id	sid	tid	token	lemma	pos
ap-1666	1	1	acta	acta	PROPN
ap-1666	1	2	polytechnica	polytechnica	PROPN
ap-1666	1	3	vol	vol	NOUN
ap-1666	1	4	.	.	PROPN
ap-1666	2	1	52	52	NUM
ap-1666	2	2	no	no	NOUN
ap-1666	2	3	.	.	PUNCT
ap-1666	3	1	6/2012	6/2012	NUM
ap-1666	3	2	energetic	energetic	ADJ
ap-1666	3	3	approach	approach	NOUN
ap-1666	3	4	to	to	ADP
ap-1666	3	5	large	large	ADJ
ap-1666	3	6	strain	strain	NOUN
ap-1666	3	7	gradient	gradient	NOUN
ap-1666	3	8	crystal	crystal	NOUN
ap-1666	3	9	plasticity	plasticity	NOUN
ap-1666	3	10	jan	jan	PROPN
ap-1666	3	11	kratochvíl1	kratochvíl1	PROPN
ap-1666	3	12	,	,	PUNCT
ap-1666	3	13	martin	martin	PROPN
ap-1666	3	14	kružík2,1	kružík2,1	PROPN
ap-1666	3	15	1czech	1czech	NUM
ap-1666	3	16	technical	technical	ADJ
ap-1666	3	17	university	university	NOUN
ap-1666	3	18	,	,	PUNCT
ap-1666	3	19	faculty	faculty	NOUN
ap-1666	3	20	of	of	ADP
ap-1666	3	21	civil	civil	ADJ
ap-1666	3	22	engineering	engineering	NOUN
ap-1666	3	23	,	,	PUNCT
ap-1666	3	24	thákurova	thákurova	X
ap-1666	3	25	7	7	NUM
ap-1666	3	26	,	,	PUNCT
ap-1666	3	27	166	166	NUM
ap-1666	3	28	29	29	NUM
ap-1666	3	29	prague	prague	NOUN
ap-1666	3	30	,	,	PUNCT
ap-1666	3	31	czech	czech	PROPN
ap-1666	3	32	republic	republic	NOUN
ap-1666	3	33	2institute	2institute	NUM
ap-1666	3	34	of	of	ADP
ap-1666	3	35	information	information	NOUN
ap-1666	3	36	theory	theory	NOUN
ap-1666	3	37	and	and	CCONJ
ap-1666	3	38	automation	automation	NOUN
ap-1666	3	39	of	of	ADP
ap-1666	3	40	the	the	DET
ap-1666	3	41	ascr	ascr	NOUN
ap-1666	3	42	,	,	PUNCT
ap-1666	3	43	pod	pod	NOUN
ap-1666	3	44	vodárenskou	vodárenskou	PROPN
ap-1666	3	45	věží	věží	VERB
ap-1666	3	46	4	4	NUM
ap-1666	3	47	,	,	PUNCT
ap-1666	3	48	182	182	NUM
ap-1666	3	49	08	08	NUM
ap-1666	3	50	prague	prague	NOUN
ap-1666	3	51	,	,	PUNCT
ap-1666	3	52	czech	czech	PROPN
ap-1666	3	53	republic	republic	PROPN
ap-1666	3	54	corresponding	correspond	VERB
ap-1666	3	55	author	author	NOUN
ap-1666	3	56	:	:	PUNCT
ap-1666	3	57	kruzik@utia.cas.cz	kruzik@utia.cas.cz	NOUN
ap-1666	3	58	abstract	abstract	ADJ
ap-1666	3	59	we	we	PRON
ap-1666	3	60	formulate	formulate	VERB
ap-1666	3	61	a	a	DET
ap-1666	3	62	problem	problem	NOUN
ap-1666	3	63	of	of	ADP
ap-1666	3	64	the	the	DET
ap-1666	3	65	evolution	evolution	NOUN
ap-1666	3	66	of	of	ADP
ap-1666	3	67	elasto	elasto	NOUN
ap-1666	3	68	-	-	PUNCT
ap-1666	3	69	plastic	plastic	NOUN
ap-1666	3	70	materials	material	NOUN
ap-1666	3	71	subjected	subject	VERB
ap-1666	3	72	to	to	ADP
ap-1666	3	73	external	external	ADJ
ap-1666	3	74	loads	load	NOUN
ap-1666	3	75	in	in	ADP
ap-1666	3	76	the	the	DET
ap-1666	3	77	framework	framework	NOUN
ap-1666	3	78	of	of	ADP
ap-1666	3	79	large	large	ADJ
ap-1666	3	80	deformations	deformation	NOUN
ap-1666	3	81	and	and	CCONJ
ap-1666	3	82	multiplicative	multiplicative	ADJ
ap-1666	3	83	plasticity	plasticity	NOUN
ap-1666	3	84	.	.	PUNCT
ap-1666	4	1	we	we	PRON
ap-1666	4	2	focus	focus	VERB
ap-1666	4	3	on	on	ADP
ap-1666	4	4	a	a	DET
ap-1666	4	5	spontaneous	spontaneous	ADJ
ap-1666	4	6	inhomogenization	inhomogenization	NOUN
ap-1666	4	7	interpreted	interpret	VERB
ap-1666	4	8	as	as	ADP
ap-1666	4	9	a	a	DET
ap-1666	4	10	structuralization	structuralization	NOUN
ap-1666	4	11	process	process	NOUN
ap-1666	4	12	.	.	PUNCT
ap-1666	5	1	our	our	PRON
ap-1666	5	2	model	model	NOUN
ap-1666	5	3	includes	include	VERB
ap-1666	5	4	gradients	gradient	NOUN
ap-1666	5	5	of	of	ADP
ap-1666	5	6	the	the	DET
ap-1666	5	7	plastic	plastic	NOUN
ap-1666	5	8	strain	strain	NOUN
ap-1666	5	9	and	and	CCONJ
ap-1666	5	10	of	of	ADP
ap-1666	5	11	hardening	harden	VERB
ap-1666	5	12	variables	variable	NOUN
ap-1666	5	13	which	which	PRON
ap-1666	5	14	provide	provide	VERB
ap-1666	5	15	a	a	DET
ap-1666	5	16	relevant	relevant	ADJ
ap-1666	5	17	length	length	NOUN
ap-1666	5	18	scale	scale	NOUN
ap-1666	5	19	of	of	ADP
ap-1666	5	20	the	the	DET
ap-1666	5	21	model	model	NOUN
ap-1666	5	22	.	.	PUNCT
ap-1666	6	1	a	a	DET
ap-1666	6	2	simple	simple	ADJ
ap-1666	6	3	computational	computational	ADJ
ap-1666	6	4	experiment	experiment	NOUN
ap-1666	6	5	interpreted	interpret	VERB
ap-1666	6	6	as	as	ADP
ap-1666	6	7	a	a	DET
ap-1666	6	8	hint	hint	NOUN
ap-1666	6	9	of	of	ADP
ap-1666	6	10	a	a	DET
ap-1666	6	11	deformation	deformation	NOUN
ap-1666	6	12	substructure	substructure	NOUN
ap-1666	6	13	formation	formation	NOUN
ap-1666	6	14	is	be	AUX
ap-1666	6	15	included	include	VERB
ap-1666	6	16	.	.	PUNCT
ap-1666	7	1	keywords	keyword	NOUN
ap-1666	7	2	:	:	PUNCT
ap-1666	7	3	energetic	energetic	ADJ
ap-1666	7	4	solution	solution	NOUN
ap-1666	7	5	,	,	PUNCT
ap-1666	7	6	crystal	crystal	NOUN
ap-1666	7	7	plasticity	plasticity	NOUN
ap-1666	7	8	,	,	PUNCT
ap-1666	7	9	gradient	gradient	NOUN
ap-1666	7	10	plasticity	plasticity	NOUN
ap-1666	7	11	,	,	PUNCT
ap-1666	7	12	slip	slip	NOUN
ap-1666	7	13	system	system	NOUN
ap-1666	7	14	.	.	PUNCT
ap-1666	8	1	1	1	NUM
ap-1666	8	2	introduction	introduction	NOUN
ap-1666	8	3	the	the	DET
ap-1666	8	4	elastic	elastic	ADJ
ap-1666	8	5	-	-	PUNCT
ap-1666	8	6	plastic	plastic	NOUN
ap-1666	8	7	behavior	behavior	NOUN
ap-1666	8	8	of	of	ADP
ap-1666	8	9	crystalline	crystalline	NOUN
ap-1666	8	10	materials	material	NOUN
ap-1666	8	11	poses	pose	VERB
ap-1666	8	12	a	a	DET
ap-1666	8	13	challenge	challenge	NOUN
ap-1666	8	14	for	for	ADP
ap-1666	8	15	mathematical	mathematical	ADJ
ap-1666	8	16	analysis	analysis	NOUN
ap-1666	8	17	on	on	ADP
ap-1666	8	18	the	the	DET
ap-1666	8	19	microscopic	microscopic	NOUN
ap-1666	8	20	,	,	PUNCT
ap-1666	8	21	the	the	DET
ap-1666	8	22	mesoscopic	mesoscopic	NOUN
ap-1666	8	23	,	,	PUNCT
ap-1666	8	24	and	and	CCONJ
ap-1666	8	25	the	the	DET
ap-1666	8	26	macroscopic	macroscopic	ADJ
ap-1666	8	27	scales	scale	NOUN
ap-1666	8	28	.	.	PUNCT
ap-1666	9	1	here	here	ADV
ap-1666	9	2	,	,	PUNCT
ap-1666	9	3	we	we	PRON
ap-1666	9	4	study	study	VERB
ap-1666	9	5	a	a	DET
ap-1666	9	6	rate	rate	NOUN
ap-1666	9	7	-	-	PUNCT
ap-1666	9	8	independent	independent	ADJ
ap-1666	9	9	model	model	NOUN
ap-1666	9	10	arising	arise	VERB
ap-1666	9	11	in	in	ADP
ap-1666	9	12	the	the	DET
ap-1666	9	13	crystal	crystal	NOUN
ap-1666	9	14	plasticity	plasticity	NOUN
ap-1666	9	15	.	.	PUNCT
ap-1666	10	1	a	a	DET
ap-1666	10	2	common	common	ADJ
ap-1666	10	3	and	and	CCONJ
ap-1666	10	4	successful	successful	ADJ
ap-1666	10	5	approach	approach	NOUN
ap-1666	10	6	to	to	ADP
ap-1666	10	7	the	the	DET
ap-1666	10	8	analysis	analysis	NOUN
ap-1666	10	9	of	of	ADP
ap-1666	10	10	crystalline	crystalline	ADJ
ap-1666	10	11	materials	material	NOUN
ap-1666	10	12	is	be	AUX
ap-1666	10	13	by	by	ADP
ap-1666	10	14	means	mean	NOUN
ap-1666	10	15	of	of	ADP
ap-1666	10	16	energy	energy	NOUN
ap-1666	10	17	minimization	minimization	NOUN
ap-1666	10	18	;	;	PUNCT
ap-1666	10	19	see	see	VERB
ap-1666	10	20	e.g.	e.g.	ADV
ap-1666	10	21	ortiz	ortiz	PROPN
ap-1666	10	22	&	&	CCONJ
ap-1666	10	23	repetto	repetto	PROPN
ap-1666	11	1	[	[	X
ap-1666	11	2	30	30	NUM
ap-1666	11	3	]	]	PUNCT
ap-1666	11	4	.	.	PUNCT
ap-1666	12	1	this	this	PRON
ap-1666	12	2	is	be	AUX
ap-1666	12	3	manifested	manifest	VERB
ap-1666	12	4	for	for	ADP
ap-1666	12	5	various	various	ADJ
ap-1666	12	6	elastic	elastic	ADJ
ap-1666	12	7	crystals	crystal	NOUN
ap-1666	12	8	,	,	PUNCT
ap-1666	12	9	even	even	ADV
ap-1666	12	10	for	for	ADP
ap-1666	12	11	those	those	PRON
ap-1666	12	12	with	with	ADP
ap-1666	12	13	the	the	DET
ap-1666	12	14	potential	potential	NOUN
ap-1666	12	15	of	of	ADP
ap-1666	12	16	undergoing	undergo	VERB
ap-1666	12	17	phase	phase	NOUN
ap-1666	12	18	transitions	transition	NOUN
ap-1666	12	19	.	.	PUNCT
ap-1666	13	1	the	the	DET
ap-1666	13	2	applicability	applicability	NOUN
ap-1666	13	3	of	of	ADP
ap-1666	13	4	variational	variational	ADJ
ap-1666	13	5	methods	method	NOUN
ap-1666	13	6	has	have	AUX
ap-1666	13	7	been	be	AUX
ap-1666	13	8	broadened	broaden	VERB
ap-1666	13	9	to	to	PART
ap-1666	13	10	include	include	VERB
ap-1666	13	11	rate	rate	NOUN
ap-1666	13	12	-	-	PUNCT
ap-1666	13	13	independent	independent	ADJ
ap-1666	13	14	evolution	evolution	NOUN
ap-1666	13	15	.	.	PUNCT
ap-1666	14	1	typically	typically	ADV
ap-1666	14	2	,	,	PUNCT
ap-1666	14	3	these	these	DET
ap-1666	14	4	models	model	NOUN
ap-1666	14	5	are	be	AUX
ap-1666	14	6	characterized	characterize	VERB
ap-1666	14	7	by	by	ADP
ap-1666	14	8	energy	energy	NOUN
ap-1666	14	9	minimization	minimization	NOUN
ap-1666	14	10	of	of	ADP
ap-1666	14	11	a	a	DET
ap-1666	14	12	functional	functional	ADJ
ap-1666	14	13	including	include	VERB
ap-1666	14	14	macroscopic	macroscopic	ADJ
ap-1666	14	15	quantities	quantity	NOUN
ap-1666	14	16	such	such	ADJ
ap-1666	14	17	as	as	ADP
ap-1666	14	18	the	the	DET
ap-1666	14	19	macroscopic	macroscopic	ADJ
ap-1666	14	20	deformation	deformation	NOUN
ap-1666	14	21	gradient	gradient	NOUN
ap-1666	14	22	as	as	ADV
ap-1666	14	23	well	well	ADV
ap-1666	14	24	as	as	ADP
ap-1666	14	25	a	a	DET
ap-1666	14	26	dissipation	dissipation	NOUN
ap-1666	14	27	functional	functional	ADJ
ap-1666	14	28	.	.	PUNCT
ap-1666	15	1	in	in	ADP
ap-1666	15	2	order	order	NOUN
ap-1666	15	3	to	to	PART
ap-1666	15	4	introduce	introduce	VERB
ap-1666	15	5	a	a	DET
ap-1666	15	6	physically	physically	ADV
ap-1666	15	7	relevant	relevant	ADJ
ap-1666	15	8	scale	scale	NOUN
ap-1666	15	9	to	to	ADP
ap-1666	15	10	our	our	PRON
ap-1666	15	11	problem	problem	NOUN
ap-1666	15	12	we	we	PRON
ap-1666	15	13	assume	assume	VERB
ap-1666	15	14	,	,	PUNCT
ap-1666	15	15	following	follow	VERB
ap-1666	15	16	earlier	early	ADJ
ap-1666	15	17	works	work	NOUN
ap-1666	15	18	of	of	ADP
ap-1666	15	19	bažant	bažant	PROPN
ap-1666	15	20	&	&	CCONJ
ap-1666	15	21	jirásek	jirásek	PROPN
ap-1666	16	1	[	[	X
ap-1666	16	2	3	3	NUM
ap-1666	16	3	]	]	PUNCT
ap-1666	16	4	,	,	PUNCT
ap-1666	16	5	dillon	dillon	PROPN
ap-1666	16	6	&	&	CCONJ
ap-1666	16	7	kratochvíl	kratochvíl	PROPN
ap-1666	16	8	[	[	X
ap-1666	16	9	9	9	NUM
ap-1666	16	10	]	]	PUNCT
ap-1666	16	11	,	,	PUNCT
ap-1666	16	12	gurtin	gurtin	NOUN
ap-1666	16	13	and	and	CCONJ
ap-1666	16	14	gurtin	gurtin	NOUN
ap-1666	16	15	&	&	CCONJ
ap-1666	16	16	anand	anand	PROPN
ap-1666	16	17	[	[	X
ap-1666	16	18	15	15	NUM
ap-1666	16	19	,	,	PUNCT
ap-1666	16	20	16	16	NUM
ap-1666	16	21	]	]	PUNCT
ap-1666	16	22	,	,	PUNCT
ap-1666	16	23	mainik	mainik	PROPN
ap-1666	16	24	&	&	CCONJ
ap-1666	16	25	mielke	mielke	PROPN
ap-1666	17	1	[	[	X
ap-1666	17	2	22	22	NUM
ap-1666	17	3	]	]	PUNCT
ap-1666	17	4	and	and	CCONJ
ap-1666	17	5	others	other	NOUN
ap-1666	17	6	,	,	PUNCT
ap-1666	17	7	that	that	SCONJ
ap-1666	17	8	our	our	PRON
ap-1666	17	9	energy	energy	NOUN
ap-1666	17	10	functional	functional	ADJ
ap-1666	17	11	depends	depend	VERB
ap-1666	17	12	also	also	ADV
ap-1666	17	13	on	on	ADP
ap-1666	17	14	the	the	DET
ap-1666	17	15	gradient	gradient	NOUN
ap-1666	17	16	of	of	ADP
ap-1666	17	17	the	the	DET
ap-1666	17	18	plastic	plastic	NOUN
ap-1666	17	19	tensor	tensor	NOUN
ap-1666	17	20	.	.	PUNCT
ap-1666	18	1	the	the	DET
ap-1666	18	2	gradient	gradient	ADJ
ap-1666	18	3	term	term	NOUN
ap-1666	18	4	models	model	NOUN
ap-1666	18	5	nonlocal	nonlocal	ADJ
ap-1666	18	6	effects	effect	NOUN
ap-1666	18	7	caused	cause	VERB
ap-1666	18	8	by	by	ADP
ap-1666	18	9	short	short	ADJ
ap-1666	18	10	-	-	PUNCT
ap-1666	18	11	range	range	NOUN
ap-1666	18	12	interactions	interaction	NOUN
ap-1666	18	13	among	among	ADP
ap-1666	18	14	dislocations	dislocation	NOUN
ap-1666	18	15	.	.	PUNCT
ap-1666	19	1	it	it	PRON
ap-1666	19	2	is	be	AUX
ap-1666	19	3	not	not	PART
ap-1666	19	4	clear	clear	ADJ
ap-1666	19	5	,	,	PUNCT
ap-1666	19	6	however	however	ADV
ap-1666	19	7	,	,	PUNCT
ap-1666	19	8	which	which	DET
ap-1666	19	9	function	function	NOUN
ap-1666	19	10	of	of	ADP
ap-1666	19	11	the	the	DET
ap-1666	19	12	gradient	gradient	NOUN
ap-1666	19	13	should	should	AUX
ap-1666	19	14	be	be	AUX
ap-1666	19	15	used	use	VERB
ap-1666	19	16	.	.	PUNCT
ap-1666	20	1	for	for	ADP
ap-1666	20	2	further	further	ADJ
ap-1666	20	3	details	detail	NOUN
ap-1666	20	4	we	we	PRON
ap-1666	20	5	refer	refer	VERB
ap-1666	20	6	to	to	ADP
ap-1666	20	7	kratochvíl	kratochvíl	PROPN
ap-1666	20	8	&	&	CCONJ
ap-1666	20	9	sedláček	sedláček	PROPN
ap-1666	21	1	[	[	X
ap-1666	21	2	18	18	NUM
ap-1666	21	3	]	]	PUNCT
ap-1666	21	4	,	,	PUNCT
ap-1666	21	5	and	and	CCONJ
ap-1666	21	6	to	to	ADP
ap-1666	21	7	bakó	bakó	PROPN
ap-1666	21	8	&	&	CCONJ
ap-1666	21	9	groma	groma	PROPN
ap-1666	22	1	[	[	X
ap-1666	22	2	1	1	NUM
ap-1666	22	3	]	]	PUNCT
ap-1666	22	4	for	for	ADP
ap-1666	22	5	attempts	attempt	NOUN
ap-1666	22	6	to	to	PART
ap-1666	22	7	derive	derive	VERB
ap-1666	22	8	it	it	PRON
ap-1666	22	9	from	from	ADP
ap-1666	22	10	statistical	statistical	ADJ
ap-1666	22	11	physics	physics	NOUN
ap-1666	22	12	revealing	reveal	VERB
ap-1666	22	13	thus	thus	ADV
ap-1666	22	14	complexity	complexity	NOUN
ap-1666	22	15	of	of	ADP
ap-1666	22	16	the	the	DET
ap-1666	22	17	problem	problem	NOUN
ap-1666	22	18	,	,	PUNCT
ap-1666	22	19	for	for	ADP
ap-1666	22	20	more	more	ADJ
ap-1666	22	21	details	detail	NOUN
ap-1666	22	22	.	.	PUNCT
ap-1666	23	1	a	a	DET
ap-1666	23	2	related	related	ADJ
ap-1666	23	3	approach	approach	NOUN
ap-1666	23	4	to	to	ADP
ap-1666	23	5	non	non	ADJ
ap-1666	23	6	-	-	ADJ
ap-1666	23	7	local	local	ADJ
ap-1666	23	8	models	model	NOUN
ap-1666	23	9	in	in	ADP
ap-1666	23	10	damage	damage	NOUN
ap-1666	23	11	and	and	CCONJ
ap-1666	23	12	plasticity	plasticity	NOUN
ap-1666	23	13	was	be	AUX
ap-1666	23	14	undertaken	undertake	VERB
ap-1666	23	15	in	in	ADP
ap-1666	23	16	bažant	bažant	NOUN
ap-1666	23	17	&	&	CCONJ
ap-1666	23	18	jirásek	jirásek	PROPN
ap-1666	24	1	[	[	X
ap-1666	24	2	3	3	NUM
ap-1666	24	3	]	]	PUNCT
ap-1666	24	4	,	,	PUNCT
ap-1666	24	5	see	see	VERB
ap-1666	24	6	also	also	ADV
ap-1666	24	7	[	[	X
ap-1666	24	8	8	8	NUM
ap-1666	24	9	,	,	PUNCT
ap-1666	24	10	10	10	NUM
ap-1666	24	11	,	,	PUNCT
ap-1666	24	12	12	12	NUM
ap-1666	24	13	,	,	PUNCT
ap-1666	24	14	23	23	NUM
ap-1666	24	15	]	]	PUNCT
ap-1666	24	16	.	.	PUNCT
ap-1666	25	1	in	in	ADP
ap-1666	25	2	this	this	DET
ap-1666	25	3	paper	paper	NOUN
ap-1666	25	4	,	,	PUNCT
ap-1666	25	5	we	we	PRON
ap-1666	25	6	formulate	formulate	VERB
ap-1666	25	7	the	the	DET
ap-1666	25	8	so	so	ADV
ap-1666	25	9	-	-	PUNCT
ap-1666	25	10	called	call	VERB
ap-1666	25	11	energetic	energetic	ADJ
ap-1666	25	12	solution	solution	NOUN
ap-1666	25	13	due	due	ADP
ap-1666	25	14	to	to	ADP
ap-1666	25	15	mielke	mielke	PROPN
ap-1666	25	16	et	et	PROPN
ap-1666	25	17	al	al	PROPN
ap-1666	25	18	.	.	PUNCT
ap-1666	26	1	[	[	X
ap-1666	26	2	28	28	NUM
ap-1666	26	3	]	]	PUNCT
ap-1666	26	4	to	to	ADP
ap-1666	26	5	our	our	PRON
ap-1666	26	6	problem	problem	NOUN
ap-1666	26	7	.	.	PUNCT
ap-1666	27	1	this	this	DET
ap-1666	27	2	concept	concept	NOUN
ap-1666	27	3	of	of	ADP
ap-1666	27	4	a	a	DET
ap-1666	27	5	solution	solution	NOUN
ap-1666	27	6	is	be	AUX
ap-1666	27	7	based	base	VERB
ap-1666	27	8	on	on	ADP
ap-1666	27	9	two	two	NUM
ap-1666	27	10	requirements	requirement	NOUN
ap-1666	27	11	.	.	PUNCT
ap-1666	28	1	first	first	ADV
ap-1666	28	2	,	,	PUNCT
ap-1666	28	3	as	as	ADP
ap-1666	28	4	a	a	DET
ap-1666	28	5	consequence	consequence	NOUN
ap-1666	28	6	of	of	ADP
ap-1666	28	7	the	the	DET
ap-1666	28	8	conservation	conservation	NOUN
ap-1666	28	9	law	law	NOUN
ap-1666	28	10	for	for	ADP
ap-1666	28	11	linear	linear	PROPN
ap-1666	28	12	momentum	momentum	NOUN
ap-1666	28	13	,	,	PUNCT
ap-1666	28	14	all	all	DET
ap-1666	28	15	work	work	NOUN
ap-1666	28	16	put	put	VERB
ap-1666	28	17	into	into	ADP
ap-1666	28	18	the	the	DET
ap-1666	28	19	system	system	NOUN
ap-1666	28	20	by	by	ADP
ap-1666	28	21	external	external	ADJ
ap-1666	28	22	forces	force	NOUN
ap-1666	28	23	or	or	CCONJ
ap-1666	28	24	boundary	boundary	ADJ
ap-1666	28	25	conditions	condition	NOUN
ap-1666	28	26	is	be	AUX
ap-1666	28	27	spent	spend	VERB
ap-1666	28	28	on	on	ADP
ap-1666	28	29	increasing	increase	VERB
ap-1666	28	30	the	the	DET
ap-1666	28	31	stored	store	VERB
ap-1666	28	32	energy	energy	NOUN
ap-1666	28	33	or	or	CCONJ
ap-1666	28	34	it	it	PRON
ap-1666	28	35	is	be	AUX
ap-1666	28	36	dissipated	dissipate	VERB
ap-1666	28	37	.	.	PUNCT
ap-1666	29	1	secondly	secondly	ADV
ap-1666	29	2	,	,	PUNCT
ap-1666	29	3	the	the	DET
ap-1666	29	4	formulation	formulation	NOUN
ap-1666	29	5	must	must	AUX
ap-1666	29	6	satisfy	satisfy	VERB
ap-1666	29	7	the	the	DET
ap-1666	29	8	second	second	ADJ
ap-1666	29	9	law	law	NOUN
ap-1666	29	10	of	of	ADP
ap-1666	29	11	thermodynamics	thermodynamic	NOUN
ap-1666	29	12	,	,	PUNCT
ap-1666	29	13	which	which	PRON
ap-1666	29	14	in	in	ADP
ap-1666	29	15	the	the	DET
ap-1666	29	16	present	present	ADJ
ap-1666	29	17	mechanical	mechanical	ADJ
ap-1666	29	18	framework	framework	NOUN
ap-1666	29	19	has	have	VERB
ap-1666	29	20	the	the	DET
