	19	the	the	DET
ap-614	112	20	integration	integration	NOUN
ap-614	112	21	of	of	ADP
ap-614	112	22	the	the	DET
ap-614	112	23	stiffness	stiffness	ADJ
ap-614	112	24	matrix	matrix	NOUN
ap-614	112	25	.	.	PUNCT
ap-614	113	1	this	this	PRON
ap-614	113	2	means	mean	VERB
ap-614	113	3	that	that	SCONJ
ap-614	113	4	the	the	DET
ap-614	113	5	integration	integration	NOUN
ap-614	113	6	must	must	AUX
ap-614	113	7	only	only	ADV
ap-614	113	8	be	be	AUX
ap-614	113	9	performed	perform	VERB
ap-614	113	10	on	on	ADP
ap-614	113	11	the	the	DET
ap-614	113	12	side	side	NOUN
ap-614	113	13	of	of	ADP
ap-614	113	14	the	the	DET
ap-614	113	15	element	element	NOUN
ap-614	113	16	where	where	SCONJ
ap-614	113	17	the	the	DET
ap-614	113	18	heaviside	heaviside	ADJ
ap-614	113	19	function	function	NOUN
ap-614	113	20	equals	equal	VERB
ap-614	113	21	one	one	NUM
ap-614	113	22	,	,	PUNCT
ap-614	113	23	i.e.	i.e.	X
ap-614	113	24	�	�	X
ap-614	113	25	i	i	PRON
ap-614	113	26	�	�	PROPN
ap-614	113	27	.	.	PUNCT
ap-614	114	1	obviously	obviously	ADV
ap-614	114	2	,	,	PUNCT
ap-614	114	3	enough	enough	ADJ
ap-614	114	4	integration	integration	NOUN
ap-614	114	5	points	point	NOUN
ap-614	114	6	must	must	AUX
ap-614	114	7	be	be	AUX
ap-614	114	8	present	present	ADJ
ap-614	114	9	on	on	ADP
ap-614	114	10	that	that	DET
ap-614	114	11	side	side	NOUN
ap-614	114	12	so	so	SCONJ
ap-614	114	13	that	that	SCONJ
ap-614	114	14	an	an	DET
ap-614	114	15	adequate	adequate	ADJ
ap-614	114	16	integration	integration	NOUN
ap-614	114	17	is	be	AUX
ap-614	114	18	performed	perform	VERB
ap-614	114	19	.	.	PUNCT
ap-614	115	1	since	since	SCONJ
ap-614	115	2	a	a	DET
ap-614	115	3	discontinuity	discontinuity	NOUN
ap-614	115	4	can	can	AUX
ap-614	115	5	cross	cross	VERB
ap-614	115	6	the	the	DET
ap-614	115	7	element	element	NOUN
ap-614	115	8	arbitrarily	arbitrarily	ADV
ap-614	115	9	,	,	PUNCT
ap-614	115	10	the	the	DET
ap-614	115	11	safest	safe	ADJ
ap-614	115	12	solution	solution	NOUN
ap-614	115	13	is	be	AUX
ap-614	115	14	to	to	PART
ap-614	115	15	redefine	redefine	VERB
ap-614	115	16	the	the	DET
ap-614	115	17	integration	integration	NOUN
ap-614	115	18	scheme	scheme	NOUN
ap-614	115	19	.	.	PUNCT
ap-614	116	1	when	when	SCONJ
ap-614	116	2	only	only	ADV
ap-614	116	3	one	one	NUM
ap-614	116	4	discontinuity	discontinuity	NOUN
ap-614	116	5	crosses	cross	VERB
ap-614	116	6	the	the	DET
ap-614	116	7	considered	consider	VERB
ap-614	116	8	element	element	NOUN
ap-614	116	9	,	,	PUNCT
ap-614	116	10	the	the	DET
ap-614	116	11	integration	integration	NOUN
ap-614	116	12	rule	rule	NOUN
ap-614	116	13	is	be	AUX
ap-614	116	14	adapted	adapt	VERB
ap-614	116	15	following	follow	VERB
ap-614	116	16	wells	well	NOUN
ap-614	116	17	and	and	CCONJ
ap-614	116	18	sluys	sluy	NOUN
ap-614	116	19	[	[	X
ap-614	116	20	17	17	NUM
ap-614	116	21	]	]	PUNCT
ap-614	116	22	.	.	PUNCT
ap-614	117	1	for	for	ADP
ap-614	117	2	the	the	DET
ap-614	117	3	triangular	triangular	ADJ
ap-614	117	4	quadratic	quadratic	ADJ
ap-614	117	5	element	element	NOUN
ap-614	117	6	as	as	ADP
ap-614	117	7	the	the	DET
ap-614	117	8	underlying	underlying	ADJ
ap-614	117	9	finite	finite	ADJ
ap-614	117	10	element	element	NOUN
ap-614	117	11	,	,	PUNCT
ap-614	117	12	23	23	NUM
ap-614	117	13	integration	integration	NOUN
ap-614	117	14	points	point	NOUN
ap-614	117	15	–	–	PUNCT
ap-614	117	16	21	21	NUM
ap-614	117	17	in	in	ADP
ap-614	117	18	the	the	DET
ap-614	117	19	continuum	continuum	ADJ
ap-614	117	20	and	and	CCONJ
ap-614	117	21	2	2	NUM
ap-614	117	22	for	for	ADP
ap-614	117	23	the	the	DET
ap-614	117	24	discontinuity	discontinuity	NOUN
ap-614	117	25	–	–	PUNCT
ap-614	117	26	are	be	AUX
ap-614	117	27	inserted	insert	VERB
ap-614	117	28	as	as	SCONJ
ap-614	117	29	shown	show	VERB
ap-614	117	30	in	in	ADP
ap-614	117	31	fig	fig	NOUN
ap-614	117	32	.	.	PUNCT
ap-614	118	1	2a	2a	NUM
ap-614	118	2	.	.	PUNCT
ap-614	119	1	when	when	SCONJ
ap-614	119	2	2	2	NUM
ap-614	119	3	non	non	ADJ
ap-614	119	4	-	-	ADJ
ap-614	119	5	intersection	intersection	ADJ
ap-614	119	6	discontinuities	discontinuity	NOUN
ap-614	119	7	cross	cross	VERB
ap-614	119	8	the	the	DET
ap-614	119	9	same	same	ADJ
ap-614	119	10	element	element	NOUN
ap-614	119	11	,	,	PUNCT
ap-614	119	12	the	the	DET
ap-614	119	13	integration	integration	NOUN
ap-614	119	14	rule	rule	NOUN
ap-614	119	15	is	be	AUX
ap-614	119	16	re	re	VERB
ap-614	119	17	-	-	VERB
ap-614	119	18	adapted	adapt	VERB
ap-614	119	19	again	again	ADV
ap-614	119	20	as	as	SCONJ
ap-614	119	21	shown	show	VERB
ap-614	119	22	in	in	ADP
ap-614	119	23	fig	fig	NOUN
ap-614	119	24	.	.	PUNCT
ap-614	120	1	2b	2b	NUM
ap-614	120	2	.	.	PUNCT
ap-614	121	1	in	in	ADP
ap-614	121	2	this	this	DET
ap-614	121	3	case	case	NOUN
ap-614	121	4	,	,	PUNCT
ap-614	121	5	15	15	NUM
ap-614	121	6	integration	integration	NOUN
ap-614	121	7	points	point	VERB
ap-614	121	8	for	for	ADP
ap-614	121	9	the	the	DET
ap-614	121	10	continuum	continuum	ADJ
ap-614	121	11	and	and	CCONJ
ap-614	121	12	4	4	NUM
ap-614	121	13	integration	integration	NOUN
ap-614	121	14	points	point	NOUN
ap-614	121	15	for	for	ADP
ap-614	121	16	the	the	DET
ap-614	121	17	discontinuity	discontinuity	NOUN
ap-614	121	18	are	be	AUX
ap-614	121	19	used	use	VERB
ap-614	121	20	.	.	PUNCT
ap-614	122	1	of	of	ADP
ap-614	122	2	course	course	ADV
ap-614	122	3	,	,	PUNCT
ap-614	122	4	depending	depend	VERB
ap-614	122	5	on	on	ADP
ap-614	122	6	the	the	DET
ap-614	122	7	position	position	NOUN
ap-614	122	8	of	of	ADP
ap-614	122	9	the	the	DET
ap-614	122	10	discontinuities	discontinuity	NOUN
ap-614	122	11	,	,	PUNCT
ap-614	122	12	the	the	DET
ap-614	122	13	integration	integration	NOUN
ap-614	122	14	rule	rule	NOUN
ap-614	122	15	might	might	AUX
ap-614	122	16	change	change	VERB
ap-614	122	17	.	.	PUNCT
ap-614	123	1	2.4.2	2.4.2	NUM
ap-614	123	2	enhanced	enhance	VERB
ap-614	123	3	nodes	node	NOUN
ap-614	123	4	another	another	DET
ap-614	123	5	implementation	implementation	NOUN
ap-614	123	6	issue	issue	NOUN
ap-614	123	7	is	be	AUX
ap-614	123	8	the	the	DET
ap-614	123	9	enhancement	enhancement	NOUN
ap-614	123	10	of	of	ADP
ap-614	123	11	the	the	DET
ap-614	123	12	nodes	node	NOUN
ap-614	123	13	.	.	PUNCT
ap-614	124	1	only	only	ADV
ap-614	124	2	nodes	node	NOUN
ap-614	124	3	whose	whose	DET
ap-614	124	4	support	support	NOUN
ap-614	124	5	is	be	AUX
ap-614	124	6	crossed	cross	VERB
ap-614	124	7	by	by	ADP
ap-614	124	8	a	a	DET
ap-614	124	9	discontinuity	discontinuity	NOUN
ap-614	124	10	should	should	AUX
ap-614	124	11	be	be	AUX
ap-614	124	12	enhanced	enhance	VERB
ap-614	124	13	.	.	PUNCT
ap-614	125	1	furthermore	furthermore	ADV
ap-614	125	2	,	,	PUNCT
ap-614	125	3	the	the	DET
ap-614	125	4	enhanced	enhance	VERB
ap-614	125	5	degrees	degree	NOUN
ap-614	125	6	of	of	ADP
ap-614	125	7	freedom	freedom	NOUN
ap-614	125	8	of	of	ADP
ap-614	125	9	the	the	DET
ap-614	125	10	nodes	node	NOUN
ap-614	125	11	on	on	ADP
ap-614	125	12	the	the	DET
ap-614	125	13	support	support	NOUN
ap-614	125	14	of	of	ADP
ap-614	125	15	the	the	DET
ap-614	125	16	crack	crack	NOUN
ap-614	125	17	tip	tip	NOUN
ap-614	125	18	remain	remain	VERB
ap-614	125	19	constrained	constrain	VERB
ap-614	125	20	.	.	PUNCT
ap-614	126	1	consequently	consequently	ADV
ap-614	126	2	,	,	PUNCT
ap-614	126	3	the	the	DET
ap-614	126	4	separation	separation	NOUN
ap-614	126	5	of	of	ADP
ap-614	126	6	the	the	DET
ap-614	126	7	crack	crack	NOUN
ap-614	126	8	tip	tip	NOUN
ap-614	126	9	is	be	AUX
ap-614	126	10	zero	zero	NUM
ap-614	126	11	.	.	PUNCT
ap-614	127	1	an	an	DET
ap-614	127	2	overview	overview	NOUN
ap-614	127	3	of	of	ADP
ap-614	127	4	which	which	PRON
ap-614	127	5	nodes	node	NOUN
ap-614	127	6	should	should	AUX
ap-614	127	7	be	be	AUX
ap-614	127	8	enhanced	enhance	VERB
ap-614	127	9	is	be	AUX
ap-614	127	10	given	give	VERB
ap-614	127	11	in	in	ADP
ap-614	127	12	fig	fig	NOUN
ap-614	127	13	.	.	PUNCT
ap-614	128	1	3	3	X
ap-614	128	2	.	.	X
ap-614	128	3	the	the	DET
ap-614	128	4	enhanced	enhance	VERB
ap-614	128	5	nodes	node	NOUN
ap-614	128	6	are	be	AUX
ap-614	128	7	represented	represent	VERB
ap-614	128	8	by	by	ADP
ap-614	128	9	squares	square	NOUN
ap-614	128	10	,	,	PUNCT
ap-614	128	11	while	while	SCONJ
ap-614	128	12	circles	circle	NOUN
ap-614	128	13	represent	represent	VERB
ap-614	128	14	the	the	DET
ap-614	128	15	nodes	node	NOUN
ap-614	128	16	at	at	ADP
ap-614	128	17	the	the	DET
ap-614	128	18	support	support	NOUN
ap-614	128	19	of	of	ADP
ap-614	128	20	the	the	DET
ap-614	128	21	crack	crack	NOUN
ap-614	128	22	tip	tip	NOUN
ap-614	128	23	.	.	PUNCT
ap-614	129	1	since	since	SCONJ
ap-614	129	2	the	the	DET
ap-614	129	3	crack	crack	NOUN
ap-614	129	4	can	can	AUX
ap-614	129	5	freely	freely	ADV
ap-614	129	6	run	run	VERB
ap-614	129	7	through	through	ADP
ap-614	129	8	the	the	DET
ap-614	129	9	finite	finite	ADJ
ap-614	129	10	elements	element	NOUN
ap-614	129	11	,	,	PUNCT
ap-614	129	12	it	it	PRON
ap-614	129	13	is	be	AUX
ap-614	129	14	possible	possible	ADJ
ap-614	129	15	that	that	SCONJ
ap-614	129	16	a	a	DET
ap-614	129	17	discontinuity	discontinuity	NOUN
ap-614	129	18	runs	run	VERB
ap-614	129	19	close	close	ADV
ap-614	129	20	to	to	ADP
ap-614	129	21	a	a	DET
ap-614	129	22	node	node	NOUN
ap-614	129	23	.	.	PUNCT
ap-614	130	1	as	as	ADP
ap-614	130	2	a	a	DET
ap-614	130	3	result	result	NOUN
ap-614	130	4	,	,	PUNCT
ap-614	130	5	a	a	DET
ap-614	130	6	small	small	ADJ
ap-614	130	7	proportion	proportion	NOUN
ap-614	130	8	of	of	ADP
ap-614	130	9	the	the	DET
ap-614	130	10	support	support	NOUN
ap-614	130	11	of	of	ADP
ap-614	130	12	the	the	DET
ap-614	130	13	node	node	NOUN
ap-614	130	14	lies	lie	VERB
ap-614	130	15	in	in	ADP
ap-614	130	16	either	either	DET
ap-614	130	17	�	�	PROPN
ap-614	130	18	i	i	PRON
ap-614	130	19	�	�	PROPN
ap-614	130	20	or	or	CCONJ
ap-614	130	21	�	�	PROPN
ap-614	130	22	i	i	PRON
ap-614	130	23	.	.	PUNCT
ap-614	131	1	in	in	ADP
ap-614	131	2	this	this	DET
ap-614	131	3	case	case	NOUN
ap-614	131	4	,	,	PUNCT
ap-614	131	5	the	the	DET
ap-614	131	6	global	global	ADJ
ap-614	131	7	stiffness	stiffness	NOUN
ap-614	131	8	matrix	matrix	NOUN
ap-614	131	9	is	be	AUX
ap-614	131	10	not	not	PART
ap-614	131	11	necessarily	necessarily	ADV
ap-614	131	12	well	well	ADV
ap-614	131	13	conditioned	condition	VERB
ap-614	131	14	.	.	PUNCT
ap-614	132	1	for	for	ADP
ap-614	132	2	this	this	DET
ap-614	132	3	reason	reason	NOUN
ap-614	132	4	,	,	PUNCT
ap-614	132	5	an	an	DET
ap-614	132	6	extra	extra	ADJ
ap-614	132	7	condition	condition	NOUN
ap-614	132	8	is	be	AUX
ap-614	132	9	introduced	introduce	VERB
ap-614	132	10	:	:	PUNCT
ap-614	132	11	min	min	NOUN
ap-614	132	12	(	(	PUNCT
ap-614	132	13	,	,	PUNCT
ap-614	132	14	)	)	PUNCT
ap-614	132	15	�	�	PROPN
ap-614	132	16	�	�	PROPN
ap-614	132	17	�	�	PROPN
ap-614	132	18	s	s	PART
ap-614	132	19	s	s	NOUN
ap-614	132	20	s	s	NOUN
ap-614	132	21	tol	tol	NOUN
ap-614	132	22	�	�	PROPN
ap-614	132	23	�	�	PROPN
ap-614	132	24	(	(	PUNCT
ap-614	132	25	17	17	NUM
ap-614	132	26	)	)	PUNCT
ap-614	132	27	where	where	SCONJ
ap-614	132	28	�	�	PROPN
ap-614	132	29	s	s	VERB
ap-614	132	30	is	be	AUX
ap-614	132	31	the	the	DET
ap-614	132	32	volume	volume	NOUN
ap-614	132	33	of	of	ADP
ap-614	132	34	the	the	DET
ap-614	132	35	support	support	NOUN
ap-614	132	36	of	of	ADP
ap-614	132	37	a	a	DET
ap-614	132	38	node	node	NOUN
ap-614	132	39	.	.	PUNCT
ap-614	133	1	the	the	DET
ap-614	133	2	tolerance	tolerance	NOUN
ap-614	133	3	is	be	AUX
ap-614	133	4	dependent	dependent	ADJ
ap-614	133	5	on	on	ADP
ap-614	133	6	the	the	DET
ap-614	133	7	precision	precision	NOUN
ap-614	133	8	of	of	ADP
ap-614	133	9	the	the	DET
ap-614	133	10	solver	solver	NOUN
ap-614	133	11	.	.	PUNCT
ap-614	134	1	when	when	SCONJ
ap-614	134	2	condition	condition	NOUN
ap-614	134	3	(	(	PUNCT
ap-614	134	4	17	17	NUM
ap-614	134	5	)	)	PUNCT
ap-614	134	6	is	be	AUX
ap-614	134	7	not	not	PART
ap-614	134	8	met	meet	VERB
ap-614	134	9	,	,	PUNCT
ap-614	134	10	the	the	DET
ap-614	134	11	considered	consider	VERB
ap-614	134	12	node	node	NOUN
ap-614	134	13	is	be	AUX
ap-614	134	14	constrained	constrain	VERB
ap-614	134	15	.	.	PUNCT
ap-614	135	1	the	the	DET
ap-614	135	2	influence	influence	NOUN
ap-614	135	3	will	will	AUX
ap-614	135	4	be	be	AUX
ap-614	135	5	spread	spread	VERB
ap-614	135	6	out	out	ADP
ap-614	135	7	over	over	ADP
ap-614	135	8	the	the	DET
ap-614	135	9	other	other	ADJ
ap-614	135	10	nodes	node	NOUN
ap-614	135	11	.	.	PUNCT
ap-614	136	1	44	44	NUM
ap-614	136	2	©	©	PROPN
ap-614	136	3	czech	czech	PROPN
ap-614	136	4	technical	technical	PROPN
ap-614	136	5	university	university	PROPN
ap-614	136	6	publishing	publishing	NOUN
ap-614	136	7	house	house	NOUN
ap-614	136	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	136	9	acta	acta	PROPN
ap-614	136	10	polytechnica	polytechnica	PROPN
ap-614	136	11	vol	vol	NOUN
ap-614	136	12	.	.	PROPN
ap-614	137	1	44	44	NUM
ap-614	137	2	no	no	NOUN
ap-614	137	3	.	.	PUNCT
ap-614	138	1	5–6/2004	5–6/2004	NUM
ap-614	138	2	fig	fig	NOUN
ap-614	138	3	.	.	PUNCT
ap-614	139	1	3	3	NUM
ap-614	139	2	:	:	PUNCT
ap-614	139	3	definition	definition	NOUN
ap-614	139	4	for	for	ADP
ap-614	139	5	enhancement	enhancement	NOUN
ap-614	139	6	of	of	ADP
ap-614	139	7	nodes	node	NOUN
ap-614	139	8	(	(	PUNCT
ap-614	139	9	squares	square	NOUN
ap-614	139	10	represent	represent	VERB
ap-614	139	11	enhanced	enhanced	ADJ
ap-614	139	12	nodes	node	NOUN
ap-614	139	13	)	)	PUNCT
ap-614	139	14	(	(	PUNCT
ap-614	139	15	a	a	X
ap-614	139	16	)	)	PUNCT
ap-614	139	17	(	(	PUNCT
ap-614	139	18	b	b	X
ap-614	139	19	)	)	PUNCT
ap-614	139	20	fig	fig	NOUN
ap-614	139	21	.	.	PUNCT
ap-614	140	1	2	2	NUM
ap-614	140	2	:	:	PUNCT
ap-614	140	3	location	location	NOUN
ap-614	140	4	of	of	ADP
ap-614	140	5	integration	integration	NOUN
ap-614	140	6	points	point	VERB
ap-614	140	7	for	for	ADP
ap-614	140	8	an	an	DET
ap-614	140	9	element	element	NOUN
ap-614	140	10	crossed	cross	VERB
ap-614	140	11	by	by	ADP
ap-614	140	12	(	(	PUNCT
ap-614	140	13	a	a	X
ap-614	140	14	)	)	PUNCT
ap-614	140	15	1	1	NUM
ap-614	140	16	discontinuity	discontinuity	NOUN
ap-614	140	17	and	and	CCONJ
ap-614	140	18	(	(	PUNCT
ap-614	140	19	b	b	NOUN
ap-614	140	20	)	)	PUNCT
ap-614	140	21	2	2	NUM
ap-614	140	22	discontinuities	discontinuity	NOUN
ap-614	140	23	initiation	initiation	NOUN
ap-614	140	24	and	and	CCONJ
ap-614	140	25	propagation	propagation	NOUN
ap-614	140	26	rules	rule	VERB
ap-614	140	27	an	an	DET
ap-614	140	28	important	important	ADJ
ap-614	140	29	issue	issue	NOUN
ap-614	140	30	is	be	AUX
ap-614	140	31	the	the	DET
ap-614	140	32	initiation	initiation	NOUN
ap-614	140	33	of	of	ADP
ap-614	140	34	the	the	DET
ap-614	140	35	discontinuity	discontinuity	NOUN
ap-614	140	36	.	.	PUNCT
ap-614	141	1	a	a	DET
ap-614	141	2	criterion	criterion	NOUN
ap-614	141	3	is	be	AUX
ap-614	141	4	needed	need	VERB
ap-614	141	5	to	to	PART
ap-614	141	6	decide	decide	VERB
ap-614	141	7	when	when	SCONJ
ap-614	141	8	a	a	DET
ap-614	141	9	discontinuity	discontinuity	NOUN
ap-614	141	10	should	should	AUX
ap-614	141	11	be	be	AUX
ap-614	141	12	initiated	initiate	VERB
ap-614	141	13	and	and	CCONJ
ap-614	141	14	should	should	AUX
ap-614	141	15	propagate	propagate	VERB
ap-614	141	16	.	.	PUNCT
ap-614	142	1	a	a	DET
ap-614	142	2	typical	typical	ADJ
ap-614	142	3	example	example	NOUN
ap-614	142	4	of	of	ADP
ap-614	142	5	an	an	DET
ap-614	142	6	initiation	initiation	NOUN
ap-614	142	7	criterion	criterion	NOUN
ap-614	142	8	is	be	AUX
ap-614	142	9	a	a	DET
ap-614	142	10	plasticity	plasticity	NOUN
ap-614	142	11	yield	yield	NOUN
ap-614	142	12	surface	surface	NOUN
ap-614	142	13	:	:	PUNCT
ap-614	142	14	whenever	whenever	SCONJ
ap-614	142	15	the	the	DET
ap-614	142	16	stress	stress	NOUN
ap-614	142	17	state	state	NOUN
ap-614	142	18	in	in	ADP
ap-614	142	19	one	one	NUM
ap-614	142	20	integration	integration	NOUN
ap-614	142	21	point	point	NOUN
ap-614	142	22	of	of	ADP
ap-614	142	23	the	the	DET
ap-614	142	24	considered	consider	VERB
ap-614	142	25	element	element	NOUN
ap-614	142	26	is	be	AUX
ap-614	142	27	situated	situate	VERB
ap-614	142	28	outside	outside	ADP
ap-614	142	29	the	the	DET
ap-614	142	30	elastic	elastic	ADJ
ap-614	142	31	domain	domain	NOUN
ap-614	142	32	bounded	bound	VERB
ap-614	142	33	by	by	ADP
ap-614	142	34	the	the	DET
ap-614	142	35	yield	yield	NOUN
ap-614	142	36	surface	surface	NOUN
ap-614	142	37	,	,	PUNCT
ap-614	142	38	a	a	DET
ap-614	142	39	discontinuity	discontinuity	NOUN
ap-614	142	40	is	be	AUX
ap-614	142	41	initiated	initiate	VERB
ap-614	142	42	,	,	PUNCT
ap-614	142	43	as	as	SCONJ
ap-614	142	44	will	will	AUX
ap-614	142	45	be	be	AUX
ap-614	142	46	explained	explain	VERB
ap-614	142	47	in	in	ADP
ap-614	142	48	section	section	NOUN
ap-614	142	49	7	7	NUM
ap-614	142	50	.	.	PUNCT
ap-614	143	1	another	another	DET
ap-614	143	2	important	important	ADJ
ap-614	143	3	item	item	NOUN
ap-614	143	4	is	be	AUX
ap-614	143	5	the	the	DET
ap-614	143	6	direction	direction	NOUN
ap-614	143	7	of	of	ADP
ap-614	143	8	the	the	DET
ap-614	143	9	discontinuity	discontinuity	NOUN
ap-614	143	10	.	.	PUNCT
ap-614	144	1	oliver	oliver	PROPN
ap-614	145	1	[	[	X
ap-614	145	2	16	16	NUM
ap-614	145	3	]	]	PUNCT
ap-614	145	4	stated	state	VERB
ap-614	145	5	that	that	SCONJ
ap-614	145	6	the	the	DET
ap-614	145	7	direction	direction	NOUN
ap-614	145	8	of	of	ADP
ap-614	145	9	the	the	DET
ap-614	145	10	discontinuity	discontinuity	NOUN
ap-614	145	11	could	could	AUX
ap-614	145	12	be	be	AUX
ap-614	145	13	found	find	VERB
ap-614	145	14	from	from	ADP
ap-614	145	15	the	the	DET
ap-614	145	16	stress	stress	NOUN
ap-614	145	17	state	state	NOUN
ap-614	145	18	at	at	ADP
ap-614	145	19	the	the	DET
ap-614	145	20	moment	moment	NOUN
ap-614	145	21	of	of	ADP
ap-614	145	22	initiation	initiation	NOUN
ap-614	145	23	.	.	PUNCT
ap-614	146	1	when	when	SCONJ
ap-614	146	2	using	use	VERB
ap-614	146	3	a	a	DET
ap-614	146	4	plasticity	plasticity	NOUN
ap-614	146	5	yield	yield	NOUN
ap-614	146	6	surface	surface	NOUN
ap-614	146	7	as	as	ADP
ap-614	146	8	the	the	DET
ap-614	146	9	initiation	initiation	NOUN
ap-614	146	10	criterion	criterion	NOUN
ap-614	146	11	,	,	PUNCT
ap-614	146	12	the	the	DET
ap-614	146	13	direction	direction	NOUN
ap-614	146	14	can	can	AUX
ap-614	146	15	be	be	AUX
ap-614	146	16	obtained	obtain	VERB
ap-614	146	17	by	by	ADP
ap-614	146	18	means	mean	NOUN
ap-614	146	19	of	of	ADP
ap-614	146	20	a	a	DET
ap-614	146	21	bifurcation	bifurcation	NOUN
ap-614	146	22	analysis	analysis	NOUN
ap-614	146	23	.	.	PUNCT
ap-614	147	1	furthermore	furthermore	ADV
ap-614	147	2	,	,	PUNCT
ap-614	147	3	a	a	DET
ap-614	147	4	discontinuity	discontinuity	NOUN
ap-614	147	5	can	can	AUX
ap-614	147	6	only	only	ADV
ap-614	147	7	grow	grow	VERB
ap-614	147	8	from	from	ADP
ap-614	147	9	a	a	DET
ap-614	147	10	previous	previous	ADJ
ap-614	147	11	crack	crack	NOUN
ap-614	147	12	tip	tip	NOUN
ap-614	147	13	to	to	PART
ap-614	147	14	introduce	introduce	VERB
ap-614	147	15	path	path	NOUN
ap-614	147	16	continuity	continuity	NOUN
ap-614	147	17	,	,	PUNCT
ap-614	147	18	and	and	CCONJ
ap-614	147	19	discontinuities	discontinuity	NOUN
ap-614	147	20	can	can	AUX
ap-614	147	21	only	only	ADV
ap-614	147	22	grow	grow	VERB
ap-614	147	23	at	at	ADP
ap-614	147	24	the	the	DET
ap-614	147	25	end	end	NOUN
ap-614	147	26	of	of	ADP
ap-614	147	27	a	a	DET
ap-614	147	28	time	time	NOUN
ap-614	147	29	step	step	NOUN
ap-614	147	30	.	.	PUNCT
ap-614	148	1	in	in	ADP
ap-614	148	2	this	this	DET
ap-614	148	3	case	case	NOUN
ap-614	148	4	,	,	PUNCT
ap-614	148	5	no	no	DET
ap-614	148	6	discontinuities	discontinuity	NOUN
ap-614	148	7	are	be	AUX
ap-614	148	8	introduced	introduce	VERB
ap-614	148	9	in	in	ADP
ap-614	148	10	non	non	ADJ
ap-614	148	11	-	-	ADJ
ap-614	148	12	equilibrium	equilibrium	ADJ
ap-614	148	13	states	state	NOUN
ap-614	148	14	and	and	CCONJ
ap-614	148	15	the	the	DET
ap-614	148	16	quadratic	quadratic	ADJ
ap-614	148	17	convergence	convergence	NOUN
ap-614	148	18	of	of	ADP
ap-614	148	19	the	the	DET
ap-614	148	20	newton	newton	PROPN
ap-614	148	21	-	-	PUNCT
ap-614	148	22	raphson	raphson	NOUN
ap-614	148	23	process	process	NOUN
ap-614	148	24	is	be	AUX
ap-614	148	25	ensured	ensure	VERB
ap-614	148	26	[	[	X
ap-614	148	27	17	17	NUM
ap-614	148	28	]	]	PUNCT
ap-614	148	29	.	.	PUNCT
ap-614	149	1	a	a	DET
ap-614	149	2	discontinuity	discontinuity	NOUN
ap-614	149	3	crosses	crosse	NOUN
ap-614	149	4	each	each	DET
ap-614	149	5	time	time	NOUN
ap-614	149	6	through	through	ADP
ap-614	149	7	the	the	DET
ap-614	149	8	whole	whole	ADJ
ap-614	149	9	element	element	NOUN
ap-614	149	10	.	.	PUNCT
ap-614	150	1	when	when	SCONJ
ap-614	150	2	allowing	allow	VERB
ap-614	150	3	multiple	multiple	ADJ
ap-614	150	4	discontinuities	discontinuity	NOUN
ap-614	150	5	to	to	PART
ap-614	150	6	grow	grow	VERB
ap-614	150	7	without	without	ADP
ap-614	150	8	intersection	intersection	NOUN
ap-614	150	9	,	,	PUNCT
ap-614	150	10	specific	specific	ADJ
ap-614	150	11	interaction	interaction	NOUN
ap-614	150	12	rules	rule	NOUN
ap-614	150	13	should	should	AUX
ap-614	150	14	be	be	AUX
ap-614	150	15	defined	define	VERB
ap-614	150	16	.	.	PUNCT
ap-614	151	1	different	different	ADJ
ap-614	151	2	cases	case	NOUN
ap-614	151	3	can	can	AUX
ap-614	151	4	be	be	AUX
ap-614	151	5	considered	consider	VERB
ap-614	151	6	,	,	PUNCT
ap-614	151	7	namely	namely	ADV
ap-614	151	8	a	a	X
ap-614	151	9	)	)	PUNCT
ap-614	151	10	only	only	ADV
ap-614	151	11	one	one	NUM
ap-614	151	12	crack	crack	NOUN
ap-614	151	13	tip	tip	NOUN
ap-614	151	14	touches	touch	VERB
ap-614	151	15	the	the	DET
ap-614	151	16	considered	consider	VERB
ap-614	151	17	element	element	NOUN
ap-614	151	18	,	,	PUNCT
ap-614	151	19	b	b	NOUN
ap-614	151	20	)	)	PUNCT
ap-614	151	21	two	two	NUM
ap-614	151	22	crack	crack	NOUN
ap-614	151	23	tips	tip	NOUN
ap-614	151	24	touch	touch	VERB
ap-614	151	25	the	the	DET
ap-614	151	26	considered	consider	VERB
ap-614	151	27	element	element	NOUN
ap-614	151	28	,	,	PUNCT
ap-614	151	29	c	c	NOUN
ap-614	151	30	)	)	PUNCT
ap-614	151	31	three	three	NUM
ap-614	151	32	crack	crack	NOUN
ap-614	151	33	tips	tip	NOUN
ap-614	151	34	touch	touch	VERB
ap-614	151	35	the	the	DET
ap-614	151	36	considered	consider	VERB
ap-614	151	37	element	element	NOUN
ap-614	151	38	,	,	PUNCT
ap-614	151	39	d	d	NOUN
ap-614	151	40	)	)	PUNCT
ap-614	151	41	one	one	NUM
ap-614	151	42	crack	crack	NOUN
ap-614	151	43	tip	tip	NOUN
ap-614	151	44	touches	touch	VERB
ap-614	151	45	an	an	DET
ap-614	151	46	element	element	NOUN
ap-614	151	47	that	that	PRON
ap-614	151	48	is	be	AUX
ap-614	151	49	already	already	ADV
ap-614	151	50	crossed	cross	VERB
ap-614	151	51	.	.	PUNCT
ap-614	152	1	the	the	DET
ap-614	152	2	first	first	ADJ
ap-614	152	3	case	case	NOUN
ap-614	152	4	is	be	AUX
ap-614	152	5	the	the	DET
ap-614	152	6	most	most	ADV
ap-614	152	7	common	common	ADJ
ap-614	152	8	case	case	NOUN
ap-614	152	9	.	.	PUNCT
ap-614	153	1	the	the	DET
ap-614	153	2	stress	stress	NOUN
ap-614	153	3	state	state	NOUN
ap-614	153	4	in	in	ADP
ap-614	153	5	the	the	DET
ap-614	153	6	considered	consider	VERB
ap-614	153	7	element	element	NOUN
ap-614	153	8	is	be	AUX
ap-614	153	9	checked	check	VERB
ap-614	153	10	and	and	CCONJ
ap-614	153	11	the	the	DET
ap-614	153	12	initiation	initiation	NOUN
ap-614	153	13	criterion	criterion	NOUN
ap-614	153	14	decides	decide	VERB
ap-614	153	15	whether	whether	SCONJ
ap-614	153	16	the	the	DET
ap-614	153	17	discontinuity	discontinuity	NOUN
ap-614	153	18	should	should	AUX
ap-614	153	19	propagate	propagate	VERB
ap-614	153	20	along	along	ADP
ap-614	153	21	the	the	DET
ap-614	153	22	computed	computed	ADJ
ap-614	153	23	direction	direction	NOUN
ap-614	153	24	or	or	CCONJ
ap-614	153	25	not	not	PART
ap-614	153	26	.	.	PUNCT
ap-614	154	1	the	the	DET
ap-614	154	2	second	second	ADJ
ap-614	154	3	case	case	NOUN
ap-614	154	4	implies	imply	VERB
ap-614	154	5	several	several	ADJ
ap-614	154	6	possibilities	possibility	NOUN
ap-614	154	7	:	:	PUNCT
ap-614	154	8	�	�	PROPN
ap-614	154	9	the	the	DET
ap-614	154	10	two	two	NUM
ap-614	154	11	crack	crack	NOUN
ap-614	154	12	tips	tip	NOUN
ap-614	154	13	link	link	VERB
ap-614	154	14	and	and	CCONJ
ap-614	154	15	form	form	VERB
ap-614	154	16	one	one	NUM
ap-614	154	17	crack	crack	NOUN
ap-614	154	18	,	,	PUNCT
ap-614	154	19	�	�	PROPN
ap-614	154	20	one	one	NUM
ap-614	154	21	crack	crack	NOUN
ap-614	154	22	propagates	propagate	VERB
ap-614	154	23	while	while	SCONJ
ap-614	154	24	the	the	DET
ap-614	154	25	other	other	ADJ
ap-614	154	26	stops	stop	NOUN
ap-614	154	27	,	,	PUNCT
ap-614	154	28	�	�	PROPN
ap-614	154	29	both	both	DET
ap-614	154	30	cracks	crack	NOUN
ap-614	154	31	grow	grow	VERB
ap-614	154	32	,	,	PUNCT
ap-614	154	33	without	without	ADP
ap-614	154	34	intersecting	intersect	VERB
ap-614	154	35	.	.	PUNCT
ap-614	155	1	to	to	PART
ap-614	155	2	decide	decide	VERB
ap-614	155	3	which	which	DET
ap-614	155	4	case	case	NOUN
ap-614	155	5	occurs	occur	VERB
ap-614	155	6	,	,	PUNCT
ap-614	155	7	the	the	DET
ap-614	155	8	normal	normal	ADJ
ap-614	155	9	ncomp	ncomp	NOUN
ap-614	155	10	is	be	AUX
ap-614	155	11	computed	compute	VERB
ap-614	155	12	according	accord	VERB
ap-614	155	13	to	to	ADP
ap-614	155	14	the	the	DET
ap-614	155	15	present	present	ADJ
ap-614	155	16	stress	stress	NOUN
ap-614	155	17	state	state	NOUN
ap-614	155	18	in	in	ADP
ap-614	155	19	the	the	DET
ap-614	155	20	considered	consider	VERB
ap-614	155	21	element	element	NOUN
ap-614	155	22	.	.	PUNCT
ap-614	156	1	then	then	ADV
ap-614	156	2	the	the	DET
ap-614	156	3	normal	normal	ADJ
ap-614	156	4	ncon	ncon	NOUN
ap-614	156	5	to	to	ADP
ap-614	156	6	the	the	DET
ap-614	156	7	connecting	connect	VERB
ap-614	156	8	line	line	NOUN
ap-614	156	9	,	,	PUNCT
ap-614	156	10	i.e.	i.e.	X
ap-614	156	11	the	the	DET
ap-614	156	12	line	line	NOUN
ap-614	156	13	that	that	PRON
ap-614	156	14	connects	connect	VERB
ap-614	156	15	the	the	DET
ap-614	156	16	crack	crack	NOUN
ap-614	156	17	tips	tip	NOUN
ap-614	156	18	,	,	PUNCT
ap-614	156	19	is	be	AUX
ap-614	156	20	computed	compute	VERB
ap-614	156	21	.	.	PUNCT
ap-614	157	1	from	from	ADP
ap-614	157	2	this	this	DET
ap-614	157	3	normal	normal	ADJ
ap-614	157	4	,	,	PUNCT
ap-614	157	5	a	a	DET
ap-614	157	6	3	3	NUM
ap-614	157	7	cohesive	cohesive	ADJ
ap-614	157	8	zone	zone	NOUN
ap-614	157	9	model	model	NOUN
ap-614	157	10	the	the	DET
ap-614	157	11	behaviour	behaviour	NOUN
ap-614	157	12	within	within	ADP
ap-614	157	13	the	the	DET
ap-614	157	14	discontinuity	discontinuity	NOUN
ap-614	157	15	is	be	AUX
ap-614	157	16	described	describe	VERB
ap-614	157	17	by	by	ADP
ap-614	157	18	a	a	DET
ap-614	157	19	plasticity	plasticity	NOUN
ap-614	157	20	based	base	VERB
ap-614	157	21	cohesive	cohesive	ADJ
ap-614	157	22	zone	zone	NOUN
ap-614	157	23	model	model	NOUN
ap-614	157	24	.	.	PUNCT
ap-614	158	1	the	the	DET
ap-614	158	2	adopted	adopt	VERB
ap-614	158	3	plasticity	plasticity	NOUN
ap-614	158	4	model	model	NOUN
ap-614	158	5	was	be	AUX
ap-614	158	6	proposed	propose	VERB
ap-614	158	7	by	by	ADP
ap-614	158	8	carol	carol	PROPN
ap-614	158	9	et	et	PROPN
ap-614	158	10	al	al	PROPN
ap-614	158	11	.	.	PUNCT
ap-614	159	1	[	[	X
ap-614	159	2	22	22	NUM
ap-614	159	3	]	]	PUNCT
ap-614	159	4	for	for	ADP
ap-614	159	5	use	use	NOUN
ap-614	159	6	in	in	ADP
ap-614	159	7	interface	interface	NOUN
ap-614	159	8	elements	element	NOUN
ap-614	159	9	.	.	PUNCT
ap-614	160	1	consequently	consequently	ADV
ap-614	160	2	,	,	PUNCT
ap-614	160	3	the	the	DET
ap-614	160	4	plastic	plastic	NOUN
ap-614	160	5	yield	yield	NOUN
ap-614	160	6	function	function	NOUN
ap-614	160	7	is	be	AUX
ap-614	160	8	given	give	VERB
ap-614	160	9	in	in	ADP
ap-614	160	10	the	the	DET
ap-614	160	11	traction	traction	NOUN
ap-614	160	12	space	space	NOUN
ap-614	160	13	instead	instead	ADV
ap-614	160	14	of	of	ADP
ap-614	160	15	the	the	DET
ap-614	160	16	stress	stress	NOUN
ap-614	160	17	space	space	NOUN
ap-614	160	18	.	.	PUNCT
ap-614	161	1	a	a	DET
ap-614	161	2	hyperbolic	hyperbolic	ADJ
ap-614	161	3	yield	yield	NOUN