ap-1666	29	21	form	form	NOUN
ap-1666	29	22	of	of	ADP
ap-1666	29	23	a	a	DET
ap-1666	29	24	dissipation	dissipation	NOUN
ap-1666	29	25	inequality	inequality	NOUN
ap-1666	29	26	.	.	PUNCT
ap-1666	30	1	the	the	DET
ap-1666	30	2	last	last	ADJ
ap-1666	30	3	requirement	requirement	NOUN
ap-1666	30	4	enters	enter	VERB
ap-1666	30	5	the	the	DET
ap-1666	30	6	framework	framework	NOUN
ap-1666	30	7	as	as	ADP
ap-1666	30	8	the	the	DET
ap-1666	30	9	assumption	assumption	NOUN
ap-1666	30	10	of	of	ADP
ap-1666	30	11	the	the	DET
ap-1666	30	12	existence	existence	NOUN
ap-1666	30	13	of	of	ADP
ap-1666	30	14	a	a	DET
ap-1666	30	15	nonnegative	nonnegative	ADJ
ap-1666	30	16	convex	convex	NOUN
ap-1666	30	17	potential	potential	NOUN
ap-1666	30	18	of	of	ADP
ap-1666	30	19	dissipative	dissipative	ADJ
ap-1666	30	20	forces	force	NOUN
ap-1666	30	21	.	.	PUNCT
ap-1666	31	1	as	as	ADP
ap-1666	31	2	a	a	DET
ap-1666	31	3	consequence	consequence	NOUN
ap-1666	31	4	,	,	PUNCT
ap-1666	31	5	the	the	DET
ap-1666	31	6	imposed	impose	VERB
ap-1666	31	7	deformation	deformation	NOUN
ap-1666	31	8	evolves	evolve	NOUN
ap-1666	31	9	in	in	ADP
ap-1666	31	10	such	such	DET
ap-1666	31	11	a	a	DET
ap-1666	31	12	way	way	NOUN
ap-1666	31	13	that	that	PRON
ap-1666	31	14	the	the	DET
ap-1666	31	15	sum	sum	NOUN
ap-1666	31	16	of	of	ADP
ap-1666	31	17	the	the	DET
ap-1666	31	18	stored	store	VERB
ap-1666	31	19	and	and	CCONJ
ap-1666	31	20	dissipated	dissipate	VERB
ap-1666	31	21	energies	energy	NOUN
ap-1666	31	22	is	be	AUX
ap-1666	31	23	always	always	ADV
ap-1666	31	24	minimized	minimize	VERB
ap-1666	31	25	.	.	PUNCT
ap-1666	32	1	the	the	DET
ap-1666	32	2	main	main	ADJ
ap-1666	32	3	advantage	advantage	NOUN
ap-1666	32	4	of	of	ADP
ap-1666	32	5	this	this	DET
ap-1666	32	6	approach	approach	NOUN
ap-1666	32	7	is	be	AUX
ap-1666	32	8	that	that	SCONJ
ap-1666	32	9	it	it	PRON
ap-1666	32	10	allows	allow	VERB
ap-1666	32	11	us	we	PRON
ap-1666	32	12	to	to	PART
ap-1666	32	13	exploit	exploit	VERB
ap-1666	32	14	the	the	DET
ap-1666	32	15	theory	theory	NOUN
ap-1666	32	16	of	of	ADP
ap-1666	32	17	the	the	DET
ap-1666	32	18	modern	modern	ADJ
ap-1666	32	19	calculus	calculus	NOUN
ap-1666	32	20	of	of	ADP
ap-1666	32	21	variations	variation	NOUN
ap-1666	32	22	and	and	CCONJ
ap-1666	32	23	suggests	suggest	VERB
ap-1666	32	24	a	a	DET
ap-1666	32	25	numerical	numerical	ADJ
ap-1666	32	26	approach	approach	NOUN
ap-1666	32	27	to	to	ADP
ap-1666	32	28	this	this	DET
ap-1666	32	29	problem	problem	NOUN
ap-1666	32	30	.	.	PUNCT
ap-1666	33	1	to	to	PART
ap-1666	33	2	expose	expose	VERB
ap-1666	33	3	the	the	DET
ap-1666	33	4	essence	essence	NOUN
ap-1666	33	5	of	of	ADP
ap-1666	33	6	the	the	DET
ap-1666	33	7	mathematical	mathematical	ADJ
ap-1666	33	8	structure	structure	NOUN
ap-1666	33	9	of	of	ADP
ap-1666	33	10	the	the	DET
ap-1666	33	11	energetic	energetic	ADJ
ap-1666	33	12	approach	approach	NOUN
ap-1666	33	13	,	,	PUNCT
ap-1666	33	14	we	we	PRON
ap-1666	33	15	first	first	ADV
ap-1666	33	16	analyze	analyze	VERB
ap-1666	33	17	a	a	DET
ap-1666	33	18	proto	proto	NOUN
ap-1666	33	19	-	-	PUNCT
ap-1666	33	20	model	model	NOUN
ap-1666	33	21	called	call	VERB
ap-1666	33	22	here	here	ADV
ap-1666	33	23	a	a	DET
ap-1666	33	24	material	material	NOUN
ap-1666	33	25	with	with	ADP
ap-1666	33	26	internal	internal	ADJ
ap-1666	33	27	variables	variable	NOUN
ap-1666	33	28	.	.	PUNCT
ap-1666	34	1	it	it	PRON
ap-1666	34	2	freely	freely	ADV
ap-1666	34	3	follows	follow	VERB
ap-1666	34	4	the	the	DET
ap-1666	34	5	exposition	exposition	NOUN
ap-1666	34	6	of	of	ADP
ap-1666	34	7	francfort	francfort	NOUN
ap-1666	34	8	&	&	CCONJ
ap-1666	34	9	mielke	mielke	PROPN
ap-1666	35	1	[	[	X
ap-1666	35	2	11	11	NUM
ap-1666	35	3	]	]	PUNCT
ap-1666	35	4	and	and	CCONJ
ap-1666	35	5	we	we	PRON
ap-1666	35	6	recall	recall	VERB
ap-1666	35	7	it	it	PRON
ap-1666	35	8	here	here	ADV
ap-1666	35	9	to	to	PART
ap-1666	35	10	motivate	motivate	VERB
ap-1666	35	11	the	the	DET
ap-1666	35	12	notion	notion	NOUN
ap-1666	35	13	of	of	ADP
ap-1666	35	14	the	the	DET
ap-1666	35	15	energetic	energetic	ADJ
ap-1666	35	16	solution	solution	NOUN
ap-1666	35	17	.	.	PUNCT
ap-1666	36	1	in	in	ADP
ap-1666	36	2	the	the	DET
ap-1666	36	3	second	second	ADJ
ap-1666	36	4	step	step	NOUN
ap-1666	36	5	,	,	PUNCT
ap-1666	36	6	the	the	DET
ap-1666	36	7	framework	framework	NOUN
ap-1666	36	8	is	be	AUX
ap-1666	36	9	applied	apply	VERB
ap-1666	36	10	to	to	ADP
ap-1666	36	11	elasto	elasto	NOUN
ap-1666	36	12	-	-	PUNCT
ap-1666	36	13	plastic	plastic	NOUN
ap-1666	36	14	materials	material	NOUN
ap-1666	36	15	by	by	ADP
ap-1666	36	16	specifications	specification	NOUN
ap-1666	36	17	of	of	ADP
ap-1666	36	18	some	some	DET
ap-1666	36	19	internal	internal	ADJ
ap-1666	36	20	variables	variable	NOUN
ap-1666	36	21	.	.	PUNCT
ap-1666	37	1	one	one	NUM
ap-1666	37	2	of	of	ADP
ap-1666	37	3	the	the	DET
ap-1666	37	4	main	main	ADJ
ap-1666	37	5	results	result	NOUN
ap-1666	37	6	is	be	AUX
ap-1666	37	7	that	that	SCONJ
ap-1666	37	8	the	the	DET
ap-1666	37	9	described	describe	VERB
ap-1666	37	10	energetic	energetic	ADJ
ap-1666	37	11	approach	approach	NOUN
ap-1666	37	12	can	can	AUX
ap-1666	37	13	be	be	AUX
ap-1666	37	14	identified	identify	VERB
ap-1666	37	15	with	with	ADP
ap-1666	37	16	crystal	crystal	NOUN
ap-1666	37	17	plasticity	plasticity	NOUN
ap-1666	37	18	with	with	ADP
ap-1666	37	19	strain	strain	ADJ
ap-1666	37	20	gradients	gradient	NOUN
ap-1666	37	21	in	in	ADP
ap-1666	37	22	the	the	DET
ap-1666	37	23	version	version	NOUN
ap-1666	37	24	formulated	formulate	VERB
ap-1666	37	25	by	by	ADP
ap-1666	37	26	gurtin	gurtin	NOUN
ap-1666	37	27	[	[	X
ap-1666	37	28	15	15	NUM
ap-1666	37	29	]	]	PUNCT
ap-1666	37	30	.	.	PUNCT
ap-1666	38	1	gurtin	gurtin	NOUN
ap-1666	38	2	’s	’s	PART
ap-1666	38	3	model	model	NOUN
ap-1666	38	4	is	be	AUX
ap-1666	38	5	formulated	formulate	VERB
ap-1666	38	6	in	in	ADP
ap-1666	38	7	the	the	DET
ap-1666	38	8	mathematical	mathematical	ADJ
ap-1666	38	9	language	language	NOUN
ap-1666	38	10	of	of	ADP
ap-1666	38	11	differential	differential	ADJ
ap-1666	38	12	equations	equation	NOUN
ap-1666	38	13	.	.	PUNCT
ap-1666	39	1	from	from	ADP
ap-1666	39	2	the	the	DET
ap-1666	39	3	point	point	NOUN
ap-1666	39	4	of	of	ADP
ap-1666	39	5	view	view	NOUN
ap-1666	39	6	of	of	ADP
ap-1666	39	7	numerical	numerical	ADJ
ap-1666	39	8	solution	solution	NOUN
ap-1666	39	9	of	of	ADP
ap-1666	39	10	a	a	DET
ap-1666	39	11	boundary	boundary	ADJ
ap-1666	39	12	value	value	NOUN
ap-1666	39	13	problem	problem	NOUN
ap-1666	39	14	of	of	ADP
ap-1666	39	15	crystal	crystal	NOUN
ap-1666	39	16	plasticity	plasticity	NOUN
ap-1666	39	17	the	the	DET
ap-1666	39	18	energetic	energetic	ADJ
ap-1666	39	19	formulation	formulation	NOUN
ap-1666	39	20	is	be	AUX
ap-1666	39	21	more	more	ADV
ap-1666	39	22	convenient	convenient	ADJ
ap-1666	39	23	.	.	PUNCT
ap-1666	40	1	our	our	PRON
ap-1666	40	2	results	result	NOUN
ap-1666	40	3	are	be	AUX
ap-1666	40	4	closely	closely	ADV
ap-1666	40	5	related	relate	VERB
ap-1666	40	6	to	to	ADP
ap-1666	40	7	[	[	X
ap-1666	40	8	22	22	NUM
ap-1666	40	9	]	]	PUNCT
ap-1666	40	10	,	,	PUNCT
ap-1666	40	11	where	where	SCONJ
ap-1666	40	12	the	the	DET
ap-1666	40	13	authors	author	NOUN
ap-1666	40	14	proved	prove	VERB
ap-1666	40	15	the	the	DET
ap-1666	40	16	existence	existence	NOUN
ap-1666	40	17	of	of	ADP
ap-1666	40	18	energetic	energetic	ADJ
ap-1666	40	19	solutions	solution	NOUN
ap-1666	40	20	to	to	PART
ap-1666	40	21	strain	strain	VERB
ap-1666	40	22	gradient	gradient	ADJ
ap-1666	40	23	plasticity	plasticity	NOUN
ap-1666	40	24	with	with	ADP
ap-1666	40	25	polyconvex	polyconvex	NOUN
ap-1666	40	26	energy	energy	NOUN
ap-1666	40	27	density	density	NOUN
ap-1666	40	28	allowing	allow	VERB
ap-1666	40	29	even	even	ADV
ap-1666	40	30	for	for	ADP
ap-1666	40	31	+	+	ADJ
ap-1666	40	32	∞	∞	NOUN
ap-1666	40	33	;	;	PUNCT
ap-1666	40	34	see	see	VERB
ap-1666	40	35	[	[	X
ap-1666	40	36	2	2	X
ap-1666	40	37	]	]	PUNCT
ap-1666	40	38	and	and	CCONJ
ap-1666	40	39	to	to	PART
ap-1666	40	40	giacomini	giacomini	VERB
ap-1666	40	41	&	&	CCONJ
ap-1666	40	42	lussardi	lussardi	ADJ
ap-1666	41	1	[	[	X
ap-1666	41	2	13	13	NUM
ap-1666	41	3	]	]	PUNCT
ap-1666	41	4	where	where	SCONJ
ap-1666	41	5	the	the	DET
ap-1666	41	6	linear	linear	ADJ
ap-1666	41	7	-	-	PUNCT
ap-1666	41	8	elastoplasticity	elastoplasticity	NOUN
ap-1666	41	9	9	9	NUM
ap-1666	41	10	acta	acta	PROPN
ap-1666	41	11	polytechnica	polytechnica	PROPN
ap-1666	41	12	vol	vol	NOUN
ap-1666	41	13	.	.	PROPN
ap-1666	42	1	52	52	NUM
ap-1666	42	2	no	no	NOUN
ap-1666	42	3	.	.	PUNCT
ap-1666	43	1	6/2012	6/2012	NUM
ap-1666	43	2	framework	framework	NOUN
ap-1666	43	3	is	be	AUX
ap-1666	43	4	considered	consider	VERB
ap-1666	43	5	.	.	PUNCT
ap-1666	44	1	here	here	ADV
ap-1666	44	2	we	we	PRON
ap-1666	44	3	allow	allow	VERB
ap-1666	44	4	for	for	ADP
ap-1666	44	5	finite	finite	ADJ
ap-1666	44	6	quasiconvex	quasiconvex	NOUN
ap-1666	44	7	stored	store	VERB
ap-1666	44	8	energy	energy	NOUN
ap-1666	44	9	density	density	NOUN
ap-1666	44	10	and	and	CCONJ
ap-1666	44	11	large	large	ADJ
ap-1666	44	12	deformations	deformation	NOUN
ap-1666	44	13	.	.	PUNCT
ap-1666	45	1	this	this	PRON
ap-1666	45	2	is	be	AUX
ap-1666	45	3	motivated	motivate	VERB
ap-1666	45	4	by	by	ADP
ap-1666	45	5	relaxation	relaxation	NOUN
ap-1666	45	6	theory	theory	NOUN
ap-1666	45	7	in	in	ADP
ap-1666	45	8	the	the	DET
ap-1666	45	9	calculus	calculus	NOUN
ap-1666	45	10	of	of	ADP
ap-1666	45	11	variation	variation	NOUN
ap-1666	45	12	,	,	PUNCT
ap-1666	45	13	where	where	SCONJ
ap-1666	45	14	the	the	DET
ap-1666	45	15	effective	effective	ADJ
ap-1666	45	16	macroscopic	macroscopic	ADJ
ap-1666	45	17	energy	energy	NOUN
ap-1666	45	18	density	density	NOUN
ap-1666	45	19	is	be	AUX
ap-1666	45	20	quasiconvexification	quasiconvexification	NOUN
ap-1666	45	21	of	of	ADP
ap-1666	45	22	the	the	DET
ap-1666	45	23	microscopic	microscopic	ADJ
ap-1666	45	24	energy	energy	NOUN
ap-1666	45	25	density	density	NOUN
ap-1666	45	26	.	.	PUNCT
ap-1666	46	1	thus	thus	ADV
ap-1666	46	2	,	,	PUNCT
ap-1666	46	3	our	our	PRON
ap-1666	46	4	results	result	NOUN
ap-1666	46	5	may	may	AUX
ap-1666	46	6	be	be	AUX
ap-1666	46	7	applied	apply	VERB
ap-1666	46	8	to	to	ADP
ap-1666	46	9	plasticity	plasticity	NOUN
ap-1666	46	10	of	of	ADP
ap-1666	46	11	materials	material	NOUN
ap-1666	46	12	with	with	ADP
ap-1666	46	13	developing	develop	VERB
ap-1666	46	14	microstructures	microstructure	NOUN
ap-1666	46	15	,	,	PUNCT
ap-1666	46	16	as	as	ADP
ap-1666	46	17	in	in	ADP
ap-1666	46	18	shape	shape	NOUN
ap-1666	46	19	memory	memory	NOUN
ap-1666	46	20	alloys	alloy	NOUN
ap-1666	46	21	,	,	PUNCT
ap-1666	46	22	[	[	X
ap-1666	46	23	4	4	NUM
ap-1666	46	24	]	]	PUNCT
ap-1666	46	25	,	,	PUNCT
ap-1666	46	26	or	or	CCONJ
ap-1666	46	27	[	[	X
ap-1666	46	28	26	26	NUM
ap-1666	46	29	]	]	PUNCT
ap-1666	46	30	for	for	ADP
ap-1666	46	31	instance	instance	NOUN
ap-1666	46	32	.	.	PUNCT
ap-1666	47	1	we	we	PRON
ap-1666	47	2	refer	refer	VERB
ap-1666	47	3	an	an	DET
ap-1666	47	4	interested	interested	ADJ
ap-1666	47	5	reader	reader	NOUN
ap-1666	47	6	to	to	ADP
ap-1666	47	7	[	[	X
ap-1666	47	8	19	19	NUM
ap-1666	47	9	]	]	PUNCT
ap-1666	47	10	for	for	ADP
ap-1666	47	11	a	a	DET
ap-1666	47	12	model	model	NOUN
ap-1666	47	13	describing	describe	VERB
ap-1666	47	14	cyclic	cyclic	ADJ
ap-1666	47	15	plasticity	plasticity	NOUN
ap-1666	47	16	in	in	ADP
ap-1666	47	17	these	these	DET
ap-1666	47	18	materials	material	NOUN
ap-1666	47	19	.	.	PUNCT
ap-1666	48	1	another	another	DET
ap-1666	48	2	related	related	ADJ
ap-1666	48	3	paper	paper	NOUN
ap-1666	48	4	is	be	AUX
ap-1666	48	5	carstensen	carstensen	VERB
ap-1666	48	6	et	et	PROPN
ap-1666	48	7	al	al	PROPN
ap-1666	48	8	.	.	PUNCT
ap-1666	49	1	[	[	X
ap-1666	49	2	6	6	NUM
ap-1666	49	3	]	]	PUNCT
ap-1666	49	4	,	,	PUNCT
ap-1666	49	5	where	where	SCONJ
ap-1666	49	6	the	the	DET
ap-1666	49	7	authors	author	NOUN
ap-1666	49	8	use	use	VERB
ap-1666	49	9	the	the	DET
ap-1666	49	10	energetic	energetic	ADJ
ap-1666	49	11	approach	approach	NOUN
ap-1666	49	12	to	to	ADP
ap-1666	49	13	plasticity	plasticity	NOUN
ap-1666	49	14	without	without	ADP
ap-1666	49	15	strain	strain	NOUN
ap-1666	49	16	gradients	gradient	NOUN
ap-1666	49	17	.	.	PUNCT
ap-1666	50	1	in	in	ADP
ap-1666	50	2	what	what	PRON
ap-1666	50	3	follows	follow	VERB
ap-1666	50	4	,	,	PUNCT
ap-1666	50	5	ω	ω	PROPN
ap-1666	50	6	⊂	⊂	PROPN
ap-1666	50	7	rn	rn	PROPN
ap-1666	50	8	,	,	PUNCT
ap-1666	50	9	is	be	AUX
ap-1666	50	10	an	an	DET
ap-1666	50	11	open	open	ADJ
ap-1666	50	12	bounded	bounded	ADJ
ap-1666	50	13	domain	domain	NOUN
ap-1666	50	14	and	and	CCONJ
ap-1666	50	15	lβ(ω	lβ(ω	NUM
ap-1666	50	16	;	;	PUNCT
ap-1666	50	17	rn	rn	PROPN
ap-1666	50	18	)	)	PUNCT
ap-1666	50	19	,	,	PUNCT
ap-1666	50	20	1	1	NUM
ap-1666	50	21	≤	≤	NUM
ap-1666	50	22	β	β	X
ap-1666	50	23	<	<	X
ap-1666	50	24	+	+	PROPN
ap-1666	50	25	∞	∞	PROPN
ap-1666	50	26	denotes	denote	VERB
ap-1666	50	27	the	the	DET
ap-1666	50	28	usual	usual	ADJ
ap-1666	50	29	lebesgue	lebesgue	NOUN
ap-1666	50	30	space	space	NOUN
ap-1666	50	31	of	of	ADP
ap-1666	50	32	mappings	mapping	NOUN
ap-1666	50	33	ω	ω	PROPN
ap-1666	50	34	→	→	SYM
ap-1666	50	35	rn	rn	PROPN
ap-1666	50	36	whose	whose	DET
ap-1666	50	37	modulus	modulus	NOUN
ap-1666	50	38	is	be	AUX
ap-1666	50	39	integrable	integrable	ADJ
ap-1666	50	40	with	with	ADP
ap-1666	50	41	the	the	DET
ap-1666	50	42	power	power	NOUN
ap-1666	50	43	β	β	NOUN
ap-1666	50	44	,	,	PUNCT
ap-1666	50	45	and	and	CCONJ
ap-1666	50	46	l∞(ω	l∞(ω	ADV
ap-1666	50	47	;	;	PUNCT
ap-1666	50	48	rn	rn	NOUN
ap-1666	50	49	)	)	PUNCT
ap-1666	50	50	is	be	AUX
ap-1666	50	51	the	the	DET
ap-1666	50	52	space	space	NOUN
ap-1666	50	53	of	of	ADP
ap-1666	50	54	measurable	measurable	ADJ
ap-1666	50	55	and	and	CCONJ
ap-1666	50	56	essentially	essentially	ADV
ap-1666	50	57	bounded	bound	VERB
ap-1666	50	58	mappings	mapping	NOUN
ap-1666	50	59	ω	ω	PROPN
ap-1666	50	60	→	→	SYM
ap-1666	50	61	rn	rn	PROPN
ap-1666	50	62	.	.	PROPN
ap-1666	50	63	further	far	ADV
ap-1666	50	64	,	,	PUNCT
ap-1666	50	65	w	w	PROPN
ap-1666	50	66	1,β(ω	1,β(ω	NUM
ap-1666	50	67	;	;	PUNCT
ap-1666	50	68	rn	rn	NOUN
ap-1666	50	69	)	)	PUNCT
ap-1666	50	70	standardly	standardly	ADV
ap-1666	50	71	represents	represent	VERB
ap-1666	50	72	the	the	DET
ap-1666	50	73	space	space	NOUN
ap-1666	50	74	of	of	ADP
ap-1666	50	75	mappings	mapping	NOUN
ap-1666	50	76	which	which	PRON
ap-1666	50	77	live	live	VERB
ap-1666	50	78	in	in	ADP
ap-1666	50	79	lβ(ω	lβ(ω	NUM
ap-1666	50	80	;	;	PUNCT
ap-1666	50	81	rn	rn	NOUN
ap-1666	50	82	)	)	PUNCT
ap-1666	50	83	and	and	CCONJ
ap-1666	50	84	their	their	PRON
ap-1666	50	85	gradients	gradient	NOUN
ap-1666	50	86	belong	belong	VERB
ap-1666	50	87	to	to	ADP
ap-1666	50	88	lβ(ω	lβ(ω	NUM
ap-1666	50	89	;	;	PUNCT
ap-1666	50	90	rn×n	rn×n	NOUN
ap-1666	50	91	)	)	PUNCT
ap-1666	50	92	.	.	PUNCT
ap-1666	51	1	if	if	SCONJ
ap-1666	51	2	f	f	PROPN
ap-1666	51	3	:	:	PUNCT
ap-1666	51	4	rn	rn	PROPN
ap-1666	51	5	→	→	SYM
ap-1666	51	6	r	r	NOUN
ap-1666	51	7	is	be	AUX
ap-1666	51	8	convex	convex	ADJ
ap-1666	51	9	but	but	CCONJ
ap-1666	51	10	possibly	possibly	ADV
ap-1666	51	11	nonsmooth	nonsmooth	VERB
ap-1666	51	12	we	we	PRON
ap-1666	51	13	define	define	VERB
ap-1666	51	14	its	its	PRON
ap-1666	51	15	subdifferential	subdifferential	NOUN
ap-1666	51	16	at	at	ADP
ap-1666	51	17	a	a	DET
ap-1666	51	18	point	point	NOUN
ap-1666	51	19	x0	x0	PROPN
ap-1666	51	20	∈	∈	PROPN
ap-1666	51	21	rn	rn	PROPN
ap-1666	51	22	as	as	ADP
ap-1666	51	23	the	the	DET
ap-1666	51	24	set	set	NOUN
ap-1666	51	25	of	of	ADP
ap-1666	51	26	all	all	DET
ap-1666	51	27	v	v	ADP
ap-1666	51	28	∈	∈	NUM
ap-1666	51	29	rn	rn	NOUN
ap-1666	51	30	such	such	ADJ
ap-1666	51	31	that	that	SCONJ
ap-1666	51	32	f(x	f(x	PROPN
ap-1666	51	33	)	)	PUNCT
ap-1666	51	34	≥	≥	NOUN
ap-1666	51	35	f(x0	f(x0	PROPN
ap-1666	51	36	)	)	PUNCT
ap-1666	52	1	+	+	CCONJ
ap-1666	52	2	v	v	X
ap-1666	52	3	·	·	PUNCT
ap-1666	52	4	(	(	PUNCT
ap-1666	52	5	x−	x−	PROPN
ap-1666	52	6	x0	x0	PROPN
ap-1666	52	7	)	)	PUNCT
ap-1666	52	8	for	for	ADP
ap-1666	52	9	all	all	DET
ap-1666	52	10	x	x	PROPN
ap-1666	52	11	∈	∈	PROPN
ap-1666	52	12	rn	rn	PROPN
ap-1666	52	13	.	.	PUNCT
ap-1666	53	1	the	the	DET
ap-1666	53	2	subdifferential	subdifferential	NOUN
ap-1666	53	3	of	of	ADP
ap-1666	53	4	f	f	PROPN
ap-1666	53	5	will	will	AUX
ap-1666	53	6	be	be	AUX
ap-1666	53	7	denoted	denote	VERB
ap-1666	53	8	∂subf	∂subf	ADJ
ap-1666	53	9	and	and	CCONJ
ap-1666	53	10	its	its	PRON
ap-1666	53	11	elements	element	NOUN
ap-1666	53	12	will	will	AUX
ap-1666	53	13	be	be	AUX
ap-1666	53	14	called	call	VERB
ap-1666	53	15	subgradients	subgradient	NOUN
ap-1666	53	16	of	of	ADP
ap-1666	53	17	f	f	PROPN