ap-614	161	4	surface	surface	NOUN
ap-614	161	5	is	be	AUX
ap-614	161	6	introduced	introduce	VERB
ap-614	161	7	,	,	PUNCT
ap-614	161	8	f	f	PROPN
ap-614	161	9	t	t	PROPN
ap-614	161	10	c	c	PROPN
ap-614	161	11	t	t	PROPN
ap-614	161	12	c	c	PROPN
ap-614	161	13	ft	ft	PROPN
ap-614	161	14	n	n	PROPN
ap-614	161	15	t	t	PROPN
ap-614	161	16	�	�	PROPN
ap-614	161	17	�	�	PROPN
ap-614	161	18	2	2	NUM
ap-614	161	19	2	2	NUM
ap-614	161	20	2	2	NUM
ap-614	161	21	(	(	PUNCT
ap-614	161	22	tan	tan	PROPN
ap-614	161	23	)	)	PUNCT
ap-614	161	24	(	(	PUNCT
ap-614	161	25	tan	tan	PROPN
ap-614	161	26	)	)	PUNCT
ap-614	161	27	�	�	PROPN
ap-614	161	28	�	�	PROPN
ap-614	161	29	(	(	PUNCT
ap-614	161	30	18	18	NUM
ap-614	161	31	)	)	PUNCT
ap-614	161	32	where	where	SCONJ
ap-614	161	33	!	!	PUNCT
ap-614	161	34	t	t	PROPN
ap-614	161	35	�	�	PROPN
ap-614	161	36	t	t	PROPN
ap-614	161	37	tn	tn	PROPN
ap-614	161	38	t	t	PROPN
ap-614	161	39	,	,	PUNCT
ap-614	161	40	are	be	AUX
ap-614	161	41	the	the	DET
ap-614	161	42	normal	normal	ADJ
ap-614	161	43	and	and	CCONJ
ap-614	161	44	tangential	tangential	ADJ
ap-614	161	45	component	component	NOUN
ap-614	161	46	of	of	ADP
ap-614	161	47	the	the	DET
ap-614	161	48	traction	traction	PROPN
ap-614	161	49	vector	vector	NOUN
ap-614	161	50	,	,	PUNCT
ap-614	161	51	c	c	PROPN
ap-614	161	52	is	be	AUX
ap-614	161	53	the	the	DET
ap-614	161	54	cohesion	cohesion	NOUN
ap-614	161	55	,	,	PUNCT
ap-614	161	56	ft	ft	PROPN
ap-614	161	57	the	the	DET
ap-614	161	58	tensile	tensile	NOUN
ap-614	161	59	strength	strength	NOUN
ap-614	161	60	and	and	CCONJ
ap-614	161	61	�	�	PROPN
ap-614	161	62	the	the	DET
ap-614	161	63	internal	internal	ADJ
ap-614	161	64	friction	friction	NOUN
ap-614	161	65	angle	angle	NOUN
ap-614	161	66	of	of	ADP
ap-614	161	67	the	the	DET
ap-614	161	68	material	material	NOUN
ap-614	161	69	.	.	PUNCT
ap-614	162	1	for	for	ADP
ap-614	162	2	tension	tension	NOUN
ap-614	162	3	,	,	PUNCT
ap-614	162	4	an	an	DET
ap-614	162	5	associative	associative	ADJ
ap-614	162	6	flow	flow	NOUN
ap-614	162	7	rule	rule	NOUN
ap-614	162	8	is	be	AUX
ap-614	162	9	adopted	adopt	VERB
ap-614	162	10	.	.	PUNCT
ap-614	163	1	the	the	DET
ap-614	163	2	evolution	evolution	NOUN
ap-614	163	3	of	of	ADP
ap-614	163	4	the	the	DET
ap-614	163	5	yield	yield	NOUN
ap-614	163	6	surface	surface	NOUN
ap-614	163	7	is	be	AUX
ap-614	163	8	governed	govern	VERB
ap-614	163	9	by	by	ADP
ap-614	163	10	the	the	DET
ap-614	163	11	decrease	decrease	NOUN
ap-614	163	12	of	of	ADP
ap-614	163	13	tensile	tensile	NOUN
ap-614	163	14	strength	strength	NOUN
ap-614	163	15	and	and	CCONJ
ap-614	163	16	cohesion	cohesion	NOUN
ap-614	163	17	throughout	throughout	ADP
ap-614	163	18	the	the	DET
ap-614	163	19	computation	computation	NOUN
ap-614	163	20	:	:	PUNCT
ap-614	164	1	f	f	PROPN
ap-614	164	2	f	f	PROPN
ap-614	164	3	w	w	PROPN
ap-614	164	4	gt	gt	PROPN
ap-614	164	5	t	t	PROPN
ap-614	164	6	cr	cr	PROPN
ap-614	164	7	fi	fi	PROPN
ap-614	164	8	�	�	PROPN
ap-614	164	9	�	�	PROPN
ap-614	164	10	�	�	PROPN
ap-614	164	11	�	�	PROPN
ap-614	164	12	�	�	PROPN
ap-614	164	13	�	�	PROPN
ap-614	164	14	�	�	PROPN
ap-614	164	15	�	�	PROPN
ap-614	164	16	�	�	PROPN
ap-614	164	17	0	0	NUM
ap-614	164	18	1	1	NUM
ap-614	164	19	,	,	PUNCT
ap-614	164	20	(	(	PUNCT
ap-614	164	21	19a	19a	NUM
ap-614	164	22	)	)	PUNCT
ap-614	164	23	c	c	PROPN
ap-614	164	24	c	c	PROPN
ap-614	164	25	w	w	PROPN
ap-614	164	26	g	g	PROPN
ap-614	164	27	cr	cr	PROPN
ap-614	164	28	fii	fii	PROPN
ap-614	164	29	�	�	PROPN
ap-614	164	30	�	�	PROPN
ap-614	164	31	�	�	PROPN
ap-614	164	32	�	�	PROPN
ap-614	164	33	�	�	PROPN
ap-614	164	34	�	�	PROPN
ap-614	164	35	�	�	PROPN
ap-614	164	36	�	�	PROPN
ap-614	164	37	�	�	PROPN
ap-614	164	38	0	0	NUM
ap-614	164	39	1	1	NUM
ap-614	164	40	,	,	PUNCT
ap-614	164	41	(	(	PUNCT
ap-614	164	42	19b	19b	NOUN
ap-614	164	43	)	)	PUNCT
ap-614	164	44	where	where	SCONJ
ap-614	164	45	ft0	ft0	NOUN
ap-614	164	46	and	and	CCONJ
ap-614	164	47	c0	c0	PROPN
ap-614	164	48	are	be	AUX
ap-614	164	49	the	the	DET
ap-614	164	50	initial	initial	ADJ
ap-614	164	51	values	value	NOUN
ap-614	164	52	for	for	ADP
ap-614	164	53	the	the	DET
ap-614	164	54	tensile	tensile	NOUN
ap-614	164	55	strength	strength	NOUN
ap-614	164	56	and	and	CCONJ
ap-614	164	57	the	the	DET
ap-614	164	58	cohesion	cohesion	NOUN
ap-614	164	59	,	,	PUNCT
ap-614	164	60	gfi	gfi	PROPN
ap-614	164	61	is	be	AUX
ap-614	164	62	the	the	DET
ap-614	164	63	mode	mode	NOUN
ap-614	164	64	-	-	PUNCT
ap-614	164	65	i	i	PRON
ap-614	164	66	fracture	fracture	PROPN
ap-614	164	67	energy	energy	NOUN
ap-614	164	68	,	,	PUNCT
ap-614	164	69	gfii	gfii	PROPN
ap-614	164	70	is	be	AUX
ap-614	164	71	the	the	DET
ap-614	164	72	mode	mode	PROPN
ap-614	164	73	-	-	PUNCT
ap-614	164	74	ii	ii	PROPN
ap-614	164	75	fracture	fracture	NOUN
ap-614	164	76	energy	energy	NOUN
ap-614	164	77	and	and	CCONJ
ap-614	164	78	wcr	wcr	PROPN
ap-614	164	79	is	be	AUX
ap-614	164	80	the	the	DET
ap-614	164	81	energy	energy	NOUN
ap-614	164	82	dissipated	dissipate	VERB
ap-614	164	83	during	during	ADP
ap-614	164	84	fracture	fracture	NOUN
ap-614	164	85	processes	process	NOUN
ap-614	164	86	.	.	PUNCT
ap-614	165	1	the	the	DET
ap-614	165	2	energy	energy	NOUN
ap-614	165	3	is	be	AUX
ap-614	165	4	defined	define	VERB
ap-614	165	5	as	as	ADP
ap-614	165	6	:	:	PUNCT
ap-614	165	7	d	d	PROPN
ap-614	165	8	d	d	X
ap-614	165	9	dw	dw	PROPN
ap-614	165	10	t	t	PROPN
ap-614	165	11	tcr	tcr	PROPN
ap-614	165	12	n	n	PROPN
ap-614	165	13	n	n	PROPN
ap-614	165	14	pl	pl	PROPN
ap-614	165	15	t	t	PROPN
ap-614	165	16	t	t	PROPN
ap-614	165	17	pl	pl	PROPN
ap-614	165	18	�	�	PROPN
ap-614	165	19	�	�	PROPN
ap-614	165	20	�	�	PROPN
ap-614	165	21	�	�	PROPN
ap-614	165	22	(	(	PUNCT
ap-614	165	23	20a	20a	NOUN
ap-614	165	24	)	)	PUNCT
ap-614	165	25	and	and	CCONJ
ap-614	165	26	w	w	PROPN
ap-614	165	27	wcr	wcr	PROPN
ap-614	165	28	cr	cr	PROPN
ap-614	165	29	t	t	PROPN
ap-614	165	30	�	�	PROPN
ap-614	165	31	�	�	PROPN
ap-614	165	32	d	d	PROPN
ap-614	165	33	0	0	NUM
ap-614	165	34	(	(	PUNCT
ap-614	165	35	20b	20b	NOUN
ap-614	165	36	)	)	PUNCT
ap-614	165	37	where	where	SCONJ
ap-614	165	38	!	!	PUNCT
ap-614	165	39	�	�	PROPN
ap-614	165	40	�	�	PROPN
ap-614	165	41	�	�	PROPN
ap-614	165	42	�	�	PROPN
ap-614	165	43	n	n	PART
ap-614	165	44	pl	pl	PROPN
ap-614	165	45	t	t	PROPN
ap-614	165	46	pl	pl	PROPN
ap-614	165	47	,	,	PUNCT
ap-614	165	48	are	be	AUX
ap-614	165	49	the	the	DET
ap-614	165	50	normal	normal	ADJ
ap-614	165	51	and	and	CCONJ
ap-614	165	52	tangential	tangential	ADJ
ap-614	165	53	component	component	NOUN
ap-614	165	54	of	of	ADP
ap-614	165	55	the	the	DET
ap-614	165	56	plastic	plastic	NOUN
ap-614	165	57	separation	separation	NOUN
ap-614	165	58	vector	vector	NOUN
ap-614	165	59	.	.	PUNCT
ap-614	166	1	the	the	DET
ap-614	166	2	decrease	decrease	NOUN
ap-614	166	3	of	of	ADP
ap-614	166	4	tensile	tensile	NOUN
ap-614	166	5	strength	strength	NOUN
ap-614	166	6	and	and	CCONJ
ap-614	166	7	cohesion	cohesion	NOUN
ap-614	166	8	is	be	AUX
ap-614	166	9	coupled	couple	VERB
ap-614	166	10	to	to	ADP
ap-614	166	11	the	the	DET
ap-614	166	12	energy	energy	NOUN
ap-614	166	13	dissipated	dissipate	VERB
ap-614	166	14	during	during	ADP
ap-614	166	15	the	the	DET
ap-614	166	16	fracture	fracture	NOUN
ap-614	166	17	processes	process	NOUN
ap-614	166	18	.	.	PUNCT
ap-614	167	1	moreover	moreover	ADV
ap-614	167	2	,	,	PUNCT
ap-614	167	3	the	the	DET
ap-614	167	4	choice	choice	NOUN
ap-614	167	5	of	of	ADP
ap-614	167	6	eq	eq	PROPN
ap-614	167	7	.	.	PUNCT
ap-614	168	1	(	(	PUNCT
ap-614	168	2	19a)/(19b	19a)/(19b	X
ap-614	168	3	)	)	PUNCT
ap-614	168	4	ensures	ensure	VERB
ap-614	168	5	that	that	SCONJ
ap-614	168	6	the	the	DET
ap-614	168	7	total	total	ADJ
ap-614	168	8	mode	mode	NOUN
ap-614	168	9	-	-	PUNCT
ap-614	168	10	i	i	PRON
ap-614	168	11	fracture	fracture	VERB
ap-614	168	12	energy	energy	NOUN
ap-614	168	13	/	/	SYM
ap-614	168	14	mode	mode	NOUN
ap-614	168	15	-	-	PUNCT
ap-614	168	16	ii	ii	PROPN
ap-614	168	17	fracture	fracture	NOUN
ap-614	168	18	energy	energy	NOUN
ap-614	168	19	is	be	AUX
ap-614	168	20	dissipated	dissipate	VERB
ap-614	168	21	when	when	SCONJ
ap-614	168	22	the	the	DET
ap-614	168	23	tensile	tensile	NOUN
ap-614	168	24	strength	strength	NOUN
ap-614	168	25	/	/	SYM
ap-614	168	26	cohesion	cohesion	NOUN
ap-614	168	27	vanishes	vanish	VERB
ap-614	168	28	.	.	PUNCT
ap-614	169	1	furthermore	furthermore	ADV
ap-614	169	2	,	,	PUNCT
ap-614	169	3	the	the	DET
ap-614	169	4	decrease	decrease	NOUN
ap-614	169	5	of	of	ADP
ap-614	169	6	tensile	tensile	NOUN
ap-614	169	7	strength	strength	NOUN
ap-614	169	8	and	and	CCONJ
ap-614	169	9	cohesion	cohesion	NOUN
ap-614	169	10	is	be	AUX
ap-614	169	11	coupled	couple	VERB
ap-614	169	12	:	:	PUNCT
ap-614	169	13	when	when	SCONJ
ap-614	169	14	a	a	DET
ap-614	169	15	material	material	NOUN
ap-614	169	16	is	be	AUX
ap-614	169	17	damaged	damage	VERB
ap-614	169	18	due	due	ADJ
ap-614	169	19	to	to	ADP
ap-614	169	20	tensile	tensile	NOUN
ap-614	169	21	loading	loading	NOUN
ap-614	169	22	,	,	PUNCT
ap-614	169	23	the	the	DET
ap-614	169	24	tensile	tensile	NOUN
ap-614	169	25	strength	strength	NOUN
ap-614	169	26	but	but	CCONJ
ap-614	169	27	also	also	ADV
ap-614	169	28	the	the	DET
ap-614	169	29	cohesion	cohesion	NOUN
ap-614	169	30	decreases	decrease	VERB
ap-614	169	31	.	.	PUNCT
ap-614	170	1	the	the	DET
ap-614	170	2	tangential	tangential	ADJ
ap-614	170	3	stiffness	stiffness	NOUN
ap-614	170	4	and	and	CCONJ
ap-614	170	5	the	the	DET
ap-614	170	6	stress	stress	NOUN
ap-614	170	7	update	update	NOUN
ap-614	170	8	are	be	AUX
ap-614	170	9	obtained	obtain	VERB
ap-614	170	10	with	with	ADP
ap-614	170	11	classical	classical	ADJ
ap-614	170	12	elasto	elasto	NOUN
ap-614	170	13	-	-	PUNCT
ap-614	170	14	plastic	plastic	NOUN
ap-614	170	15	equations	equation	NOUN
ap-614	170	16	.	.	PUNCT
ap-614	171	1	the	the	DET
ap-614	171	2	tractions	traction	NOUN
ap-614	171	3	are	be	AUX
ap-614	171	4	defined	define	VERB
ap-614	171	5	through	through	ADP
ap-614	171	6	:	:	PUNCT
ap-614	171	7	t	t	PROPN
ap-614	171	8	d	d	PROPN
ap-614	171	9	�	�	PROPN
ap-614	171	10	e	e	PROPN
ap-614	171	11	pl	pl	PROPN
ap-614	171	12	(	(	PUNCT
ap-614	171	13	)	)	PUNCT
ap-614	171	14	�	�	PROPN
ap-614	171	15	�	�	PROPN
ap-614	171	16	.	.	PUNCT
ap-614	172	1	(	(	PUNCT
ap-614	172	2	21	21	NUM
ap-614	172	3	)	)	PUNCT
ap-614	172	4	the	the	DET
ap-614	172	5	plastic	plastic	ADJ
ap-614	172	6	deformation	deformation	NOUN
ap-614	172	7	rate	rate	NOUN
ap-614	172	8	is	be	AUX
ap-614	172	9	defined	define	VERB
ap-614	172	10	as	as	ADP
ap-614	172	11	:	:	PUNCT
ap-614	172	12	�	�	PROPN
ap-614	172	13	�	�	PROPN
ap-614	172	14	�	�	PROPN
ap-614	172	15	�	�	PROPN
ap-614	172	16	pl	pl	PROPN
ap-614	172	17	f	f	PROPN
ap-614	172	18	�	�	PROPN
ap-614	172	19	�	�	PROPN
ap-614	172	20	t	t	PROPN
ap-614	172	21	n	n	PROPN
ap-614	172	22	,	,	PUNCT
ap-614	172	23	(	(	PUNCT
ap-614	172	24	22	22	NUM
ap-614	172	25	)	)	PUNCT
ap-614	172	26	where	where	SCONJ
ap-614	172	27	�	�	PROPN
ap-614	172	28	is	be	AUX
ap-614	172	29	the	the	DET
ap-614	172	30	plastic	plastic	ADJ
ap-614	172	31	multiplier	multipli	ADJ
ap-614	172	32	rate	rate	NOUN
ap-614	172	33	.	.	PUNCT
ap-614	173	1	for	for	ADP
ap-614	173	2	tension	tension	NOUN
ap-614	173	3	,	,	PUNCT
ap-614	173	4	an	an	DET
ap-614	173	5	associative	associative	ADJ
ap-614	173	6	flow	flow	NOUN
ap-614	173	7	rule	rule	NOUN
ap-614	173	8	is	be	AUX
ap-614	173	9	adopted	adopt	VERB
ap-614	173	10	.	.	PUNCT
ap-614	174	1	the	the	DET
ap-614	174	2	plastic	plastic	ADJ
ap-614	174	3	deformation	deformation	NOUN
ap-614	174	4	rate	rate	NOUN
ap-614	174	5	can	can	AUX
ap-614	174	6	be	be	AUX
ap-614	174	7	introduced	introduce	VERB
ap-614	174	8	in	in	ADP
ap-614	174	9	eq	eq	ADP
ap-614	174	10	.	.	PUNCT
ap-614	175	1	(	(	PUNCT
ap-614	175	2	22	22	NUM
ap-614	175	3	):	):	PUNCT
ap-614	175	4	�	�	PROPN
ap-614	175	5	(	(	PUNCT
ap-614	175	6	�	�	PROPN
ap-614	175	7	�	�	PROPN
ap-614	175	8	)	)	PUNCT
ap-614	175	9	t	t	PROPN
ap-614	175	10	d	d	PROPN
ap-614	175	11	n	n	CCONJ
ap-614	175	12	�	�	PROPN
ap-614	175	13	e	e	X
ap-614	175	14	�	�	PROPN
ap-614	175	15	(	(	PUNCT
ap-614	175	16	23	23	NUM
ap-614	175	17	)	)	PUNCT
ap-614	175	18	the	the	DET
ap-614	175	19	plastic	plastic	ADJ
ap-614	175	20	multiplier	multipli	ADJ
ap-614	175	21	rate	rate	NOUN
ap-614	175	22	can	can	AUX
ap-614	175	23	be	be	AUX
ap-614	175	24	obtained	obtain	VERB
ap-614	175	25	through	through	ADP
ap-614	175	26	the	the	DET
ap-614	175	27	consistency	consistency	NOUN
ap-614	175	28	equation	equation	NOUN
ap-614	175	29	:	:	PUNCT
ap-614	175	30	�	�	PROPN
ap-614	175	31	�	�	PROPN
ap-614	175	32	�	�	PROPN
ap-614	175	33	n	n	CCONJ
ap-614	175	34	d	d	PROPN
ap-614	175	35	n	n	PROPN
ap-614	175	36	d	d	PROPN
ap-614	175	37	n	n	NOUN
ap-614	175	38	t	t	NOUN
ap-614	175	39	t	t	NOUN
ap-614	175	40	h	h	NOUN
ap-614	175	41	e	e	PROPN
ap-614	175	42	e	e	X
ap-614	175	43	�	�	PROPN
ap-614	175	44	,	,	PUNCT
ap-614	175	45	(	(	PUNCT
ap-614	175	46	24	24	NUM
ap-614	175	47	)	)	PUNCT
ap-614	175	48	where	where	SCONJ
ap-614	175	49	h	h	NOUN
ap-614	175	50	is	be	AUX
ap-614	175	51	the	the	DET
ap-614	175	52	hardening	hardening	NOUN
ap-614	175	53	/	/	SYM
ap-614	175	54	softening	soften	VERB
ap-614	175	55	modulus	modulus	NOUN
ap-614	175	56	.	.	PUNCT
ap-614	176	1	inserting	insert	VERB
ap-614	176	2	the	the	DET
ap-614	176	3	result	result	NOUN
ap-614	176	4	for	for	ADP
ap-614	176	5	the	the	DET
ap-614	176	6	plastic	plastic	NOUN
ap-614	176	7	multiplier	multipli	ADJ
ap-614	176	8	into	into	ADP
ap-614	176	9	equation	equation	NOUN
ap-614	176	10	(	(	PUNCT
ap-614	176	11	23	23	NUM
ap-614	176	12	)	)	PUNCT
ap-614	176	13	yields	yield	VERB
ap-614	176	14	the	the	DET
ap-614	176	15	tangential	tangential	ADJ
ap-614	176	16	stiffness	stiffness	NOUN
ap-614	176	17	:	:	PUNCT
ap-614	176	18	�	�	PROPN
ap-614	176	19	�	�	PROPN
ap-614	176	20	�	�	PROPN
ap-614	176	21	t	t	PROPN
ap-614	176	22	d	d	PROPN
ap-614	176	23	d	d	PROPN
ap-614	176	24	nn	nn	PROPN
ap-614	176	25	d	d	PROPN