ap-1666	53	18	at	at	ADP
ap-1666	53	19	x0	x0	PROPN
ap-1666	53	20	.	.	PUNCT
ap-1666	54	1	2	2	NUM
ap-1666	54	2	materials	material	NOUN
ap-1666	54	3	with	with	ADP
ap-1666	54	4	internal	internal	ADJ
ap-1666	54	5	variables	variable	NOUN
ap-1666	54	6	consider	consider	VERB
ap-1666	54	7	a	a	DET
ap-1666	54	8	material	material	NOUN
ap-1666	54	9	whose	whose	DET
ap-1666	54	10	elastic	elastic	ADJ
ap-1666	54	11	properties	property	NOUN
ap-1666	54	12	depend	depend	VERB
ap-1666	54	13	on	on	ADP
ap-1666	54	14	internal	internal	ADJ
ap-1666	54	15	variables	variable	NOUN
ap-1666	54	16	z	z	PROPN
ap-1666	54	17	∈	∈	PROPN
ap-1666	54	18	z	z	PROPN
ap-1666	54	19	⊂	⊂	PROPN
ap-1666	54	20	rm	rm	PROPN
ap-1666	54	21	.	.	PUNCT
ap-1666	55	1	the	the	DET
ap-1666	55	2	stored	store	VERB
ap-1666	55	3	energy	energy	NOUN
ap-1666	55	4	density	density	NOUN
ap-1666	55	5	is	be	AUX
ap-1666	55	6	then	then	ADV
ap-1666	55	7	w	w	PROPN
ap-1666	55	8	=	=	NOUN
ap-1666	55	9	w(fe	w(fe	NOUN
ap-1666	55	10	,	,	PUNCT
ap-1666	55	11	z	z	NOUN
ap-1666	55	12	)	)	PUNCT
ap-1666	55	13	,	,	PUNCT
ap-1666	55	14	where	where	SCONJ
ap-1666	55	15	fe	fe	X
ap-1666	55	16	∈	∈	PROPN
ap-1666	55	17	rn×n	rn×n	PROPN
ap-1666	55	18	is	be	AUX
ap-1666	55	19	the	the	DET
ap-1666	55	20	elastic	elastic	ADJ
ap-1666	55	21	strain	strain	NOUN
ap-1666	55	22	.	.	PUNCT
ap-1666	56	1	we	we	PRON
ap-1666	56	2	are	be	AUX
ap-1666	56	3	interested	interested	ADJ
ap-1666	56	4	in	in	ADP
ap-1666	56	5	the	the	DET
ap-1666	56	6	rateindependent	rateindependent	NOUN
ap-1666	56	7	evolution	evolution	NOUN
ap-1666	56	8	of	of	ADP
ap-1666	56	9	the	the	DET
ap-1666	56	10	material	material	NOUN
ap-1666	56	11	.	.	PUNCT
ap-1666	57	1	to	to	ADP
ap-1666	57	2	this	this	DET
ap-1666	57	3	end	end	NOUN
ap-1666	57	4	,	,	PUNCT
ap-1666	57	5	we	we	PRON
ap-1666	57	6	assume	assume	VERB
ap-1666	57	7	the	the	DET
ap-1666	57	8	existence	existence	NOUN
ap-1666	57	9	of	of	ADP
ap-1666	57	10	a	a	DET
ap-1666	57	11	nonnegative	nonnegative	ADJ
ap-1666	57	12	convex	convex	NOUN
ap-1666	57	13	potential	potential	ADJ
ap-1666	57	14	δ	δ	PROPN
ap-1666	57	15	=	=	SYM
ap-1666	57	16	δ(ż	δ(ż	PROPN
ap-1666	57	17	)	)	PUNCT
ap-1666	57	18	of	of	ADP
ap-1666	57	19	dissipative	dissipative	ADJ
ap-1666	57	20	forces	force	NOUN
ap-1666	57	21	,	,	PUNCT
ap-1666	57	22	where	where	SCONJ
ap-1666	57	23	ż	ż	NOUN
ap-1666	57	24	denotes	denote	VERB
ap-1666	57	25	the	the	DET
ap-1666	57	26	time	time	NOUN
ap-1666	57	27	derivative	derivative	ADJ
ap-1666	57	28	of	of	ADP
ap-1666	57	29	z.	z.	PROPN
ap-1666	57	30	in	in	ADP
ap-1666	57	31	order	order	NOUN
ap-1666	57	32	to	to	PART
ap-1666	57	33	ensure	ensure	VERB
ap-1666	57	34	rateindependence	rateindependence	NOUN
ap-1666	57	35	,	,	PUNCT
ap-1666	57	36	δ	δ	PROPN
ap-1666	57	37	must	must	AUX
ap-1666	57	38	be	be	AUX
ap-1666	57	39	positively	positively	ADV
ap-1666	57	40	one	one	NUM
ap-1666	57	41	-	-	PUNCT
ap-1666	57	42	homogeneous	homogeneous	ADJ
ap-1666	57	43	,	,	PUNCT
ap-1666	57	44	i.e.	i.e.	X
ap-1666	57	45	,	,	PUNCT
ap-1666	57	46	δ(αż	δ(αż	NOUN
ap-1666	57	47	)	)	PUNCT
ap-1666	58	1	=	=	SYM
ap-1666	58	2	αδ(ż	αδ(ż	NOUN
ap-1666	58	3	)	)	PUNCT
ap-1666	58	4	for	for	ADP
ap-1666	58	5	all	all	DET
ap-1666	58	6	α	α	PROPN
ap-1666	58	7	>	>	X
ap-1666	58	8	0	0	X
ap-1666	58	9	.	.	PUNCT
ap-1666	59	1	finally	finally	ADV
ap-1666	59	2	,	,	PUNCT
ap-1666	59	3	we	we	PRON
ap-1666	59	4	define	define	VERB
ap-1666	59	5	for	for	ADP
ap-1666	59	6	z	z	PROPN
ap-1666	59	7	∈	∈	PROPN
ap-1666	59	8	z	z	NOUN
ap-1666	59	9	a	a	DET
ap-1666	59	10	thermodynamic	thermodynamic	ADJ
ap-1666	59	11	force	force	NOUN
ap-1666	59	12	q	q	PROPN
ap-1666	60	1	:	:	PUNCT
ap-1666	60	2	=	=	SYM
ap-1666	60	3	−	−	PROPN
ap-1666	60	4	∂	∂	NUM
ap-1666	60	5	∂z	∂z	PROPN
ap-1666	60	6	w(fe	w(fe	PROPN
ap-1666	60	7	,	,	PUNCT
ap-1666	60	8	z	z	NOUN
ap-1666	60	9	)	)	PUNCT
ap-1666	60	10	.	.	PUNCT
ap-1666	61	1	(	(	PUNCT
ap-1666	61	2	1	1	X
ap-1666	61	3	)	)	PUNCT
ap-1666	61	4	the	the	DET
ap-1666	61	5	evolution	evolution	NOUN
ap-1666	61	6	rule	rule	NOUN
ap-1666	61	7	is	be	AUX
ap-1666	61	8	introduced	introduce	VERB
ap-1666	61	9	in	in	ADP
ap-1666	61	10	the	the	DET
ap-1666	61	11	form	form	NOUN
ap-1666	61	12	q(t	q(t	NOUN
ap-1666	61	13	)	)	PUNCT
ap-1666	61	14	∈	∈	PROPN
ap-1666	61	15	∂subδ(ż(t	∂subδ(ż(t	NOUN
ap-1666	61	16	)	)	PUNCT
ap-1666	61	17	)	)	PUNCT
ap-1666	61	18	,	,	PUNCT
ap-1666	61	19	(	(	PUNCT
ap-1666	61	20	2	2	X
ap-1666	61	21	)	)	PUNCT
ap-1666	61	22	where	where	SCONJ
ap-1666	61	23	∂subδ	∂subδ	PROPN
ap-1666	61	24	is	be	AUX
ap-1666	61	25	the	the	DET
ap-1666	61	26	subdifferential	subdifferential	NOUN
ap-1666	61	27	of	of	ADP
ap-1666	61	28	δ	δ	PROPN
ap-1666	61	29	.	.	PUNCT
ap-1666	62	1	hence	hence	ADV
ap-1666	62	2	,	,	PUNCT
ap-1666	62	3	there	there	PRON
ap-1666	62	4	is	be	VERB
ap-1666	62	5	ω(t	ω(t	NOUN
ap-1666	62	6	)	)	PUNCT
ap-1666	62	7	∈	∈	PROPN
ap-1666	62	8	∂subδ(ż(t	∂subδ(ż(t	NOUN
ap-1666	62	9	)	)	PUNCT
ap-1666	62	10	)	)	PUNCT
ap-1666	62	11	such	such	ADJ
ap-1666	62	12	that	that	DET
ap-1666	62	13	q(t	q(t	NOUN
ap-1666	62	14	)	)	PUNCT
ap-1666	62	15	=	=	SYM
ap-1666	62	16	ω(t	ω(t	NOUN
ap-1666	62	17	)	)	PUNCT
ap-1666	62	18	.	.	PUNCT
ap-1666	63	1	maximal	maximal	ADJ
ap-1666	63	2	monotonicity	monotonicity	NOUN
ap-1666	63	3	of	of	ADP
ap-1666	63	4	the	the	DET
ap-1666	63	5	subdifferential	subdifferential	NOUN
ap-1666	63	6	implies	imply	VERB
ap-1666	63	7	that	that	SCONJ
ap-1666	63	8	for	for	ADP
ap-1666	63	9	all	all	PRON
ap-1666	63	10	θ	θ	PROPN
ap-1666	63	11	∈	∈	PROPN
ap-1666	63	12	∂subδ(ξ	∂subδ(ξ	AUX
ap-1666	63	13	)	)	PUNCT
ap-1666	64	1	we	we	PRON
ap-1666	64	2	have	have	VERB
ap-1666	64	3	〈	〈	VERB
ap-1666	64	4	ω(t)−	ω(t)−	PROPN
ap-1666	64	5	θ	θ	PROPN
ap-1666	64	6	,	,	PUNCT
ap-1666	64	7	ż(t)−	ż(t)−	PROPN
ap-1666	64	8	ξ	ξ	PROPN
ap-1666	64	9	〉	〉	PROPN
ap-1666	64	10	≥	≥	NOUN
ap-1666	64	11	0	0	NUM
ap-1666	64	12	.	.	PUNCT
ap-1666	65	1	(	(	PUNCT
ap-1666	65	2	3	3	X
ap-1666	65	3	)	)	PUNCT
ap-1666	65	4	remark	remark	NOUN
ap-1666	65	5	2.1	2.1	NUM
ap-1666	65	6	.	.	PUNCT
ap-1666	66	1	in	in	ADP
ap-1666	66	2	particular	particular	ADJ
ap-1666	66	3	,	,	PUNCT
ap-1666	66	4	taking	take	VERB
ap-1666	66	5	ξ	ξ	NOUN
ap-1666	66	6	=	=	SYM
ap-1666	66	7	0	0	PUNCT
ap-1666	66	8	and	and	CCONJ
ap-1666	66	9	realizing	realize	VERB
ap-1666	66	10	that	that	SCONJ
ap-1666	66	11	the	the	DET
ap-1666	66	12	one	one	NUM
ap-1666	66	13	-	-	PUNCT
ap-1666	66	14	homogeneity	homogeneity	NOUN
ap-1666	66	15	of	of	ADP
ap-1666	66	16	δ	δ	PROPN
ap-1666	66	17	yields	yield	VERB
ap-1666	66	18	δ(ż	δ(ż	NOUN
ap-1666	66	19	)	)	PUNCT
ap-1666	66	20	=	=	PUNCT
ap-1666	66	21	〈	〈	PROPN
ap-1666	66	22	ω	ω	PROPN
ap-1666	66	23	,	,	PUNCT
ap-1666	66	24	ż	ż	NOUN
ap-1666	66	25	〉	〉	NOUN
ap-1666	66	26	for	for	ADP
ap-1666	66	27	all	all	DET
ap-1666	66	28	ω	ω	NUM
ap-1666	66	29	∈	∈	PROPN
ap-1666	66	30	∂subδ(ż	∂subδ(ż	NOUN
ap-1666	66	31	)	)	PUNCT
ap-1666	66	32	we	we	PRON
ap-1666	66	33	get	get	VERB
ap-1666	66	34	δ(ż(t	δ(ż(t	NOUN
ap-1666	66	35	)	)	PUNCT
ap-1666	66	36	)	)	PUNCT
ap-1666	67	1	=	=	PUNCT
ap-1666	67	2	〈	〈	PROPN
ap-1666	67	3	ω(t	ω(t	NOUN
ap-1666	67	4	)	)	PUNCT
ap-1666	67	5	,	,	PUNCT
ap-1666	67	6	ż(t	ż(t	PROPN
ap-1666	67	7	)	)	PUNCT
ap-1666	67	8	〉	〉	NOUN
ap-1666	67	9	=	=	SYM
ap-1666	67	10	〈	〈	PROPN
ap-1666	67	11	q(t	q(t	NOUN
ap-1666	67	12	)	)	PUNCT
ap-1666	67	13	,	,	PUNCT
ap-1666	67	14	ż(t	ż(t	PROPN
ap-1666	67	15	)	)	PUNCT
ap-1666	67	16	〉	〉	PROPN
ap-1666	67	17	≥	≥	NUM
ap-1666	67	18	〈	〈	PROPN
ap-1666	67	19	θ	θ	PROPN
ap-1666	67	20	,	,	PUNCT
ap-1666	67	21	ż(t	ż(t	NUM
ap-1666	67	22	)	)	PUNCT
ap-1666	67	23	)	)	PUNCT
ap-1666	67	24	〉	〉	NOUN
ap-1666	67	25	(	(	PUNCT
ap-1666	67	26	4	4	NUM
ap-1666	67	27	)	)	PUNCT
ap-1666	67	28	for	for	ADP
ap-1666	67	29	all	all	DET
ap-1666	67	30	θ	θ	PROPN
ap-1666	67	31	∈	∈	PROPN
ap-1666	67	32	∂subδ(0	∂subδ(0	PROPN
ap-1666	67	33	)	)	PUNCT
ap-1666	67	34	.	.	PUNCT
ap-1666	68	1	inequality	inequality	NOUN
ap-1666	68	2	(	(	PUNCT
ap-1666	68	3	4	4	X
ap-1666	68	4	)	)	PUNCT
ap-1666	68	5	expresses	express	VERB
ap-1666	68	6	the	the	DET
ap-1666	68	7	socalled	socalled	ADJ
ap-1666	68	8	maximum	maximum	ADJ
ap-1666	68	9	dissipation	dissipation	NOUN
ap-1666	68	10	principle	principle	NOUN
ap-1666	68	11	(	(	PUNCT
ap-1666	68	12	see	see	VERB
ap-1666	68	13	e.g.	e.g.	ADV
ap-1666	68	14	hill	hill	NOUN
ap-1666	69	1	[	[	X
ap-1666	69	2	17	17	NUM
ap-1666	69	3	]	]	PUNCT
ap-1666	69	4	or	or	CCONJ
ap-1666	69	5	simo	simo	NOUN
ap-1666	69	6	[	[	X
ap-1666	69	7	31	31	NUM
ap-1666	69	8	]	]	PUNCT
ap-1666	69	9	)	)	PUNCT
ap-1666	69	10	,	,	PUNCT
ap-1666	69	11	which	which	PRON
ap-1666	69	12	says	say	VERB
ap-1666	69	13	that	that	SCONJ
ap-1666	69	14	thermodynamic	thermodynamic	ADJ
ap-1666	69	15	forces	force	NOUN
ap-1666	69	16	“	"	PUNCT
ap-1666	69	17	available	available	ADJ
ap-1666	69	18	”	"	PUNCT
ap-1666	69	19	in	in	ADP
ap-1666	69	20	the	the	DET
ap-1666	69	21	so	so	ADV
ap-1666	69	22	-	-	PUNCT
ap-1666	69	23	called	call	VERB
ap-1666	69	24	elastic	elastic	ADJ
ap-1666	69	25	domain	domain	NOUN
ap-1666	69	26	∂subδ(0	∂subδ(0	NOUN
ap-1666	69	27	)	)	PUNCT
ap-1666	69	28	are	be	AUX
ap-1666	69	29	not	not	PART
ap-1666	69	30	strong	strong	ADJ
ap-1666	69	31	enough	enough	ADV
ap-1666	69	32	to	to	PART
ap-1666	69	33	overcome	overcome	VERB
ap-1666	69	34	frictional	frictional	ADJ
ap-1666	69	35	forces	force	NOUN
ap-1666	69	36	.	.	PUNCT
ap-1666	70	1	in	in	ADP
ap-1666	70	2	what	what	PRON
ap-1666	70	3	follows	follow	VERB
ap-1666	70	4	,	,	PUNCT
ap-1666	70	5	ω	ω	PROPN
ap-1666	70	6	⊂	⊂	PROPN
ap-1666	70	7	rn	rn	PROPN
ap-1666	70	8	,	,	PUNCT
ap-1666	70	9	is	be	AUX
ap-1666	70	10	a	a	DET
ap-1666	70	11	bounded	bounded	ADJ
ap-1666	70	12	lipschitz	lipschitz	NOUN
ap-1666	70	13	domain	domain	NOUN
ap-1666	70	14	representing	represent	VERB
ap-1666	70	15	the	the	DET
ap-1666	70	16	so	so	ADV
ap-1666	70	17	-	-	PUNCT
ap-1666	70	18	called	call	VERB
ap-1666	70	19	reference	reference	NOUN
ap-1666	70	20	configuration	configuration	NOUN
ap-1666	70	21	,	,	PUNCT
ap-1666	70	22	ν	ν	PROPN
ap-1666	70	23	is	be	AUX
ap-1666	70	24	the	the	DET
ap-1666	70	25	outer	outer	ADJ
ap-1666	70	26	unit	unit	NOUN
ap-1666	70	27	normal	normal	ADJ
ap-1666	70	28	to	to	ADP
ap-1666	70	29	∂ω	∂ω	PROPN
ap-1666	70	30	,	,	PUNCT
ap-1666	70	31	and	and	CCONJ
ap-1666	70	32	∂ω	∂ω	ADJ
ap-1666	70	33	⊃	⊃	PROPN
ap-1666	70	34	γ0,γ1	γ0,γ1	PROPN
ap-1666	70	35	which	which	PRON
ap-1666	70	36	are	be	AUX
ap-1666	70	37	disjoint	disjoint	ADJ
ap-1666	70	38	.	.	PUNCT
ap-1666	71	1	the	the	DET
ap-1666	71	2	deformation	deformation	NOUN
ap-1666	71	3	will	will	AUX
ap-1666	71	4	be	be	AUX
ap-1666	71	5	denoted	denote	VERB
ap-1666	71	6	y	y	PROPN
ap-1666	71	7	:	:	PUNCT
ap-1666	71	8	ω	ω	PROPN
ap-1666	71	9	→	→	SYM
ap-1666	71	10	rn	rn	PROPN
ap-1666	71	11	.	.	PUNCT
ap-1666	72	1	the	the	DET
ap-1666	72	2	evolution	evolution	NOUN
ap-1666	72	3	of	of	ADP
ap-1666	72	4	the	the	DET
ap-1666	72	5	system	system	NOUN
ap-1666	72	6	will	will	AUX
ap-1666	72	7	be	be	AUX
ap-1666	72	8	controlled	control	VERB
ap-1666	72	9	by	by	ADP
ap-1666	72	10	external	external	ADJ
ap-1666	72	11	forces	force	NOUN
ap-1666	72	12	.	.	PUNCT
ap-1666	73	1	let	let	VERB
ap-1666	73	2	f(t	f(t	NOUN
ap-1666	73	3	)	)	PUNCT
ap-1666	73	4	:	:	PUNCT
ap-1666	73	5	ω→	ω→	PUNCT
ap-1666	73	6	rn	rn	AUX
ap-1666	73	7	be	be	AUX
ap-1666	73	8	the	the	DET
ap-1666	73	9	(	(	PUNCT
ap-1666	73	10	volume	volume	NOUN
ap-1666	73	11	)	)	PUNCT
ap-1666	73	12	density	density	NOUN
ap-1666	73	13	of	of	ADP
ap-1666	73	14	the	the	DET
ap-1666	73	15	external	external	ADJ
ap-1666	73	16	body	body	NOUN
ap-1666	73	17	forces	force	NOUN
ap-1666	73	18	and	and	CCONJ
ap-1666	73	19	g(t	g(t	PROPN
ap-1666	73	20	)	)	PUNCT
ap-1666	73	21	:	:	PUNCT
ap-1666	73	22	γ1	γ1	NOUN
ap-1666	73	23	⊂	⊂	PROPN
ap-1666	73	24	∂ω	∂ω	PROPN
ap-1666	73	25	→	→	SYM
ap-1666	73	26	rn	rn	PROPN
ap-1666	73	27	be	be	AUX
ap-1666	73	28	the	the	DET
ap-1666	73	29	(	(	PUNCT
ap-1666	73	30	surface	surface	NOUN
ap-1666	73	31	)	)	PUNCT
ap-1666	73	32	density	density	NOUN
ap-1666	73	33	of	of	ADP
ap-1666	73	34	the	the	DET
ap-1666	73	35	surface	surface	NOUN
ap-1666	73	36	forces	force	NOUN
ap-1666	73	37	.	.	PUNCT
ap-1666	74	1	the	the	DET
ap-1666	74	2	equilibrium	equilibrium	NOUN
ap-1666	74	3	equations	equation	NOUN
ap-1666	74	4	governing	govern	VERB
ap-1666	74	5	the	the	DET
ap-1666	74	6	mechanical	mechanical	ADJ
ap-1666	74	7	behavior	behavior	NOUN
ap-1666	74	8	of	of	ADP
ap-1666	74	9	the	the	DET
ap-1666	74	10	system	system	NOUN
ap-1666	74	11	are	be	AUX
ap-1666	74	12	:	:	PUNCT
ap-1666	74	13	−div	−div	X
ap-1666	74	14	(	(	PUNCT
ap-1666	74	15	∂	∂	X
ap-1666	74	16	∂∇y	∂∇y	X
ap-1666	74	17	w(∇y(t	w(∇y(t	PROPN
ap-1666	74	18	)	)	PUNCT
ap-1666	74	19	,	,	PUNCT
ap-1666	74	20	z(t	z(t	NOUN
ap-1666	74	21	)	)	PUNCT
ap-1666	74	22	)	)	PUNCT
ap-1666	74	23	)	)	PUNCT
ap-1666	75	1	=	=	SYM
ap-1666	75	2	f(t	f(t	NOUN
ap-1666	75	3	)	)	PUNCT
ap-1666	75	4	in	in	ADP
ap-1666	75	5	ω	ω	NUM
ap-1666	75	6	,	,	PUNCT
ap-1666	75	7	(	(	PUNCT
ap-1666	75	8	5	5	NUM
ap-1666	75	9	)	)	PUNCT
ap-1666	75	10	y(t	y(t	PROPN
ap-1666	75	11	,	,	PUNCT
ap-1666	75	12	x	x	X
ap-1666	75	13	)	)	PUNCT
ap-1666	75	14	=	=	SYM
ap-1666	75	15	y0(x	y0(x	NOUN
ap-1666	75	16	)	)	PUNCT
ap-1666	75	17	on	on	ADP
ap-1666	75	18	γ0	γ0	NOUN
ap-1666	75	19	,	,	PUNCT
ap-1666	75	20	(	(	PUNCT
ap-1666	75	21	6	6	NUM
ap-1666	75	22	)	)	PUNCT
ap-1666	75	23	∂	∂	NOUN
ap-1666	75	24	∂∇y	∂∇y	X
ap-1666	75	25	w(∇y(t	w(∇y(t	PROPN
ap-1666	75	26	)	)	PUNCT
ap-1666	75	27	,	,	PUNCT
ap-1666	75	28	z(t))ν(x	z(t))ν(x	PROPN
ap-1666	75	29	)	)	PUNCT
ap-1666	75	30	=	=	SYM
ap-1666	75	31	g(t	g(t	PROPN
ap-1666	75	32	,	,	PUNCT
ap-1666	75	33	x	x	NOUN
ap-1666	75	34	)	)	PUNCT
ap-1666	75	35	on	on	ADP
ap-1666	75	36	γ1	γ1	PROPN
ap-1666	75	37	.	.	PUNCT
ap-1666	76	1	(	(	PUNCT
ap-1666	76	2	7	7	X
ap-1666	76	3	)	)	PUNCT
ap-1666	76	4	the	the	DET
ap-1666	76	5	full	full	ADJ
ap-1666	76	6	system	system	NOUN
ap-1666	76	7	characterizing	characterize	VERB
ap-1666	76	8	the	the	DET
ap-1666	76	9	proto	proto	NOUN
ap-1666	76	10	-	-	PUNCT
ap-1666	76	11	model	model	NOUN
ap-1666	76	12	consists	consist	VERB
ap-1666	76	13	of	of	ADP
ap-1666	76	14	(	(	PUNCT
ap-1666	76	15	5)–(7	5)–(7	NOUN
ap-1666	76	16	)	)	PUNCT
ap-1666	76	17	supplemented	supplement	VERB
ap-1666	76	18	by	by	ADP
ap-1666	76	19	(	(	PUNCT
ap-1666	76	20	2	2	NUM
ap-1666	76	21	):	):	PUNCT
ap-1666	76	22	−	−	PROPN
ap-1666	76	23	∂	∂	NOUN
ap-1666	76	24	∂z	∂z	PROPN
ap-1666	76	25	w(∇y(t	w(∇y(t	PROPN
ap-1666	76	26	)	)	PUNCT
ap-1666	76	27	,	,	PUNCT
ap-1666	76	28	z(t	z(t	PROPN
ap-1666	76	29	)	)	PUNCT
ap-1666	76	30	)	)	PUNCT
ap-1666	77	1	∈	∈	PROPN
ap-1666	77	2	∂δ(ż(t	∂δ(ż(t	NOUN
ap-1666	77	3	)	)	PUNCT
ap-1666	77	4	)	)	PUNCT
ap-1666	77	5	,	,	PUNCT
ap-1666	77	6	z(0	z(0	X
ap-1666	77	7	)	)	PUNCT
ap-1666	77	8	=	=	SYM
ap-1666	77	9	z0	z0	PROPN
ap-1666	77	10	,	,	PUNCT
ap-1666	77	11	z	z	PROPN
ap-1666	77	12	∈	∈	PROPN
ap-1666	77	13	z	z	PROPN
ap-1666	77	14	,	,	PUNCT
ap-1666	77	15	(	(	PUNCT
ap-1666	77	16	8)	8)	NUM
ap-1666	77	17	where	where	SCONJ
ap-1666	77	18	z0	z0	PROPN
ap-1666	77	19	∈	∈	PROPN
ap-1666	77	20	z	z	NOUN
ap-1666	77	21	is	be	AUX
ap-1666	77	22	an	an	DET
ap-1666	77	23	initial	initial	ADJ
ap-1666	77	24	condition	condition	NOUN
ap-1666	77	25	for	for	ADP
ap-1666	77	26	the	the	DET
ap-1666	77	27	internal	internal	ADJ
ap-1666	77	28	variable	variable	NOUN
ap-1666	77	29	.	.	PUNCT
ap-1666	78	1	in	in	ADP
ap-1666	78	2	order	order	NOUN
ap-1666	78	3	to	to	PART
ap-1666	78	4	regularize	regularize	VERB
ap-1666	78	5	our	our	PRON
ap-1666	78	6	problem	problem	NOUN
ap-1666	78	7	we	we	PRON
ap-1666	78	8	may	may	AUX
ap-1666	78	9	add	add	VERB
ap-1666	78	10	the	the	DET
ap-1666	78	11	gradient	gradient	NOUN
ap-1666	78	12	of	of	ADP
ap-1666	78	13	the	the	DET
ap-1666	78	14	internal	internal	ADJ
ap-1666	78	15	variable	variable	NOUN
ap-1666	78	16	,	,	PUNCT
ap-1666	78	17	i.e.	i.e.	X
ap-1666	78	18	,	,	PUNCT
ap-1666	78	19	for	for	ADP
ap-1666	78	20	ω	ω	PROPN
ap-1666	78	21	≥	≥	NOUN
ap-1666	78	22	1	1	NUM
ap-1666	78	23	and	and	CCONJ
ap-1666	78	24	ε	ε	PROPN
ap-1666	78	25	>	>	X
ap-1666	78	26	0	0	PUNCT
ap-1666	78	27	put	put	PROPN
ap-1666	78	28	w(∇y	w(∇y	NUM
ap-1666	78	29	,	,	PUNCT
ap-1666	78	30	z	z	NOUN
ap-1666	78	31	)	)	PUNCT
ap-1666	79	1	+	+	CCONJ
ap-1666	79	2	ε	ε	PROPN
ap-1666	79	3	ω	ω	NUM
ap-1666	79	4	|∇z|ω	|∇z|ω	NOUN
ap-1666	79	5	.	.	PUNCT
ap-1666	80	1	(	(	PUNCT
ap-1666	80	2	9	9	X
ap-1666	80	3	)	)	PUNCT
ap-1666	80	4	the	the	DET
ap-1666	80	5	evolution	evolution	NOUN
ap-1666	80	6	rule	rule	NOUN
ap-1666	80	7	changes	change	NOUN
ap-1666	80	8	to	to	PART
ap-1666	80	9	ε	ε	PROPN
ap-1666	80	10	div	div	X
ap-1666	80	11	(	(	PUNCT
ap-1666	80	12	|∇z(t)|ω−2∇z(t	|∇z(t)|ω−2∇z(t	NOUN
ap-1666	80	13	)	)	PUNCT
ap-1666	80	14	)	)	PUNCT
ap-1666	80	15	−	−	PROPN
ap-1666	80	16	∂	∂	NOUN
ap-1666	80	17	∂z	∂z	PROPN
ap-1666	80	18	w(∇y(t	w(∇y(t	PROPN
ap-1666	80	19	)	)	PUNCT
ap-1666	80	20	,	,	PUNCT
ap-1666	80	21	z(t	z(t	PROPN
ap-1666	80	22	)	)	PUNCT
ap-1666	80	23	)	)	PUNCT
ap-1666	81	1	∈	∈	PROPN
ap-1666	81	2	∂δ(ż(t	∂δ(ż(t	NOUN
ap-1666	81	3	)	)	PUNCT
ap-1666	81	4	)	)	PUNCT
ap-1666	81	5	,	,	PUNCT
ap-1666	81	6	z(0	z(0	X
ap-1666	81	7	)	)	PUNCT
ap-1666	81	8	=	=	SYM
ap-1666	81	9	z0	z0	PROPN
ap-1666	81	10	,	,	PUNCT
ap-1666	81	11	z	z	PROPN
ap-1666	81	12	∈	∈	PROPN
ap-1666	82	1	z	z	PROPN
ap-1666	82	2	,	,	PUNCT
ap-1666	82	3	(	(	PUNCT
ap-1666	82	4	10	10	NUM
ap-1666	82	5	)	)	PUNCT
ap-1666	82	6	so	so	SCONJ
ap-1666	82	7	we	we	PRON
ap-1666	82	8	have	have	VERB
ap-1666	82	9	the	the	DET
ap-1666	82	10	thermodynamic	thermodynamic	ADJ
ap-1666	82	11	force	force	NOUN
ap-1666	82	12	q(t	q(t	PROPN
ap-1666	82	13	)	)	PUNCT
ap-1666	82	14	:	:	PUNCT
ap-1666	82	15	=	=	SYM
ap-1666	82	16	εdiv(|∇z(t)|ω−2∇z(t	εdiv(|∇z(t)|ω−2∇z(t	NOUN
ap-1666	82	17	)	)	PUNCT
ap-1666	82	18	)	)	PUNCT
ap-1666	83	1	−	−	PROPN
ap-1666	83	2	∂	∂	NUM
ap-1666	83	3	∂z(t	∂z(t	PROPN
ap-1666	83	4	)	)	PUNCT
ap-1666	83	5	w(∇y(t	w(∇y(t	PROPN
ap-1666	83	6	)	)	PUNCT
ap-1666	83	7	,	,	PUNCT
ap-1666	83	8	z(t	z(t	PROPN
ap-1666	83	9	)	)	PUNCT
ap-1666	83	10	)	)	PUNCT
ap-1666	83	11	.	.	PUNCT
ap-1666	84	1	10	10	NUM
ap-1666	84	2	acta	acta	PROPN
ap-1666	84	3	polytechnica	polytechnica	PROPN
ap-1666	84	4	vol	vol	NOUN
ap-1666	84	5	.	.	PROPN
ap-1666	85	1	52	52	NUM
ap-1666	85	2	no	no	NOUN
ap-1666	85	3	.	.	PUNCT
ap-1666	86	1	6/2012	6/2012	NUM
ap-1666	87	1	the	the	DET
ap-1666	87	2	potential	potential	ADJ
ap-1666	87	3	energy	energy	NOUN
ap-1666	87	4	of	of	ADP
ap-1666	87	5	our	our	PRON
ap-1666	87	6	system	system	NOUN
ap-1666	87	7	can	can	AUX
ap-1666	87	8	be	be	AUX
ap-1666	87	9	written	write	VERB
ap-1666	87	10	(	(	PUNCT
ap-1666	87	11	ε	ε	PROPN
ap-1666	87	12	:	:	PUNCT
ap-1666	87	13	=	=	PUNCT
ap-1666	87	14	ε	ε	PROPN
ap-1666	87	15	/	/	SYM
ap-1666	87	16	ω	ω	PROPN
ap-1666	87	17	)	)	PUNCT
ap-1666	87	18	i(t	i(t	PROPN
ap-1666	87	19	,	,	PUNCT
ap-1666	87	20	y(t	y(t	PROPN
ap-1666	87	21	)	)	PUNCT
ap-1666	87	22	,	,	PUNCT
ap-1666	87	23	z(t	z(t	PROPN
ap-1666	87	24	)	)	PUNCT
ap-1666	87	25	)	)	PUNCT
ap-1666	87	26	:	:	PUNCT
ap-1666	88	1	=	=	SYM
ap-1666	88	2	∫	∫	PROPN
ap-1666	88	3	ω	ω	NUM
ap-1666	88	4	w(∇y(t	w(∇y(t	PROPN
ap-1666	88	5	)	)	PUNCT
ap-1666	88	6	,	,	PUNCT
ap-1666	88	7	z(t	z(t	NOUN
ap-1666	88	8	)	)	PUNCT
ap-1666	88	9	)	)	PUNCT
ap-1666	88	10	dx	dx	PROPN
ap-1666	89	1	+	+	CCONJ
ap-1666	89	2	ε	ε	PROPN
ap-1666	89	3	∫	∫	PROPN
ap-1666	89	4	ω	ω	PROPN
ap-1666	89	5	|∇z(t)|ω	|∇z(t)|ω	PROPN
ap-1666	89	6	dx−	dx−	NUM
ap-1666	89	7	l(t	l(t	PROPN
ap-1666	89	8	,	,	PUNCT
ap-1666	89	9	y(t	y(t	NOUN
ap-1666	89	10	)	)	PUNCT
ap-1666	89	11	)	)	PUNCT
ap-1666	89	12	,	,	PUNCT
ap-1666	89	13	(	(	PUNCT
ap-1666	89	14	11	11	NUM
ap-1666	89	15	)	)	PUNCT
ap-1666	89	16	where	where	SCONJ
ap-1666	89	17	the	the	DET
ap-1666	89	18	work	work	NOUN
ap-1666	89	19	done	do	VERB
ap-1666	89	20	by	by	ADP
ap-1666	89	21	external	external	ADJ
ap-1666	89	22	forces	force	NOUN
ap-1666	89	23	is	be	AUX
ap-1666	89	24	l(t	l(t	NOUN
ap-1666	89	25	,	,	PUNCT
ap-1666	89	26	y(t	y(t	NOUN
ap-1666	89	27	)	)	PUNCT
ap-1666	89	28	)	)	PUNCT
ap-1666	89	29	:	:	PUNCT
ap-1666	89	30	=	=	SYM
ap-1666	89	31	∫	∫	PROPN
ap-1666	89	32	ω	ω	NUM
ap-1666	89	33	f(t	f(t	PROPN
ap-1666	89	34	)	)	PUNCT
ap-1666	89	35	·	·	PUNCT
ap-1666	90	1	y(t	y(t	NUM
ap-1666	90	2	)	)	PUNCT
ap-1666	90	3	dx	dx	PROPN
ap-1666	91	1	+	+	CCONJ
ap-1666	91	2	∫	∫	PROPN
ap-1666	91	3	γ1	γ1	PROPN
ap-1666	91	4	g(t	g(t	PROPN
ap-1666	91	5	)	)	PUNCT
ap-1666	91	6	·	·	PUNCT
ap-1666	92	1	y(t	y(t	X
ap-1666	92	2	)	)	PUNCT
ap-1666	92	3	ds	ds	NOUN
ap-1666	92	4	(	(	PUNCT
ap-1666	92	5	12	12	NUM
ap-1666	92	6	)	)	PUNCT
ap-1666	92	7	and	and	CCONJ
ap-1666	92	8	the	the	DET
ap-1666	92	9	following	follow	VERB
ap-1666	92	10	energy	energy	NOUN
ap-1666	92	11	balance	balance	NOUN
ap-1666	92	12	is	be	AUX
ap-1666	92	13	satisfied	satisfied	ADJ
ap-1666	92	14	d	d	X
ap-1666	92	15	dt	dt	X
ap-1666	92	16	i(t	i(t	PROPN
ap-1666	92	17	,	,	PUNCT
ap-1666	92	18	y(t	y(t	PROPN
ap-1666	92	19	)	)	PUNCT
ap-1666	92	20	,	,	PUNCT
ap-1666	92	21	z(t	z(t	NOUN
ap-1666	92	22	)	)	PUNCT
ap-1666	92	23	)	)	PUNCT
ap-1666	93	1	=	=	SYM
ap-1666	93	2	l̇	l̇	PROPN
ap-1666	93	3	(	(	PUNCT
ap-1666	93	4	t	t	PROPN
ap-1666	93	5	,	,	PUNCT
ap-1666	93	6	y(t	y(t	PROPN
ap-1666	93	7	)	)	PUNCT
ap-1666	93	8	)	)	PUNCT
ap-1666	94	1	−	−	PROPN
ap-1666	95	1	d	d	INTJ
ap-1666	95	2	dt	dt	X
ap-1666	95	3	diss	diss	PROPN
ap-1666	95	4	(	(	PUNCT
ap-1666	95	5	z	z	NOUN
ap-1666	95	6	;	;	PUNCT
ap-1666	95	7	[	[	X
ap-1666	95	8	0	0	NUM
ap-1666	95	9	,	,	PUNCT
ap-1666	95	10	t	t	PROPN
ap-1666	95	11	]	]	PUNCT
ap-1666	95	12	)	)	PUNCT
ap-1666	95	13	,	,	PUNCT
ap-1666	95	14	(	(	PUNCT
ap-1666	95	15	13	13	NUM
ap-1666	95	16	)	)	PUNCT
ap-1666	95	17	where	where	SCONJ
ap-1666	95	18	diss	diss	PROPN
ap-1666	95	19	(	(	PUNCT
ap-1666	95	20	z	z	NOUN
ap-1666	95	21	;	;	PUNCT
ap-1666	95	22	[	[	X
ap-1666	95	23	0	0	NUM
ap-1666	95	24	,	,	PUNCT
ap-1666	95	25	t	t	PROPN
ap-1666	95	26	]	]	PUNCT
ap-1666	95	27	)	)	PUNCT
ap-1666	95	28	:	:	PUNCT
ap-1666	96	1	=	=	X
ap-1666	96	2	∫	∫	PROPN
ap-1666	96	3	t	t	PROPN
ap-1666	96	4	0	0	NUM
ap-1666	96	5	∫	∫	PROPN
ap-1666	96	6	ω	ω	PROPN
ap-1666	96	7	δ	δ	PROPN
ap-1666	96	8	(	(	PUNCT
ap-1666	96	9	ż(s	ż(s	PROPN
ap-1666	96	10	)	)	PUNCT
ap-1666	96	11	)	)	PUNCT
ap-1666	96	12	dxds	dxds	NOUN
ap-1666	96	13	.	.	PUNCT
ap-1666	97	1	hence	hence	ADV
ap-1666	97	2	,	,	PUNCT
ap-1666	97	3	the	the	DET
ap-1666	97	4	integration	integration	NOUN
ap-1666	97	5	with	with	ADP
ap-1666	97	6	respect	respect	NOUN
ap-1666	97	7	to	to	ADP
ap-1666	97	8	time	time	NOUN
ap-1666	97	9	gives	give	VERB
ap-1666	97	10	i(t	i(t	PROPN
ap-1666	97	11	,	,	PUNCT
ap-1666	97	12	y(t	y(t	PROPN
ap-1666	97	13	)	)	PUNCT
ap-1666	97	14	,	,	PUNCT
ap-1666	97	15	z(t	z(t	NOUN
ap-1666	97	16	)	)	PUNCT
ap-1666	97	17	)	)	PUNCT
ap-1666	98	1	+	+	CCONJ
ap-1666	99	1	diss(z	diss(z	NOUN
ap-1666	99	2	;	;	PUNCT
ap-1666	99	3	[	[	X
ap-1666	99	4	0	0	NUM
ap-1666	99	5	,	,	PUNCT
ap-1666	99	6	t	t	PROPN
ap-1666	99	7	]	]	PUNCT
ap-1666	99	8	)	)	PUNCT
ap-1666	99	9	=	=	SYM
ap-1666	100	1	i(0	i(0	PROPN
ap-1666	100	2	,	,	PUNCT
ap-1666	100	3	y(0	y(0	PROPN
ap-1666	100	4	)	)	PUNCT
ap-1666	100	5	,	,	PUNCT
ap-1666	100	6	z(0	z(0	NOUN
ap-1666	100	7	)	)	PUNCT
ap-1666	100	8	)	)	PUNCT
ap-1666	101	1	+	+	CCONJ
ap-1666	101	2	∫	∫	PROPN
ap-1666	101	3	t	t	PROPN
ap-1666	101	4	0	0	NUM
ap-1666	101	5	l̇(s	l̇(s	PROPN
ap-1666	101	6	,	,	PUNCT
ap-1666	101	7	y(s	y(s	PROPN
ap-1666	101	8	)	)	PUNCT
ap-1666	101	9	)	)	PUNCT
ap-1666	102	1	ds	ds	PROPN
ap-1666	102	2	.	.	PUNCT
ap-1666	103	1	we	we	PRON
ap-1666	103	2	can	can	AUX
ap-1666	103	3	also	also	ADV
ap-1666	103	4	consider	consider	VERB
ap-1666	103	5	a	a	DET
ap-1666	103	6	more	more	ADV
ap-1666	103	7	general	general	ADJ
ap-1666	103	8	form	form	NOUN
ap-1666	103	9	of	of	ADP
ap-1666	103	10	δ	δ	PROPN
ap-1666	103	11	which	which	PRON
ap-1666	103	12	can	can	AUX
ap-1666	103	13	also	also	ADV
ap-1666	103	14	depend	depend	VERB
ap-1666	103	15	on	on	ADP
ap-1666	103	16	(	(	PUNCT
ap-1666	103	17	x	x	X
ap-1666	103	18	,	,	PUNCT
ap-1666	103	19	z	z	NOUN
ap-1666	103	20	)	)	PUNCT
ap-1666	103	21	,	,	PUNCT
ap-1666	103	22	i.e.	i.e.	X
ap-1666	103	23	δ	δ	NOUN
ap-1666	103	24	:	:	PUNCT
ap-1666	103	25	=	=	SYM
ap-1666	103	26	δ(x	δ(x	PROPN
ap-1666	103	27	,	,	PUNCT
ap-1666	103	28	z	z	PROPN
ap-1666	103	29	,	,	PUNCT
ap-1666	103	30	ż	ż	NOUN
ap-1666	103	31	)	)	PUNCT
ap-1666	103	32	.	.	PUNCT
ap-1666	104	1	typically	typically	ADV
ap-1666	104	2	,	,	PUNCT
ap-1666	104	3	however	however	ADV
ap-1666	104	4	,	,	PUNCT
ap-1666	104	5	we	we	PRON
ap-1666	104	6	do	do	AUX
ap-1666	104	7	not	not	PART
ap-1666	104	8	have	have	VERB
ap-1666	104	9	enough	enough	ADJ
ap-1666	104	10	smoothness	smoothness	NOUN
ap-1666	104	11	in	in	ADP
ap-1666	104	12	the	the	DET
ap-1666	104	13	internal	internal	ADJ
ap-1666	104	14	variable	variable	NOUN
ap-1666	104	15	to	to	PART
ap-1666	104	16	compute	compute	VERB
ap-1666	104	17	the	the	DET
ap-1666	104	18	time	time	NOUN
ap-1666	104	19	derivative	derivative	ADJ
ap-1666	104	20	on	on	ADP
ap-1666	104	21	the	the	DET
ap-1666	104	22	right	right	ADJ
ap-1666	104	23	-	-	PUNCT
ap-1666	104	24	hand	hand	NOUN
ap-1666	104	25	side	side	NOUN
ap-1666	104	26	of	of	ADP
ap-1666	104	27	(	(	PUNCT
ap-1666	104	28	13	13	NUM
ap-1666	104	29	)	)	PUNCT
ap-1666	104	30	.	.	PUNCT
ap-1666	105	1	following	follow	VERB
ap-1666	105	2	mielke	mielke	PROPN
ap-1666	106	1	[	[	X
ap-1666	106	2	24	24	NUM
ap-1666	106	3	]	]	PUNCT
ap-1666	106	4	,	,	PUNCT
ap-1666	106	5	we	we	PRON
ap-1666	106	6	define	define	VERB
ap-1666	106	7	the	the	DET
ap-1666	106	8	dissipation	dissipation	NOUN
ap-1666	106	9	distance	distance	NOUN
ap-1666	106	10	between	between	ADP
ap-1666	106	11	two	two	NUM
ap-1666	106	12	values	value	NOUN
ap-1666	106	13	of	of	ADP
ap-1666	106	14	internal	internal	ADJ
ap-1666	106	15	variables	variable	NOUN
ap-1666	106	16	z0	z0	NOUN
ap-1666	106	17	,	,	PUNCT
ap-1666	106	18	z1	z1	PROPN
ap-1666	106	19	∈	∈	PROPN
ap-1666	106	20	z	z	NOUN
ap-1666	106	21	as	as	ADP
ap-1666	106	22	d(x	d(x	PROPN
ap-1666	106	23	,	,	PUNCT
ap-1666	106	24	z0	z0	NOUN
ap-1666	106	25	,	,	PUNCT
ap-1666	106	26	z1	z1	PROPN
ap-1666	106	27	)	)	PUNCT
ap-1666	106	28	:	:	PUNCT
ap-1666	107	1	=	=	SYM
ap-1666	107	2	inf	inf	PROPN
ap-1666	107	3	z	z	PROPN
ap-1666	107	4	{	{	PUNCT
ap-1666	107	5	∫	∫	PROPN
ap-1666	107	6	1	1	NUM
ap-1666	107	7	0	0	NUM
ap-1666	107	8	δ(x	δ(x	PROPN
ap-1666	107	9	,	,	PUNCT
ap-1666	107	10	z(s	z(s	PROPN
ap-1666	107	11	)	)	PUNCT
ap-1666	107	12	,	,	PUNCT
ap-1666	107	13	ż(s	ż(s	PROPN
ap-1666	107	14	)	)	PUNCT
ap-1666	107	15	)	)	PUNCT
ap-1666	107	16	ds	ds	ADJ
ap-1666	107	17	;	;	PUNCT
ap-1666	107	18	z(0	z(0	X
ap-1666	107	19	)	)	PUNCT
ap-1666	107	20	=	=	SYM
ap-1666	107	21	z0	z0	PROPN
ap-1666	107	22	,	,	PUNCT
ap-1666	107	23	z(1	z(1	PROPN
ap-1666	107	24	)	)	PUNCT
ap-1666	107	25	=	=	SYM
ap-1666	107	26	z1	z1	PROPN
ap-1666	107	27	}	}	PUNCT
ap-1666	107	28	,	,	PUNCT
ap-1666	107	29	(	(	PUNCT
ap-1666	107	30	14	14	NUM
ap-1666	107	31	)	)	PUNCT
ap-1666	107	32	where	where	SCONJ
ap-1666	107	33	z	z	PROPN
ap-1666	107	34	∈	∈	PROPN
ap-1666	107	35	c1([0	c1([0	PROPN
ap-1666	107	36	,	,	PUNCT
ap-1666	107	37	1];z	1];z	NUM
ap-1666	107	38	)	)	PUNCT
ap-1666	107	39	,	,	PUNCT
ap-1666	107	40	and	and	CCONJ
ap-1666	107	41	set	set	VERB
ap-1666	107	42	d(z1	d(z1	NOUN
ap-1666	107	43	,	,	PUNCT
ap-1666	107	44	z2	z2	NOUN
ap-1666	107	45	)	)	PUNCT
ap-1666	107	46	=	=	SYM
ap-1666	108	1	∫	∫	PROPN
ap-1666	109	1	ω	ω	PROPN
ap-1666	109	2	d	d	X
ap-1666	109	3	(	(	PUNCT
ap-1666	109	4	x	x	X
ap-1666	109	5	,	,	PUNCT
ap-1666	109	6	z1(x	z1(x	NUM
ap-1666	109	7	)	)	PUNCT
ap-1666	109	8	,	,	PUNCT
ap-1666	109	9	z2(x	z2(x	NOUN
ap-1666	109	10	)	)	PUNCT
ap-1666	109	11	)	)	PUNCT
ap-1666	109	12	dx	dx	PROPN
ap-1666	109	13	,	,	PUNCT
ap-1666	109	14	(	(	PUNCT
ap-1666	109	15	15	15	NUM
ap-1666	109	16	)	)	PUNCT
ap-1666	109	17	where	where	SCONJ
ap-1666	109	18	z1	z1	ADJ
ap-1666	109	19	,	,	PUNCT
ap-1666	109	20	z2	z2	PROPN
ap-1666	109	21	∈	∈	PROPN
ap-1666	109	22	z	z	NOUN
ap-1666	109	23	:	:	PUNCT
ap-1666	109	24	=	=	SYM
ap-1666	109	25	{	{	PUNCT
ap-1666	109	26	z	z	NOUN
ap-1666	109	27	:	:	PUNCT
ap-1666	109	28	ω	ω	PROPN
ap-1666	109	29	→	→	SYM
ap-1666	109	30	rm	rm	PROPN
ap-1666	109	31	;	;	PUNCT
ap-1666	109	32	z(x	z(x	NUM
ap-1666	109	33	)	)	PUNCT
ap-1666	109	34	∈	∈	PROPN
ap-1666	109	35	z	z	PROPN
ap-1666	109	36	a.e	a.e	PROPN
ap-1666	109	37	.	.	PROPN
ap-1666	109	38	in	in	ADP
ap-1666	109	39	ω	ω	NUM
ap-1666	109	40	}	}	PUNCT
ap-1666	109	41	.	.	PUNCT
ap-1666	110	1	we	we	PRON
ap-1666	110	2	assume	assume	VERB
ap-1666	110	3	that	that	SCONJ
ap-1666	110	4	z	z	NOUN
ap-1666	110	5	is	be	AUX
ap-1666	110	6	equipped	equip	VERB
ap-1666	110	7	with	with	ADP
ap-1666	110	8	strong	strong	ADJ
ap-1666	110	9	and	and	CCONJ
ap-1666	110	10	weak	weak	ADJ
ap-1666	110	11	topologies	topology	NOUN
ap-1666	110	12	which	which	PRON
ap-1666	110	13	define	define	VERB
ap-1666	110	14	the	the	DET
ap-1666	110	15	notions	notion	NOUN
ap-1666	110	16	of	of	ADP
ap-1666	110	17	convergence	convergence	NOUN
ap-1666	110	18	used	use	VERB
ap-1666	110	19	below	below	ADV
ap-1666	110	20	.	.	PUNCT
ap-1666	111	1	following	follow	VERB
ap-1666	111	2	[	[	X
ap-1666	111	3	11	11	NUM
ap-1666	111	4	,	,	PUNCT
ap-1666	111	5	22	22	NUM
ap-1666	111	6	]	]	PUNCT
ap-1666	111	7	,	,	PUNCT
ap-1666	111	8	we	we	PRON
ap-1666	111	9	impose	impose	VERB
ap-1666	111	10	the	the	DET
ap-1666	111	11	following	follow	VERB
ap-1666	111	12	assumptions	assumption	NOUN
ap-1666	111	13	on	on	ADP
ap-1666	111	14	d	d	NOUN
ap-1666	111	15	:	:	PUNCT
ap-1666	111	16	(	(	PUNCT
ap-1666	111	17	i	i	NOUN
ap-1666	111	18	)	)	PUNCT
ap-1666	111	19	weak	weak	ADJ
ap-1666	111	20	lower	low	ADJ
ap-1666	111	21	semicontinuity	semicontinuity	NOUN
ap-1666	111	22	:	:	PUNCT
ap-1666	111	23	d(z	d(z	PROPN
ap-1666	111	24	,	,	PUNCT
ap-1666	111	25	z̃	z̃	PROPN
ap-1666	111	26	)	)	PUNCT
ap-1666	111	27	≤	≤	NOUN
ap-1666	111	28	lim	lim	PROPN
ap-1666	111	29	inf	inf	PROPN
ap-1666	111	30	k→∞	k→∞	PROPN
ap-1666	111	31	d(zk	d(zk	PROPN
ap-1666	111	32	,	,	PUNCT
ap-1666	111	33	z̃k	z̃k	NOUN
ap-1666	111	34	)	)	PUNCT
ap-1666	111	35	,	,	PUNCT
ap-1666	111	36	(	(	PUNCT
ap-1666	111	37	16	16	NUM
ap-1666	111	38	)	)	PUNCT
ap-1666	111	39	whenever	whenever	SCONJ
ap-1666	111	40	zk	zk	PROPN
ap-1666	111	41	⇀	⇀	PROPN
ap-1666	111	42	z	z	PROPN
ap-1666	111	43	and	and	CCONJ
ap-1666	111	44	z̃k	z̃k	ADP
ap-1666	111	45	⇀	⇀	PROPN
ap-1666	111	46	z̃.	z̃.	PROPN
ap-1666	111	47	(	(	PUNCT
ap-1666	111	48	ii	ii	NOUN
ap-1666	111	49	)	)	PUNCT
ap-1666	111	50	positivity	positivity	NOUN
ap-1666	111	51	:	:	PUNCT
ap-1666	111	52	if	if	SCONJ
ap-1666	111	53	{	{	PUNCT
ap-1666	111	54	zk	zk	PROPN
ap-1666	111	55	}	}	PUNCT
ap-1666	111	56	⊂	⊂	PROPN
ap-1666	111	57	z	z	PROPN
ap-1666	111	58	is	be	AUX
ap-1666	111	59	bounded	bound	VERB
ap-1666	111	60	and	and	CCONJ
ap-1666	111	61	at	at	ADP
ap-1666	111	62	the	the	DET
ap-1666	111	63	same	same	ADJ
ap-1666	111	64	time	time	NOUN
ap-1666	111	65	min{d(zk	min{d(zk	PROPN
ap-1666	111	66	,	,	PUNCT
ap-1666	111	67	z),d(z	z),d(z	NUM
ap-1666	111	68	,	,	PUNCT
ap-1666	111	69	zk	zk	PROPN
ap-1666	111	70	)	)	PUNCT
ap-1666	111	71	}	}	PUNCT
ap-1666	111	72	→	→	SYM
ap-1666	111	73	0	0	NUM
ap-1666	111	74	then	then	ADV
ap-1666	111	75	zk	zk	PROPN
ap-1666	111	76	⇀	⇀	PROPN
ap-1666	111	77	z.	z.	PROPN
ap-1666	111	78	(	(	PUNCT
ap-1666	111	79	17	17	NUM
ap-1666	111	80	)	)	PUNCT
ap-1666	111	81	2.1	2.1	NUM
ap-1666	111	82	energetic	energetic	ADJ
ap-1666	111	83	solution	solution	NOUN
ap-1666	111	84	suppose	suppose	VERB
ap-1666	111	85	that	that	SCONJ
ap-1666	111	86	we	we	PRON
ap-1666	111	87	look	look	VERB
ap-1666	111	88	for	for	ADP
ap-1666	111	89	the	the	DET
ap-1666	111	90	time	time	NOUN
ap-1666	111	91	evolution	evolution	NOUN
ap-1666	111	92	of	of	ADP
ap-1666	111	93	y(t	y(t	PROPN
ap-1666	111	94	)	)	PUNCT
ap-1666	112	1	∈	∈	PROPN
ap-1666	112	2	y	y	PROPN
ap-1666	112	3	⊂	⊂	PROPN
ap-1666	112	4	{	{	PUNCT
ap-1666	112	5	y	y	NOUN
ap-1666	112	6	:	:	PUNCT
ap-1666	112	7	ω	ω	PROPN
ap-1666	112	8	→	→	SYM
ap-1666	112	9	rn	rn	PROPN
ap-1666	112	10	}	}	PUNCT
ap-1666	112	11	and	and	CCONJ
ap-1666	112	12	z(t	z(t	NOUN
ap-1666	112	13	)	)	PUNCT
ap-1666	112	14	∈	∈	PROPN
ap-1666	112	15	z	z	NOUN
ap-1666	112	16	during	during	ADP
ap-1666	112	17	the	the	DET
ap-1666	112	18	time	time	NOUN
ap-1666	112	19	interval	interval	NOUN
ap-1666	112	20	[	[	X
ap-1666	112	21	0	0	NUM
ap-1666	112	22	,	,	PUNCT
ap-1666	112	23	t	t	X
ap-1666	112	24	]	]	PUNCT
ap-1666	112	25	.	.	PUNCT
ap-1666	113	1	the	the	DET
ap-1666	113	2	following	follow	VERB
ap-1666	113	3	two	two	NUM
ap-1666	113	4	properties	property	NOUN
ap-1666	113	5	are	be	AUX
ap-1666	113	6	the	the	DET
ap-1666	113	7	key	key	ADJ
ap-1666	113	8	ingredients	ingredient	NOUN
ap-1666	113	9	of	of	ADP
ap-1666	113	10	the	the	DET
ap-1666	113	11	so	so	ADV
ap-1666	113	12	-	-	PUNCT
ap-1666	113	13	called	call	VERB
ap-1666	113	14	energetic	energetic	ADJ
ap-1666	113	15	solution	solution	NOUN
ap-1666	113	16	due	due	ADP
ap-1666	113	17	to	to	ADP
ap-1666	113	18	mielke	mielke	ADJ
ap-1666	113	19	and	and	CCONJ
ap-1666	113	20	theil	theil	PROPN
ap-1666	113	21	[	[	X
ap-1666	113	22	27	27	NUM
ap-1666	113	23	,	,	PUNCT
ap-1666	113	24	28	28	NUM
ap-1666	113	25	]	]	PUNCT
ap-1666	113	26	.	.	PUNCT
ap-1666	114	1	(	(	PUNCT
ap-1666	114	2	i	i	NOUN
ap-1666	114	3	)	)	PUNCT
ap-1666	114	4	stability	stability	NOUN