ap-614	176	26	n	n	PROPN
ap-614	176	27	d	d	PROPN
ap-614	176	28	n	n	SYM
ap-614	176	29	d	d	PROPN
ap-614	176	30	�	�	PROPN
ap-614	176	31	�	�	PROPN
ap-614	176	32	�	�	PROPN
ap-614	176	33	�	�	PROPN
ap-614	176	34	�	�	PROPN
ap-614	176	35	�	�	PROPN
ap-614	176	36	�	�	PROPN
ap-614	176	37	�	�	PROPN
ap-614	176	38	�	�	PROPN
ap-614	176	39	�	�	PROPN
ap-614	176	40	e	e	X
ap-614	176	41	e	e	X
ap-614	176	42	e	e	PROPN
ap-614	176	43	t	t	PROPN
ap-614	176	44	t	t	PROPN
ap-614	176	45	h	h	PROPN
ap-614	176	46	�	�	PROPN
ap-614	176	47	�	�	PROPN
ap-614	176	48	.	.	PUNCT
ap-614	177	1	(	(	PUNCT
ap-614	177	2	25	25	NUM
ap-614	177	3	)	)	PUNCT
ap-614	177	4	the	the	DET
ap-614	177	5	tangential	tangential	ADJ
ap-614	177	6	stiffness	stiffness	NOUN
ap-614	177	7	can	can	AUX
ap-614	177	8	be	be	AUX
ap-614	177	9	inserted	insert	VERB
ap-614	177	10	in	in	ADP
ap-614	177	11	the	the	DET
ap-614	177	12	finite	finite	ADJ
ap-614	177	13	element	element	NOUN
ap-614	177	14	equations	equation	NOUN
ap-614	177	15	(	(	PUNCT
ap-614	177	16	see	see	VERB
ap-614	177	17	eq	eq	ADP
ap-614	177	18	.	.	PROPN
ap-614	177	19	14	14	NUM
ap-614	177	20	)	)	PUNCT
ap-614	177	21	.	.	PUNCT
ap-614	178	1	the	the	DET
ap-614	178	2	elastic	elastic	ADJ
ap-614	178	3	stiffness	stiffness	NOUN
ap-614	178	4	is	be	AUX
ap-614	178	5	chosen	choose	VERB
ap-614	178	6	very	very	ADV
ap-614	178	7	high	high	ADJ
ap-614	178	8	,	,	PUNCT
ap-614	178	9	in	in	ADP
ap-614	178	10	theory	theory	NOUN
ap-614	178	11	infinite	infinite	VERB
ap-614	178	12	,	,	PUNCT
ap-614	178	13	in	in	ADP
ap-614	178	14	order	order	NOUN
ap-614	178	15	to	to	PART
ap-614	178	16	suppress	suppress	VERB
ap-614	178	17	the	the	DET
ap-614	178	18	artificial	artificial	ADJ
ap-614	178	19	elastic	elastic	ADJ
ap-614	178	20	part	part	NOUN
ap-614	178	21	of	of	ADP
ap-614	178	22	the	the	DET
ap-614	178	23	solution	solution	NOUN
ap-614	178	24	.	.	PUNCT
ap-614	179	1	since	since	SCONJ
ap-614	179	2	a	a	DET
ap-614	179	3	discontinuity	discontinuity	NOUN
ap-614	179	4	is	be	AUX
ap-614	179	5	only	only	ADV
ap-614	179	6	inserted	insert	VERB
ap-614	179	7	when	when	SCONJ
ap-614	179	8	the	the	DET
ap-614	179	9	yield	yield	NOUN
ap-614	179	10	surface	surface	NOUN
ap-614	179	11	is	be	AUX
ap-614	179	12	violated	violate	VERB
ap-614	179	13	,	,	PUNCT
ap-614	179	14	the	the	DET
ap-614	179	15	jump	jump	NOUN
ap-614	179	16	is	be	AUX
ap-614	179	17	completely	completely	ADV
ap-614	179	18	inelastic	inelastic	ADJ
ap-614	179	19	.	.	PUNCT
ap-614	180	1	4	4	NUM
ap-614	180	2	numerical	numerical	PROPN
ap-614	180	3	example	example	NOUN
ap-614	180	4	nooru	nooru	PROPN
ap-614	180	5	-	-	PUNCT
ap-614	180	6	mohamed	mohamed	PROPN
ap-614	180	7	[	[	X
ap-614	180	8	23	23	NUM
ap-614	180	9	]	]	PUNCT
ap-614	180	10	examined	examine	VERB
ap-614	180	11	double	double	ADJ
ap-614	180	12	edge	edge	NOUN
ap-614	180	13	notched	notch	VERB
ap-614	180	14	specimens	specimen	NOUN
ap-614	180	15	of	of	ADP
ap-614	180	16	different	different	ADJ
ap-614	180	17	sizes	size	NOUN
ap-614	180	18	(	(	PUNCT
ap-614	180	19	200×200×50	200×200×50	NOUN
ap-614	180	20	,	,	PUNCT
ap-614	180	21	100×100×50	100×100×50	NUM
ap-614	180	22	,	,	PUNCT
ap-614	180	23	50×50×50	50×50×50	NUM
ap-614	180	24	mm	mm	NOUN
ap-614	180	25	)	)	PUNCT
ap-614	180	26	,	,	PUNCT
ap-614	180	27	subjected	subject	VERB
ap-614	180	28	to	to	ADP
ap-614	180	29	different	different	ADJ
ap-614	180	30	loading	loading	NOUN
ap-614	180	31	paths	path	NOUN
ap-614	180	32	.	.	PUNCT
ap-614	181	1	all	all	DET
ap-614	181	2	specimens	specimen	NOUN
ap-614	181	3	were	be	AUX
ap-614	181	4	placed	place	VERB
ap-614	181	5	in	in	ADP
ap-614	181	6	a	a	DET
ap-614	181	7	special	special	ADJ
ap-614	181	8	loading	loading	NOUN
ap-614	181	9	frame	frame	NOUN
ap-614	181	10	,	,	PUNCT
ap-614	181	11	allowing	allow	VERB
ap-614	181	12	a	a	DET
ap-614	181	13	combination	combination	NOUN
ap-614	181	14	of	of	ADP
ap-614	181	15	shear	shear	NOUN
ap-614	181	16	and	and	CCONJ
ap-614	181	17	tensile	tensile	NOUN
ap-614	181	18	loading	loading	NOUN
ap-614	181	19	.	.	PUNCT
ap-614	182	1	for	for	ADP
ap-614	182	2	the	the	DET
ap-614	182	3	numerical	numerical	ADJ
ap-614	182	4	simulations	simulation	NOUN
ap-614	182	5	presented	present	VERB
ap-614	182	6	in	in	ADP
ap-614	182	7	this	this	DET
ap-614	182	8	section	section	NOUN
ap-614	182	9	,	,	PUNCT
ap-614	182	10	only	only	ADV
ap-614	182	11	one	one	NUM
ap-614	182	12	loading	loading	NOUN
ap-614	182	13	path	path	NOUN
ap-614	182	14	is	be	AUX
ap-614	182	15	considered	consider	VERB
ap-614	182	16	(	(	PUNCT
ap-614	182	17	path	path	NOUN
ap-614	182	18	4	4	NUM
ap-614	182	19	in	in	ADP
ap-614	182	20	the	the	DET
ap-614	182	21	experiments	experiment	NOUN
ap-614	182	22	)	)	PUNCT
ap-614	182	23	.	.	PUNCT
ap-614	183	1	double	double	ADJ
ap-614	183	2	-	-	PUNCT
ap-614	183	3	edge	edge	NOUN
ap-614	183	4	notched	notch	VERB
ap-614	183	5	specimens	specimen	NOUN
ap-614	183	6	,	,	PUNCT
ap-614	183	7	shown	show	VERB
ap-614	183	8	in	in	ADP
ap-614	183	9	fig	fig	NOUN
ap-614	183	10	.	.	PUNCT
ap-614	184	1	4	4	NUM
ap-614	184	2	,	,	PUNCT
ap-614	184	3	are	be	AUX
ap-614	184	4	first	first	ADV
ap-614	184	5	loaded	load	VERB
ap-614	184	6	in	in	ADP
ap-614	184	7	shear	shear	NOUN
ap-614	184	8	until	until	SCONJ
ap-614	184	9	a	a	DET
ap-614	184	10	certain	certain	ADJ
ap-614	184	11	value	value	NOUN
ap-614	184	12	of	of	ADP
ap-614	184	13	the	the	DET
ap-614	184	14	lateral	lateral	ADJ
ap-614	184	15	force	force	NOUN
ap-614	184	16	ps	ps	PROPN
ap-614	184	17	is	be	AUX
ap-614	184	18	reached	reach	VERB
ap-614	184	19	.	.	PUNCT
ap-614	185	1	afterwards	afterwards	ADV
ap-614	185	2	,	,	PUNCT
ap-614	185	3	the	the	DET
ap-614	185	4	lateral	lateral	ADJ
ap-614	185	5	shear	shear	NOUN
ap-614	185	6	force	force	NOUN
ap-614	185	7	is	be	AUX
ap-614	185	8	kept	keep	VERB
ap-614	185	9	constant	constant	ADJ
ap-614	185	10	©	©	PROPN
ap-614	185	11	czech	czech	PROPN
ap-614	185	12	technical	technical	PROPN
ap-614	185	13	university	university	PROPN
ap-614	185	14	publishing	publishing	NOUN
ap-614	185	15	house	house	NOUN
ap-614	185	16	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	185	17	45	45	NUM
ap-614	185	18	acta	acta	PROPN
ap-614	185	19	polytechnica	polytechnica	PROPN
ap-614	185	20	vol	vol	NOUN
ap-614	185	21	.	.	PROPN
ap-614	186	1	44	44	NUM
ap-614	186	2	no	no	NOUN
ap-614	186	3	.	.	PUNCT
ap-614	187	1	5–6/2004	5–6/2004	NUM
ap-614	187	2	tolerance	tolerance	NOUN
ap-614	187	3	is	be	AUX
ap-614	187	4	computed	compute	VERB
ap-614	187	5	.	.	PUNCT
ap-614	188	1	the	the	DET
ap-614	188	2	obtained	obtain	VERB
ap-614	188	3	limit	limit	NOUN
ap-614	188	4	values	value	NOUN
ap-614	188	5	for	for	ADP
ap-614	188	6	the	the	DET
ap-614	188	7	normal	normal	ADJ
ap-614	188	8	are	be	AUX
ap-614	188	9	ntol1	ntol1	NOUN
ap-614	188	10	and	and	CCONJ
ap-614	188	11	ntol2	ntol2	PROPN
ap-614	188	12	.	.	PUNCT
ap-614	189	1	when	when	SCONJ
ap-614	189	2	the	the	DET
ap-614	189	3	normal	normal	ADJ
ap-614	189	4	computed	compute	VERB
ap-614	189	5	from	from	ADP
ap-614	189	6	the	the	DET
ap-614	189	7	stress	stress	NOUN
ap-614	189	8	field	field	NOUN
ap-614	189	9	lies	lie	VERB
ap-614	189	10	within	within	ADP
ap-614	189	11	the	the	DET
ap-614	189	12	zone	zone	NOUN
ap-614	189	13	defined	define	VERB
ap-614	189	14	by	by	ADP
ap-614	189	15	ntol1	ntol1	PROPN
ap-614	189	16	and	and	CCONJ
ap-614	189	17	ntol2	ntol2	PROPN
ap-614	189	18	,	,	PUNCT
ap-614	189	19	the	the	DET
ap-614	189	20	cracks	crack	NOUN
ap-614	189	21	are	be	AUX
ap-614	189	22	connected	connect	VERB
ap-614	189	23	.	.	PUNCT
ap-614	190	1	in	in	ADP
ap-614	190	2	the	the	DET
ap-614	190	3	other	other	ADJ
ap-614	190	4	case	case	NOUN
ap-614	190	5	,	,	PUNCT
ap-614	190	6	one	one	NUM
ap-614	190	7	crack	crack	NOUN
ap-614	190	8	propagates	propagate	VERB
ap-614	190	9	along	along	ADP
ap-614	190	10	the	the	DET
ap-614	190	11	normal	normal	ADJ
ap-614	190	12	computed	compute	VERB
ap-614	190	13	from	from	ADP
ap-614	190	14	the	the	DET
ap-614	190	15	stress	stress	NOUN
ap-614	190	16	field	field	NOUN
ap-614	190	17	while	while	SCONJ
ap-614	190	18	the	the	DET
ap-614	190	19	other	other	ADJ
ap-614	190	20	crack	crack	NOUN
ap-614	190	21	is	be	AUX
ap-614	190	22	stopped	stop	VERB
ap-614	190	23	.	.	PUNCT
ap-614	191	1	the	the	DET
ap-614	191	2	propagating	propagate	VERB
ap-614	191	3	crack	crack	NOUN
ap-614	191	4	can	can	AUX
ap-614	191	5	be	be	AUX
ap-614	191	6	chosen	choose	VERB
ap-614	191	7	arbitrarily	arbitrarily	ADV
ap-614	191	8	.	.	PUNCT
ap-614	192	1	another	another	DET
ap-614	192	2	possibility	possibility	NOUN
ap-614	192	3	is	be	AUX
ap-614	192	4	to	to	PART
ap-614	192	5	allow	allow	VERB
ap-614	192	6	the	the	DET
ap-614	192	7	crack	crack	NOUN
ap-614	192	8	with	with	ADP
ap-614	192	9	the	the	DET
ap-614	192	10	highest	high	ADJ
ap-614	192	11	energy	energy	NOUN
ap-614	192	12	dissipation	dissipation	NOUN
ap-614	192	13	(	(	PUNCT
ap-614	192	14	main	main	ADJ
ap-614	192	15	crack	crack	NOUN
ap-614	192	16	)	)	PUNCT
ap-614	192	17	to	to	PART
ap-614	192	18	propagate	propagate	VERB
ap-614	192	19	.	.	PUNCT
ap-614	193	1	another	another	DET
ap-614	193	2	option	option	NOUN
ap-614	193	3	is	be	AUX
ap-614	193	4	to	to	PART
ap-614	193	5	let	let	VERB
ap-614	193	6	both	both	DET
ap-614	193	7	cracks	crack	NOUN
ap-614	193	8	propagate	propagate	VERB
ap-614	193	9	.	.	PUNCT
ap-614	194	1	in	in	ADP
ap-614	194	2	this	this	DET
ap-614	194	3	case	case	NOUN
ap-614	194	4	,	,	PUNCT
ap-614	194	5	the	the	DET
ap-614	194	6	cracks	crack	NOUN
ap-614	194	7	may	may	AUX
ap-614	194	8	or	or	CCONJ
ap-614	194	9	may	may	AUX
ap-614	194	10	not	not	PART
ap-614	194	11	intersect	intersect	VERB
ap-614	194	12	.	.	PUNCT
ap-614	195	1	the	the	DET
ap-614	195	2	case	case	NOUN
ap-614	195	3	of	of	ADP
ap-614	195	4	intersecting	intersecting	ADJ
ap-614	195	5	cracks	crack	NOUN
ap-614	195	6	is	be	AUX
ap-614	195	7	not	not	PART
ap-614	195	8	considered	consider	VERB
ap-614	195	9	in	in	ADP
ap-614	195	10	this	this	DET
ap-614	195	11	paper	paper	NOUN
ap-614	195	12	.	.	PUNCT
ap-614	196	1	the	the	DET
ap-614	196	2	third	third	ADJ
ap-614	196	3	case	case	NOUN
ap-614	196	4	can	can	AUX
ap-614	196	5	be	be	AUX
ap-614	196	6	solved	solve	VERB
ap-614	196	7	in	in	ADP
ap-614	196	8	the	the	DET
ap-614	196	9	same	same	ADJ
ap-614	196	10	way	way	NOUN
ap-614	196	11	,	,	PUNCT
ap-614	196	12	only	only	ADV
ap-614	196	13	more	more	ADJ
ap-614	196	14	linking	link	VERB
ap-614	196	15	possibilities	possibility	NOUN
ap-614	196	16	should	should	AUX
ap-614	196	17	be	be	AUX
ap-614	196	18	considered	consider	VERB
ap-614	196	19	here	here	ADV
ap-614	196	20	.	.	PUNCT
ap-614	197	1	the	the	DET
ap-614	197	2	last	last	ADJ
ap-614	197	3	case	case	NOUN
ap-614	197	4	is	be	AUX
ap-614	197	5	simply	simply	ADV
ap-614	197	6	solved	solve	VERB
ap-614	197	7	by	by	ADP
ap-614	197	8	arresting	arrest	VERB
ap-614	197	9	the	the	DET
ap-614	197	10	crack	crack	NOUN
ap-614	197	11	tip	tip	NOUN
ap-614	197	12	.	.	PUNCT
ap-614	198	1	it	it	PRON
ap-614	198	2	would	would	AUX
ap-614	198	3	also	also	ADV
ap-614	198	4	be	be	AUX
ap-614	198	5	possible	possible	ADJ
ap-614	198	6	to	to	PART
ap-614	198	7	let	let	VERB
ap-614	198	8	the	the	DET
ap-614	198	9	crack	crack	NOUN
ap-614	198	10	grow	grow	VERB
ap-614	198	11	,	,	PUNCT
ap-614	198	12	but	but	CCONJ
ap-614	198	13	only	only	ADV
ap-614	198	14	if	if	SCONJ
ap-614	198	15	the	the	DET
ap-614	198	16	discontinuities	discontinuity	NOUN
ap-614	198	17	inside	inside	ADP
ap-614	198	18	the	the	DET
ap-614	198	19	element	element	NOUN
ap-614	198	20	do	do	AUX
ap-614	198	21	not	not	PART
ap-614	198	22	intersect	intersect	VERB
ap-614	198	23	.	.	PUNCT
ap-614	199	1	this	this	PRON
ap-614	199	2	is	be	AUX
ap-614	199	3	however	however	ADV
ap-614	199	4	not	not	PART
ap-614	199	5	considered	consider	VERB
ap-614	199	6	.	.	PUNCT
ap-614	200	1	it	it	PRON
ap-614	200	2	is	be	AUX
ap-614	200	3	clear	clear	ADJ
ap-614	200	4	that	that	SCONJ
ap-614	200	5	the	the	DET
ap-614	200	6	defined	define	VERB
ap-614	200	7	interaction	interaction	NOUN
ap-614	200	8	rules	rule	NOUN
ap-614	200	9	are	be	AUX
ap-614	200	10	more	more	ADV
ap-614	200	11	or	or	CCONJ
ap-614	200	12	less	less	ADV
ap-614	200	13	arbitrary	arbitrary	ADJ
ap-614	200	14	.	.	PUNCT
ap-614	201	1	nevertheless	nevertheless	ADV
ap-614	201	2	,	,	PUNCT
ap-614	201	3	the	the	DET
ap-614	201	4	rules	rule	NOUN
ap-614	201	5	are	be	AUX
ap-614	201	6	straightforward	straightforward	ADJ
ap-614	201	7	and	and	CCONJ
ap-614	201	8	relatively	relatively	ADV
ap-614	201	9	easy	easy	ADJ
ap-614	201	10	to	to	PART
ap-614	201	11	implement	implement	VERB
ap-614	201	12	.	.	PUNCT
ap-614	202	1	if	if	SCONJ
ap-614	202	2	necessary	necessary	ADJ
ap-614	202	3	,	,	PUNCT
ap-614	202	4	the	the	DET
ap-614	202	5	adopted	adopt	VERB
ap-614	202	6	rules	rule	NOUN
ap-614	202	7	will	will	AUX
ap-614	202	8	be	be	AUX
ap-614	202	9	refined	refine	VERB
ap-614	202	10	.	.	PUNCT
ap-614	203	1	ps	ps	PROPN
ap-614	203	2	pn	pn	PROPN
ap-614	203	3	25	25	NUM
ap-614	203	4	25150	25150	NUM
ap-614	203	5	65	65	NUM
ap-614	203	6	100	100	NUM
ap-614	203	7	100	100	NUM
ap-614	203	8	a	a	DET
ap-614	203	9	a	a	DET
ap-614	203	10	’	'	PUNCT
ap-614	203	11	b	b	NOUN
ap-614	203	12	’	'	PUNCT
ap-614	203	13	b	b	NOUN
ap-614	203	14	3	3	NUM
ap-614	203	15	0	0	NUM
ap-614	203	16	c	c	NOUN
ap-614	203	17	fig	fig	NOUN
ap-614	203	18	.	.	PUNCT
ap-614	204	1	4	4	NUM
ap-614	204	2	:	:	PUNCT
ap-614	204	3	geometry	geometry	NOUN
ap-614	204	4	of	of	ADP
ap-614	204	5	the	the	DET
ap-614	204	6	specimen	speciman	NOUN
ap-614	204	7	(	(	PUNCT
ap-614	204	8	all	all	DET
ap-614	204	9	dimensions	dimension	NOUN
ap-614	204	10	in	in	ADP
ap-614	204	11	mm	mm	PROPN
ap-614	204	12	)	)	PUNCT
ap-614	204	13	while	while	SCONJ
ap-614	204	14	a	a	DET
ap-614	204	15	tensile	tensile	NOUN
ap-614	204	16	load	load	NOUN
ap-614	204	17	(	(	PUNCT
ap-614	204	18	pn	pn	NOUN
ap-614	204	19	)	)	PUNCT
ap-614	204	20	is	be	AUX
ap-614	204	21	applied	apply	VERB
ap-614	204	22	.	.	PUNCT
ap-614	205	1	the	the	DET
ap-614	205	2	specimen	speciman	NOUN
ap-614	205	3	is	be	AUX
ap-614	205	4	supported	support	VERB
ap-614	205	5	at	at	ADP
ap-614	205	6	the	the	DET
ap-614	205	7	bottom	bottom	NOUN
ap-614	205	8	and	and	CCONJ
ap-614	205	9	along	along	ADP
ap-614	205	10	the	the	DET
ap-614	205	11	right	right	ADJ
ap-614	205	12	side	side	NOUN
ap-614	205	13	below	below	ADP
ap-614	205	14	the	the	DET
ap-614	205	15	notch	notch	NOUN
ap-614	205	16	.	.	PUNCT
ap-614	206	1	nooru	nooru	PROPN
ap-614	206	2	-	-	PUNCT
ap-614	206	3	mohamed	mohamed	PROPN
ap-614	206	4	[	[	X
ap-614	206	5	23	23	NUM
ap-614	206	6	]	]	PUNCT
ap-614	206	7	applied	apply	VERB
ap-614	206	8	three	three	NUM
ap-614	206	9	different	different	ADJ
ap-614	206	10	values	value	NOUN
ap-614	206	11	for	for	ADP
ap-614	206	12	the	the	DET
ap-614	206	13	lateral	lateral	ADJ
ap-614	206	14	shear	shear	NOUN
ap-614	206	15	force	force	NOUN
ap-614	206	16	,	,	PUNCT
ap-614	206	17	i.e.	i.e.	X
ap-614	206	18	(	(	PUNCT
ap-614	206	19	a	a	X
ap-614	206	20	)	)	PUNCT
ap-614	206	21	ps	ps	NOUN
ap-614	206	22	�	�	PROPN
ap-614	206	23	5	5	NUM
ap-614	206	24	kn	kn	PROPN
ap-614	206	25	,	,	PUNCT
ap-614	206	26	(	(	PUNCT
ap-614	206	27	b	b	X
ap-614	206	28	)	)	PUNCT
ap-614	206	29	ps	ps	PROPN
ap-614	206	30	�	�	PROPN
ap-614	206	31	10	10	NUM
ap-614	206	32	kn	kn	PROPN
ap-614	206	33	and	and	CCONJ
ap-614	206	34	(	(	PUNCT
ap-614	206	35	c	c	X
ap-614	206	36	)	)	PUNCT
ap-614	206	37	ps	ps	PROPN
ap-614	206	38	�	�	PROPN
ap-614	206	39	max	max	PROPN
ap-614	206	40	.	.	PROPN
ap-614	207	1	for	for	ADP
ap-614	207	2	the	the	DET
ap-614	207	3	last	last	ADJ
ap-614	207	4	case	case	NOUN
ap-614	207	5	,	,	PUNCT
ap-614	207	6	the	the	DET
ap-614	207	7	specimen	speciman	NOUN
ap-614	207	8	is	be	AUX
ap-614	207	9	loaded	load	VERB
ap-614	207	10	laterally	laterally	ADV
ap-614	207	11	until	until	SCONJ
ap-614	207	12	it	it	PRON
ap-614	207	13	no	no	ADV
ap-614	207	14	longer	long	ADV
ap-614	207	15	sustains	sustain	VERB
ap-614	207	16	the	the	DET
ap-614	207	17	lateral	lateral	ADJ
ap-614	207	18	forces	force	NOUN
ap-614	207	19	.	.	PUNCT
ap-614	208	1	�	�	PROPN
ap-614	208	2	c0	c0	PROPN
ap-614	208	3	�	�	PROPN
ap-614	208	4	20	20	NUM
ap-614	208	5	mpa	mpa	PROPN
ap-614	208	6	,	,	PUNCT
ap-614	208	7	�	�	PROPN
ap-614	208	8	gfii	gfii	PROPN
ap-614	208	9	�	�	PROPN
ap-614	208	10	0.1	0.1	NUM
ap-614	208	11	n	n	CCONJ
ap-614	208	12	/	/	SYM
ap-614	208	13	mm	mm	PROPN
ap-614	208	14	,	,	PUNCT
ap-614	208	15	�	�	PROPN
ap-614	208	16	tan	tan	PROPN
ap-614	208	17	�	�	PROPN
ap-614	208	18	�	�	PROPN
ap-614	208	19	0.5	0.5	NUM
ap-614	208	20	.	.	PUNCT
ap-614	209	1	for	for	ADP
ap-614	209	2	the	the	DET
ap-614	209	3	continuum	continuum	PROPN
ap-614	209	4	,	,	PUNCT
ap-614	209	5	the	the	DET
ap-614	209	6	material	material	NOUN
ap-614	209	7	paramters	paramter	NOUN
ap-614	209	8	are	be	AUX
ap-614	209	9	:	:	PUNCT
ap-614	209	10	young	young	ADJ
ap-614	209	11	’s	’s	PART
ap-614	209	12	modulus	modulus	PROPN
ap-614	209	13	e	e	PROPN
ap-614	209	14	�	�	PROPN
ap-614	209	15	25000	25000	NUM
ap-614	209	16	mpa	mpa	PROPN
ap-614	209	17	and	and	CCONJ
ap-614	209	18	poisson	poisson	PROPN
ap-614	209	19	’s	’s	PART
ap-614	209	20	ratio	ratio	PROPN
ap-614	209	21	�	�	PROPN
ap-614	209	22	�	�	PROPN
ap-614	209	23	0.2	0.2	NUM
ap-614	209	24	.	.	PUNCT
ap-614	210	1	the	the	DET
ap-614	210	2	obtained	obtain	VERB
ap-614	210	3	load	load	NOUN
ap-614	210	4	-	-	PUNCT
ap-614	210	5	deformation	deformation	NOUN
ap-614	210	6	curve	curve	NOUN
ap-614	210	7	is	be	AUX
ap-614	210	8	shown	show	VERB
ap-614	210	9	in	in	ADP
ap-614	210	10	fig	fig	NOUN
ap-614	210	11	.	.	PUNCT
ap-614	211	1	6a	6a	NOUN
ap-614	211	2	.	.	PUNCT
ap-614	212	1	when	when	SCONJ
ap-614	212	2	compared	compare	VERB
ap-614	212	3	with	with	ADP
ap-614	212	4	the	the	DET
ap-614	212	5	experimental	experimental	ADJ
ap-614	212	6	curve	curve	NOUN
ap-614	212	7	,	,	PUNCT
ap-614	212	8	a	a	DET
ap-614	212	9	good	good	ADJ
ap-614	212	10	agreement	agreement	NOUN
ap-614	212	11	is	be	AUX
ap-614	212	12	found	find	VERB
ap-614	212	13	.	.	PUNCT
ap-614	213	1	especially	especially	ADV
ap-614	213	2	the	the	DET
ap-614	213	3	peak	peak	NOUN
ap-614	213	4	load	load	NOUN
ap-614	213	5	is	be	AUX
ap-614	213	6	simulated	simulate	VERB
ap-614	213	7	remarkably	remarkably	ADV
ap-614	213	8	well	well	ADV
ap-614	213	9	.	.	PUNCT
ap-614	214	1	the	the	DET
ap-614	214	2	post	post	NOUN
ap-614	214	3	peak	peak	NOUN
ap-614	214	4	response	response	NOUN
ap-614	214	5	in	in	ADP
ap-614	214	6	the	the	DET
ap-614	214	7	finite	finite	PROPN
ap-614	214	8	element	element	NOUN
ap-614	214	9	simulation	simulation	NOUN
ap-614	214	10	is	be	AUX
ap-614	214	11	more	more	ADV
ap-614	214	12	brittle	brittle	ADJ
ap-614	214	13	.	.	PUNCT
ap-614	215	1	the	the	DET
ap-614	215	2	computed	compute	VERB
ap-614	215	3	crack	crack	NOUN
ap-614	215	4	path	path	NOUN
ap-614	215	5	is	be	AUX
ap-614	215	6	compared	compare	VERB
ap-614	215	7	with	with	ADP
ap-614	215	8	the	the	DET
ap-614	215	9	experimentally	experimentally	ADV
ap-614	215	10	obtained	obtain	VERB
ap-614	215	11	path	path	NOUN
ap-614	215	12	.	.	PUNCT
ap-614	216	1	as	as	SCONJ
ap-614	216	2	can	can	AUX
ap-614	216	3	be	be	AUX
ap-614	216	4	seen	see	VERB
ap-614	216	5	in	in	ADP
ap-614	216	6	fig	fig	NOUN
ap-614	216	7	.	.	PUNCT
ap-614	217	1	6b	6b	NOUN
ap-614	217	2	,	,	PUNCT
ap-614	217	3	the	the	DET
ap-614	217	4	computed	compute	VERB
ap-614	217	5	crack	crack	NOUN
ap-614	217	6	path	path	NOUN
ap-614	217	7	is	be	AUX
ap-614	217	8	in	in	ADP
ap-614	217	9	good	good	ADJ
ap-614	217	10	agreement	agreement	NOUN
ap-614	217	11	with	with	ADP
ap-614	217	12	the	the	DET
ap-614	217	13	experimentally	experimentally	ADV
ap-614	217	14	observed	observe	VERB
ap-614	217	15	crack	crack	NOUN
ap-614	217	16	path	path	NOUN
ap-614	217	17	.	.	PUNCT
ap-614	218	1	during	during	ADP
ap-614	218	2	the	the	DET
ap-614	218	3	experiments	experiment	NOUN
ap-614	218	4	,	,	PUNCT
ap-614	218	5	nooru	nooru	PROPN
ap-614	218	6	-	-	PUNCT
ap-614	218	7	mohamed	mohame	VERB
ap-614	218	8	also	also	ADV
ap-614	218	9	connected	connect	VERB
ap-614	218	10	lvdts	lvdts	ADV
ap-614	218	11	to	to	ADP
ap-614	218	12	the	the	DET
ap-614	218	13	specimen	speciman	NOUN
ap-614	218	14	in	in	ADP
ap-614	218	15	order	order	NOUN
ap-614	218	16	to	to	PART
ap-614	218	17	study	study	VERB
ap-614	218	18	local	local	ADJ
ap-614	218	19	deformations	deformation	NOUN
ap-614	218	20	.	.	PUNCT
ap-614	219	1	the	the	DET
ap-614	219	2	position	position	NOUN
ap-614	219	3	of	of	ADP
ap-614	219	4	these	these	DET
ap-614	219	5	additional	additional	ADJ
ap-614	219	6	lvdts	lvdts	NOUN
ap-614	219	7	is	be	AUX
ap-614	219	8	visualized	visualize	VERB
ap-614	219	9	in	in	ADP
ap-614	219	10	fig	fig	NOUN
ap-614	219	11	.	.	PUNCT
ap-614	220	1	7	7	X
ap-614	220	2	.	.	X
ap-614	220	3	the	the	DET
ap-614	220	4	recorded	recorded	ADJ
ap-614	220	5	deformations	deformation	NOUN
ap-614	220	6	are	be	AUX
ap-614	220	7	plotted	plot	VERB
ap-614	220	8	versus	versus	ADP
ap-614	220	9	the	the	DET
ap-614	220	10	shear	shear	NOUN
ap-614	220	11	deformation	deformation	NOUN
ap-614	220	12	�	�	PROPN
ap-614	220	13	s	s	PART
ap-614	220	14	,	,	PUNCT
ap-614	220	15	and	and	CCONJ
ap-614	220	16	compared	compare	VERB
ap-614	220	17	with	with	ADP
ap-614	220	18	the	the	DET
ap-614	220	19	computed	compute	VERB
ap-614	220	20	values	value	NOUN
ap-614	220	21	in	in	ADP
ap-614	220	22	fig	fig	NOUN
ap-614	220	23	.	.	PUNCT
ap-614	221	1	8a	8a	NUM
ap-614	221	2	–	–	PUNCT
ap-614	221	3	e.	e.	NOUN
ap-614	221	4	examining	examine	VERB
ap-614	221	5	fig	fig	NOUN
ap-614	221	6	.	.	PUNCT
ap-614	222	1	8a	8a	NUM
ap-614	222	2	and	and	CCONJ
ap-614	222	3	fig	fig	NOUN
ap-614	222	4	.	.	PUNCT
ap-614	223	1	8e	8e	NUM
ap-614	223	2	,	,	PUNCT
ap-614	223	3	the	the	DET
ap-614	223	4	calculated	calculated	ADJ
ap-614	223	5	deformations	deformation	NOUN
ap-614	223	6	for	for	ADP
ap-614	223	7	lvdt	lvdt	PROPN
ap-614	223	8	1	1	NUM
ap-614	223	9	and	and	CCONJ
ap-614	223	10	lvdt	lvdt	PROPN
ap-614	223	11	5	5	NUM
ap-614	223	12	show	show	VERB
ap-614	223	13	a	a	DET
ap-614	223	14	good	good	ADJ
ap-614	223	15	agreement	agreement	NOUN
ap-614	223	16	with	with	ADP
ap-614	223	17	the	the	DET
ap-614	223	18	measured	measure	VERB
ap-614	223	19	values	value	NOUN
ap-614	223	20	.	.	PUNCT
ap-614	224	1	the	the	DET
ap-614	224	2	deformation	deformation	NOUN
ap-614	224	3	for	for	ADP
ap-614	224	4	lvdt	lvdt	PROPN
ap-614	224	5	2	2	NUM
ap-614	224	6	,	,	PUNCT
ap-614	224	7	fig	fig	NOUN
ap-614	224	8	.	.	PUNCT
ap-614	225	1	8b	8b	NUM
ap-614	225	2	,	,	PUNCT
ap-614	225	3	is	be	AUX
ap-614	225	4	not	not	PART
ap-614	225	5	captured	capture	VERB
ap-614	225	6	with	with	ADP
ap-614	225	7	the	the	DET
ap-614	225	8	calculations	calculation	NOUN
ap-614	225	9	.	.	PUNCT
ap-614	226	1	the	the	DET
ap-614	226	2	computed	compute	VERB
ap-614	226	3	crack	crack	NOUN
ap-614	226	4	path	path	NOUN
ap-614	226	5	runs	run	NOUN
ap-614	226	6	outside	outside	ADP
ap-614	226	7	the	the	DET
ap-614	226	8	measuring	measure	VERB
ap-614	226	9	range	range	NOUN
ap-614	226	10	of	of	ADP
ap-614	226	11	lvdt	lvdt	PROPN
ap-614	226	12	2	2	NUM
ap-614	226	13	.	.	PUNCT
ap-614	227	1	as	as	ADP
ap-614	227	2	a	a	DET
ap-614	227	3	result	result	NOUN
ap-614	227	4	,	,	PUNCT
ap-614	227	5	the	the	DET
ap-614	227	6	experimentally	experimentally	ADV
ap-614	227	7	observed	observe	VERB
ap-614	227	8	increase	increase	NOUN
ap-614	227	9	in	in	ADP
ap-614	227	10	deformations	deformation	NOUN
ap-614	227	11	is	be	AUX
ap-614	227	12	not	not	PART
ap-614	227	13	observed	observe	VERB
ap-614	227	14	in	in	ADP
ap-614	227	15	the	the	DET
ap-614	227	16	computations	computation	NOUN
ap-614	227	17	.	.	PUNCT
ap-614	228	1	for	for	ADP
ap-614	228	2	lvdt	lvdt	PROPN
ap-614	228	3	3	3	NUM
ap-614	228	4	and	and	CCONJ
ap-614	228	5	lvdt	lvdt	PROPN
ap-614	228	6	4	4	NUM
ap-614	228	7	,	,	PUNCT
ap-614	228	8	the	the	DET
ap-614	228	9	measured	measure	VERB
ap-614	228	10	and	and	CCONJ
ap-614	228	11	calculated	calculated	ADJ
ap-614	228	12	deformations	deformation	NOUN
ap-614	228	13	show	show	VERB
ap-614	228	14	the	the	DET
ap-614	228	15	same	same	ADJ
ap-614	228	16	tendency	tendency	NOUN
ap-614	228	17	.	.	PUNCT
ap-614	229	1	first	first	ADV
ap-614	229	2	a	a	DET
ap-614	229	3	small	small	ADJ
ap-614	229	4	increase	increase	NOUN
ap-614	229	5	is	be	AUX
ap-614	229	6	noticed	notice	VERB
ap-614	229	7	.	.	PUNCT
ap-614	230	1	when	when	SCONJ
ap-614	230	2	the	the	DET
ap-614	230	3	crack	crack	NOUN
ap-614	230	4	has	have	AUX
ap-614	230	5	passed	pass	VERB
ap-614	230	6	the	the	DET
ap-614	230	7	location	location	NOUN
ap-614	230	8	of	of	ADP
ap-614	230	9	the	the	DET
ap-614	230	10	lvdt	lvdt	PROPN
ap-614	230	11	,	,	PUNCT
ap-614	230	12	the	the	DET
ap-614	230	13	deformations	deformation	NOUN
ap-614	230	14	start	start	VERB
ap-614	230	15	to	to	PART
ap-614	230	16	decrease	decrease	VERB
ap-614	230	17	because	because	SCONJ
ap-614	230	18	the	the	DET
ap-614	230	19	crack	crack	NOUN
ap-614	230	20	passes	pass	VERB
ap-614	230	21	outside	outside	ADP
ap-614	230	22	the	the	DET
ap-614	230	23	measuring	measure	VERB
ap-614	230	24	range	range	NOUN
ap-614	230	25	of	of	ADP
ap-614	230	26	the	the	DET
ap-614	230	27	lvdt	lvdt	PROPN
ap-614	230	28	.	.	PUNCT
ap-614	231	1	the	the	DET
ap-614	231	2	overview	overview	NOUN
ap-614	231	3	in	in	ADP
ap-614	231	4	fig	fig	NOUN
ap-614	231	5	.	.	PUNCT
ap-614	232	1	8a	8a	NUM
ap-614	232	2	–	–	PUNCT
ap-614	232	3	e	e	NOUN
ap-614	232	4	shows	show	VERB
ap-614	232	5	that	that	SCONJ
ap-614	232	6	apart	apart	ADV
ap-614	232	7	from	from	ADP
ap-614	232	8	the	the	DET
ap-614	232	9	load	load	NOUN
ap-614	232	10	deformation	deformation	NOUN
ap-614	232	11	curve	curve	NOUN
ap-614	232	12	and	and	CCONJ
ap-614	232	13	the	the	DET
ap-614	232	14	final	final	ADJ
ap-614	232	15	crack	crack	NOUN
ap-614	232	16	path	path	NOUN
ap-614	232	17	,	,	PUNCT
ap-614	232	18	also	also	ADV
ap-614	232	19	local	local	ADJ
ap-614	232	20	information	information	NOUN
ap-614	232	21	is	be	AUX
ap-614	232	22	captured	capture	VERB
ap-614	232	23	in	in	ADP
ap-614	232	24	a	a	DET
ap-614	232	25	reasonable	reasonable	ADJ
ap-614	232	26	way	way	NOUN
ap-614	232	27	.	.	PUNCT
ap-614	233	1	finally	finally	ADV
ap-614	233	2	,	,	PUNCT
ap-614	233	3	the	the	DET
ap-614	233	4	same	same	ADJ
ap-614	233	5	model	model	NOUN
ap-614	233	6	and	and	CCONJ
ap-614	233	7	model	model	NOUN
ap-614	233	8	parameters	parameter	NOUN
ap-614	233	9	are	be	AUX
ap-614	233	10	used	use	VERB
ap-614	233	11	to	to	PART
ap-614	233	12	simulate	simulate	VERB
ap-614	233	13	load	load	NOUN
ap-614	233	14	case	case	NOUN
ap-614	233	15	(	(	PUNCT
ap-614	233	16	a	a	NOUN
ap-614	233	17	)	)	PUNCT
ap-614	233	18	.	.	PUNCT
ap-614	234	1	in	in	ADP
ap-614	234	2	this	this	DET
ap-614	234	3	case	case	NOUN
ap-614	234	4	,	,	PUNCT
ap-614	234	5	the	the	DET
ap-614	234	6	lateral	lateral	ADJ
ap-614	234	7	force	force	NOUN
ap-614	234	8	is	be	AUX
ap-614	234	9	increased	increase	VERB
ap-614	234	10	until	until	ADP
ap-614	234	11	ps	ps	PROPN
ap-614	234	12	�	�	PROPN
ap-614	234	13	5	5	NUM
ap-614	234	14	kn	kn	PROPN
ap-614	234	15	.	.	PUNCT
ap-614	235	1	then	then	ADV
ap-614	235	2	,	,	PUNCT
ap-614	235	3	the	the	DET
ap-614	235	4	lateral	lateral	ADJ
ap-614	235	5	force	force	NOUN
ap-614	235	6	is	be	AUX
ap-614	235	7	kept	keep	VERB
ap-614	235	8	constant	constant	ADJ
ap-614	235	9	and	and	CCONJ
ap-614	235	10	a	a	DET
ap-614	235	11	tensile	tensile	NOUN
ap-614	235	12	load	load	NOUN
ap-614	235	13	is	be	AUX
ap-614	235	14	applied	apply	VERB
ap-614	235	15	.	.	PUNCT
ap-614	236	1	the	the	DET
ap-614	236	2	comparison	comparison	NOUN
ap-614	236	3	of	of	ADP
ap-614	236	4	the	the	DET
ap-614	236	5	computed	compute	VERB
ap-614	236	6	load	load	NOUN
ap-614	236	7	deformation	deformation	NOUN
ap-614	236	8	curve	curve	NOUN
ap-614	236	9	with	with	ADP
ap-614	236	10	the	the	DET
ap-614	236	11	experimental	experimental	ADJ
ap-614	236	12	obtained	obtain	VERB
ap-614	236	13	curve	curve	NOUN
ap-614	236	14	is	be	AUX
ap-614	236	15	shown	show	VERB