ap-1666	114	5	inequality	inequality	NOUN
ap-1666	114	6	:	:	PUNCT
ap-1666	114	7	∀t	∀t	PROPN
ap-1666	114	8	∈	∈	X
ap-1666	115	1	[	[	X
ap-1666	115	2	0	0	NUM
ap-1666	115	3	,	,	PUNCT
ap-1666	115	4	t	t	X
ap-1666	115	5	]	]	PUNCT
ap-1666	115	6	,	,	PUNCT
ap-1666	115	7	z̃	z̃	PROPN
ap-1666	115	8	∈	∈	PROPN
ap-1666	115	9	z	z	PROPN
ap-1666	115	10	,	,	PUNCT
ap-1666	115	11	y	y	PROPN
ap-1666	115	12	∈	∈	PROPN
ap-1666	116	1	y	y	PROPN
ap-1666	116	2	:	:	PUNCT
ap-1666	116	3	i	i	PRON
ap-1666	116	4	(	(	PUNCT
ap-1666	116	5	t	t	PROPN
ap-1666	116	6	,	,	PUNCT
ap-1666	116	7	y(t	y(t	PROPN
ap-1666	116	8	)	)	PUNCT
ap-1666	116	9	,	,	PUNCT
ap-1666	116	10	z(t	z(t	NOUN
ap-1666	116	11	)	)	PUNCT
ap-1666	116	12	)	)	PUNCT
ap-1666	116	13	≤	≤	PUNCT
ap-1666	117	1	i	i	PRON
ap-1666	117	2	(	(	PUNCT
ap-1666	117	3	t	t	PROPN
ap-1666	117	4	,	,	PUNCT
ap-1666	117	5	ỹ	ỹ	PROPN
ap-1666	117	6	,	,	PUNCT
ap-1666	117	7	z̃	z̃	PROPN
ap-1666	117	8	)	)	PUNCT
ap-1666	118	1	+	+	PUNCT
ap-1666	118	2	d	d	X
ap-1666	118	3	(	(	PUNCT
ap-1666	118	4	z(t	z(t	NOUN
ap-1666	118	5	)	)	PUNCT
ap-1666	118	6	,	,	PUNCT
ap-1666	118	7	z̃	z̃	PROPN
ap-1666	118	8	)	)	PUNCT
ap-1666	118	9	(	(	PUNCT
ap-1666	118	10	18	18	NUM
ap-1666	118	11	)	)	PUNCT
ap-1666	118	12	(	(	PUNCT
ap-1666	118	13	ii	ii	NOUN
ap-1666	118	14	)	)	PUNCT
ap-1666	118	15	energy	energy	NOUN
ap-1666	118	16	balance	balance	NOUN
ap-1666	118	17	:	:	PUNCT
ap-1666	118	18	∀t	∀t	PROPN
ap-1666	118	19	,	,	PUNCT
ap-1666	118	20	0	0	NUM
ap-1666	118	21	≤	≤	NUM
ap-1666	118	22	t	t	PROPN
ap-1666	118	23	≤	≤	NUM
ap-1666	118	24	t	t	PROPN
ap-1666	119	1	i	i	PRON
ap-1666	119	2	(	(	PUNCT
ap-1666	119	3	t	t	PROPN
ap-1666	119	4	,	,	PUNCT
ap-1666	119	5	y(t	y(t	PROPN
ap-1666	119	6	)	)	PUNCT
ap-1666	119	7	,	,	PUNCT
ap-1666	119	8	z(t	z(t	NOUN
ap-1666	119	9	)	)	PUNCT
ap-1666	119	10	)	)	PUNCT
ap-1666	120	1	+	+	CCONJ
ap-1666	120	2	var	var	NOUN
ap-1666	120	3	(	(	PUNCT
ap-1666	120	4	d	d	NOUN
ap-1666	120	5	,	,	PUNCT
ap-1666	120	6	z	z	NOUN
ap-1666	120	7	;	;	PUNCT
ap-1666	120	8	[	[	X
ap-1666	120	9	0	0	NUM
ap-1666	120	10	,	,	PUNCT
ap-1666	120	11	t	t	PROPN
ap-1666	120	12	]	]	PUNCT
ap-1666	120	13	)	)	PUNCT
ap-1666	121	1	=	=	PUNCT
ap-1666	121	2	i	i	PRON
ap-1666	121	3	(	(	PUNCT
ap-1666	121	4	s	s	PROPN
ap-1666	121	5	,	,	PUNCT
ap-1666	121	6	y(0	y(0	PROPN
ap-1666	121	7	)	)	PUNCT
ap-1666	121	8	,	,	PUNCT
ap-1666	121	9	z(0	z(0	NOUN
ap-1666	121	10	)	)	PUNCT
ap-1666	121	11	)	)	PUNCT
ap-1666	122	1	+	+	CCONJ
ap-1666	123	1	∫	∫	PROPN
ap-1666	123	2	t	t	PROPN
ap-1666	123	3	0	0	NUM
ap-1666	124	1	l̇	l̇	PROPN
ap-1666	124	2	(	(	PUNCT
ap-1666	124	3	ξ	ξ	PROPN
ap-1666	124	4	,	,	PUNCT
ap-1666	124	5	y(ξ	y(ξ	PROPN
ap-1666	124	6	)	)	PUNCT
ap-1666	124	7	)	)	PUNCT
ap-1666	125	1	dξ	dξ	PROPN
ap-1666	125	2	,	,	PUNCT
ap-1666	125	3	(	(	PUNCT
ap-1666	125	4	19	19	NUM
ap-1666	125	5	)	)	PUNCT
ap-1666	125	6	where	where	SCONJ
ap-1666	125	7	var	var	NOUN
ap-1666	125	8	(	(	PUNCT
ap-1666	125	9	d	d	NOUN
ap-1666	125	10	,	,	PUNCT
ap-1666	125	11	z	z	NOUN
ap-1666	125	12	;	;	PUNCT
ap-1666	125	13	[	[	X
ap-1666	125	14	s	s	X
ap-1666	125	15	,	,	PUNCT
ap-1666	125	16	t	t	PROPN
ap-1666	125	17	]	]	PUNCT
ap-1666	125	18	)	)	PUNCT
ap-1666	125	19	:	:	PUNCT
ap-1666	125	20	=	=	SYM
ap-1666	125	21	sup	sup	INTJ
ap-1666	125	22	{	{	PUNCT
ap-1666	125	23	n∑	n∑	NOUN
ap-1666	125	24	i=1	i=1	PROPN
ap-1666	126	1	d	d	X
ap-1666	126	2	(	(	PUNCT
ap-1666	126	3	z(ti	z(ti	PROPN
ap-1666	126	4	)	)	PUNCT
ap-1666	126	5	,	,	PUNCT
ap-1666	126	6	z(ti−1	z(ti−1	PROPN
ap-1666	126	7	)	)	PUNCT
ap-1666	126	8	)	)	PUNCT
ap-1666	126	9	;	;	PUNCT
ap-1666	126	10	{	{	PUNCT
ap-1666	126	11	ti	ti	NOUN
ap-1666	126	12	}	}	PUNCT
ap-1666	126	13	partition	partition	NOUN
ap-1666	126	14	of	of	ADP
ap-1666	126	15	[	[	X
ap-1666	126	16	s	s	X
ap-1666	126	17	,	,	PUNCT
ap-1666	126	18	t	t	PROPN
ap-1666	126	19	]	]	PUNCT
ap-1666	126	20	}	}	PUNCT
ap-1666	126	21	.	.	PUNCT
ap-1666	127	1	definition	definition	NOUN
ap-1666	127	2	2.2	2.2	NUM
ap-1666	127	3	.	.	PUNCT
ap-1666	128	1	the	the	DET
ap-1666	128	2	mapping	mapping	NOUN
ap-1666	128	3	t	t	PROPN
ap-1666	128	4	7→	7→	NUM
ap-1666	128	5	(	(	PUNCT
ap-1666	128	6	y(t	y(t	PROPN
ap-1666	128	7	)	)	PUNCT
ap-1666	128	8	,	,	PUNCT
ap-1666	128	9	z(t	z(t	PROPN
ap-1666	128	10	)	)	PUNCT
ap-1666	128	11	)	)	PUNCT
ap-1666	129	1	∈	∈	NOUN
ap-1666	129	2	y×	y×	X
ap-1666	129	3	z	z	NOUN
ap-1666	129	4	is	be	AUX
ap-1666	129	5	an	an	DET
ap-1666	129	6	energetic	energetic	ADJ
ap-1666	129	7	solution	solution	NOUN
ap-1666	129	8	to	to	ADP
ap-1666	129	9	the	the	DET
ap-1666	129	10	problem	problem	NOUN
ap-1666	129	11	(	(	PUNCT
ap-1666	129	12	i	i	PROPN
ap-1666	129	13	,	,	PUNCT
ap-1666	129	14	δ	δ	PROPN
ap-1666	129	15	,	,	PUNCT
ap-1666	129	16	l	l	NOUN
ap-1666	129	17	)	)	PUNCT
ap-1666	129	18	if	if	SCONJ
ap-1666	129	19	the	the	DET
ap-1666	129	20	stability	stability	NOUN
ap-1666	129	21	inequality	inequality	NOUN
ap-1666	129	22	and	and	CCONJ
ap-1666	129	23	the	the	DET
ap-1666	129	24	energy	energy	NOUN
ap-1666	129	25	balance	balance	NOUN
ap-1666	129	26	are	be	AUX
ap-1666	129	27	satisfied	satisfied	ADJ
ap-1666	129	28	.	.	PUNCT
ap-1666	130	1	remark	remark	VERB
ap-1666	130	2	2.3	2.3	NUM
ap-1666	130	3	.	.	PUNCT
ap-1666	131	1	note	note	VERB
ap-1666	131	2	that	that	SCONJ
ap-1666	131	3	the	the	DET
ap-1666	131	4	stability	stability	NOUN
ap-1666	131	5	inequality	inequality	NOUN
ap-1666	131	6	(	(	PUNCT
ap-1666	131	7	i	i	NOUN
ap-1666	131	8	)	)	PUNCT
ap-1666	131	9	can	can	AUX
ap-1666	131	10	be	be	AUX
ap-1666	131	11	written	write	VERB
ap-1666	131	12	in	in	ADP
ap-1666	131	13	the	the	DET
ap-1666	131	14	form	form	NOUN
ap-1666	131	15	∀t	∀t	X
ap-1666	131	16	∈	∈	PROPN
ap-1666	132	1	[	[	X
ap-1666	132	2	0	0	NUM
ap-1666	132	3	,	,	PUNCT
ap-1666	132	4	t	t	X
ap-1666	132	5	]	]	PUNCT
ap-1666	132	6	,	,	PUNCT
ap-1666	132	7	z̃	z̃	PROPN
ap-1666	132	8	∈	∈	PROPN
ap-1666	132	9	z	z	NOUN
ap-1666	132	10	,	,	PUNCT
ap-1666	132	11	ỹ	ỹ	PROPN
ap-1666	132	12	∈	∈	PROPN
ap-1666	133	1	y	y	NOUN
ap-1666	133	2	i	i	PRON
ap-1666	133	3	(	(	PUNCT
ap-1666	133	4	t	t	PROPN
ap-1666	133	5	,	,	PUNCT
ap-1666	133	6	y(t	y(t	PROPN
ap-1666	133	7	)	)	PUNCT
ap-1666	133	8	,	,	PUNCT
ap-1666	133	9	z(t	z(t	NOUN
ap-1666	133	10	)	)	PUNCT
ap-1666	133	11	)	)	PUNCT
ap-1666	134	1	+	+	PUNCT
ap-1666	134	2	d	d	X
ap-1666	134	3	(	(	PUNCT
ap-1666	134	4	z(t	z(t	NOUN
ap-1666	134	5	)	)	PUNCT
ap-1666	134	6	,	,	PUNCT
ap-1666	134	7	z(t	z(t	NOUN
ap-1666	134	8	)	)	PUNCT
ap-1666	134	9	)	)	PUNCT
ap-1666	134	10	≤	≤	PUNCT
ap-1666	135	1	i	i	PRON
ap-1666	135	2	(	(	PUNCT
ap-1666	135	3	t	t	PROPN
ap-1666	135	4	,	,	PUNCT
ap-1666	135	5	ỹ	ỹ	PROPN
ap-1666	135	6	,	,	PUNCT
ap-1666	135	7	z̃	z̃	PROPN
ap-1666	135	8	)	)	PUNCT
ap-1666	136	1	+	+	PUNCT
ap-1666	136	2	d	d	X
ap-1666	136	3	(	(	PUNCT
ap-1666	136	4	z(t	z(t	NOUN
ap-1666	136	5	)	)	PUNCT
ap-1666	136	6	,	,	PUNCT
ap-1666	136	7	z̃	z̃	PROPN
ap-1666	136	8	)	)	PUNCT
ap-1666	136	9	,	,	PUNCT
ap-1666	136	10	which	which	PRON
ap-1666	136	11	means	mean	VERB
ap-1666	136	12	that	that	SCONJ
ap-1666	136	13	y(t	y(t	PROPN
ap-1666	136	14	)	)	PUNCT
ap-1666	136	15	,	,	PUNCT
ap-1666	136	16	z(t	z(t	NOUN
ap-1666	136	17	)	)	PUNCT
ap-1666	136	18	always	always	ADV
ap-1666	136	19	minimizes	minimize	VERB
ap-1666	136	20	(	(	PUNCT
ap-1666	136	21	ỹ	ỹ	PROPN
ap-1666	136	22	,	,	PUNCT
ap-1666	136	23	z̃	z̃	PROPN
ap-1666	136	24	)	)	PUNCT
ap-1666	136	25	7→	7→	NUM
ap-1666	136	26	i(t	i(t	NOUN
ap-1666	136	27	,	,	PUNCT
ap-1666	136	28	ỹ	ỹ	PROPN
ap-1666	136	29	,	,	PUNCT
ap-1666	136	30	z̃)+d(z(t	z̃)+d(z(t	NOUN
ap-1666	136	31	)	)	PUNCT
ap-1666	136	32	,	,	PUNCT
ap-1666	136	33	z̃	z̃	PROPN
ap-1666	136	34	)	)	PUNCT
ap-1666	136	35	.	.	PUNCT
ap-1666	137	1	this	this	PRON
ap-1666	137	2	means	mean	VERB
ap-1666	137	3	that	that	SCONJ
ap-1666	137	4	the	the	DET
ap-1666	137	5	equilibrium	equilibrium	NOUN
ap-1666	137	6	configurations	configuration	NOUN
ap-1666	137	7	are	be	AUX
ap-1666	137	8	characterized	characterize	VERB
ap-1666	137	9	by	by	ADP
ap-1666	137	10	energetic	energetic	ADJ
ap-1666	137	11	minima	minima	NOUN
ap-1666	137	12	.	.	PUNCT
ap-1666	138	1	contrary	contrary	ADJ
ap-1666	138	2	to	to	ADP
ap-1666	138	3	elasticity	elasticity	NOUN
ap-1666	138	4	theory	theory	NOUN
ap-1666	138	5	,	,	PUNCT
ap-1666	138	6	the	the	DET
ap-1666	138	7	minimized	minimized	ADJ
ap-1666	138	8	energy	energy	NOUN
ap-1666	138	9	is	be	AUX
ap-1666	138	10	not	not	PART
ap-1666	138	11	only	only	ADV
ap-1666	138	12	the	the	DET
ap-1666	138	13	overall	overall	ADJ
ap-1666	138	14	elastic	elastic	ADJ
ap-1666	138	15	energy	energy	NOUN
ap-1666	138	16	described	describe	VERB
ap-1666	138	17	by	by	ADP
ap-1666	138	18	i	i	PRON
ap-1666	138	19	but	but	CCONJ
ap-1666	138	20	the	the	DET
ap-1666	138	21	dissipated	dissipate	VERB
ap-1666	138	22	energy	energy	NOUN
ap-1666	138	23	is	be	AUX
ap-1666	138	24	added	add	VERB
ap-1666	138	25	.	.	PUNCT
ap-1666	139	1	it	it	PRON
ap-1666	139	2	is	be	AUX
ap-1666	139	3	convenient	convenient	ADJ
ap-1666	139	4	to	to	PART
ap-1666	139	5	put	put	VERB
ap-1666	139	6	q	q	NOUN
ap-1666	139	7	:	:	PUNCT
ap-1666	139	8	=	=	SYM
ap-1666	139	9	y	y	NUM
ap-1666	139	10	×	×	PROPN
ap-1666	139	11	z	z	NOUN
ap-1666	139	12	and	and	CCONJ
ap-1666	139	13	to	to	PART
ap-1666	139	14	set	set	VERB
ap-1666	139	15	q	q	NOUN
ap-1666	139	16	:	:	PUNCT
ap-1666	139	17	=	=	SYM
ap-1666	139	18	(	(	PUNCT
ap-1666	139	19	y	y	PROPN
ap-1666	139	20	,	,	PUNCT
ap-1666	139	21	z	z	NOUN
ap-1666	139	22	)	)	PUNCT
ap-1666	139	23	.	.	PUNCT
ap-1666	140	1	moreover	moreover	ADV
ap-1666	140	2	,	,	PUNCT
ap-1666	140	3	we	we	PRON
ap-1666	140	4	define	define	VERB
ap-1666	140	5	the	the	DET
ap-1666	140	6	set	set	NOUN
ap-1666	140	7	of	of	ADP
ap-1666	140	8	stable	stable	ADJ
ap-1666	140	9	states	state	NOUN
ap-1666	140	10	at	at	ADP
ap-1666	140	11	time	time	NOUN
ap-1666	140	12	t	t	PROPN
ap-1666	140	13	as	as	ADP
ap-1666	140	14	s(t	s(t	PROPN
ap-1666	140	15	)	)	PUNCT
ap-1666	140	16	:	:	PUNCT
ap-1666	141	1	=	=	X
ap-1666	141	2	{	{	PUNCT
ap-1666	141	3	q	q	PUNCT
ap-1666	141	4	∈	∈	PROPN
ap-1666	141	5	q	q	NOUN
ap-1666	141	6	;	;	PUNCT
ap-1666	141	7	∀q̃	∀q̃	NOUN
ap-1666	141	8	∈	∈	PROPN
ap-1666	141	9	q	q	X
ap-1666	141	10	:	:	PUNCT
ap-1666	141	11	i(t	i(t	NOUN
ap-1666	141	12	,	,	PUNCT
ap-1666	141	13	q	q	NOUN
ap-1666	141	14	)	)	PUNCT
ap-1666	141	15	≤	≤	NUM
ap-1666	141	16	i(t	i(t	NOUN
ap-1666	141	17	,	,	PUNCT
ap-1666	141	18	q̃	q̃	PROPN
ap-1666	141	19	)	)	PUNCT
ap-1666	141	20	+	+	NOUN
ap-1666	141	21	d(q	d(q	PROPN
ap-1666	141	22	,	,	PUNCT
ap-1666	141	23	q̃	q̃	PROPN
ap-1666	141	24	)	)	PUNCT
ap-1666	141	25	}	}	PUNCT
ap-1666	141	26	(	(	PUNCT
ap-1666	141	27	20	20	NUM
ap-1666	141	28	)	)	PUNCT
ap-1666	141	29	and	and	CCONJ
ap-1666	141	30	s[0,t	s[0,t	NOUN
ap-1666	141	31	]	]	PUNCT
ap-1666	141	32	:	:	PUNCT
ap-1666	141	33	=	=	SYM
ap-1666	142	1	⋃	⋃	PROPN
ap-1666	142	2	t∈[0,t	t∈[0,t	X
ap-1666	142	3	]	]	X
ap-1666	142	4	{	{	PUNCT
ap-1666	142	5	t	t	PROPN
ap-1666	142	6	}	}	PUNCT
ap-1666	142	7	×	×	NOUN
ap-1666	142	8	s(t	s(t	PROPN
ap-1666	142	9	)	)	PUNCT
ap-1666	142	10	.	.	PUNCT
ap-1666	143	1	(	(	PUNCT
ap-1666	143	2	21	21	NUM
ap-1666	143	3	)	)	PUNCT
ap-1666	143	4	moreover	moreover	ADV
ap-1666	143	5	,	,	PUNCT
ap-1666	143	6	a	a	DET
ap-1666	143	7	sequence	sequence	NOUN
ap-1666	143	8	{	{	PUNCT
ap-1666	143	9	(	(	PUNCT
ap-1666	143	10	tk	tk	PROPN
ap-1666	143	11	,	,	PUNCT
ap-1666	143	12	qk)}k∈n	qk)}k∈n	ADV
ap-1666	143	13	is	be	AUX
ap-1666	143	14	called	call	VERB
ap-1666	143	15	stable	stable	ADJ
ap-1666	143	16	if	if	SCONJ
ap-1666	143	17	qk	qk	VERB
ap-1666	143	18	∈	∈	PROPN
ap-1666	143	19	s(tk	s(tk	NOUN
ap-1666	143	20	)	)	PUNCT
ap-1666	143	21	.	.	PUNCT
ap-1666	144	1	11	11	NUM
ap-1666	144	2	acta	acta	PROPN
ap-1666	144	3	polytechnica	polytechnica	PROPN
ap-1666	144	4	vol	vol	NOUN
ap-1666	144	5	.	.	PROPN
ap-1666	145	1	52	52	NUM
ap-1666	145	2	no	no	NOUN
ap-1666	145	3	.	.	PUNCT
ap-1666	146	1	6/2012	6/2012	NUM
ap-1666	146	2	3	3	NUM
ap-1666	146	3	applications	application	NOUN
ap-1666	146	4	to	to	ADP
ap-1666	146	5	elasto	elasto	NOUN
ap-1666	146	6	-	-	PUNCT
ap-1666	146	7	plasticity	plasticity	NOUN
ap-1666	146	8	now	now	ADV
ap-1666	146	9	we	we	PRON
ap-1666	146	10	apply	apply	VERB
ap-1666	146	11	the	the	DET
ap-1666	146	12	energetic	energetic	ADJ
ap-1666	146	13	approach	approach	NOUN
ap-1666	146	14	to	to	ADP
ap-1666	146	15	an	an	DET
ap-1666	146	16	elastoplastic	elastoplastic	ADJ
ap-1666	146	17	problem	problem	NOUN
ap-1666	146	18	.	.	PUNCT
ap-1666	147	1	3.1	3.1	NUM
ap-1666	147	2	problem	problem	NOUN
ap-1666	147	3	statement	statement	NOUN
ap-1666	147	4	in	in	ADP
ap-1666	147	5	what	what	PRON
ap-1666	147	6	follows	follow	VERB
ap-1666	147	7	y	y	PROPN
ap-1666	147	8	:	:	PUNCT
ap-1666	147	9	ω→	ω→	PROPN
ap-1666	147	10	rn	rn	PROPN
ap-1666	147	11	will	will	AUX
ap-1666	147	12	be	be	AUX
ap-1666	147	13	a	a	DET
ap-1666	147	14	deformation	deformation	NOUN
ap-1666	147	15	of	of	ADP
ap-1666	147	16	a	a	DET
ap-1666	147	17	body	body	NOUN
ap-1666	147	18	ω	ω	PROPN
ap-1666	147	19	⊂	⊂	PROPN
ap-1666	147	20	rn	rn	PROPN
ap-1666	147	21	(	(	PUNCT
ap-1666	147	22	in	in	ADP
ap-1666	147	23	a	a	DET
ap-1666	147	24	fixed	fix	VERB
ap-1666	147	25	reference	reference	NOUN
ap-1666	147	26	configuration	configuration	NOUN
ap-1666	147	27	)	)	PUNCT
ap-1666	147	28	with	with	ADP
ap-1666	147	29	the	the	DET
ap-1666	147	30	deformation	deformation	NOUN
ap-1666	147	31	gradient	gradient	NOUN
ap-1666	147	32	f	f	PROPN
ap-1666	147	33	=	=	PROPN
ap-1666	147	34	∇y	∇y	PROPN
ap-1666	147	35	.	.	PUNCT
ap-1666	148	1	in	in	ADP
ap-1666	148	2	particular	particular	ADJ
ap-1666	148	3	,	,	PUNCT
ap-1666	148	4	y	y	PROPN
ap-1666	148	5	covers	cover	VERB
ap-1666	148	6	both	both	CCONJ
ap-1666	148	7	elastic	elastic	ADJ
ap-1666	148	8	and	and	CCONJ
ap-1666	148	9	plastic	plastic	ADJ
ap-1666	148	10	deformation	deformation	NOUN
ap-1666	148	11	.	.	PUNCT
ap-1666	149	1	we	we	PRON
ap-1666	149	2	define	define	VERB
ap-1666	149	3	the	the	DET
ap-1666	149	4	multiplicative	multiplicative	ADJ
ap-1666	149	5	split	split	NOUN
ap-1666	149	6	,	,	PUNCT
ap-1666	149	7	f	f	PROPN
ap-1666	149	8	=	=	SYM
ap-1666	149	9	fefp	fefp	PROPN
ap-1666	149	10	,	,	PUNCT
ap-1666	149	11	into	into	ADP
ap-1666	149	12	an	an	DET
ap-1666	149	13	elastic	elastic	ADJ
ap-1666	149	14	part	part	NOUN
ap-1666	149	15	fe	fe	NOUN
ap-1666	149	16	and	and	CCONJ
ap-1666	149	17	an	an	DET
ap-1666	149	18	irreversible	irreversible	ADJ
ap-1666	149	19	plastic	plastic	NOUN
ap-1666	149	20	part	part	NOUN
ap-1666	149	21	fp	fp	NOUN
ap-1666	149	22	,	,	PUNCT
ap-1666	149	23	which	which	PRON
ap-1666	149	24	belongs	belong	VERB
ap-1666	149	25	to	to	ADP
ap-1666	149	26	sl(n	sl(n	NUM
ap-1666	149	27	)	)	PUNCT
ap-1666	149	28	:	:	PUNCT
ap-1666	150	1	=	=	X
ap-1666	150	2	{	{	PUNCT
ap-1666	150	3	a	a	DET
ap-1666	150	4	∈	∈	NOUN
ap-1666	150	5	rn×n	rn×n	NOUN
ap-1666	150	6	;	;	PUNCT
ap-1666	150	7	deta	deta	NOUN
ap-1666	150	8	=	=	NOUN
ap-1666	150	9	1	1	NUM
ap-1666	150	10	}	}	PUNCT
ap-1666	150	11	.	.	PUNCT
ap-1666	151	1	the	the	DET
ap-1666	151	2	socalled	socalled	ADJ
ap-1666	151	3	plastic	plastic	NOUN
ap-1666	151	4	strain	strain	NOUN
ap-1666	151	5	fp	fp	NOUN
ap-1666	151	6	and	and	CCONJ
ap-1666	151	7	the	the	DET
ap-1666	151	8	vector	vector	NOUN
ap-1666	151	9	p	p	PROPN
ap-1666	151	10	∈	∈	PROPN
ap-1666	151	11	rm	rm	NOUN
ap-1666	151	12	of	of	ADP
ap-1666	151	13	the	the	DET
ap-1666	151	14	hardening	hardening	NOUN
ap-1666	151	15	variables	variable	NOUN
ap-1666	151	16	are	be	AUX
ap-1666	151	17	internal	internal	ADJ
ap-1666	151	18	variables	variable	NOUN
ap-1666	151	19	influencing	influence	VERB
ap-1666	151	20	elasticity	elasticity	NOUN
ap-1666	151	21	.	.	PUNCT
ap-1666	152	1	in	in	ADP
ap-1666	152	2	other	other	ADJ
ap-1666	152	3	words	word	NOUN
ap-1666	152	4	,	,	PUNCT
ap-1666	152	5	z(x	z(x	NUM
ap-1666	152	6	)	)	PUNCT
ap-1666	152	7	=	=	SYM
ap-1666	152	8	(	(	PUNCT
ap-1666	152	9	fp(x	fp(x	PROPN
ap-1666	152	10	)	)	PUNCT
ap-1666	152	11	,	,	PUNCT
ap-1666	152	12	p(x	p(x	PROPN
ap-1666	152	13	)	)	PUNCT
ap-1666	152	14	)	)	PUNCT
ap-1666	153	1	∈	∈	PROPN
ap-1666	153	2	sl(n)×	sl(n)×	PROPN
ap-1666	153	3	rm	rm	NOUN
ap-1666	153	4	for	for	ADP
ap-1666	153	5	almost	almost	ADV
ap-1666	153	6	all	all	PRON
ap-1666	153	7	x	x	SYM
ap-1666	153	8	∈	∈	PROPN
ap-1666	153	9	ω	ω	PROPN
ap-1666	153	10	.	.	PUNCT
ap-1666	154	1	the	the	DET
ap-1666	154	2	energy	energy	NOUN
ap-1666	154	3	functional	functional	NOUN
ap-1666	154	4	i	i	PRON
ap-1666	154	5	takes	take	VERB
ap-1666	154	6	the	the	DET
ap-1666	154	7	form	form	NOUN
ap-1666	154	8	i	i	PRON
ap-1666	154	9	(	(	PUNCT
ap-1666	154	10	t	t	PROPN
ap-1666	154	11	,	,	PUNCT
ap-1666	154	12	y(t	y(t	PROPN
ap-1666	154	13	)	)	PUNCT
ap-1666	154	14	,	,	PUNCT
ap-1666	154	15	z(t	z(t	NOUN