ap-614	236	16	in	in	ADP
ap-614	236	17	fig	fig	NOUN
ap-614	236	18	.	.	PUNCT
ap-614	237	1	9a	9a	NOUN
ap-614	237	2	while	while	SCONJ
ap-614	237	3	the	the	DET
ap-614	237	4	experimental	experimental	ADJ
ap-614	237	5	and	and	CCONJ
ap-614	237	6	computed	compute	VERB
ap-614	237	7	crack	crack	NOUN
ap-614	237	8	path	path	NOUN
ap-614	237	9	are	be	AUX
ap-614	237	10	visualized	visualize	VERB
ap-614	237	11	in	in	ADP
ap-614	237	12	fig	fig	NOUN
ap-614	237	13	.	.	PUNCT
ap-614	238	1	9b	9b	NOUN
ap-614	238	2	.	.	PUNCT
ap-614	239	1	again	again	ADV
ap-614	239	2	,	,	PUNCT
ap-614	239	3	the	the	DET
ap-614	239	4	peak	peak	NOUN
ap-614	239	5	load	load	NOUN
ap-614	239	6	is	be	AUX
ap-614	239	7	captured	capture	VERB
ap-614	239	8	remarkably	remarkably	ADV
ap-614	239	9	well	well	ADV
ap-614	239	10	.	.	PUNCT
ap-614	240	1	the	the	DET
ap-614	240	2	computed	computed	ADJ
ap-614	240	3	post	post	NOUN
ap-614	240	4	peak	peak	NOUN
ap-614	240	5	response	response	NOUN
ap-614	240	6	is	be	AUX
ap-614	240	7	slightly	slightly	ADV
ap-614	240	8	more	more	ADV
ap-614	240	9	brittle	brittle	ADJ
ap-614	240	10	.	.	PUNCT
ap-614	241	1	when	when	SCONJ
ap-614	241	2	the	the	DET
ap-614	241	3	crack	crack	NOUN
ap-614	241	4	path	path	NOUN
ap-614	241	5	is	be	AUX
ap-614	241	6	studied	study	VERB
ap-614	241	7	,	,	PUNCT
ap-614	241	8	it	it	PRON
ap-614	241	9	can	can	AUX
ap-614	241	10	be	be	AUX
ap-614	241	11	observed	observe	VERB
ap-614	241	12	that	that	SCONJ
ap-614	241	13	the	the	DET
ap-614	241	14	crack	crack	NOUN
ap-614	241	15	which	which	PRON
ap-614	241	16	grows	grow	VERB
ap-614	241	17	from	from	ADP
ap-614	241	18	the	the	DET
ap-614	241	19	left	left	ADJ
ap-614	241	20	notch	notch	NOUN
ap-614	241	21	is	be	AUX
ap-614	241	22	in	in	ADP
ap-614	241	23	agreement	agreement	NOUN
ap-614	241	24	with	with	ADP
ap-614	241	25	the	the	DET
ap-614	241	26	experimentally	experimentally	ADV
ap-614	241	27	observed	observe	VERB
ap-614	241	28	crack	crack	NOUN
ap-614	241	29	.	.	PUNCT
ap-614	242	1	the	the	DET
ap-614	242	2	crack	crack	NOUN
ap-614	242	3	growing	grow	VERB
ap-614	242	4	from	from	ADP
ap-614	242	5	the	the	DET
ap-614	242	6	right	right	ADJ
ap-614	242	7	notch	notch	NOUN
ap-614	242	8	is	be	AUX
ap-614	242	9	more	more	ADV
ap-614	242	10	curved	curved	ADJ
ap-614	242	11	than	than	ADP
ap-614	242	12	the	the	DET
ap-614	242	13	experimentally	experimentally	ADV
ap-614	242	14	observed	observe	VERB
ap-614	242	15	crack	crack	NOUN
ap-614	242	16	.	.	PUNCT
ap-614	243	1	46	46	NUM
ap-614	244	1	©	©	PROPN
ap-614	244	2	czech	czech	PROPN
ap-614	244	3	technical	technical	PROPN
ap-614	244	4	university	university	PROPN
ap-614	244	5	publishing	publishing	NOUN
ap-614	244	6	house	house	NOUN
ap-614	244	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	244	8	acta	acta	PROPN
ap-614	244	9	polytechnica	polytechnica	PROPN
ap-614	244	10	vol	vol	NOUN
ap-614	244	11	.	.	PROPN
ap-614	245	1	44	44	NUM
ap-614	245	2	no	no	NOUN
ap-614	245	3	.	.	PUNCT
ap-614	246	1	5–6/2004	5–6/2004	NUM
ap-614	246	2	fig	fig	NOUN
ap-614	246	3	.	.	PUNCT
ap-614	247	1	5	5	NUM
ap-614	247	2	:	:	PUNCT
ap-614	247	3	mesh	mesh	NOUN
ap-614	247	4	used	use	VERB
ap-614	247	5	for	for	ADP
ap-614	247	6	analysis	analysis	NOUN
ap-614	247	7	30	30	NUM
ap-614	247	8	3535	3535	NUM
ap-614	247	9	3535	3535	NUM
ap-614	247	10	30	30	NUM
ap-614	247	11	35	35	NUM
ap-614	247	12	1	1	NUM
ap-614	247	13	2	2	NUM
ap-614	247	14	3	3	NUM
ap-614	247	15	4	4	NUM
ap-614	247	16	5	5	NUM
ap-614	247	17	fig	fig	NOUN
ap-614	247	18	.	.	PUNCT
ap-614	248	1	7	7	NUM
ap-614	248	2	:	:	PUNCT
ap-614	248	3	location	location	NOUN
ap-614	248	4	of	of	ADP
ap-614	248	5	additional	additional	ADJ
ap-614	248	6	lvdt	lvdt	PROPN
ap-614	248	7	�	�	PROPN
ap-614	248	8	�	�	PROPN
ap-614	248	9	�	�	PROPN
ap-614	248	10	�	�	PROPN
ap-614	248	11	p	p	PROPN
ap-614	248	12	n	n	PROPN
ap-614	248	13	(	(	PUNCT
ap-614	248	14	k	k	PROPN
ap-614	248	15	n	n	PROPN
ap-614	248	16	)	)	PUNCT
ap-614	248	17	0	0	NUM
ap-614	249	1	25	25	NUM
ap-614	249	2	50	50	NUM
ap-614	249	3	75	75	NUM
ap-614	249	4	100	100	NUM
ap-614	249	5	0	0	NUM
ap-614	249	6	4	4	NUM
ap-614	249	7	8	8	NUM
ap-614	249	8	12	12	NUM
ap-614	249	9	calculation	calculation	NOUN
ap-614	249	10	experimental	experimental	PROPN
ap-614	249	11	mn	mn	PROPN
ap-614	249	12	(	(	PUNCT
ap-614	249	13	a	a	NOUN
ap-614	249	14	)	)	PUNCT
ap-614	249	15	(	(	PUNCT
ap-614	249	16	b	b	X
ap-614	249	17	)	)	PUNCT
ap-614	249	18	fig	fig	NOUN
ap-614	249	19	.	.	PUNCT
ap-614	250	1	6	6	NUM
ap-614	250	2	:	:	PUNCT
ap-614	250	3	(	(	PUNCT
ap-614	250	4	a	a	X
ap-614	250	5	)	)	PUNCT
ap-614	250	6	experimental	experimental	ADJ
ap-614	250	7	versus	versus	ADP
ap-614	250	8	computed	compute	VERB
ap-614	250	9	tensile	tensile	NOUN
ap-614	250	10	load	load	NOUN
ap-614	250	11	deformation	deformation	NOUN
ap-614	250	12	curve	curve	NOUN
ap-614	250	13	and	and	CCONJ
ap-614	250	14	(	(	PUNCT
ap-614	250	15	b	b	NOUN
ap-614	250	16	)	)	PUNCT
ap-614	250	17	experimental	experimental	ADJ
ap-614	250	18	versus	versus	ADP
ap-614	250	19	computed	compute	VERB
ap-614	250	20	crack	crack	NOUN
ap-614	250	21	path	path	NOUN
ap-614	250	22	5	5	NUM
ap-614	250	23	acknowledgments	acknowledgment	NOUN
ap-614	250	24	financial	financial	ADJ
ap-614	250	25	support	support	NOUN
ap-614	250	26	from	from	ADP
ap-614	250	27	the	the	DET
ap-614	250	28	fwo	fwo	NOUN
ap-614	250	29	-	-	PUNCT
ap-614	250	30	vlaanderen	vlaanderen	NOUN
ap-614	250	31	(	(	PUNCT
ap-614	250	32	fonds	fond	NOUN
ap-614	250	33	voor	voor	PROPN
ap-614	250	34	wetenschapelijk	wetenschapelijk	PROPN
ap-614	250	35	onderzoek	onderzoek	PROPN
ap-614	250	36	,	,	PUNCT
ap-614	250	37	fund	fund	NOUN
ap-614	250	38	for	for	ADP
ap-614	250	39	scientific	scientific	ADJ
ap-614	250	40	research	research	NOUN
ap-614	250	41	–	–	PUNCT
ap-614	250	42	flanders	flander	NOUN
ap-614	250	43	)	)	PUNCT
ap-614	250	44	is	be	AUX
ap-614	250	45	gratefully	gratefully	ADV
ap-614	250	46	acknowledged	acknowledge	VERB
ap-614	250	47	.	.	PUNCT
ap-614	251	1	references	reference	NOUN
ap-614	251	2	[	[	X
ap-614	251	3	1	1	NUM
ap-614	251	4	]	]	X
ap-614	251	5	pijaudier	pijaudier	NOUN
ap-614	251	6	-	-	PUNCT
ap-614	251	7	cabot	cabot	PROPN
ap-614	251	8	g.	g.	PROPN
ap-614	251	9	,	,	PUNCT
ap-614	251	10	bažant	bažant	PROPN
ap-614	251	11	z.	z.	PROPN
ap-614	251	12	:	:	PUNCT
ap-614	251	13	“	"	PUNCT
ap-614	251	14	non	non	ADJ
ap-614	251	15	-	-	ADJ
ap-614	251	16	local	local	ADJ
ap-614	251	17	damage	damage	NOUN
ap-614	251	18	theory	theory	NOUN
ap-614	251	19	.	.	PUNCT
ap-614	251	20	”	"	PUNCT
ap-614	252	1	asce	asce	PROPN
ap-614	252	2	journal	journal	PROPN
ap-614	252	3	of	of	ADP
ap-614	252	4	engineering	engineering	NOUN
ap-614	252	5	mechanics	mechanic	NOUN
ap-614	252	6	,	,	PUNCT
ap-614	252	7	vol	vol	NOUN
ap-614	252	8	.	.	PROPN
ap-614	252	9	113	113	NUM
ap-614	252	10	(	(	PUNCT
ap-614	252	11	1987	1987	NUM
ap-614	252	12	)	)	PUNCT
ap-614	252	13	,	,	PUNCT
ap-614	252	14	no	no	INTJ
ap-614	252	15	.	.	NOUN
ap-614	252	16	10	10	NUM
ap-614	252	17	,	,	PUNCT
ap-614	252	18	p.	p.	NOUN
ap-614	252	19	1512–1533	1512–1533	NUM
ap-614	252	20	.	.	PUNCT
ap-614	253	1	[	[	X
ap-614	253	2	2	2	NUM
ap-614	253	3	]	]	PUNCT
ap-614	253	4	peerlings	peerling	NOUN
ap-614	253	5	r.	r.	PROPN
ap-614	253	6	h.	h.	PROPN
ap-614	253	7	j.	j.	PROPN
ap-614	253	8	,	,	PUNCT
ap-614	253	9	de	de	PROPN
ap-614	253	10	borst	borst	PROPN
ap-614	253	11	r.	r.	PROPN
ap-614	253	12	,	,	PUNCT
ap-614	253	13	brekelmans	brekelman	VERB
ap-614	253	14	w.	w.	PROPN
ap-614	253	15	a.	a.	PROPN
ap-614	253	16	m.	m.	PROPN
ap-614	253	17	,	,	PUNCT
ap-614	253	18	geers	geer	NOUN
ap-614	253	19	m.	m.	PROPN
ap-614	253	20	g.	g.	PROPN
ap-614	253	21	d.	d.	PROPN
ap-614	253	22	:	:	PUNCT
ap-614	253	23	“	"	PUNCT
ap-614	253	24	gradient	gradient	NOUN
ap-614	253	25	-	-	PUNCT
ap-614	253	26	enhanced	enhance	VERB
ap-614	253	27	damage	damage	NOUN
ap-614	253	28	modelling	modelling	NOUN
ap-614	253	29	of	of	ADP
ap-614	253	30	concrete	concrete	ADJ
ap-614	253	31	fracture	fracture	NOUN
ap-614	253	32	.	.	PUNCT
ap-614	253	33	”	"	PUNCT
ap-614	254	1	mechanics	mechanic	NOUN
ap-614	254	2	of	of	ADP
ap-614	254	3	cohesive	cohesive	ADJ
ap-614	254	4	-	-	PUNCT
ap-614	254	5	frictional	frictional	ADJ
ap-614	254	6	materials	material	NOUN
ap-614	254	7	,	,	PUNCT
ap-614	254	8	vol	vol	NOUN
ap-614	254	9	.	.	NOUN
ap-614	254	10	3	3	NUM
ap-614	254	11	(	(	PUNCT
ap-614	254	12	1998	1998	NUM
ap-614	254	13	)	)	PUNCT
ap-614	254	14	,	,	PUNCT
ap-614	254	15	no	no	INTJ
ap-614	254	16	.	.	NOUN
ap-614	254	17	4	4	NUM
ap-614	254	18	,	,	PUNCT
ap-614	254	19	p.	p.	NOUN
ap-614	254	20	323–342	323–342	NUM
ap-614	254	21	.	.	PUNCT
ap-614	255	1	[	[	X
ap-614	255	2	3	3	NUM
ap-614	255	3	]	]	X
ap-614	255	4	de	de	X
ap-614	255	5	borst	borst	PROPN
ap-614	255	6	r.	r.	PROPN
ap-614	255	7	,	,	PUNCT
ap-614	255	8	sluys	sluys	PROPN
ap-614	255	9	l.	l.	PROPN
ap-614	255	10	j.	j.	PROPN
ap-614	255	11	:	:	PUNCT
ap-614	255	12	“	"	PUNCT
ap-614	255	13	localization	localization	NOUN
ap-614	255	14	in	in	ADP
ap-614	255	15	a	a	DET
ap-614	255	16	cosserat	cosserat	NOUN
ap-614	255	17	continuum	continuum	ADJ
ap-614	255	18	under	under	ADP
ap-614	255	19	static	static	ADJ
ap-614	255	20	and	and	CCONJ
ap-614	255	21	dynamic	dynamic	ADJ
ap-614	255	22	loading	loading	NOUN
ap-614	255	23	conditions	condition	NOUN
ap-614	255	24	.	.	PUNCT
ap-614	255	25	”	"	PUNCT
ap-614	256	1	computer	computer	NOUN
ap-614	256	2	methods	method	NOUN
ap-614	256	3	in	in	ADP
ap-614	256	4	applied	applied	ADJ
ap-614	256	5	mechanics	mechanic	NOUN
ap-614	256	6	and	and	CCONJ
ap-614	256	7	engineering	engineering	NOUN
ap-614	256	8	,	,	PUNCT
ap-614	256	9	vol	vol	NOUN
ap-614	256	10	.	.	PROPN
ap-614	256	11	90	90	NUM
ap-614	256	12	(	(	PUNCT
ap-614	256	13	1991	1991	NUM
ap-614	256	14	)	)	PUNCT
ap-614	256	15	,	,	PUNCT
ap-614	256	16	no	no	INTJ
ap-614	256	17	.	.	PUNCT
ap-614	257	1	1–3	1–3	NUM
ap-614	257	2	,	,	PUNCT
ap-614	257	3	p.	p.	NOUN
ap-614	257	4	805–827	805–827	NUM
ap-614	257	5	.	.	PUNCT
ap-614	258	1	[	[	X
ap-614	258	2	4	4	X
ap-614	258	3	]	]	X
ap-614	258	4	needleman	needleman	PROPN
ap-614	258	5	a.	a.	PROPN
ap-614	258	6	:	:	PUNCT
ap-614	258	7	“	"	PUNCT
ap-614	258	8	material	material	ADJ
ap-614	258	9	rate	rate	NOUN
ap-614	258	10	dependence	dependence	NOUN
ap-614	258	11	and	and	CCONJ
ap-614	258	12	mesh	mesh	NOUN
ap-614	258	13	sensitivity	sensitivity	NOUN
ap-614	258	14	in	in	ADP
ap-614	258	15	localization	localization	NOUN
ap-614	258	16	problems	problem	NOUN
ap-614	258	17	.	.	PUNCT
ap-614	258	18	”	"	PUNCT
ap-614	259	1	computer	computer	NOUN
ap-614	259	2	methods	method	NOUN
ap-614	259	3	in	in	ADP
ap-614	259	4	©	©	PROPN
ap-614	259	5	czech	czech	PROPN
ap-614	259	6	technical	technical	PROPN
ap-614	259	7	university	university	PROPN
ap-614	259	8	publishing	publishing	NOUN
ap-614	259	9	house	house	NOUN
ap-614	259	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-614	259	11	47	47	NUM
ap-614	259	12	acta	acta	PROPN
ap-614	259	13	polytechnica	polytechnica	PROPN
ap-614	259	14	vol	vol	NOUN
ap-614	259	15	.	.	PROPN
ap-614	260	1	44	44	NUM
ap-614	260	2	no	no	NOUN
ap-614	260	3	.	.	PUNCT
ap-614	261	1	5–6/2004	5–6/2004	NUM
ap-614	261	2	�	�	PROPN
ap-614	261	3	�	�	PROPN
ap-614	261	4	�	�	PROPN
ap-614	261	5	�	�	PROPN
ap-614	261	6	10	10	NUM
ap-614	261	7	20	20	NUM
ap-614	261	8	30	30	NUM
ap-614	261	9	40	40	NUM
ap-614	261	10	10	10	NUM
ap-614	261	11	20	20	NUM
ap-614	261	12	30	30	NUM
ap-614	261	13	40	40	NUM
ap-614	261	14	50	50	NUM
ap-614	261	15	calculation	calculation	NOUN
ap-614	261	16	experiment	experiment	NOUN
ap-614	261	17	s	s	PART
ap-614	261	18	m	m	VERB
ap-614	261	19	m	m	VERB
ap-614	261	20	1	1	NUM
ap-614	261	21	(	(	PUNCT
ap-614	261	22	a	a	PRON
ap-614	261	23	)	)	PUNCT
ap-614	261	24	�	�	PROPN
ap-614	261	25	�	�	PROPN
ap-614	261	26	�	�	PROPN
ap-614	261	27	�	�	PROPN
ap-614	261	28	10	10	NUM
ap-614	261	29	20	20	NUM
ap-614	261	30	30	30	NUM
ap-614	261	31	40	40	NUM
ap-614	261	32	10	10	NUM
ap-614	261	33	20	20	NUM
ap-614	261	34	30	30	NUM
ap-614	261	35	40	40	NUM
ap-614	261	36	50	50	NUM
ap-614	261	37	calculation	calculation	NOUN
ap-614	261	38	experiment	experiment	NOUN
ap-614	261	39	s	s	PART
ap-614	261	40	m	m	VERB
ap-614	261	41	m	m	VERB
ap-614	261	42	2	2	NUM
ap-614	261	43	(	(	PUNCT
ap-614	261	44	b	b	NOUN
ap-614	261	45	)	)	PUNCT
ap-614	261	46	�	�	PROPN
ap-614	261	47	�	�	PROPN
ap-614	261	48	�	�	PROPN
ap-614	261	49	�	�	PROPN
ap-614	261	50	10	10	NUM
ap-614	261	51	20	20	NUM
ap-614	261	52	30	30	NUM
ap-614	261	53	40	40	NUM
ap-614	261	54	0	0	NUM
ap-614	261	55	1	1	NUM
ap-614	261	56	2	2	NUM
ap-614	261	57	3	3	NUM
ap-614	261	58	4	4	NUM
ap-614	261	59	5	5	NUM
ap-614	261	60	calculation	calculation	NOUN
ap-614	261	61	experiment	experiment	NOUN
ap-614	261	62	s	s	PART
ap-614	261	63	m	m	VERB
ap-614	261	64	m	m	VERB
ap-614	261	65	3	3	NUM
ap-614	261	66	(	(	PUNCT
ap-614	261	67	c	c	NOUN
ap-614	261	68	)	)	PUNCT
ap-614	261	69	�	�	PROPN
ap-614	261	70	�	�	PROPN
ap-614	261	71	�	�	PROPN
ap-614	261	72	�	�	PROPN
ap-614	261	73	0	0	NUM
ap-614	261	74	10	10	NUM
ap-614	261	75	20	20	NUM
ap-614	261	76	30	30	NUM
ap-614	261	77	40	40	NUM
ap-614	261	78	0	0	NUM
ap-614	261	79	5	5	NUM
ap-614	261	80	10	10	NUM
ap-614	261	81	calculation	calculation	NOUN
ap-614	261	82	experiment	experiment	NOUN
ap-614	261	83	s	s	PART
ap-614	261	84	m	m	VERB
ap-614	261	85	m	m	VERB
ap-614	261	86	4	4	NUM
ap-614	261	87	(	(	PUNCT
ap-614	261	88	d	d	NOUN
ap-614	261	89	)	)	PUNCT
ap-614	261	90	�	�	PROPN
ap-614	261	91	�	�	PROPN
ap-614	261	92	�	�	PROPN
ap-614	261	93	�	�	PROPN
ap-614	261	94	0	0	NUM
ap-614	261	95	10	10	NUM
ap-614	261	96	20	20	NUM
ap-614	261	97	30	30	NUM
ap-614	261	98	40	40	NUM
ap-614	261	99	0	0	NUM
ap-614	261	100	5	5	NUM
ap-614	261	101	10	10	NUM
ap-614	261	102	15	15	NUM
ap-614	261	103	20	20	NUM
ap-614	261	104	25	25	NUM
ap-614	261	105	calculation	calculation	NOUN
ap-614	261	106	experiment	experiment	NOUN
ap-614	261	107	s	s	PART
ap-614	261	108	m	m	VERB
ap-614	261	109	m	m	VERB
ap-614	261	110	5	5	NUM
ap-614	261	111	(	(	PUNCT
ap-614	261	112	e	e	NOUN
ap-614	261	113	)	)	PUNCT
ap-614	261	114	fig	fig	NOUN
ap-614	261	115	.	.	PUNCT
ap-614	262	1	8	8	NUM
ap-614	262	2	:	:	PUNCT
ap-614	262	3	experimental	experimental	ADJ
ap-614	262	4	versus	versus	ADP
ap-614	262	5	calculated	calculated	ADJ
ap-614	262	6	local	local	ADJ
ap-614	262	7	deformations	deformation	NOUN
ap-614	262	8	applied	apply	VERB
ap-614	262	9	mechanics	mechanic	NOUN
ap-614	262	10	and	and	CCONJ
ap-614	262	11	engineering	engineering	NOUN
ap-614	262	12	,	,	PUNCT
ap-614	262	13	vol	vol	NOUN
ap-614	262	14	.	.	PROPN
ap-614	263	1	67	67	NUM
ap-614	263	2	(	(	PUNCT
ap-614	263	3	1988	1988	NUM
ap-614	263	4	)	)	PUNCT
ap-614	263	5	,	,	PUNCT
ap-614	263	6	no	no	INTJ
ap-614	263	7	.	.	NOUN
ap-614	263	8	1	1	NUM
ap-614	263	9	,	,	PUNCT
ap-614	263	10	p.	p.	NOUN
ap-614	263	11	69–97	69–97	NUM
ap-614	263	12	.	.	PUNCT
ap-614	264	1	[	[	X
ap-614	264	2	5	5	X
ap-614	264	3	]	]	X
ap-614	264	4	sluys	sluys	PROPN
ap-614	264	5	l.	l.	PROPN
ap-614	264	6	j.	j.	PROPN
ap-614	264	7	,	,	PUNCT
ap-614	264	8	de	de	PROPN
ap-614	264	9	borst	borst	PROPN
ap-614	264	10	r.	r.	PROPN
ap-614	264	11	:	:	PUNCT
ap-614	264	12	“	"	PUNCT
ap-614	264	13	wave	wave	NOUN
ap-614	264	14	-	-	PUNCT
ap-614	264	15	propagation	propagation	NOUN
ap-614	264	16	and	and	CCONJ
ap-614	264	17	localization	localization	NOUN
ap-614	264	18	in	in	ADP
ap-614	264	19	a	a	DET
ap-614	264	20	rate	rate	NOUN
ap-614	264	21	-	-	PUNCT
ap-614	264	22	dependent	dependent	ADJ
ap-614	264	23	cracked	crack	VERB
ap-614	264	24	medium	medium	ADJ
ap-614	264	25	:	:	PUNCT
ap-614	264	26	model	model	NOUN
ap-614	264	27	formulation	formulation	NOUN
ap-614	264	28	and	and	CCONJ
ap-614	264	29	one	one	NUM
ap-614	264	30	-	-	PUNCT
ap-614	264	31	dimensional	dimensional	ADJ
ap-614	264	32	examples	example	NOUN
ap-614	264	33	.	.	PUNCT
ap-614	264	34	”	"	PUNCT
ap-614	264	35	international	international	ADJ
ap-614	264	36	journal	journal	NOUN
ap-614	264	37	of	of	ADP
ap-614	264	38	solids	solid	NOUN
ap-614	264	39	and	and	CCONJ
ap-614	264	40	structures	structure	NOUN
ap-614	264	41	,	,	PUNCT
ap-614	264	42	vol	vol	NOUN
ap-614	264	43	.	.	PROPN
ap-614	264	44	29	29	NUM
ap-614	264	45	(	(	PUNCT
ap-614	264	46	1992	1992	NUM
ap-614	264	47	)	)	PUNCT
ap-614	264	48	,	,	PUNCT
ap-614	264	49	no	no	INTJ
ap-614	264	50	.	.	NOUN
ap-614	264	51	23	23	NUM
ap-614	264	52	,	,	PUNCT
ap-614	264	53	p.	p.	NOUN
ap-614	264	54	2945–2958	2945–2958	NUM
ap-614	264	55	.	.	PUNCT
ap-614	265	1	[	[	X
ap-614	265	2	6	6	NUM
ap-614	265	3	]	]	X
ap-614	265	4	ortiz	ortiz	PROPN
ap-614	265	5	m.	m.	NOUN
ap-614	265	6	,	,	PUNCT
ap-614	265	7	leroy	leroy	PROPN
ap-614	265	8	y.	y.	PROPN
ap-614	265	9	,	,	PUNCT
ap-614	265	10	needleman	needleman	PROPN
ap-614	265	11	a.	a.	PROPN
ap-614	265	12	:	:	PUNCT
ap-614	265	13	“	"	PUNCT
ap-614	265	14	a	a	DET
ap-614	265	15	finite	finite	ADJ
ap-614	265	16	element	element	NOUN
ap-614	265	17	method	method	NOUN
ap-614	265	18	for	for	ADP
ap-614	265	19	localized	localized	ADJ
ap-614	265	20	failure	failure	NOUN
ap-614	265	21	analysis	analysis	NOUN
ap-614	265	22	.	.	PUNCT
ap-614	265	23	”	"	PUNCT
ap-614	266	1	computer	computer	NOUN
ap-614	266	2	methods	method	NOUN
ap-614	266	3	in	in	ADP
ap-614	266	4	applied	applied	ADJ
ap-614	266	5	mechanics	mechanic	NOUN
ap-614	266	6	and	and	CCONJ
ap-614	266	7	engineering	engineering	NOUN
ap-614	266	8	,	,	PUNCT
ap-614	266	9	vol	vol	NOUN
ap-614	266	10	.	.	PROPN
ap-614	266	11	61	61	NUM
ap-614	266	12	(	(	PUNCT
ap-614	266	13	1987	1987	NUM
ap-614	266	14	)	)	PUNCT
ap-614	266	15	,	,	PUNCT
ap-614	266	16	p.189–214	p.189–214	NOUN
ap-614	266	17	.	.	PUNCT
ap-614	267	1	[	[	X
ap-614	267	2	7	7	NUM
ap-614	267	3	]	]	X
ap-614	267	4	belytschko	belytschko	PROPN
ap-614	267	5	t.	t.	PROPN
ap-614	267	6	,	,	PUNCT
ap-614	267	7	fish	fish	PROPN
ap-614	267	8	j.	j.	PROPN
ap-614	267	9	,	,	PUNCT
ap-614	267	10	engelmann	engelmann	PROPN
ap-614	267	11	b.	b.	PROPN
ap-614	267	12	e.	e.	PROPN
ap-614	267	13	:	:	PUNCT
ap-614	267	14	“	"	PUNCT
ap-614	267	15	a	a	DET
ap-614	267	16	finite	finite	ADJ
ap-614	267	17	element	element	NOUN
ap-614	267	18	with	with	ADP
ap-614	267	19	embedded	embed	VERB
ap-614	267	20	localization	localization	NOUN
ap-614	267	21	zones	zone	NOUN
ap-614	267	22	.	.	PUNCT
ap-614	267	23	”	"	PUNCT
ap-614	267	24	computer	computer	NOUN
ap-614	267	25	methods	method	NOUN
ap-614	267	26	in	in	ADP
ap-614	267	27	applied	applied	ADJ
ap-614	267	28	mechanics	mechanic	NOUN
ap-614	267	29	and	and	CCONJ
ap-614	267	30	engineering	engineering	NOUN
ap-614	267	31	,	,	PUNCT
ap-614	267	32	vol	vol	NOUN
ap-614	267	33	.	.	PROPN
ap-614	267	34	70	70	NUM
ap-614	267	35	(	(	PUNCT
ap-614	267	36	1998	1998	NUM
ap-614	267	37	)	)	PUNCT
ap-614	267	38	,	,	PUNCT
ap-614	268	1	p.	p.	NOUN
ap-614	268	2	59–89	59–89	NUM
ap-614	268	3	.	.	PUNCT
ap-614	269	1	[	[	X
ap-614	269	2	8	8	NUM
ap-614	269	3	]	]	X
ap-614	269	4	sluys	sluys	PROPN
ap-614	269	5	l.j	l.j	PROPN
ap-614	269	6	.	.	PROPN
ap-614	269	7	,	,	PUNCT
ap-614	269	8	berends	berend	VERB
ap-614	269	9	a.h	a.h	PROPN
ap-614	269	10	.	.	PROPN
ap-614	269	11	:	:	PUNCT
ap-614	269	12	“	"	PUNCT
ap-614	269	13	discontinuous	discontinuous	ADJ
ap-614	269	14	failure	failure	NOUN
ap-614	269	15	analysis	analysis	NOUN
ap-614	269	16	for	for	ADP
ap-614	269	17	mode	mode	NOUN
ap-614	269	18	-	-	PUNCT
ap-614	269	19	i	i	PROPN
ap-614	269	20	and	and	CCONJ
ap-614	269	21	mode	mode	NOUN
ap-614	269	22	-	-	PUNCT
ap-614	269	23	ii	ii	NOUN
ap-614	269	24	localization	localization	NOUN
ap-614	269	25	problems	problem	NOUN
ap-614	269	26	.	.	PUNCT
ap-614	269	27	”	"	PUNCT
ap-614	270	1	international	international	ADJ
ap-614	270	2	journal	journal	NOUN
ap-614	270	3	of	of	ADP
ap-614	270	4	solids	solid	NOUN
ap-614	270	5	and	and	CCONJ
ap-614	270	6	structures	structure	NOUN
ap-614	270	7	,	,	PUNCT
ap-614	270	8	vol	vol	NOUN
ap-614	270	9	.	.	PROPN
ap-614	270	10	35	35	NUM
ap-614	270	11	(	(	PUNCT
ap-614	270	12	1998	1998	NUM
ap-614	270	13	)	)	PUNCT
ap-614	270	14	,	,	PUNCT
ap-614	270	15	no	no	INTJ
ap-614	270	16	.	.	NOUN
ap-614	270	17	31	31	NUM
ap-614	270	18	,	,	PUNCT
ap-614	270	19	p.	p.	NOUN
ap-614	270	20	4257–4274	4257–4274	NOUN
ap-614	270	21	.	.	PUNCT
ap-614	271	1	[	[	X
ap-614	271	2	9	9	NUM
ap-614	271	3	]	]	SYM
ap-614	271	4	dvorkin	dvorkin	NOUN
ap-614	271	5	e.	e.	PROPN
ap-614	271	6	n.	n.	PROPN
ap-614	271	7	,	,	PUNCT
ap-614	271	8	cuitino	cuitino	PROPN
ap-614	271	9	a.	a.	NOUN
ap-614	271	10	m.	m.	NOUN
ap-614	271	11	,	,	PUNCT
ap-614	271	12	giogia	giogia	PROPN
ap-614	271	13	g.	g.	PROPN
ap-614	271	14	:	:	PUNCT
ap-614	271	15	“	"	PUNCT
ap-614	271	16	finite	finite	VERB
ap-614	271	17	elements	element	NOUN
ap-614	271	18	with	with	ADP
ap-614	271	19	displacement	displacement	NOUN
ap-614	271	20	interpolated	interpolate	VERB
ap-614	271	21	embedded	embed	VERB
ap-614	271	22	localization	localization	NOUN
ap-614	271	23	lines	line	NOUN
ap-614	271	24	insensitive	insensitive	ADJ
ap-614	271	25	to	to	ADP
ap-614	271	26	mesh	mesh	NOUN
ap-614	271	27	size	size	NOUN
ap-614	271	28	and	and	CCONJ
ap-614	271	29	distortions	distortion	NOUN
ap-614	271	30	.	.	PUNCT
ap-614	271	31	”	"	PUNCT
ap-614	272	1	international	international	ADJ
ap-614	272	2	journal	journal	NOUN
ap-614	272	3	of	of	ADP
ap-614	272	4	numerical	numerical	ADJ
ap-614	272	5	methods	method	NOUN
ap-614	272	6	in	in	ADP
ap-614	272	7	engineering	engineering	NOUN
ap-614	272	8	,	,	PUNCT
ap-614	272	9	vol	vol	NOUN
ap-614	272	10	.	.	PROPN
ap-614	272	11	30	30	NUM
ap-614	272	12	(	(	PUNCT
ap-614	272	13	1990	1990	NUM
ap-614	272	14	)	)	PUNCT
ap-614	272	15	,	,	PUNCT
ap-614	273	1	p.	p.	NOUN
ap-614	273	2	541–564	541–564	NUM
ap-614	273	3	.	.	PUNCT
ap-614	274	1	[	[	X
ap-614	274	2	10	10	NUM
ap-614	274	3	]	]	X
ap-614	274	4	klisinski	klisinski	NOUN
ap-614	274	5	m.	m.	NOUN
ap-614	274	6	,	,	PUNCT
ap-614	274	7	runesson	runesson	PROPN
ap-614	274	8	k.	k.	PROPN
ap-614	274	9	,	,	PUNCT
ap-614	274	10	sture	sture	PROPN
ap-614	274	11	s.	s.	PROPN
ap-614	274	12	“	"	PUNCT
ap-614	274	13	finite	finite	PROPN
ap-614	274	14	element	element	NOUN
ap-614	274	15	with	with	ADP
ap-614	274	16	inner	inner	ADJ
ap-614	274	17	softening	soften	VERB
ap-614	274	18	band	band	NOUN
ap-614	274	19	.	.	PUNCT
ap-614	274	20	”	"	PUNCT
ap-614	275	1	asce	asce	PROPN
ap-614	275	2	journal	journal	PROPN
ap-614	275	3	of	of	ADP
ap-614	275	4	engineering	engineering	NOUN
ap-614	275	5	mechanics	mechanic	NOUN
ap-614	275	6	,	,	PUNCT
ap-614	275	7	vol	vol	NOUN
ap-614	275	8	.	.	PROPN
ap-614	275	9	17	17	NUM
ap-614	275	10	(	(	PUNCT
ap-614	275	11	1991	1991	NUM
ap-614	275	12	)	)	PUNCT
ap-614	275	13	,	,	PUNCT
ap-614	276	1	p.	p.	NOUN
ap-614	276	2	575–587	575–587	NUM
ap-614	276	3	.	.	PUNCT
ap-614	277	1	[	[	X
ap-614	277	2	11	11	NUM
ap-614	277	3	]	]	X
ap-614	277	4	simo	simo	PROPN
ap-614	277	5	j.	j.	PROPN
ap-614	277	6	c.	c.	PROPN
ap-614	277	7	,	,	PUNCT
ap-614	277	8	oliver	oliver	PROPN
ap-614	277	9	j.	j.	PROPN
ap-614	277	10	,	,	PUNCT
ap-614	277	11	armero	armero	PROPN
ap-614	277	12	f.	f.	PROPN
ap-614	277	13	:	:	PUNCT
ap-614	277	14	“	"	PUNCT
ap-614	277	15	an	an	DET
ap-614	277	16	analysis	analysis	NOUN
ap-614	277	17	of	of	ADP
ap-614	277	18	strong	strong	ADJ
ap-614	277	19	discontinuities	discontinuity	NOUN
ap-614	277	20	induced	induce	VERB
ap-614	277	21	by	by	ADP
ap-614	277	22	strain	strain	NOUN
ap-614	277	23	-	-	PUNCT
ap-614	277	24	softening	softening	NOUN
ap-614	277	25	in	in	ADP
ap-614	277	26	rate	rate	NOUN
ap-614	277	27	-	-	PUNCT
ap-614	277	28	independent	independent	ADJ
ap-614	277	29	inelastic	inelastic	ADJ
ap-614	277	30	solids	solid	NOUN
ap-614	277	31	.	.	PUNCT
ap-614	277	32	”	"	PUNCT
ap-614	278	1	computational	computational	ADJ
ap-614	278	2	mechanics	mechanic	NOUN
ap-614	278	3	,	,	PUNCT
ap-614	278	4	vol	vol	NOUN
ap-614	278	5	.	.	PROPN
ap-614	278	6	12	12	NUM
ap-614	278	7	(	(	PUNCT
ap-614	278	8	1993	1993	NUM
ap-614	278	9	)	)	PUNCT
ap-614	278	10	,	,	PUNCT
ap-614	278	11	p.	p.	NOUN
ap-614	278	12	277–296	277–296	NUM
ap-614	278	13	.	.	PUNCT
ap-614	279	1	[	[	X
ap-614	279	2	12	12	NUM
ap-614	279	3	]	]	PUNCT
ap-614	279	4	armero	armero	PROPN
ap-614	279	5	f.	f.	PROPN
ap-614	279	6	,	,	PUNCT
ap-614	279	7	garikipati	garikipati	PROPN
ap-614	279	8	k.	k.	PROPN
ap-614	279	9	:	:	PUNCT
ap-614	279	10	“	"	PUNCT
ap-614	279	11	recent	recent	ADJ
ap-614	279	12	advances	advance	NOUN
ap-614	279	13	in	in	ADP
ap-614	279	14	the	the	DET
ap-614	279	15	analysis	analysis	NOUN
ap-614	279	16	and	and	CCONJ
ap-614	279	17	numerical	numerical	ADJ
ap-614	279	18	simulation	simulation	NOUN
ap-614	279	19	of	of	ADP
ap-614	279	20	strain	strain	NOUN
ap-614	279	21	localization	localization	NOUN
ap-614	279	22	in	in	ADP
ap-614	279	23	inelastic	inelastic	ADJ
ap-614	279	24	solids	solid	NOUN
ap-614	279	25	.	.	PUNCT
ap-614	279	26	”	"	PUNCT
ap-614	279	27	in	in	ADP
ap-614	279	28	computational	computational	ADJ
ap-614	279	29	plasticity	plasticity	NOUN
ap-614	279	30	,	,	PUNCT
ap-614	279	31	fundamentals	fundamental	NOUN
ap-614	279	32	and	and	CCONJ
ap-614	279	33	applications	application	NOUN
ap-614	279	34	,	,	PUNCT
ap-614	279	35	d.	d.	PROPN
ap-614	279	36	r.	r.	PROPN
ap-614	279	37	j.	j.	PROPN
ap-614	279	38	owen	owen	PROPN
ap-614	279	39	,	,	PUNCT
ap-614	279	40	e.	e.	PROPN
ap-614	279	41	onate	onate	PROPN
ap-614	279	42	and	and	CCONJ
ap-614	279	43	e.	e.	PROPN
ap-614	279	44	hinton	hinton	PROPN
ap-614	279	45	,	,	PUNCT
ap-614	279	46	eds	eds	PROPN
ap-614	279	47	.	.	PROPN
ap-614	279	48	pineridge	pineridge	NOUN
ap-614	279	49	press	press	PROPN
ap-614	279	50	,	,	PUNCT
ap-614	279	51	swansea	swansea	NOUN
ap-614	279	52	,	,	PUNCT
ap-614	279	53	1995	1995	NUM
ap-614	279	54	,	,	PUNCT
ap-614	279	55	p.	p.	NOUN
ap-614	279	56	547–561	547–561	NUM
ap-614	279	57	.	.	PUNCT
ap-614	280	1	[	[	X
ap-614	280	2	13	13	NUM
ap-614	280	3	]	]	X
ap-614	280	4	larsson	larsson	PROPN
ap-614	280	5	r.	r.	PROPN
ap-614	280	6	,	,	PUNCT
ap-614	280	7	runesson	runesson	PROPN
ap-614	280	8	k	k	PROPN
ap-614	280	9	,	,	PUNCT
ap-614	280	10	.	.	PUNCT
ap-614	280	11	akesson	akesson	PROPN
ap-614	280	12	m.	m.	PROPN
ap-614	280	13	:	:	PUNCT
ap-614	280	14	“	"	PUNCT
ap-614	280	15	embedded	embed	VERB
ap-614	280	16	localization	localization	NOUN
ap-614	280	17	based	base	VERB
ap-614	280	18	on	on	ADP
ap-614	280	19	regularized	regularize	VERB
ap-614	280	20	strong	strong	ADJ
ap-614	280	21	discontinuity	discontinuity	NOUN
ap-614	280	22	.	.	PUNCT
ap-614	280	23	”	"	PUNCT
ap-614	280	24	in	in	ADP
ap-614	280	25	computational	computational	ADJ
ap-614	280	26	plasticity	plasticity	NOUN
ap-614	280	27	,	,	PUNCT
ap-614	280	28	fundamentals	fundamental	NOUN
ap-614	280	29	and	and	CCONJ
ap-614	280	30	applications	application	NOUN
ap-614	280	31	,	,	PUNCT
ap-614	280	32	d.	d.	PROPN
ap-614	280	33	r.	r.	PROPN
ap-614	280	34	j.	j.	PROPN
ap-614	280	35	owen	owen	PROPN
ap-614	280	36	,	,	PUNCT
ap-614	280	37	e.	e.	PROPN
ap-614	280	38	onate	onate	PROPN
ap-614	280	39	and	and	CCONJ
ap-614	280	40	e.	e.	PROPN
ap-614	280	41	hinton	hinton	PROPN
ap-614	280	42	,	,	PUNCT
ap-614	280	43	eds	eds	PROPN
ap-614	280	44	.	.	PROPN
ap-614	280	45	pineridge	pineridge	NOUN
ap-614	280	46	press	press	PROPN
ap-614	280	47	,	,	PUNCT
ap-614	280	48	swansea	swansea	NOUN
ap-614	280	49	,	,	PUNCT
ap-614	280	50	1995	1995	NUM
ap-614	280	51	,	,	PUNCT
ap-614	280	52	p.	p.	NOUN
ap-614	280	53	599–610	599–610	NUM
ap-614	280	54	.	.	PUNCT
ap-614	281	1	[	[	X
ap-614	281	2	14	14	NUM
ap-614	281	3	]	]	X
ap-614	281	4	lofti	lofti	PROPN
ap-614	281	5	h.r	h.r	PROPN
ap-614	281	6	.	.	PROPN
ap-614	281	7	,	,	PUNCT
ap-614	281	8	shing	she	VERB
ap-614	281	9	p.b	p.b	PROPN
ap-614	281	10	.	.	PROPN
ap-614	281	11	:	:	PUNCT
ap-614	281	12	“	"	PUNCT
ap-614	281	13	embedded	embed	VERB
ap-614	281	14	representation	representation	NOUN
ap-614	281	15	of	of	ADP
ap-614	281	16	fracture	fracture	NOUN
ap-614	281	17	in	in	ADV
ap-614	281	18	concretewith	concretewith	ADP