ap-1666	154	16	)	)	PUNCT
ap-1666	154	17	)	)	PUNCT
ap-1666	154	18	:	:	PUNCT
ap-1666	155	1	=	=	SYM
ap-1666	155	2	∫	∫	PROPN
ap-1666	155	3	ω	ω	NUM
ap-1666	155	4	w(x,∇yf−1	w(x,∇yf−1	PROPN
ap-1666	155	5	p	p	PROPN
ap-1666	155	6	,	,	PUNCT
ap-1666	155	7	fp,∇fp	fp,∇fp	PROPN
ap-1666	155	8	,	,	PUNCT
ap-1666	155	9	p,∇p	p,∇p	NOUN
ap-1666	155	10	)	)	PUNCT
ap-1666	155	11	dx	dx	PROPN
ap-1666	155	12	−	−	PROPN
ap-1666	155	13	l(t	l(t	PROPN
ap-1666	155	14	,	,	PUNCT
ap-1666	155	15	y(t	y(t	NOUN
ap-1666	155	16	)	)	PUNCT
ap-1666	155	17	)	)	PUNCT
ap-1666	155	18	,	,	PUNCT
ap-1666	155	19	(	(	PUNCT
ap-1666	155	20	22	22	NUM
ap-1666	155	21	)	)	PUNCT
ap-1666	155	22	with	with	ADP
ap-1666	155	23	l	l	NOUN
ap-1666	155	24	given	give	VERB
ap-1666	155	25	by	by	ADP
ap-1666	155	26	(	(	PUNCT
ap-1666	155	27	12	12	NUM
ap-1666	155	28	)	)	PUNCT
ap-1666	155	29	.	.	PUNCT
ap-1666	156	1	in	in	ADP
ap-1666	156	2	order	order	NOUN
ap-1666	156	3	to	to	PART
ap-1666	156	4	ease	ease	VERB
ap-1666	156	5	the	the	DET
ap-1666	156	6	notation	notation	NOUN
ap-1666	156	7	,	,	PUNCT
ap-1666	156	8	we	we	PRON
ap-1666	156	9	omit	omit	VERB
ap-1666	156	10	the	the	DET
ap-1666	156	11	dependence	dependence	NOUN
ap-1666	156	12	of	of	ADP
ap-1666	156	13	w	w	NOUN
ap-1666	156	14	on	on	ADP
ap-1666	156	15	x.	x.	NOUN
ap-1666	156	16	however	however	ADV
ap-1666	156	17	,	,	PUNCT
ap-1666	156	18	all	all	DET
ap-1666	156	19	the	the	DET
ap-1666	156	20	theory	theory	NOUN
ap-1666	156	21	developed	develop	VERB
ap-1666	156	22	in	in	ADP
ap-1666	156	23	this	this	DET
ap-1666	156	24	paper	paper	NOUN
ap-1666	156	25	may	may	AUX
ap-1666	156	26	include	include	VERB
ap-1666	156	27	nonhomogeneous	nonhomogeneous	ADJ
ap-1666	156	28	w.	w.	NOUN
ap-1666	156	29	in	in	ADP
ap-1666	156	30	what	what	PRON
ap-1666	156	31	follows	follow	VERB
ap-1666	156	32	,	,	PUNCT
ap-1666	156	33	we	we	PRON
ap-1666	156	34	suppose	suppose	VERB
ap-1666	156	35	that	that	SCONJ
ap-1666	156	36	y	y	PROPN
ap-1666	156	37	∈	∈	PROPN
ap-1666	156	38	y	y	PROPN
ap-1666	156	39	:	:	PUNCT
ap-1666	156	40	=	=	SYM
ap-1666	156	41	{	{	PUNCT
ap-1666	156	42	y	y	PROPN
ap-1666	156	43	∈w	∈w	VERB
ap-1666	156	44	1,d(ω	1,d(ω	NUM
ap-1666	156	45	;	;	PUNCT
ap-1666	156	46	rn	rn	PROPN
ap-1666	156	47	)	)	PUNCT
ap-1666	156	48	;	;	PUNCT
ap-1666	157	1	y	y	PROPN
ap-1666	157	2	=	=	SYM
ap-1666	157	3	y0	y0	PROPN
ap-1666	157	4	on	on	ADP
ap-1666	157	5	γ0	γ0	NOUN
ap-1666	157	6	}	}	PUNCT
ap-1666	157	7	,	,	PUNCT
ap-1666	157	8	where	where	SCONJ
ap-1666	157	9	γ0	γ0	NOUN
ap-1666	157	10	⊂	⊂	PROPN
ap-1666	157	11	∂ω	∂ω	PROPN
ap-1666	157	12	with	with	ADP
ap-1666	157	13	a	a	DET
ap-1666	157	14	positive	positive	ADJ
ap-1666	157	15	surface	surface	NOUN
ap-1666	157	16	measure	measure	NOUN
ap-1666	157	17	.	.	PUNCT
ap-1666	158	1	moreover	moreover	ADV
ap-1666	158	2	,	,	PUNCT
ap-1666	158	3	we	we	PRON
ap-1666	158	4	suppose	suppose	VERB
ap-1666	158	5	that	that	SCONJ
ap-1666	158	6	γ0	γ0	NOUN
ap-1666	158	7	∩	∩	ADJ
ap-1666	158	8	γ1	γ1	NOUN
ap-1666	158	9	=	=	PUNCT
ap-1666	158	10	∅.	∅.	VERB
ap-1666	158	11	further	furth	ADJ
ap-1666	158	12	z	z	NOUN
ap-1666	158	13	:	:	PUNCT
ap-1666	158	14	=	=	SYM
ap-1666	158	15	{	{	PUNCT
ap-1666	158	16	(	(	PUNCT
ap-1666	158	17	fp	fp	INTJ
ap-1666	158	18	,	,	PUNCT
ap-1666	158	19	p	p	NOUN
ap-1666	158	20	)	)	PUNCT
ap-1666	158	21	∈w	∈w	PROPN
ap-1666	158	22	1,β(ω	1,β(ω	NUM
ap-1666	158	23	;	;	PUNCT
ap-1666	158	24	rn×n)×w	rn×n)×w	PROPN
ap-1666	158	25	1,ω(ω	1,ω(ω	NUM
ap-1666	158	26	;	;	PUNCT
ap-1666	158	27	rm	rm	NOUN
ap-1666	158	28	)	)	PUNCT
ap-1666	158	29	;	;	PUNCT
ap-1666	158	30	fp(x	fp(x	X
ap-1666	158	31	)	)	PUNCT
ap-1666	158	32	∈	∈	PROPN
ap-1666	158	33	sl(n	sl(n	NOUN
ap-1666	158	34	)	)	PUNCT
ap-1666	158	35	for	for	ADP
ap-1666	158	36	a.e	a.e	PROPN
ap-1666	158	37	.	.	PUNCT
ap-1666	158	38	x	x	SYM
ap-1666	158	39	∈	∈	PROPN
ap-1666	158	40	ω	ω	NUM
ap-1666	158	41	}	}	PUNCT
ap-1666	158	42	.	.	PUNCT
ap-1666	159	1	as	as	ADP
ap-1666	159	2	q	q	PROPN
ap-1666	159	3	=	=	SYM
ap-1666	159	4	(	(	PUNCT
ap-1666	159	5	y	y	PROPN
ap-1666	159	6	,	,	PUNCT
ap-1666	159	7	z	z	NOUN
ap-1666	159	8	)	)	PUNCT
ap-1666	159	9	it	it	PRON
ap-1666	159	10	will	will	AUX
ap-1666	159	11	be	be	AUX
ap-1666	159	12	advantageous	advantageous	ADJ
ap-1666	159	13	and	and	CCONJ
ap-1666	159	14	will	will	AUX
ap-1666	159	15	cause	cause	VERB
ap-1666	159	16	no	no	DET
ap-1666	159	17	confusion	confusion	NOUN
ap-1666	159	18	to	to	PART
ap-1666	159	19	write	write	VERB
ap-1666	159	20	d	d	PROPN
ap-1666	159	21	as	as	ADV
ap-1666	159	22	dependent	dependent	ADJ
ap-1666	159	23	on	on	ADP
ap-1666	159	24	q	q	ADJ
ap-1666	159	25	,	,	PUNCT
ap-1666	159	26	i.e.	i.e.	X
ap-1666	159	27	,	,	PUNCT
ap-1666	159	28	d(q1	d(q1	NOUN
ap-1666	159	29	,	,	PUNCT
ap-1666	159	30	q2	q2	NOUN
ap-1666	159	31	)	)	PUNCT
ap-1666	159	32	:	:	PUNCT
ap-1666	160	1	=	=	PUNCT
ap-1666	160	2	d(z1	d(z1	NOUN
ap-1666	160	3	,	,	PUNCT
ap-1666	160	4	z2	z2	PROPN
ap-1666	160	5	)	)	PUNCT
ap-1666	160	6	if	if	SCONJ
ap-1666	160	7	q1	q1	PROPN
ap-1666	160	8	=	=	SYM
ap-1666	160	9	(	(	PUNCT
ap-1666	160	10	y1	y1	PROPN
ap-1666	160	11	,	,	PUNCT
ap-1666	160	12	z1	z1	ADJ
ap-1666	160	13	)	)	PUNCT
ap-1666	160	14	and	and	CCONJ
ap-1666	160	15	q2	q2	NOUN
ap-1666	160	16	=	=	SYM
ap-1666	160	17	(	(	PUNCT
ap-1666	160	18	y2	y2	PROPN
ap-1666	160	19	,	,	PUNCT
ap-1666	160	20	z2	z2	PROPN
ap-1666	160	21	)	)	PUNCT
ap-1666	160	22	.	.	PUNCT
ap-1666	161	1	similarly	similarly	ADV
ap-1666	161	2	,	,	PUNCT
ap-1666	161	3	we	we	PRON
ap-1666	161	4	may	may	AUX
ap-1666	161	5	write	write	VERB
ap-1666	161	6	i	i	PRON
ap-1666	161	7	in	in	ADP
ap-1666	161	8	terms	term	NOUN
ap-1666	161	9	of	of	ADP
ap-1666	161	10	q	q	NOUN
ap-1666	161	11	=	=	SYM
ap-1666	161	12	(	(	PUNCT
ap-1666	161	13	y	y	PROPN
ap-1666	161	14	,	,	PUNCT
ap-1666	161	15	z	z	NOUN
ap-1666	161	16	)	)	PUNCT
ap-1666	161	17	as	as	ADP
ap-1666	161	18	i	i	PRON
ap-1666	161	19	(	(	PUNCT
ap-1666	161	20	t	t	PROPN
ap-1666	161	21	,	,	PUNCT
ap-1666	161	22	q(t	q(t	PROPN
ap-1666	161	23	)	)	PUNCT
ap-1666	161	24	)	)	PUNCT
ap-1666	162	1	=	=	SYM
ap-1666	163	1	∫	∫	PROPN
ap-1666	164	1	ω	ω	PROPN
ap-1666	164	2	w	w	PROPN
ap-1666	164	3	(	(	PUNCT
ap-1666	164	4	x,∇yf−1	x,∇yf−1	PROPN
ap-1666	164	5	p	p	X
ap-1666	164	6	,	,	PUNCT
ap-1666	164	7	fp,∇fp	fp,∇fp	PROPN
ap-1666	164	8	,	,	PUNCT
ap-1666	164	9	p,∇p	p,∇p	NOUN
ap-1666	164	10	)	)	PUNCT
ap-1666	164	11	dx	dx	PROPN
ap-1666	164	12	−	−	PROPN
ap-1666	164	13	l	l	PROPN
ap-1666	164	14	(	(	PUNCT
ap-1666	164	15	t	t	PROPN
ap-1666	164	16	,	,	PUNCT
ap-1666	164	17	q(t	q(t	PROPN
ap-1666	164	18	)	)	PUNCT
ap-1666	164	19	)	)	PUNCT
ap-1666	164	20	,	,	PUNCT
ap-1666	164	21	where	where	SCONJ
ap-1666	164	22	,	,	PUNCT
ap-1666	164	23	obviously	obviously	ADV
ap-1666	164	24	,	,	PUNCT
ap-1666	164	25	l	l	PROPN
ap-1666	164	26	(	(	PUNCT
ap-1666	164	27	t	t	PROPN
ap-1666	164	28	,	,	PUNCT
ap-1666	164	29	q(t	q(t	PROPN
ap-1666	164	30	)	)	PUNCT
ap-1666	164	31	)	)	PUNCT
ap-1666	164	32	:	:	PUNCT
ap-1666	165	1	=	=	SYM
ap-1666	165	2	l	l	NOUN
ap-1666	165	3	(	(	PUNCT
ap-1666	165	4	t	t	PROPN
ap-1666	165	5	,	,	PUNCT
ap-1666	165	6	y(t	y(t	PROPN
ap-1666	165	7	)	)	PUNCT
ap-1666	165	8	)	)	PUNCT
ap-1666	165	9	.	.	PUNCT
ap-1666	166	1	in	in	ADP
ap-1666	166	2	this	this	DET
ap-1666	166	3	situation	situation	NOUN
ap-1666	166	4	,	,	PUNCT
ap-1666	166	5	q	q	NOUN
ap-1666	166	6	=	=	SYM
ap-1666	166	7	(	(	PUNCT
ap-1666	166	8	q1	q1	PROPN
ap-1666	166	9	,	,	PUNCT
ap-1666	166	10	q2	q2	NOUN
ap-1666	166	11	)	)	PUNCT
ap-1666	166	12	are	be	AUX
ap-1666	166	13	conjugate	conjugate	ADJ
ap-1666	166	14	plastic	plastic	NOUN
ap-1666	166	15	stress	stress	NOUN
ap-1666	166	16	and	and	CCONJ
ap-1666	166	17	conjugate	conjugate	ADJ
ap-1666	166	18	hardening	harden	VERB
ap-1666	166	19	forces	force	NOUN
ap-1666	166	20	,	,	PUNCT
ap-1666	166	21	respectively	respectively	ADV
ap-1666	166	22	.	.	PUNCT
ap-1666	167	1	q1	q1	PROPN
ap-1666	167	2	=	=	SYM
ap-1666	167	3	div	div	X
ap-1666	167	4	(	(	PUNCT
ap-1666	167	5	∂w(∇yf−1	∂w(∇yf−1	PROPN
ap-1666	167	6	p	p	NOUN
ap-1666	167	7	,	,	PUNCT
ap-1666	167	8	fp,∇fp	fp,∇fp	PROPN
ap-1666	167	9	,	,	PUNCT
ap-1666	167	10	p,∇p	p,∇p	NOUN
ap-1666	167	11	)	)	PUNCT
ap-1666	167	12	∂∇fp	∂∇fp	NOUN
ap-1666	167	13	)	)	PUNCT
ap-1666	168	1	−	−	PROPN
ap-1666	168	2	∂w(∇yf−1	∂w(∇yf−1	PROPN
ap-1666	168	3	p	p	PROPN
ap-1666	168	4	,	,	PUNCT
ap-1666	168	5	fp,∇fp	fp,∇fp	PROPN
ap-1666	168	6	,	,	PUNCT
ap-1666	168	7	p,∇p	p,∇p	NOUN
ap-1666	168	8	)	)	PUNCT
ap-1666	168	9	∂fp	∂fp	PROPN
ap-1666	168	10	and	and	CCONJ
ap-1666	168	11	q2	q2	NOUN
ap-1666	168	12	=	=	SYM
ap-1666	168	13	div	div	X
ap-1666	168	14	(	(	PUNCT
ap-1666	168	15	∂w(∇yf−1	∂w(∇yf−1	PROPN
ap-1666	168	16	p	p	NOUN
ap-1666	168	17	,	,	PUNCT
ap-1666	168	18	fp,∇fp	fp,∇fp	PROPN
ap-1666	168	19	,	,	PUNCT
ap-1666	168	20	p,∇p	p,∇p	NOUN
ap-1666	168	21	)	)	PUNCT
ap-1666	168	22	∂∇p	∂∇p	NUM
ap-1666	168	23	)	)	PUNCT
ap-1666	169	1	−	−	PROPN
ap-1666	169	2	∂w(∇yf−1	∂w(∇yf−1	PROPN
ap-1666	169	3	p	p	NOUN
ap-1666	169	4	,	,	PUNCT
ap-1666	169	5	fp,∇fp	fp,∇fp	PROPN
ap-1666	169	6	,	,	PUNCT
ap-1666	169	7	p,∇p	p,∇p	NOUN
ap-1666	169	8	)	)	PUNCT
ap-1666	170	1	∂p	∂p	INTJ
ap-1666	170	2	.	.	PUNCT
ap-1666	171	1	(	(	PUNCT
ap-1666	171	2	23	23	NUM
ap-1666	171	3	)	)	PUNCT
ap-1666	171	4	the	the	DET
ap-1666	171	5	elastic	elastic	ADJ
ap-1666	171	6	domain	domain	NOUN
ap-1666	171	7	is	be	AUX
ap-1666	171	8	defined	define	VERB
ap-1666	171	9	as	as	ADP
ap-1666	171	10	q(x	q(x	NOUN
ap-1666	171	11	,	,	PUNCT
ap-1666	171	12	z	z	NOUN
ap-1666	171	13	)	)	PUNCT
ap-1666	171	14	=	=	SYM
ap-1666	172	1	∂sub	∂sub	PUNCT
ap-1666	172	2	żδ(x	żδ(x	NUM
ap-1666	172	3	,	,	PUNCT
ap-1666	172	4	z	z	PROPN
ap-1666	172	5	,	,	PUNCT
ap-1666	172	6	0	0	NUM
ap-1666	172	7	)	)	PUNCT
ap-1666	172	8	.	.	PUNCT
ap-1666	173	1	(	(	PUNCT
ap-1666	173	2	24	24	NUM
ap-1666	173	3	)	)	PUNCT
ap-1666	173	4	remark	remark	NOUN
ap-1666	173	5	3.1	3.1	NUM
ap-1666	173	6	.	.	PUNCT
ap-1666	174	1	the	the	DET
ap-1666	174	2	principle	principle	NOUN
ap-1666	174	3	of	of	ADP
ap-1666	174	4	maximal	maximal	ADJ
ap-1666	174	5	dissipation	dissipation	NOUN
ap-1666	174	6	asserts	assert	VERB
ap-1666	174	7	that	that	SCONJ
ap-1666	174	8	q1	q1	VERB
ap-1666	174	9	:	:	PUNCT
ap-1666	174	10	ḟp	ḟp	PROPN
ap-1666	175	1	+	+	PROPN
ap-1666	175	2	q2	q2	NOUN
ap-1666	175	3	·	·	PUNCT
ap-1666	176	1	ṗ	ṗ	ADJ
ap-1666	176	2	(	(	PUNCT
ap-1666	176	3	25	25	NUM
ap-1666	176	4	)	)	PUNCT
ap-1666	176	5	is	be	AUX
ap-1666	176	6	maximal	maximal	ADJ
ap-1666	176	7	if	if	SCONJ
ap-1666	176	8	ḟp	ḟp	PROPN
ap-1666	176	9	and	and	CCONJ
ap-1666	176	10	ṗ	ṗ	NOUN
ap-1666	176	11	are	be	AUX
ap-1666	176	12	kept	keep	VERB
ap-1666	176	13	fixed	fix	VERB
ap-1666	176	14	and	and	CCONJ
ap-1666	176	15	(	(	PUNCT
ap-1666	176	16	q1	q1	PROPN
ap-1666	176	17	,	,	PUNCT
ap-1666	176	18	q2	q2	NOUN
ap-1666	176	19	)	)	PUNCT
ap-1666	176	20	∈	∈	PROPN
ap-1666	176	21	q(x	q(x	PROPN
ap-1666	176	22	,	,	PUNCT
ap-1666	176	23	z	z	NOUN
ap-1666	176	24	)	)	PUNCT
ap-1666	176	25	.	.	PUNCT
ap-1666	177	1	this	this	PRON
ap-1666	177	2	means	mean	VERB
ap-1666	177	3	that	that	SCONJ
ap-1666	177	4	for	for	ADP
ap-1666	177	5	all	all	DET
ap-1666	177	6	(	(	PUNCT
ap-1666	177	7	a	a	PRON
ap-1666	177	8	,	,	PUNCT
ap-1666	177	9	b	b	NOUN
ap-1666	177	10	)	)	PUNCT
ap-1666	177	11	∈	∈	PROPN
ap-1666	177	12	q(x	q(x	PROPN
ap-1666	177	13	,	,	PUNCT
ap-1666	177	14	z	z	NOUN
ap-1666	177	15	)	)	PUNCT
ap-1666	177	16	.	.	PUNCT
ap-1666	178	1	q1	q1	PROPN
ap-1666	178	2	:	:	PUNCT
ap-1666	179	1	ḟp	ḟp	PROPN
ap-1666	180	1	+	+	PROPN
ap-1666	180	2	q2	q2	NOUN
ap-1666	180	3	·	·	PUNCT
ap-1666	181	1	ṗ	ṗ	ADJ
ap-1666	181	2	≥	≥	PRON
ap-1666	181	3	a	a	X
ap-1666	181	4	:	:	PUNCT
ap-1666	181	5	ḟp	ḟp	PROPN
ap-1666	181	6	+	+	NOUN
ap-1666	181	7	b	b	X
ap-1666	181	8	·	·	SYM
ap-1666	181	9	ṗ.	ṗ.	NOUN
ap-1666	181	10	(	(	PUNCT
ap-1666	181	11	26	26	NUM
ap-1666	181	12	)	)	PUNCT
ap-1666	181	13	finally	finally	ADV
ap-1666	181	14	,	,	PUNCT
ap-1666	181	15	we	we	PRON
ap-1666	181	16	conclude	conclude	VERB
ap-1666	181	17	with	with	ADP
ap-1666	181	18	an	an	DET
ap-1666	181	19	example	example	NOUN
ap-1666	181	20	covered	cover	VERB
ap-1666	181	21	by	by	ADP
ap-1666	181	22	our	our	PRON
ap-1666	181	23	approach	approach	NOUN
ap-1666	181	24	.	.	PUNCT
ap-1666	182	1	example	example	NOUN
ap-1666	182	2	3.2	3.2	NUM
ap-1666	182	3	(	(	PUNCT
ap-1666	182	4	simple	simple	ADJ
ap-1666	182	5	shear	shear	NOUN
ap-1666	182	6	carried	carry	VERB
ap-1666	182	7	by	by	ADP
ap-1666	182	8	a	a	DET
ap-1666	182	9	single	single	ADJ
ap-1666	182	10	slip	slip	NOUN
ap-1666	182	11	)	)	PUNCT
ap-1666	182	12	.	.	PUNCT
ap-1666	183	1	consider	consider	VERB
ap-1666	183	2	a	a	DET
ap-1666	183	3	single	single	ADJ
ap-1666	183	4	slip	slip	NOUN
ap-1666	183	5	system	system	NOUN
ap-1666	183	6	defined	define	VERB
ap-1666	183	7	by	by	ADP
ap-1666	183	8	two	two	NUM
ap-1666	183	9	orthonormal	orthonormal	ADJ
ap-1666	183	10	vectors	vector	NOUN
ap-1666	183	11	a	a	DET
ap-1666	183	12	,	,	PUNCT
ap-1666	183	13	b	b	PROPN
ap-1666	183	14	∈	∈	PROPN
ap-1666	183	15	r3	r3	NOUN
ap-1666	183	16	such	such	ADJ
ap-1666	183	17	that	that	SCONJ
ap-1666	183	18	a	a	PRON
ap-1666	183	19	is	be	AUX
ap-1666	183	20	the	the	DET
ap-1666	183	21	glide	glide	ADJ
ap-1666	183	22	direction	direction	NOUN
ap-1666	183	23	and	and	CCONJ
ap-1666	183	24	b	b	NOUN
ap-1666	183	25	is	be	AUX
ap-1666	183	26	the	the	DET
ap-1666	183	27	slip	slip	NOUN
ap-1666	183	28	-	-	PUNCT
ap-1666	183	29	plane	plane	NOUN
ap-1666	183	30	normal	normal	ADJ
ap-1666	183	31	.	.	PUNCT
ap-1666	184	1	further	far	ADV
ap-1666	184	2	suppose	suppose	VERB
ap-1666	184	3	that	that	SCONJ
ap-1666	184	4	we	we	PRON
ap-1666	184	5	have	have	VERB
ap-1666	184	6	a	a	DET
ap-1666	184	7	particular	particular	ADJ
ap-1666	184	8	case	case	NOUN
ap-1666	184	9	of	of	ADP
ap-1666	184	10	a	a	DET
ap-1666	184	11	so	so	ADV
ap-1666	184	12	-	-	PUNCT
ap-1666	184	13	called	call	VERB
ap-1666	184	14	separable	separable	ADJ
ap-1666	184	15	material	material	NOUN
ap-1666	184	16	where	where	SCONJ
ap-1666	184	17	:	:	PUNCT
ap-1666	184	18	w(x	w(x	PROPN
ap-1666	184	19	,	,	PUNCT
ap-1666	184	20	fe	fe	X
ap-1666	184	21	,	,	PUNCT
ap-1666	184	22	z	z	NOUN
ap-1666	184	23	)	)	PUNCT
ap-1666	184	24	=	=	PUNCT
ap-1666	184	25	w1(fe	w1(fe	PROPN
ap-1666	184	26	)	)	PUNCT
ap-1666	185	1	+	+	CCONJ
ap-1666	185	2	α	α	PRON
ap-1666	185	3	∣∣fp	∣∣fp	PROPN
ap-1666	185	4	∣∣2	∣∣2	PROPN
ap-1666	185	5	+	+	CCONJ
ap-1666	185	6	ε	ε	PROPN
ap-1666	185	7	2	2	NUM
ap-1666	185	8	∣∣∇fp	∣∣∇fp	PROPN
ap-1666	185	9	∣∣2	∣∣2	PROPN
ap-1666	185	10	,	,	PUNCT
ap-1666	185	11	where	where	SCONJ
ap-1666	185	12	fp(t	fp(t	NOUN
ap-1666	185	13	)	)	PUNCT
ap-1666	186	1	=	=	SYM
ap-1666	187	1	i	i	PRON
ap-1666	187	2	+	+	CCONJ
ap-1666	187	3	γ(t)a	γ(t)a	ADJ
ap-1666	187	4	⊗	⊗	PROPN
ap-1666	187	5	b	b	PROPN
ap-1666	187	6	where	where	SCONJ
ap-1666	187	7	γ	γ	PROPN
ap-1666	187	8	is	be	AUX
ap-1666	187	9	the	the	DET
ap-1666	187	10	plastic	plastic	ADJ
ap-1666	187	11	slip	slip	NOUN
ap-1666	187	12	.	.	PUNCT
ap-1666	188	1	the	the	DET
ap-1666	188	2	slip	slip	NOUN
ap-1666	188	3	system	system	NOUN
ap-1666	188	4	is	be	AUX
ap-1666	188	5	generally	generally	ADV
ap-1666	188	6	not	not	PART
ap-1666	188	7	fixed	fix	VERB
ap-1666	188	8	in	in	ADP
ap-1666	188	9	the	the	DET
ap-1666	188	10	reference	reference	NOUN
ap-1666	188	11	configuration	configuration	NOUN
ap-1666	188	12	.	.	PUNCT
ap-1666	189	1	the	the	DET
ap-1666	189	2	slip	slip	NOUN
ap-1666	189	3	-	-	PUNCT
ap-1666	189	4	plane	plane	NOUN
ap-1666	189	5	normal	normal	ADJ
ap-1666	189	6	b̃	b̃	PROPN
ap-1666	189	7	in	in	ADP
ap-1666	189	8	the	the	DET
ap-1666	189	9	reference	reference	NOUN
ap-1666	189	10	configuration	configuration	NOUN
ap-1666	189	11	has	have	VERB
ap-1666	189	12	the	the	DET
ap-1666	189	13	form	form	NOUN
ap-1666	189	14	b̃	b̃	PROPN
ap-1666	189	15	=	=	PROPN
ap-1666	189	16	(	(	PUNCT
ap-1666	189	17	fp)>b	fp)>b	X
ap-1666	189	18	.	.	PUNCT
ap-1666	190	1	however	however	ADV
ap-1666	190	2	,	,	PUNCT
ap-1666	190	3	in	in	ADP
ap-1666	190	4	this	this	DET
ap-1666	190	5	special	special	ADJ
ap-1666	190	6	case	case	NOUN
ap-1666	190	7	we	we	PRON
ap-1666	190	8	have	have	VERB
ap-1666	190	9	that	that	DET
ap-1666	190	10	b̃	b̃	PROPN
ap-1666	190	11	=	=	SYM
ap-1666	190	12	b	b	PROPN
ap-1666	190	13	,	,	PUNCT
ap-1666	190	14	so	so	SCONJ
ap-1666	190	15	that	that	SCONJ
ap-1666	190	16	the	the	DET
ap-1666	190	17	slip	slip	NOUN
ap-1666	190	18	-	-	PUNCT
ap-1666	190	19	plane	plane	NOUN
ap-1666	190	20	normal	normal	NOUN
ap-1666	190	21	is	be	AUX
ap-1666	190	22	kept	keep	VERB
ap-1666	190	23	constant	constant	ADJ
ap-1666	190	24	during	during	ADP
ap-1666	190	25	the	the	DET
ap-1666	190	26	process	process	NOUN
ap-1666	190	27	[	[	X
ap-1666	190	28	15	15	NUM