ap-614	281	19	mixed	mixed	ADJ
ap-614	281	20	finite	finite	ADJ
ap-614	281	21	elements	element	NOUN
ap-614	281	22	.	.	PUNCT
ap-614	281	23	”	"	PUNCT
ap-614	282	1	international	international	ADJ
ap-614	282	2	journal	journal	NOUN
ap-614	282	3	of	of	ADP
ap-614	282	4	numerical	numerical	ADJ
ap-614	282	5	methods	method	NOUN
ap-614	282	6	in	in	ADP
ap-614	282	7	engineering	engineering	NOUN
ap-614	282	8	,	,	PUNCT
ap-614	282	9	vol	vol	NOUN
ap-614	282	10	.	.	PROPN
ap-614	283	1	38	38	NUM
ap-614	283	2	(	(	PUNCT
ap-614	283	3	1995	1995	NUM
ap-614	283	4	)	)	PUNCT
ap-614	283	5	,	,	PUNCT
ap-614	284	1	p.	p.	NOUN
ap-614	284	2	1307–1325	1307–1325	NUM
ap-614	284	3	.	.	PUNCT
ap-614	285	1	[	[	X
ap-614	285	2	15	15	NUM
ap-614	285	3	]	]	X
ap-614	285	4	larsson	larsson	PROPN
ap-614	285	5	r.	r.	PROPN
ap-614	285	6	,	,	PUNCT
ap-614	285	7	runesson	runesson	PROPN
ap-614	285	8	k	k	PROPN
ap-614	285	9	..	..	PUNCT
ap-614	285	10	“	"	PUNCT
ap-614	285	11	element	element	NOUN
ap-614	285	12	-	-	PUNCT
ap-614	285	13	embedded	embed	VERB
ap-614	285	14	localization	localization	NOUN
ap-614	285	15	band	band	NOUN
ap-614	285	16	based	base	VERB
ap-614	285	17	on	on	ADP
ap-614	285	18	regularized	regularize	VERB
ap-614	285	19	displacement	displacement	ADJ
ap-614	285	20	discontinuity	discontinuity	NOUN
ap-614	285	21	.	.	PUNCT
ap-614	285	22	”	"	PUNCT
ap-614	286	1	journal	journal	NOUN
ap-614	286	2	of	of	ADP
ap-614	286	3	engineering	engineering	NOUN
ap-614	286	4	mechanics	mechanic	NOUN
ap-614	286	5	,	,	PUNCT
ap-614	286	6	vol	vol	NOUN
ap-614	286	7	.	.	PROPN
ap-614	286	8	122	122	NUM
ap-614	286	9	(	(	PUNCT
ap-614	286	10	1996	1996	NUM
ap-614	286	11	)	)	PUNCT
ap-614	286	12	,	,	PUNCT
ap-614	287	1	p.	p.	NOUN
ap-614	287	2	402–411	402–411	NUM
ap-614	287	3	.	.	PUNCT
ap-614	288	1	[	[	X
ap-614	288	2	16	16	NUM
ap-614	288	3	]	]	X
ap-614	288	4	oliver	oliver	PROPN
ap-614	288	5	j.	j.	PROPN
ap-614	288	6	:	:	PUNCT
ap-614	288	7	“	"	PUNCT
ap-614	288	8	modelling	model	VERB
ap-614	288	9	strong	strong	ADJ
ap-614	288	10	discontinuities	discontinuity	NOUN
ap-614	288	11	in	in	ADP
ap-614	288	12	solid	solid	ADJ
ap-614	288	13	mechanics	mechanic	NOUN
ap-614	288	14	via	via	ADP
ap-614	288	15	strain	strain	NOUN
ap-614	288	16	softening	soften	VERB
ap-614	288	17	constitutive	constitutive	ADJ
ap-614	288	18	equations	equation	NOUN
ap-614	288	19	.	.	PUNCT
ap-614	289	1	part	part	NOUN
ap-614	289	2	1	1	NUM
ap-614	289	3	:	:	PUNCT
ap-614	289	4	fundamentals	fundamental	NOUN
ap-614	289	5	.	.	PUNCT
ap-614	289	6	”	"	PUNCT
ap-614	290	1	international	international	ADJ
ap-614	290	2	journal	journal	NOUN
ap-614	290	3	for	for	ADP
ap-614	290	4	numerical	numerical	ADJ
ap-614	290	5	methods	method	NOUN
ap-614	290	6	in	in	ADP
ap-614	290	7	engineering	engineering	NOUN
ap-614	290	8	,	,	PUNCT
ap-614	290	9	vol	vol	NOUN
ap-614	290	10	.	.	PROPN
ap-614	290	11	39	39	NUM
ap-614	290	12	(	(	PUNCT
ap-614	290	13	1996	1996	NUM
ap-614	290	14	)	)	PUNCT
ap-614	290	15	,	,	PUNCT
ap-614	290	16	p.	p.	NOUN
ap-614	290	17	3575–3600	3575–3600	NUM
ap-614	290	18	.	.	PUNCT
ap-614	291	1	[	[	X
ap-614	291	2	17	17	NUM
ap-614	291	3	]	]	PUNCT
ap-614	291	4	wells	wells	PROPN
ap-614	291	5	g.	g.	PROPN
ap-614	291	6	n.	n.	PROPN
ap-614	291	7	,	,	PUNCT
ap-614	291	8	sluys	sluys	PROPN
ap-614	291	9	l.	l.	PROPN
ap-614	291	10	j.	j.	PROPN
ap-614	291	11	:	:	PUNCT
ap-614	291	12	“	"	PUNCT
ap-614	291	13	a	a	DET
ap-614	291	14	new	new	ADJ
ap-614	291	15	method	method	NOUN
ap-614	291	16	for	for	ADP
ap-614	291	17	modeling	model	VERB
ap-614	291	18	cohesive	cohesive	ADJ
ap-614	291	19	cracks	crack	NOUN
ap-614	291	20	using	use	VERB
ap-614	291	21	finite	finite	ADJ
ap-614	291	22	elements	element	NOUN
ap-614	291	23	.	.	PUNCT
ap-614	291	24	”	"	PUNCT
ap-614	292	1	international	international	ADJ
ap-614	292	2	journal	journal	NOUN
ap-614	292	3	for	for	ADP
ap-614	292	4	numerical	numerical	ADJ
ap-614	292	5	methods	method	NOUN
ap-614	292	6	in	in	ADP
ap-614	292	7	engineering	engineering	NOUN
ap-614	292	8	,	,	PUNCT
ap-614	292	9	vol	vol	NOUN
ap-614	292	10	.	.	PROPN
ap-614	292	11	50	50	NUM
ap-614	292	12	(	(	PUNCT
ap-614	292	13	2001	2001	NUM
ap-614	292	14	)	)	PUNCT
ap-614	292	15	,	,	PUNCT
ap-614	292	16	no	no	INTJ
ap-614	292	17	.	.	NOUN
ap-614	292	18	12	12	NUM
ap-614	292	19	,	,	PUNCT
ap-614	292	20	p.	p.	NOUN
ap-614	292	21	2667–2682	2667–2682	NUM
ap-614	292	22	.	.	PUNCT
ap-614	293	1	[	[	X
ap-614	293	2	18	18	NUM
ap-614	293	3	]	]	X
ap-614	293	4	jirasek	jirasek	PROPN
ap-614	293	5	m.	m.	NOUN
ap-614	293	6	:	:	PUNCT
ap-614	293	7	“	"	PUNCT
ap-614	293	8	comparative	comparative	ADJ
ap-614	293	9	study	study	NOUN
ap-614	293	10	on	on	ADP
ap-614	293	11	finite	finite	ADJ
ap-614	293	12	elements	element	NOUN
ap-614	293	13	with	with	ADP
ap-614	293	14	embedded	embed	VERB
ap-614	293	15	discontinuities	discontinuity	NOUN
ap-614	293	16	.	.	PUNCT
ap-614	293	17	“	"	PUNCT
ap-614	293	18	computer	computer	NOUN
ap-614	293	19	methods	method	NOUN
ap-614	293	20	in	in	ADP
ap-614	293	21	applied	applied	ADJ
ap-614	293	22	mechanics	mechanic	NOUN
ap-614	293	23	and	and	CCONJ
ap-614	293	24	engineering	engineering	NOUN
ap-614	293	25	,	,	PUNCT
ap-614	293	26	vol	vol	NOUN
ap-614	293	27	.	.	PROPN
ap-614	293	28	188	188	NUM
ap-614	293	29	(	(	PUNCT
ap-614	293	30	2000	2000	NUM
ap-614	293	31	)	)	PUNCT
ap-614	293	32	,	,	PUNCT
ap-614	293	33	p.	p.	NOUN
ap-614	293	34	307–330	307–330	NUM
ap-614	293	35	.	.	PUNCT
ap-614	294	1	[	[	X
ap-614	294	2	19	19	NUM
ap-614	294	3	]	]	X
ap-614	294	4	duarte	duarte	PROPN
ap-614	294	5	c.	c.	PROPN
ap-614	294	6	a.	a.	PROPN
ap-614	294	7	,	,	PUNCT
ap-614	294	8	oden	oden	PROPN
ap-614	294	9	j.	j.	PROPN
ap-614	294	10	t.	t.	PROPN
ap-614	294	11	:	:	PUNCT
ap-614	294	12	“	"	PUNCT
ap-614	294	13	h	h	NOUN
ap-614	294	14	-	-	PUNCT
ap-614	294	15	p	p	ADJ
ap-614	294	16	clouds	cloud	NOUN
ap-614	294	17	and	and	CCONJ
ap-614	294	18	h	h	NOUN
ap-614	294	19	-	-	PUNCT
ap-614	294	20	p	p	ADJ
ap-614	294	21	meshless	meshless	ADJ
ap-614	294	22	method	method	NOUN
ap-614	294	23	.	.	PUNCT
ap-614	294	24	”	"	PUNCT
ap-614	294	25	numerical	numerical	ADJ
ap-614	294	26	methods	method	NOUN
ap-614	294	27	for	for	ADP
ap-614	294	28	partial	partial	ADJ
ap-614	294	29	differential	differential	NOUN
ap-614	294	30	equations	equation	NOUN
ap-614	294	31	,	,	PUNCT
ap-614	294	32	vol	vol	NOUN
ap-614	294	33	.	.	PROPN
ap-614	294	34	12	12	NUM
ap-614	294	35	(	(	PUNCT
ap-614	294	36	1996	1996	NUM
ap-614	294	37	)	)	PUNCT
ap-614	294	38	,	,	PUNCT
ap-614	294	39	no	no	INTJ
ap-614	294	40	.	.	NOUN
ap-614	294	41	6	6	NUM
ap-614	294	42	,	,	PUNCT
ap-614	294	43	p.	p.	NOUN
ap-614	294	44	673–705	673–705	NUM
ap-614	294	45	.	.	PUNCT
ap-614	295	1	[	[	X
ap-614	295	2	20	20	NUM
ap-614	295	3	]	]	X
ap-614	295	4	belytschko	belytschko	PROPN
ap-614	295	5	t.	t.	PROPN
ap-614	295	6	,	,	PUNCT
ap-614	295	7	black	black	ADJ
ap-614	295	8	t.	t.	NOUN
ap-614	295	9	:	:	PUNCT
ap-614	295	10	“	"	PUNCT
ap-614	295	11	elastic	elastic	ADJ
ap-614	295	12	crack	crack	NOUN
ap-614	295	13	growth	growth	NOUN
ap-614	295	14	in	in	ADP
ap-614	295	15	finite	finite	ADJ
ap-614	295	16	elements	element	NOUN
ap-614	295	17	with	with	ADP
ap-614	295	18	minimal	minimal	ADJ
ap-614	295	19	remeshing	remeshing	NOUN
ap-614	295	20	.	.	PUNCT
ap-614	295	21	”	"	PUNCT
ap-614	296	1	international	international	ADJ
ap-614	296	2	journal	journal	NOUN
ap-614	296	3	for	for	ADP
ap-614	296	4	numerical	numerical	ADJ
ap-614	296	5	methods	method	NOUN
ap-614	296	6	in	in	ADP
ap-614	296	7	engineering	engineering	NOUN
ap-614	296	8	,	,	PUNCT
ap-614	296	9	vol	vol	NOUN
ap-614	296	10	.	.	PROPN
ap-614	297	1	45	45	NUM
ap-614	297	2	(	(	PUNCT
ap-614	297	3	1999	1999	NUM
ap-614	297	4	)	)	PUNCT
ap-614	297	5	,	,	PUNCT
ap-614	297	6	p.	p.	NOUN
ap-614	297	7	601–620	601–620	NUM
ap-614	297	8	.	.	PUNCT
ap-614	298	1	[	[	X
ap-614	298	2	21	21	NUM
ap-614	298	3	]	]	X
ap-614	298	4	moës	moës	NOUN
ap-614	298	5	n.	n.	NOUN
ap-614	298	6	,	,	PUNCT
ap-614	298	7	dolbow	dolbow	PROPN
ap-614	298	8	j.	j.	PROPN
ap-614	298	9	,	,	PUNCT
ap-614	298	10	belytschko	belytschko	PROPN
ap-614	298	11	t.	t.	PROPN
ap-614	298	12	:	:	PUNCT
ap-614	298	13	“	"	PUNCT
ap-614	298	14	a	a	DET
ap-614	298	15	finite	finite	ADJ
ap-614	298	16	element	element	NOUN
ap-614	298	17	method	method	NOUN
ap-614	298	18	for	for	ADP
ap-614	298	19	crack	crack	NOUN
ap-614	298	20	growth	growth	NOUN
ap-614	298	21	without	without	ADP
ap-614	298	22	remeshing	remeshe	VERB
ap-614	298	23	”	"	PUNCT
ap-614	298	24	.	.	PUNCT
ap-614	299	1	international	international	ADJ
ap-614	299	2	journal	journal	PROPN
ap-614	299	3	for	for	ADP
ap-614	299	4	numerical	numerical	ADJ
ap-614	299	5	methods	method	NOUN
ap-614	299	6	in	in	ADP
ap-614	299	7	engineering	engineering	NOUN
ap-614	299	8	,	,	PUNCT
ap-614	299	9	vol	vol	NOUN
ap-614	299	10	.	.	PROPN
ap-614	300	1	46	46	NUM
ap-614	300	2	(	(	PUNCT
ap-614	300	3	1999	1999	NUM
ap-614	300	4	)	)	PUNCT
ap-614	300	5	,	,	PUNCT
ap-614	301	1	p.	p.	NOUN
ap-614	301	2	131–150	131–150	NUM
ap-614	301	3	.	.	PUNCT
ap-614	302	1	[	[	X
ap-614	302	2	22	22	NUM
ap-614	302	3	]	]	PUNCT
ap-614	302	4	carol	carol	NOUN
ap-614	302	5	i.	i.	PROPN
ap-614	302	6	,	,	PUNCT
ap-614	302	7	prat	prat	NOUN
ap-614	302	8	p.	p.	PROPN
ap-614	302	9	c.	c.	PROPN
ap-614	302	10	,	,	PUNCT
ap-614	302	11	lopez	lopez	PROPN
ap-614	302	12	c.	c.	PROPN
ap-614	302	13	m.	m.	PROPN
ap-614	302	14	:	:	PUNCT
ap-614	302	15	“	"	PUNCT
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ap-614	302	17	/	/	SYM
ap-614	302	18	shear	shear	NOUN
ap-614	302	19	cracking	crack	VERB
ap-614	302	20	model	model	NOUN
ap-614	302	21	:	:	PUNCT
ap-614	302	22	application	application	NOUN
ap-614	302	23	to	to	PART
ap-614	302	24	discrete	discrete	VERB
ap-614	302	25	crack	crack	VERB
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ap-614	302	27	.	.	PUNCT
ap-614	302	28	”	"	PUNCT
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ap-614	302	31	engineering	engineering	NOUN
ap-614	302	32	mechanics	mechanic	NOUN
ap-614	302	33	,	,	PUNCT
ap-614	302	34	vol	vol	NOUN
ap-614	302	35	.	.	PROPN
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ap-614	302	37	(	(	PUNCT
ap-614	302	38	1997	1997	NUM
ap-614	302	39	)	)	PUNCT
ap-614	302	40	,	,	PUNCT
ap-614	302	41	p.	p.	NOUN
ap-614	302	42	765–773	765–773	NUM
ap-614	302	43	.	.	PUNCT
ap-614	303	1	[	[	X
ap-614	303	2	23	23	NUM
ap-614	303	3	]	]	X
ap-614	303	4	nooru	nooru	PROPN
ap-614	303	5	-	-	PUNCT
ap-614	303	6	mohamed	mohamed	PROPN
ap-614	303	7	m.	m.	PROPN
ap-614	303	8	b.	b.	PROPN
ap-614	303	9	:	:	PUNCT
ap-614	303	10	“	"	PUNCT
ap-614	303	11	mixed	mixed	ADJ
ap-614	303	12	-	-	PUNCT
ap-614	303	13	mode	mode	NOUN
ap-614	303	14	fracture	fracture	NOUN
ap-614	303	15	of	of	ADP
ap-614	303	16	concrete	concrete	NOUN
ap-614	303	17	:	:	PUNCT
ap-614	303	18	an	an	DET
ap-614	303	19	experimental	experimental	ADJ
ap-614	303	20	approach	approach	NOUN
ap-614	303	21	”	"	PUNCT
ap-614	303	22	.	.	PUNCT
ap-614	304	1	phd	phd	NOUN
ap-614	304	2	thesis	thesis	PROPN
ap-614	304	3	,	,	PUNCT
ap-614	304	4	delft	delft	PROPN
ap-614	304	5	university	university	PROPN
ap-614	304	6	of	of	ADP
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ap-614	304	8	,	,	PUNCT
ap-614	304	9	1992	1992	NUM
ap-614	304	10	.	.	PUNCT
ap-614	305	1	k.	k.	PROPN
ap-614	305	2	de	de	PROPN
ap-614	305	3	proft	proft	PROPN
ap-614	305	4	,	,	PUNCT
ap-614	305	5	w.p	w.p	PROPN
ap-614	305	6	.	.	PROPN
ap-614	305	7	de	de	PROPN
ap-614	305	8	wilde	wilde	PROPN
ap-614	305	9	department	department	PROPN
ap-614	305	10	of	of	ADP
ap-614	305	11	mechanics	mechanic	NOUN
ap-614	305	12	of	of	ADP
ap-614	305	13	materials	material	NOUN
ap-614	305	14	and	and	CCONJ
ap-614	305	15	constructions	construction	NOUN
ap-614	305	16	,	,	PUNCT
ap-614	305	17	vrije	vrije	PROPN
ap-614	305	18	universiteit	universiteit	PROPN
ap-614	305	19	brussel	brussel	PROPN
ap-614	305	20	pleinlaan	pleinlaan	VERB
ap-614	305	21	2	2	NUM
ap-614	305	22	1050	1050	NUM
ap-614	305	23	brussels	brussel	NOUN
ap-614	305	24	,	,	PUNCT
ap-614	305	25	belgium	belgium	NOUN
ap-614	305	26	48	48	NUM
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ap-614	305	28	czech	czech	PROPN
ap-614	305	29	technical	technical	PROPN
ap-614	305	30	university	university	PROPN
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ap-614	305	32	house	house	NOUN
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ap-614	305	34	acta	acta	PROPN
ap-614	305	35	polytechnica	polytechnica	PROPN
ap-614	305	36	vol	vol	NOUN
ap-614	305	37	.	.	PROPN
ap-614	306	1	44	44	NUM
ap-614	306	2	no	no	NOUN
ap-614	306	3	.	.	PUNCT
ap-614	307	1	5–6/2004	5–6/2004	NUM
ap-614	307	2	�	�	PROPN
ap-614	307	3	�	�	PROPN
ap-614	307	4	p	p	PROPN
ap-614	307	5	(	(	PUNCT
ap-614	307	6	k	k	PROPN
ap-614	307	7	n	n	PROPN
ap-614	307	8	)	)	PUNCT
ap-614	307	9	0	0	NUM
ap-614	307	10	25	25	NUM
ap-614	307	11	50	50	NUM
ap-614	307	12	75	75	NUM
ap-614	307	13	100	100	NUM
ap-614	307	14	0	0	NUM
ap-614	307	15	5	5	NUM
ap-614	307	16	10	10	NUM
ap-614	307	17	15	15	NUM
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ap-614	307	19	experimental	experimental	ADJ
ap-614	307	20	n	n	X
ap-614	307	21	m	m	VERB
ap-614	307	22	(	(	PUNCT
ap-614	307	23	a	a	NOUN
ap-614	307	24	)	)	PUNCT
ap-614	307	25	(	(	PUNCT
ap-614	307	26	b	b	X
ap-614	307	27	)	)	PUNCT
ap-614	307	28	fig	fig	NOUN
ap-614	307	29	.	.	PUNCT
ap-614	308	1	9	9	NUM
ap-614	308	2	:	:	PUNCT
ap-614	308	3	(	(	PUNCT
ap-614	308	4	a	a	X
ap-614	308	5	)	)	PUNCT
ap-614	308	6	experimental	experimental	ADJ
ap-614	308	7	versus	versus	ADP
ap-614	308	8	computed	computed	ADJ
ap-614	308	9	load	load	NOUN
ap-614	308	10	deformation	deformation	NOUN
ap-614	308	11	curve	curve	NOUN
ap-614	308	12	and	and	CCONJ
ap-614	308	13	(	(	PUNCT
ap-614	308	14	b	b	NOUN
ap-614	308	15	)	)	PUNCT
ap-614	308	16	experimental	experimental	ADJ
ap-614	308	17	versus	versus	ADP
ap-614	308	18	computed	compute	VERB
ap-614	308	19	crack	crack	NOUN
ap-614	308	20	path	path	NOUN