ap-1666	190	29	]	]	PUNCT
ap-1666	190	30	.	.	PUNCT
ap-1666	191	1	due	due	ADP
ap-1666	191	2	to	to	ADP
ap-1666	191	3	the	the	DET
ap-1666	191	4	special	special	ADJ
ap-1666	191	5	case	case	NOUN
ap-1666	191	6	of	of	ADP
ap-1666	191	7	fp	fp	INTJ
ap-1666	191	8	we	we	PRON
ap-1666	191	9	may	may	AUX
ap-1666	191	10	identify	identify	VERB
ap-1666	191	11	z	z	NOUN
ap-1666	191	12	:	:	PUNCT
ap-1666	191	13	=	=	SYM
ap-1666	191	14	(	(	PUNCT
ap-1666	191	15	γ	γ	X
ap-1666	191	16	,	,	PUNCT
ap-1666	191	17	p	p	NOUN
ap-1666	191	18	)	)	PUNCT
ap-1666	191	19	because	because	SCONJ
ap-1666	191	20	fp	fp	NOUN
ap-1666	191	21	depends	depend	VERB
ap-1666	191	22	only	only	ADV
ap-1666	191	23	on	on	ADP
ap-1666	191	24	γ	γ	PROPN
ap-1666	191	25	.	.	PROPN
ap-1666	191	26	choose	choose	VERB
ap-1666	191	27	the	the	DET
ap-1666	191	28	dissipation	dissipation	NOUN
ap-1666	191	29	metric	metric	ADJ
ap-1666	191	30	:	:	PUNCT
ap-1666	191	31	δ(z	δ(z	NOUN
ap-1666	191	32	,	,	PUNCT
ap-1666	191	33	ż	ż	NOUN
ap-1666	191	34	)	)	PUNCT
ap-1666	191	35	=	=	PUNCT
ap-1666	192	1	δ(γ	δ(γ	NOUN
ap-1666	192	2	,	,	PUNCT
ap-1666	192	3	p	p	X
ap-1666	192	4	,	,	PUNCT
ap-1666	192	5	γ̇	γ̇	PROPN
ap-1666	192	6	,	,	PUNCT
ap-1666	192	7	ṗ	ṗ	ADJ
ap-1666	192	8	)	)	PUNCT
ap-1666	192	9	,	,	PUNCT
ap-1666	192	10	δ(γ	δ(γ	PROPN
ap-1666	192	11	,	,	PUNCT
ap-1666	192	12	p	p	X
ap-1666	192	13	,	,	PUNCT
ap-1666	192	14	γ̇	γ̇	PROPN
ap-1666	192	15	,	,	PUNCT
ap-1666	192	16	ṗ	ṗ	ADJ
ap-1666	192	17	)	)	PUNCT
ap-1666	192	18	=	=	PRON
ap-1666	192	19	{	{	PUNCT
ap-1666	192	20	p|γ̇|	p|γ̇|	NOUN
ap-1666	192	21	if	if	SCONJ
ap-1666	192	22	ṗ	ṗ	ADJ
ap-1666	192	23	≥	≥	NUM
ap-1666	192	24	h|γ̇|	h|γ̇|	NOUN
ap-1666	192	25	,	,	PUNCT
ap-1666	192	26	+	+	NOUN
ap-1666	192	27	∞	∞	NOUN
ap-1666	192	28	otherwise	otherwise	ADV
ap-1666	192	29	,	,	PUNCT
ap-1666	192	30	where	where	SCONJ
ap-1666	192	31	h	h	NOUN
ap-1666	192	32	is	be	AUX
ap-1666	192	33	the	the	DET
ap-1666	192	34	so	so	ADV
ap-1666	192	35	-	-	PUNCT
ap-1666	192	36	called	call	VERB
ap-1666	192	37	hardening	harden	VERB
ap-1666	192	38	function	function	NOUN
ap-1666	192	39	.	.	PUNCT
ap-1666	193	1	the	the	DET
ap-1666	193	2	evolution	evolution	NOUN
ap-1666	193	3	rule	rule	NOUN
ap-1666	193	4	reads	read	VERB
ap-1666	193	5	:	:	PUNCT
ap-1666	193	6	ε∆γ	ε∆γ	PROPN
ap-1666	193	7	∈	∈	PROPN
ap-1666	193	8	∂sub(p|γ̇|	∂sub(p|γ̇|	PROPN
ap-1666	193	9	)	)	PUNCT
ap-1666	193	10	the	the	DET
ap-1666	193	11	elastic	elastic	ADJ
ap-1666	193	12	domain	domain	NOUN
ap-1666	193	13	∂subδ(γ	∂subδ(γ	PROPN
ap-1666	193	14	,	,	PUNCT
ap-1666	193	15	p	p	X
ap-1666	193	16	,	,	PUNCT
ap-1666	193	17	0	0	NUM
ap-1666	193	18	,	,	PUNCT
ap-1666	193	19	0	0	NUM
ap-1666	193	20	)	)	PUNCT
ap-1666	193	21	=	=	NOUN
ap-1666	194	1	[	[	X
ap-1666	194	2	−p	−p	NOUN
ap-1666	194	3	,	,	PUNCT
ap-1666	194	4	p	p	X
ap-1666	194	5	]	]	X
ap-1666	194	6	if	if	SCONJ
ap-1666	194	7	ṗ	ṗ	ADJ
ap-1666	194	8	≥	≥	NUM
ap-1666	194	9	h|γ̇|	h|γ̇|	NOUN
ap-1666	194	10	and	and	CCONJ
ap-1666	194	11	(	(	PUNCT
ap-1666	194	12	−∞,∞	−∞,∞	NOUN
ap-1666	194	13	)	)	PUNCT
ap-1666	194	14	otherwise	otherwise	ADV
ap-1666	194	15	.	.	PUNCT
ap-1666	195	1	the	the	DET
ap-1666	195	2	boundary	boundary	NOUN
ap-1666	195	3	of	of	ADP
ap-1666	195	4	the	the	DET
ap-1666	195	5	elastic	elastic	ADJ
ap-1666	195	6	domain	domain	NOUN
ap-1666	195	7	±p	±p	NOUN
ap-1666	195	8	−	−	PROPN
ap-1666	195	9	ε∆γ	ε∆γ	NOUN
ap-1666	195	10	=	=	SYM
ap-1666	195	11	0	0	NUM
ap-1666	195	12	defines	define	VERB
ap-1666	195	13	the	the	DET
ap-1666	195	14	yield	yield	NOUN
ap-1666	195	15	surface	surface	NOUN
ap-1666	195	16	.	.	PUNCT
ap-1666	196	1	thus	thus	ADV
ap-1666	196	2	,	,	PUNCT
ap-1666	196	3	the	the	DET
ap-1666	196	4	energetic	energetic	ADJ
ap-1666	196	5	approach	approach	NOUN
ap-1666	196	6	recovers	recover	VERB
ap-1666	196	7	gurtin	gurtin	NOUN
ap-1666	196	8	’s	’s	PART
ap-1666	196	9	calculations	calculation	NOUN
ap-1666	196	10	on	on	ADP
ap-1666	196	11	shear	shear	NOUN
ap-1666	196	12	bands	band	NOUN
ap-1666	196	13	in	in	ADP
ap-1666	196	14	single	single	ADJ
ap-1666	196	15	-	-	PUNCT
ap-1666	196	16	slip	slip	NOUN
ap-1666	196	17	,	,	PUNCT
ap-1666	196	18	see	see	VERB
ap-1666	196	19	gurtin	gurtin	NOUN
ap-1666	196	20	(	(	PUNCT
ap-1666	196	21	2000	2000	NUM
ap-1666	196	22	)	)	PUNCT
ap-1666	196	23	.	.	PUNCT
ap-1666	197	1	12	12	NUM
ap-1666	197	2	acta	acta	PROPN
ap-1666	197	3	polytechnica	polytechnica	PROPN
ap-1666	197	4	vol	vol	NOUN
ap-1666	197	5	.	.	PROPN
ap-1666	198	1	52	52	NUM
ap-1666	198	2	no	no	NOUN
ap-1666	198	3	.	.	PUNCT
ap-1666	199	1	6/2012	6/2012	NUM
ap-1666	200	1	the	the	DET
ap-1666	200	2	dissipation	dissipation	NOUN
ap-1666	200	3	distance	distance	NOUN
ap-1666	200	4	is	be	AUX
ap-1666	200	5	:	:	PUNCT
ap-1666	200	6	d(γ1	d(γ1	NOUN
ap-1666	200	7	,	,	PUNCT
ap-1666	200	8	p1	p1	NOUN
ap-1666	200	9	,	,	PUNCT
ap-1666	200	10	γ2	γ2	NOUN
ap-1666	200	11	,	,	PUNCT
ap-1666	200	12	p2	p2	X
ap-1666	200	13	)	)	PUNCT
ap-1666	201	1	=	=	PRON
ap-1666	201	2	{	{	PUNCT
ap-1666	201	3	p2|γ2	p2|γ2	NOUN
ap-1666	201	4	−	−	NOUN
ap-1666	201	5	γ1|	γ1|	NOUN
ap-1666	202	1	if	if	SCONJ
ap-1666	202	2	p2	p2	PROPN
ap-1666	202	3	−	−	PROPN
ap-1666	202	4	p1	p1	PROPN
ap-1666	202	5	≥	≥	NUM
ap-1666	202	6	h|γ2	h|γ2	PROPN
ap-1666	202	7	−	−	PROPN
ap-1666	202	8	γ1|	γ1|	PROPN
ap-1666	202	9	,	,	PUNCT
ap-1666	202	10	+	+	NOUN
ap-1666	202	11	∞	∞	NOUN
ap-1666	202	12	otherwise	otherwise	ADV
ap-1666	202	13	.	.	PUNCT
ap-1666	203	1	if	if	SCONJ
ap-1666	203	2	h	h	PROPN
ap-1666	203	3	>	>	X
ap-1666	203	4	0	0	PUNCT
ap-1666	204	1	we	we	PRON
ap-1666	204	2	get	get	VERB
ap-1666	204	3	that	that	SCONJ
ap-1666	204	4	the	the	DET
ap-1666	204	5	optimal	optimal	ADJ
ap-1666	204	6	choice	choice	NOUN
ap-1666	204	7	is	be	AUX
ap-1666	204	8	p2	p2	NOUN
ap-1666	204	9	=	=	SYM
ap-1666	204	10	p1	p1	NOUN
ap-1666	204	11	+	+	NOUN
ap-1666	204	12	h|γ2−γ1|	h|γ2−γ1|	NOUN
ap-1666	204	13	which	which	PRON
ap-1666	204	14	gives	give	VERB
ap-1666	204	15	d(γ1	d(γ1	NOUN
ap-1666	204	16	,	,	PUNCT
ap-1666	204	17	p1	p1	NOUN
ap-1666	204	18	,	,	PUNCT
ap-1666	204	19	γ2	γ2	NOUN
ap-1666	204	20	,	,	PUNCT
ap-1666	204	21	p2	p2	X
ap-1666	204	22	)	)	PUNCT
ap-1666	205	1	=	=	SYM
ap-1666	205	2	p1|γ2−	p1|γ2−	NUM
ap-1666	205	3	γ1|+h(γ2	γ1|+h(γ2	NUM
ap-1666	205	4	−	−	NOUN
ap-1666	205	5	γ1)2	γ1)2	PROPN
ap-1666	205	6	.	.	PUNCT
ap-1666	206	1	the	the	DET
ap-1666	206	2	following	follow	VERB
ap-1666	206	3	finite	finite	PROPN
ap-1666	206	4	element	element	NOUN
ap-1666	206	5	computation	computation	NOUN
ap-1666	206	6	illustrates	illustrate	VERB
ap-1666	206	7	the	the	DET
ap-1666	206	8	performance	performance	NOUN
ap-1666	206	9	of	of	ADP
ap-1666	206	10	our	our	PRON
ap-1666	206	11	model	model	NOUN
ap-1666	206	12	.	.	PUNCT
ap-1666	207	1	we	we	PRON
ap-1666	207	2	take	take	VERB
ap-1666	207	3	n	n	NOUN
ap-1666	207	4	=	=	SYM
ap-1666	207	5	2	2	NUM
ap-1666	207	6	,	,	PUNCT
ap-1666	207	7	ω	ω	NUM
ap-1666	207	8	=	=	SYM
ap-1666	207	9	(	(	PUNCT
ap-1666	207	10	0	0	NUM
ap-1666	207	11	,	,	PUNCT
ap-1666	207	12	1	1	NUM
ap-1666	207	13	)	)	PUNCT
ap-1666	207	14	×	×	NOUN
ap-1666	207	15	(	(	PUNCT
ap-1666	207	16	0	0	NUM
ap-1666	207	17	,	,	PUNCT
ap-1666	207	18	3	3	NUM
ap-1666	207	19	)	)	PUNCT
ap-1666	207	20	,	,	PUNCT
ap-1666	207	21	t	t	PROPN
ap-1666	207	22	∈	∈	PROPN
ap-1666	208	1	[	[	X
ap-1666	208	2	0	0	NUM
ap-1666	208	3	,	,	PUNCT
ap-1666	208	4	1	1	NUM
ap-1666	208	5	]	]	PUNCT
ap-1666	208	6	.	.	PUNCT
ap-1666	209	1	further	far	ADV
ap-1666	209	2	,	,	PUNCT
ap-1666	209	3	we	we	PRON
ap-1666	209	4	apply	apply	VERB
ap-1666	209	5	a	a	DET
ap-1666	209	6	zero	zero	NUM
ap-1666	209	7	dirichlet	dirichlet	NOUN
ap-1666	209	8	boundary	boundary	ADJ
ap-1666	209	9	condition	condition	NOUN
ap-1666	209	10	on	on	ADP
ap-1666	209	11	(	(	PUNCT
ap-1666	209	12	0	0	NUM
ap-1666	209	13	,	,	PUNCT
ap-1666	209	14	1)×	1)×	NUM
ap-1666	209	15	{	{	PUNCT
ap-1666	209	16	0	0	NUM
ap-1666	209	17	}	}	PUNCT
ap-1666	209	18	and	and	CCONJ
ap-1666	209	19	u(t	u(t	NOUN
ap-1666	209	20	,	,	PUNCT
ap-1666	209	21	x	x	NOUN
ap-1666	209	22	)	)	PUNCT
ap-1666	209	23	=	=	PUNCT
ap-1666	210	1	−0.6	−0.6	PROPN
ap-1666	210	2	t	t	X
ap-1666	210	3	for	for	ADP
ap-1666	210	4	x	x	SYM
ap-1666	210	5	=	=	SYM
ap-1666	210	6	(	(	PUNCT
ap-1666	210	7	0	0	NUM
ap-1666	210	8	,	,	PUNCT
ap-1666	210	9	1	1	X
ap-1666	210	10	)	)	PUNCT
ap-1666	210	11	×	×	NOUN
ap-1666	210	12	{	{	PUNCT
ap-1666	210	13	3	3	NUM
ap-1666	210	14	}	}	PUNCT
ap-1666	210	15	.	.	PUNCT
ap-1666	211	1	as	as	ADP
ap-1666	211	2	to	to	ADP
ap-1666	211	3	material	material	NOUN
ap-1666	211	4	properties	property	NOUN
ap-1666	211	5	we	we	PRON
ap-1666	211	6	consider	consider	VERB
ap-1666	211	7	a	a	DET
ap-1666	211	8	homogeneous	homogeneous	ADJ
ap-1666	211	9	isotropic	isotropic	NOUN
ap-1666	211	10	material	material	NOUN
ap-1666	211	11	with	with	ADP
ap-1666	211	12	a	a	DET
ap-1666	211	13	young	young	ADJ
ap-1666	211	14	modulus	modulus	ADJ
ap-1666	211	15	200gpa	200gpa	NUM
ap-1666	211	16	,	,	PUNCT
ap-1666	211	17	poisson	poisson	PROPN
ap-1666	211	18	’s	’s	PART
ap-1666	211	19	ratio	ratio	NOUN
ap-1666	211	20	0.3	0.3	NUM
ap-1666	211	21	,	,	PUNCT
ap-1666	211	22	a	a	DET
ap-1666	211	23	=	=	X
ap-1666	211	24	(	(	PUNCT
ap-1666	211	25	−1	−1	NOUN
ap-1666	211	26	,	,	PUNCT
ap-1666	211	27	1)/	1)/	PROPN
ap-1666	211	28	√	√	NUM
ap-1666	211	29	2	2	NUM
ap-1666	211	30	,	,	PUNCT
ap-1666	211	31	b	b	X
ap-1666	211	32	=	=	SYM
ap-1666	211	33	(	(	PUNCT
ap-1666	211	34	1	1	NUM
ap-1666	211	35	,	,	PUNCT
ap-1666	211	36	1)/	1)/	NOUN
ap-1666	211	37	√	√	NUM
ap-1666	211	38	2	2	NUM
ap-1666	211	39	and	and	CCONJ
ap-1666	211	40	the	the	DET
ap-1666	211	41	w1(e	w1(e	PROPN
ap-1666	211	42	)	)	PUNCT
ap-1666	211	43	=	=	SYM
ap-1666	211	44	λ	λ	NOUN
ap-1666	211	45	2	2	NUM
ap-1666	211	46	tr|e|2	tr|e|2	NOUN
ap-1666	212	1	+	+	X
ap-1666	213	1	µ|e|2	µ|e|2	NOUN
ap-1666	213	2	where	where	SCONJ
ap-1666	213	3	λ	λ	PROPN
ap-1666	213	4	and	and	CCONJ
ap-1666	213	5	µ	µ	PROPN
ap-1666	213	6	are	be	AUX
ap-1666	213	7	lamé	lamé	NOUN
ap-1666	213	8	constants	constant	NOUN
ap-1666	213	9	corresponding	correspond	VERB
ap-1666	213	10	to	to	ADP
ap-1666	213	11	the	the	DET
ap-1666	213	12	used	use	VERB
ap-1666	213	13	young	young	ADJ
ap-1666	213	14	modulus	modulus	NOUN
ap-1666	213	15	and	and	CCONJ
ap-1666	213	16	to	to	ADP
ap-1666	213	17	the	the	DET
ap-1666	213	18	poisson	poisson	NOUN
ap-1666	213	19	’s	’s	PART
ap-1666	213	20	ratio	ratio	NOUN
ap-1666	213	21	.	.	PUNCT
ap-1666	214	1	the	the	DET
ap-1666	214	2	other	other	ADJ
ap-1666	214	3	model	model	NOUN
ap-1666	214	4	constants	constant	NOUN
ap-1666	214	5	were	be	AUX
ap-1666	214	6	set	set	VERB
ap-1666	214	7	as	as	SCONJ
ap-1666	214	8	follows	follow	VERB
ap-1666	214	9	:	:	PUNCT
ap-1666	214	10	ε	ε	PROPN
ap-1666	214	11	=	=	SYM
ap-1666	214	12	40	40	NUM
ap-1666	214	13	gpa	gpa	PROPN
ap-1666	214	14	·	·	SYM
ap-1666	214	15	m2	m2	PROPN
ap-1666	214	16	,	,	PUNCT
ap-1666	214	17	α	α	NOUN
ap-1666	214	18	=	=	SYM
ap-1666	214	19	2	2	NUM
ap-1666	214	20	mpa	mpa	NOUN
ap-1666	214	21	,	,	PUNCT
ap-1666	214	22	and	and	CCONJ
ap-1666	214	23	h	h	NOUN
ap-1666	214	24	=	=	NUM
ap-1666	214	25	0.2	0.2	NUM
ap-1666	214	26	mpa	mpa	NOUN
ap-1666	214	27	.	.	PUNCT
ap-1666	215	1	the	the	DET
ap-1666	215	2	initial	initial	ADJ
ap-1666	215	3	condition	condition	NOUN
ap-1666	215	4	was	be	AUX
ap-1666	215	5	chosen	choose	VERB
ap-1666	215	6	γ	γ	X
ap-1666	215	7	=	=	SYM
ap-1666	215	8	0	0	PUNCT
ap-1666	215	9	(	(	PUNCT
ap-1666	215	10	no	no	DET
ap-1666	215	11	plastic	plastic	ADJ
ap-1666	215	12	deformation	deformation	NOUN
ap-1666	215	13	)	)	PUNCT
ap-1666	215	14	and	and	CCONJ
ap-1666	215	15	initial	initial	ADJ
ap-1666	215	16	yield	yield	NOUN
ap-1666	215	17	stress	stress	NOUN
ap-1666	215	18	p	p	NOUN
ap-1666	215	19	=	=	NOUN
ap-1666	215	20	200mpa	200mpa	NUM
ap-1666	215	21	.	.	PUNCT
ap-1666	216	1	note	note	VERB
ap-1666	216	2	that	that	SCONJ
ap-1666	216	3	the	the	DET
ap-1666	216	4	constant	constant	ADJ
ap-1666	216	5	defining	define	VERB
ap-1666	216	6	the	the	DET
ap-1666	216	7	energy	energy	NOUN
ap-1666	216	8	stored	store	VERB
ap-1666	216	9	in	in	ADP
ap-1666	216	10	defects	defect	NOUN
ap-1666	216	11	,	,	PUNCT
ap-1666	216	12	i.e.	i.e.	X
ap-1666	216	13	,	,	PUNCT
ap-1666	216	14	α	α	X
ap-1666	216	15	,	,	PUNCT
ap-1666	216	16	is	be	AUX
ap-1666	216	17	much	much	ADV
ap-1666	216	18	smaller	small	ADJ
ap-1666	216	19	than	than	ADP
ap-1666	216	20	the	the	DET
ap-1666	216	21	elastic	elastic	ADJ
ap-1666	216	22	constants	constant	NOUN
ap-1666	216	23	of	of	ADP
ap-1666	216	24	the	the	DET
ap-1666	216	25	material	material	NOUN
ap-1666	216	26	.	.	PUNCT
ap-1666	217	1	the	the	DET
ap-1666	217	2	specimen	speciman	NOUN
ap-1666	217	3	was	be	AUX
ap-1666	217	4	discretized	discretize	VERB
ap-1666	217	5	using	use	VERB
ap-1666	217	6	piecewise	piecewise	NOUN
ap-1666	217	7	affine	affine	NOUN
ap-1666	217	8	finite	finite	ADJ
ap-1666	217	9	elements	element	NOUN
ap-1666	217	10	for	for	ADP
ap-1666	217	11	the	the	DET
ap-1666	217	12	displacement	displacement	NOUN
ap-1666	217	13	as	as	ADV
ap-1666	217	14	well	well	ADV
ap-1666	217	15	as	as	ADP
ap-1666	217	16	for	for	ADP
ap-1666	217	17	fp	fp	NOUN
ap-1666	217	18	.	.	PUNCT
ap-1666	218	1	a	a	DET
ap-1666	218	2	sequence	sequence	NOUN
ap-1666	218	3	of	of	ADP
ap-1666	218	4	resulting	result	VERB
ap-1666	218	5	minimization	minimization	NOUN
ap-1666	218	6	problems	problem	NOUN
ap-1666	218	7	was	be	AUX
ap-1666	218	8	solved	solve	VERB
ap-1666	218	9	by	by	ADP
ap-1666	218	10	a	a	DET
ap-1666	218	11	fortran	fortran	ADJ
ap-1666	218	12	77	77	NUM
ap-1666	218	13	routine	routine	NOUN
ap-1666	218	14	described	describe	VERB
ap-1666	218	15	in	in	ADP
ap-1666	218	16	[	[	X
ap-1666	218	17	5	5	NUM
ap-1666	218	18	]	]	PUNCT
ap-1666	218	19	,	,	PUNCT
ap-1666	218	20	which	which	PRON
ap-1666	218	21	is	be	AUX
ap-1666	218	22	based	base	VERB
ap-1666	218	23	on	on	ADP
ap-1666	218	24	a	a	DET
ap-1666	218	25	quasinewton	quasinewton	NOUN
ap-1666	218	26	method	method	NOUN
ap-1666	218	27	.	.	PUNCT
ap-1666	219	1	it	it	PRON
ap-1666	219	2	is	be	AUX
ap-1666	219	3	designed	design	VERB
ap-1666	219	4	to	to	PART
ap-1666	219	5	solve	solve	VERB
ap-1666	219	6	large	large	ADJ
ap-1666	219	7	-	-	PUNCT
ap-1666	219	8	scale	scale	NOUN
ap-1666	219	9	nonlinear	nonlinear	ADJ
ap-1666	219	10	optimization	optimization	NOUN
ap-1666	219	11	problems	problem	NOUN
ap-1666	219	12	with	with	ADP
ap-1666	219	13	box	box	NOUN
ap-1666	219	14	constraints	constraint	NOUN
ap-1666	219	15	.	.	PUNCT
ap-1666	220	1	we	we	PRON
ap-1666	220	2	first	first	ADV
ap-1666	220	3	observe	observe	VERB
ap-1666	220	4	the	the	DET
ap-1666	220	5	development	development	NOUN
ap-1666	220	6	of	of	ADP
ap-1666	220	7	45	45	NUM
ap-1666	220	8	-	-	PUNCT
ap-1666	220	9	degree	degree	NOUN
ap-1666	220	10	bands	band	NOUN
ap-1666	220	11	in	in	ADP
ap-1666	220	12	the	the	DET
ap-1666	220	13	vicinity	vicinity	NOUN
ap-1666	220	14	of	of	ADP
ap-1666	220	15	the	the	DET
ap-1666	220	16	boundary	boundary	NOUN
ap-1666	220	17	where	where	SCONJ
ap-1666	220	18	the	the	DET
ap-1666	220	19	dirichlet	dirichlet	PROPN
ap-1666	220	20	boundary	boundary	PROPN
ap-1666	220	21	conditions	condition	NOUN
ap-1666	220	22	are	be	AUX
ap-1666	220	23	applied	apply	VERB
ap-1666	220	24	.	.	PUNCT
ap-1666	221	1	at	at	ADP
ap-1666	221	2	the	the	DET
ap-1666	221	3	final	final	ADJ
ap-1666	221	4	stage	stage	NOUN
ap-1666	221	5	a	a	DET
ap-1666	221	6	large	large	ADJ
ap-1666	221	7	plastic	plastic	ADJ
ap-1666	221	8	deformation	deformation	NOUN
ap-1666	221	9	appears	appear	VERB
ap-1666	221	10	in	in	ADP
ap-1666	221	11	the	the	DET
ap-1666	221	12	middle	middle	NOUN
ap-1666	221	13	of	of	ADP
ap-1666	221	14	the	the	DET
ap-1666	221	15	specimen	speciman	NOUN
ap-1666	221	16	(	(	PUNCT
ap-1666	221	17	see	see	VERB
ap-1666	222	1	e.g.	e.g.	ADV
ap-1666	222	2	[	[	X
ap-1666	222	3	20	20	NUM
ap-1666	222	4	]	]	PUNCT
ap-1666	222	5	for	for	ADP
ap-1666	222	6	similar	similar	ADJ
ap-1666	222	7	calculations	calculation	NOUN
ap-1666	222	8	)	)	PUNCT
ap-1666	222	9	.	.	PUNCT
ap-1666	223	1	the	the	DET
ap-1666	223	2	spontaneously	spontaneously	ADV
ap-1666	223	3	-	-	PUNCT
ap-1666	223	4	formed	form	VERB
ap-1666	223	5	inhomogeneity	inhomogeneity	NOUN
ap-1666	223	6	provides	provide	VERB
ap-1666	223	7	a	a	DET
ap-1666	223	8	hint	hint	NOUN
ap-1666	223	9	of	of	ADP
ap-1666	223	10	a	a	DET
ap-1666	223	11	deformation	deformation	NOUN
ap-1666	223	12	structuralization	structuralization	NOUN
ap-1666	223	13	process	process	NOUN
ap-1666	223	14	.	.	PUNCT
ap-1666	224	1	the	the	DET
ap-1666	224	2	characteristic	characteristic	ADJ
ap-1666	224	3	length	length	NOUN
ap-1666	224	4	scale	scale	NOUN
ap-1666	224	5	introduced	introduce	VERB
ap-1666	224	6	through	through	ADP
ap-1666	224	7	the	the	DET
ap-1666	224	8	higher	high	ADJ
ap-1666	224	9	gradients	gradient	NOUN
ap-1666	224	10	guarantees	guarantee	VERB
ap-1666	224	11	the	the	DET
ap-1666	224	12	intrinsic	intrinsic	ADJ
ap-1666	224	13	size	size	NOUN
ap-1666	224	14	of	of	ADP
ap-1666	224	15	the	the	DET
ap-1666	224	16	inhomogeneity	inhomogeneity	NOUN
ap-1666	224	17	independent	independent	NOUN
ap-1666	224	18	of	of	ADP
ap-1666	224	19	the	the	DET
ap-1666	224	20	fem	fem	NOUN
ap-1666	224	21	mesh	mesh	NOUN
ap-1666	224	22	size	size	NOUN
ap-1666	224	23	.	.	PUNCT
ap-1666	225	1	acknowledgements	acknowledgement	NOUN
ap-1666	225	2	this	this	DET
ap-1666	225	3	work	work	NOUN
ap-1666	225	4	was	be	AUX
ap-1666	225	5	supported	support	VERB
ap-1666	225	6	by	by	ADP
ap-1666	225	7	gačr	gačr	NOUN
ap-1666	225	8	through	through	ADP
ap-1666	225	9	projects	project	NOUN
ap-1666	225	10	p107/12/0121	p107/12/0121	VERB
ap-1666	225	11	,	,	PUNCT
ap-1666	225	12	p201/10/0357	p201/10/0357	NOUN
ap-1666	225	13	,	,	PUNCT
ap-1666	225	14	and	and	CCONJ
ap-1666	225	15	by	by	ADP
ap-1666	225	16	the	the	DET
ap-1666	225	17	research	research	NOUN
ap-1666	225	18	project	project	NOUN
ap-1666	225	19	vz	vz	NOUN
ap-1666	225	20	-	-	PUNCT
ap-1666	225	21	mšmt	mšmt	ADJ
ap-1666	225	22	6840770003	6840770003	NUM
ap-1666	225	23	.	.	PUNCT
ap-1666	226	1	references	reference	NOUN
ap-1666	226	2	[	[	X
ap-1666	226	3	1	1	NUM
ap-1666	226	4	]	]	SYM
ap-1666	226	5	bakó	bakó	NOUN
ap-1666	226	6	,	,	PUNCT
ap-1666	226	7	b.	b.	PROPN
ap-1666	226	8	,	,	PUNCT
ap-1666	226	9	groma	groma	PROPN
ap-1666	226	10	,	,	PUNCT
ap-1666	226	11	i.	i.	NOUN
ap-1666	226	12	:	:	PUNCT
ap-1666	226	13	stochastic	stochastic	ADJ
ap-1666	226	14	approach	approach	NOUN
ap-1666	226	15	for	for	ADP
ap-1666	226	16	modeling	model	VERB
ap-1666	226	17	dislocation	dislocation	NOUN
ap-1666	226	18	patterning	patterning	NOUN
ap-1666	226	19	,	,	PUNCT
ap-1666	226	20	phys	phy	NOUN
ap-1666	226	21	.	.	PUNCT
ap-1666	227	1	rev	rev	PROPN
ap-1666	227	2	.	.	PROPN
ap-1666	227	3	b.	b.	PROPN
ap-1666	227	4	,	,	PUNCT
ap-1666	227	5	60	60	NUM
ap-1666	227	6	,	,	PUNCT
ap-1666	227	7	1999	1999	NUM
ap-1666	227	8	,	,	PUNCT
ap-1666	227	9	122–127	122–127	NUM
ap-1666	227	10	.	.	PUNCT
ap-1666	228	1	−0.3	−0.3	PROPN
ap-1666	228	2	γ	γ	X
ap-1666	228	3	0	0	NUM
ap-1666	228	4	figure	figure	NOUN
ap-1666	228	5	1	1	NUM
ap-1666	228	6	:	:	PUNCT
ap-1666	228	7	elasto	elasto	NOUN
ap-1666	228	8	-	-	PUNCT
ap-1666	228	9	plastic	plastic	NOUN
ap-1666	228	10	deformation	deformation	NOUN
ap-1666	228	11	of	of	ADP
ap-1666	228	12	a	a	DET
ap-1666	228	13	twodimensional	twodimensional	ADJ
ap-1666	228	14	specimen	speciman	NOUN
ap-1666	228	15	at	at	ADP
ap-1666	228	16	four	four	NUM
ap-1666	228	17	time	time	NOUN
ap-1666	228	18	instants	instant	NOUN
ap-1666	228	19	.	.	PUNCT
ap-1666	229	1	the	the	DET
ap-1666	229	2	darker	dark	ADJ
ap-1666	229	3	the	the	DET
ap-1666	229	4	shade	shade	NOUN
ap-1666	229	5	of	of	ADP
ap-1666	229	6	gray	gray	ADJ
ap-1666	229	7	color	color	NOUN
ap-1666	229	8	,	,	PUNCT
ap-1666	229	9	the	the	DET
ap-1666	229	10	larger	large	ADJ
ap-1666	229	11	is	be	AUX
ap-1666	229	12	the	the	DET
ap-1666	229	13	plastic	plastic	ADJ
ap-1666	229	14	deformation	deformation	NOUN
ap-1666	229	15	,	,	PUNCT
ap-1666	229	16	i.e.	i.e.	X
ap-1666	229	17	,	,	PUNCT
ap-1666	229	18	|γ|	|γ|	PROPN
ap-1666	229	19	.	.	PUNCT
ap-1666	230	1	the	the	DET
ap-1666	230	2	loading	loading	NOUN
ap-1666	230	3	increases	increase	NOUN
ap-1666	230	4	from	from	ADP
ap-1666	230	5	left	left	ADJ
ap-1666	230	6	to	to	ADP
ap-1666	230	7	right	right	NOUN
ap-1666	230	8	.	.	PUNCT
ap-1666	231	1	[	[	X
ap-1666	231	2	2	2	NUM
ap-1666	231	3	]	]	PUNCT
ap-1666	231	4	ball	ball	NOUN
ap-1666	231	5	,	,	PUNCT
ap-1666	231	6	j.m	j.m	PROPN
ap-1666	231	7	.	.	PROPN
ap-1666	231	8	:	:	PUNCT
ap-1666	232	1	convexity	convexity	NOUN
ap-1666	232	2	conditions	condition	NOUN
ap-1666	232	3	and	and	CCONJ
ap-1666	232	4	existence	existence	NOUN
ap-1666	232	5	theorems	theorem	VERB
ap-1666	232	6	in	in	ADP
ap-1666	232	7	nonlinear	nonlinear	ADJ
ap-1666	232	8	elasticity	elasticity	NOUN
ap-1666	232	9	,	,	PUNCT
ap-1666	232	10	arch	arch	NOUN
ap-1666	232	11	.	.	PUNCT
ap-1666	233	1	ration	ration	NOUN
ap-1666	233	2	.	.	PUNCT
ap-1666	234	1	mech	mech	PROPN
ap-1666	234	2	.	.	PUNCT
ap-1666	235	1	anal	anal	PROPN
ap-1666	235	2	.	.	PROPN
ap-1666	235	3	,	,	PUNCT
ap-1666	235	4	63	63	NUM
ap-1666	235	5	,	,	PUNCT
ap-1666	235	6	1997	1997	NUM
ap-1666	235	7	,	,	PUNCT
ap-1666	235	8	337–403	337–403	NUM
ap-1666	235	9	.	.	PUNCT
ap-1666	236	1	[	[	X
ap-1666	236	2	3	3	NUM
ap-1666	236	3	]	]	PUNCT
ap-1666	236	4	bažant	bažant	NOUN
ap-1666	236	5	,	,	PUNCT
ap-1666	236	6	z.p	z.p	PROPN
ap-1666	236	7	.	.	PROPN
ap-1666	236	8	,	,	PUNCT
ap-1666	236	9	jirásek	jirásek	NOUN
ap-1666	236	10	,	,	PUNCT
ap-1666	236	11	m.	m.	NOUN
ap-1666	236	12	:	:	PUNCT
ap-1666	236	13	nonlocal	nonlocal	ADJ
ap-1666	236	14	integral	integral	ADJ
ap-1666	236	15	formulation	formulation	NOUN
ap-1666	236	16	of	of	ADP
ap-1666	236	17	plasticity	plasticity	NOUN
ap-1666	236	18	and	and	CCONJ
ap-1666	236	19	damage	damage	NOUN
ap-1666	236	20	:	:	PUNCT
ap-1666	236	21	a	a	DET
ap-1666	236	22	survey	survey	NOUN
ap-1666	236	23	of	of	ADP
ap-1666	236	24	progress	progress	NOUN
ap-1666	236	25	,	,	PUNCT
ap-1666	236	26	j.	j.	PROPN
ap-1666	236	27	engrg	engrg	PROPN
ap-1666	236	28	.	.	PROPN
ap-1666	236	29	mech	mech	PROPN
ap-1666	236	30	.	.	PROPN
ap-1666	236	31	,	,	PUNCT
ap-1666	236	32	128	128	NUM
ap-1666	236	33	,	,	PUNCT
ap-1666	236	34	2002	2002	NUM
ap-1666	236	35	,	,	PUNCT
ap-1666	236	36	1119	1119	NUM
ap-1666	236	37	–	–	PUNCT
ap-1666	236	38	1149	1149	NUM
ap-1666	236	39	.	.	PUNCT
ap-1666	237	1	[	[	X
ap-1666	237	2	4	4	NUM
ap-1666	237	3	]	]	X
ap-1666	237	4	bhattacharya	bhattacharya	NOUN
ap-1666	237	5	,	,	PUNCT
ap-1666	237	6	k.	k.	PROPN
ap-1666	237	7	:	:	PUNCT
ap-1666	237	8	microstructure	microstructure	NOUN
ap-1666	237	9	of	of	ADP
ap-1666	237	10	martensite	martensite	NOUN
ap-1666	237	11	.	.	PUNCT
ap-1666	238	1	why	why	SCONJ
ap-1666	238	2	it	it	PRON
ap-1666	238	3	forms	form	VERB
ap-1666	238	4	and	and	CCONJ
ap-1666	238	5	how	how	SCONJ
ap-1666	238	6	it	it	PRON
ap-1666	238	7	gives	give	VERB
ap-1666	238	8	rise	rise	NOUN
ap-1666	238	9	to	to	ADP
ap-1666	238	10	the	the	DET
ap-1666	238	11	shapememory	shapememory	ADJ
ap-1666	238	12	effect	effect	NOUN
ap-1666	238	13	.	.	PUNCT
ap-1666	239	1	oxford	oxford	NOUN
ap-1666	239	2	:	:	PUNCT
ap-1666	239	3	oxford	oxford	PROPN
ap-1666	239	4	university	university	PROPN
ap-1666	239	5	press	press	NOUN
ap-1666	239	6	,	,	PUNCT
ap-1666	239	7	2003	2003	NUM
ap-1666	239	8	.	.	PUNCT
ap-1666	240	1	[	[	X
ap-1666	240	2	5	5	NUM
ap-1666	240	3	]	]	X
ap-1666	240	4	byrd	byrd	PROPN
ap-1666	240	5	,	,	PUNCT
ap-1666	240	6	r.h	r.h	PROPN
ap-1666	240	7	.	.	PROPN
ap-1666	240	8	,	,	PUNCT
ap-1666	240	9	lu	lu	PROPN
ap-1666	240	10	,	,	PUNCT
ap-1666	240	11	p.	p.	NOUN
ap-1666	240	12	,	,	PUNCT
ap-1666	240	13	nocedal	nocedal	PROPN
ap-1666	240	14	,	,	PUNCT
ap-1666	240	15	j.	j.	PROPN
ap-1666	240	16	,	,	PUNCT
ap-1666	240	17	zhu	zhu	PROPN
ap-1666	240	18	,	,	PUNCT
ap-1666	240	19	c.	c.	PROPN
ap-1666	240	20	:	:	PUNCT
ap-1666	240	21	a	a	DET
ap-1666	240	22	limited	limited	ADJ
ap-1666	240	23	memory	memory	NOUN
ap-1666	240	24	algorithm	algorithm	NOUN
ap-1666	240	25	for	for	ADP
ap-1666	240	26	bound	bind	VERB
ap-1666	240	27	constrained	constrain	VERB
ap-1666	240	28	optimization	optimization	NOUN
ap-1666	240	29	problems	problem	NOUN
ap-1666	240	30	,	,	PUNCT
ap-1666	240	31	siam	siam	PROPN
ap-1666	240	32	j.	j.	PROPN
ap-1666	240	33	scientific	scientific	PROPN
ap-1666	240	34	computing	computing	NOUN
ap-1666	240	35	,	,	PUNCT
ap-1666	240	36	16	16	NUM
ap-1666	240	37	,	,	PUNCT
ap-1666	240	38	1995	1995	NUM
ap-1666	240	39	,	,	PUNCT
ap-1666	240	40	1190–1208	1190–1208	NUM
ap-1666	240	41	.	.	PUNCT
ap-1666	241	1	[	[	X
ap-1666	241	2	6	6	NUM
ap-1666	241	3	]	]	X
ap-1666	241	4	carstensen	carstensen	NOUN
ap-1666	241	5	,	,	PUNCT
ap-1666	241	6	c.	c.	PROPN
ap-1666	241	7	,	,	PUNCT
ap-1666	241	8	hackl	hackl	PROPN
ap-1666	241	9	,	,	PUNCT
ap-1666	241	10	k.	k.	PROPN
ap-1666	241	11	mielke	mielke	PROPN
ap-1666	241	12	,	,	PUNCT
ap-1666	241	13	a.	a.	NOUN
ap-1666	241	14	:	:	PUNCT
ap-1666	241	15	nonconvex	nonconvex	NOUN
ap-1666	241	16	potentials	potential	NOUN
ap-1666	241	17	and	and	CCONJ
ap-1666	241	18	microstructures	microstructure	NOUN
ap-1666	241	19	in	in	ADP
ap-1666	241	20	finite	finite	ADJ
ap-1666	241	21	-	-	ADJ
ap-1666	241	22	strain	strain	ADJ
ap-1666	241	23	plasticity	plasticity	NOUN
ap-1666	241	24	,	,	PUNCT
ap-1666	241	25	proc	proc	NOUN
ap-1666	241	26	.	.	PUNCT
ap-1666	242	1	roy	roy	PROPN
ap-1666	242	2	.	.	PROPN
ap-1666	242	3	soc	soc	PROPN
ap-1666	242	4	.	.	PUNCT
ap-1666	243	1	lond	lond	PROPN
ap-1666	243	2	.	.	PUNCT
ap-1666	244	1	a	a	DET
ap-1666	244	2	,	,	PUNCT
ap-1666	244	3	458	458	NUM
ap-1666	244	4	,	,	PUNCT
ap-1666	244	5	2002	2002	NUM
ap-1666	244	6	,	,	PUNCT
ap-1666	244	7	299–317	299–317	NUM
ap-1666	244	8	.	.	PUNCT
ap-1666	245	1	[	[	X
ap-1666	245	2	7	7	NUM
ap-1666	245	3	]	]	X
ap-1666	245	4	dacorogna	dacorogna	PROPN
ap-1666	245	5	,	,	PUNCT
ap-1666	245	6	b.	b.	PROPN
ap-1666	245	7	:	:	PUNCT
ap-1666	245	8	direct	direct	ADJ
ap-1666	245	9	methods	method	NOUN
ap-1666	245	10	in	in	ADP
ap-1666	245	11	the	the	DET
ap-1666	245	12	calculus	calculus	NOUN
ap-1666	245	13	of	of	ADP
ap-1666	245	14	variations	variation	NOUN
ap-1666	245	15	2nd	2nd	PROPN
ap-1666	245	16	ed	ed	NOUN
ap-1666	245	17	.	.	PUNCT
ap-1666	246	1	new	new	PROPN
ap-1666	246	2	york	york	PROPN
ap-1666	246	3	:	:	PUNCT
ap-1666	246	4	springer	springer	NOUN
ap-1666	246	5	,	,	PUNCT
ap-1666	246	6	2008	2008	NUM
ap-1666	246	7	.	.	PUNCT
ap-1666	247	1	[	[	X
ap-1666	247	2	8	8	X
ap-1666	247	3	]	]	X
ap-1666	247	4	dal	dal	NOUN
ap-1666	247	5	maso	maso	PROPN
ap-1666	247	6	,	,	PUNCT
ap-1666	247	7	g.	g.	PROPN
ap-1666	247	8	,	,	PUNCT
ap-1666	247	9	francfort	francfort	NOUN
ap-1666	247	10	,	,	PUNCT
ap-1666	247	11	g.	g.	NOUN
ap-1666	247	12	,	,	PUNCT
ap-1666	247	13	toader	toader	NOUN
ap-1666	247	14	,	,	PUNCT
ap-1666	247	15	r.	r.	PROPN
ap-1666	247	16	:	:	PUNCT
ap-1666	247	17	a	a	DET
ap-1666	247	18	model	model	NOUN
ap-1666	247	19	of	of	ADP
ap-1666	247	20	quasistatic	quasistatic	ADJ
ap-1666	247	21	crack	crack	NOUN
ap-1666	247	22	growth	growth	NOUN
ap-1666	247	23	of	of	ADP
ap-1666	247	24	brittle	brittle	ADJ
ap-1666	247	25	fractures	fracture	NOUN
ap-1666	247	26	:	:	PUNCT
ap-1666	247	27	existence	existence	NOUN
ap-1666	247	28	and	and	CCONJ
ap-1666	247	29	approximation	approximation	NOUN
ap-1666	247	30	results	result	NOUN
ap-1666	247	31	,	,	PUNCT
ap-1666	247	32	arch	arch	NOUN
ap-1666	247	33	.	.	PUNCT
ap-1666	248	1	ration	ration	NOUN
ap-1666	248	2	.	.	PUNCT
ap-1666	249	1	mech	mech	PROPN
ap-1666	249	2	.	.	PUNCT
ap-1666	250	1	anal	anal	PROPN
ap-1666	250	2	.	.	PROPN
ap-1666	250	3	,	,	PUNCT
ap-1666	250	4	176	176	NUM
ap-1666	250	5	,	,	PUNCT
ap-1666	250	6	2005	2005	NUM
ap-1666	250	7	,	,	PUNCT
ap-1666	250	8	165–225	165–225	NUM
ap-1666	250	9	.	.	PUNCT
ap-1666	251	1	[	[	X
ap-1666	251	2	9	9	NUM
ap-1666	251	3	]	]	SYM
ap-1666	251	4	dillon	dillon	PROPN
ap-1666	251	5	,	,	PUNCT
ap-1666	251	6	o.w	o.w	PROPN
ap-1666	251	7	.	.	PROPN
ap-1666	251	8	,	,	PUNCT
ap-1666	251	9	kratochvíl	kratochvíl	PROPN
ap-1666	251	10	,	,	PUNCT
ap-1666	251	11	j.	j.	PROPN
ap-1666	251	12	:	:	PUNCT
ap-1666	251	13	a	a	DET
ap-1666	251	14	strain	strain	NOUN
ap-1666	251	15	gradient	gradient	NOUN
ap-1666	251	16	theory	theory	NOUN
ap-1666	251	17	of	of	ADP
ap-1666	251	18	plasticity	plasticity	NOUN
ap-1666	251	19	,	,	PUNCT
ap-1666	251	20	int	int	NOUN
ap-1666	251	21	.	.	PUNCT
ap-1666	252	1	j.	j.	PROPN
ap-1666	252	2	solid	solid	PROPN
ap-1666	252	3	struct	struct	NOUN
ap-1666	252	4	.	.	PUNCT
ap-1666	252	5	,	,	PUNCT
ap-1666	252	6	6	6	NUM
ap-1666	252	7	,	,	PUNCT
ap-1666	252	8	1970	1970	NUM
ap-1666	252	9	,	,	PUNCT
ap-1666	252	10	1513–1533	1513–1533	NUM
ap-1666	252	11	.	.	PUNCT
ap-1666	253	1	[	[	X
ap-1666	253	2	10	10	NUM
ap-1666	253	3	]	]	X
ap-1666	253	4	fleck	fleck	NOUN
ap-1666	253	5	,	,	PUNCT
ap-1666	253	6	n.	n.	NOUN
ap-1666	253	7	,	,	PUNCT
ap-1666	253	8	hutchinson	hutchinson	PROPN
ap-1666	253	9	,	,	PUNCT
ap-1666	253	10	j.w	j.w	PROPN
ap-1666	253	11	.	.	PROPN
ap-1666	253	12	:	:	PUNCT
ap-1666	254	1	a	a	DET
ap-1666	254	2	phenomenological	phenomenological	ADJ
ap-1666	254	3	theory	theory	NOUN
ap-1666	254	4	for	for	ADP
ap-1666	254	5	strain	strain	NOUN
ap-1666	254	6	gradient	gradient	ADJ
ap-1666	254	7	effects	effect	NOUN
ap-1666	254	8	in	in	ADP
ap-1666	254	9	plasticity	plasticity	NOUN
ap-1666	254	10	.	.	PUNCT
ap-1666	255	1	j.	j.	PROPN
ap-1666	255	2	mech	mech	PROPN
ap-1666	255	3	.	.	PUNCT
ap-1666	256	1	phys	phy	NOUN
ap-1666	256	2	.	.	PUNCT
ap-1666	257	1	solids	solid	NOUN
ap-1666	257	2	,	,	PUNCT
ap-1666	257	3	41	41	NUM
ap-1666	257	4	,	,	PUNCT
ap-1666	257	5	1993	1993	NUM
ap-1666	257	6	,	,	PUNCT
ap-1666	257	7	1825–1857	1825–1857	NUM
ap-1666	257	8	.	.	PUNCT
ap-1666	257	9	13	13	NUM
ap-1666	257	10	acta	acta	PROPN
ap-1666	257	11	polytechnica	polytechnica	PROPN
ap-1666	257	12	vol	vol	NOUN
ap-1666	257	13	.	.	PROPN
ap-1666	258	1	52	52	NUM
ap-1666	258	2	no	no	NOUN
ap-1666	258	3	.	.	PUNCT
ap-1666	259	1	6/2012	6/2012	NUM
ap-1666	260	1	[	[	X
ap-1666	260	2	11	11	NUM
ap-1666	260	3	]	]	PUNCT
ap-1666	260	4	francfort	francfort	NOUN
ap-1666	260	5	,	,	PUNCT
ap-1666	260	6	g.	g.	PROPN
ap-1666	260	7	,	,	PUNCT
ap-1666	260	8	mielke	mielke	PROPN
ap-1666	260	9	,	,	PUNCT
ap-1666	260	10	a.	a.	NOUN
ap-1666	260	11	:	:	PUNCT
ap-1666	260	12	existence	existence	NOUN
ap-1666	260	13	results	result	VERB
ap-1666	260	14	for	for	ADP
ap-1666	260	15	a	a	DET
ap-1666	260	16	class	class	NOUN
ap-1666	260	17	of	of	ADP
ap-1666	260	18	rate	rate	NOUN
ap-1666	260	19	-	-	PUNCT
ap-1666	260	20	independent	independent	ADJ
ap-1666	260	21	material	material	NOUN
ap-1666	260	22	models	model	NOUN
ap-1666	260	23	with	with	ADP
ap-1666	260	24	nonconvex	nonconvex	NOUN
ap-1666	260	25	elastic	elastic	ADJ
ap-1666	260	26	energies	energy	NOUN
ap-1666	260	27	,	,	PUNCT
ap-1666	260	28	j.	j.	PROPN
ap-1666	260	29	reine	reine	PROPN
ap-1666	260	30	angew	angew	PROPN
ap-1666	260	31	.	.	PUNCT
ap-1666	261	1	math	math	NOUN
ap-1666	261	2	.	.	PUNCT
ap-1666	261	3	,	,	PUNCT
ap-1666	261	4	595	595	NUM
ap-1666	261	5	,	,	PUNCT
ap-1666	261	6	2006	2006	NUM
ap-1666	261	7	,	,	PUNCT
ap-1666	261	8	55–91	55–91	NUM
ap-1666	261	9	.	.	PUNCT
ap-1666	262	1	[	[	X
ap-1666	262	2	12	12	NUM
ap-1666	262	3	]	]	SYM
ap-1666	262	4	frémond	frémond	NOUN
ap-1666	262	5	,	,	PUNCT
ap-1666	262	6	m.	m.	NOUN
ap-1666	262	7	:	:	PUNCT
ap-1666	262	8	non	non	ADJ
ap-1666	262	9	-	-	ADJ
ap-1666	262	10	smooth	smooth	ADJ
ap-1666	262	11	thermomechanics	thermomechanic	NOUN
ap-1666	262	12	.	.	PUNCT
ap-1666	263	1	berlin	berlin	ADJ
ap-1666	263	2	:	:	PUNCT
ap-1666	263	3	springer	springer	NOUN
ap-1666	263	4	,	,	PUNCT
ap-1666	263	5	2002	2002	NUM
ap-1666	263	6	.	.	PUNCT
ap-1666	264	1	[	[	X
ap-1666	264	2	13	13	NUM
ap-1666	264	3	]	]	PUNCT
ap-1666	264	4	giacomini	giacomini	PROPN
ap-1666	264	5	,	,	PUNCT
ap-1666	264	6	a.	a.	NOUN
ap-1666	264	7	,	,	PUNCT
ap-1666	264	8	lusardi	lusardi	PROPN
ap-1666	264	9	l.	l.	PROPN
ap-1666	264	10	:	:	PUNCT
ap-1666	264	11	quasistatic	quasistatic	ADJ
ap-1666	264	12	evolution	evolution	NOUN
ap-1666	264	13	for	for	ADP
ap-1666	264	14	a	a	DET
ap-1666	264	15	model	model	NOUN
ap-1666	264	16	in	in	ADP
ap-1666	264	17	strain	strain	NOUN
ap-1666	264	18	gradient	gradient	NOUN
ap-1666	264	19	plasticity	plasticity	NOUN
ap-1666	264	20	,	,	PUNCT
ap-1666	264	21	siam	siam	PROPN
ap-1666	264	22	j.	j.	PROPN
ap-1666	264	23	math	math	PROPN
ap-1666	264	24	.	.	PUNCT
ap-1666	265	1	anal	anal	PROPN
ap-1666	265	2	.	.	PROPN
ap-1666	265	3	,	,	PUNCT
ap-1666	265	4	40	40	NUM
ap-1666	265	5	,	,	PUNCT
ap-1666	265	6	2008	2008	NUM
ap-1666	265	7	,	,	PUNCT
ap-1666	265	8	1201–1245	1201–1245	NUM
ap-1666	265	9	.	.	PUNCT
ap-1666	266	1	[	[	X
ap-1666	266	2	14	14	NUM
ap-1666	266	3	]	]	X
ap-1666	266	4	groma	groma	PROPN
ap-1666	266	5	,	,	PUNCT
ap-1666	266	6	i.	i.	PROPN
ap-1666	266	7	:	:	PUNCT
ap-1666	266	8	link	link	VERB
ap-1666	266	9	between	between	ADP
ap-1666	266	10	the	the	DET
ap-1666	266	11	microscopic	microscopic	NOUN
ap-1666	266	12	and	and	CCONJ
ap-1666	266	13	mesoscopic	mesoscopic	VERB
ap-1666	266	14	length	length	NOUN
ap-1666	266	15	-	-	PUNCT
ap-1666	266	16	scale	scale	NOUN
ap-1666	266	17	description	description	NOUN
ap-1666	266	18	of	of	ADP
ap-1666	266	19	the	the	DET
ap-1666	266	20	collective	collective	ADJ
ap-1666	266	21	behaviour	behaviour	NOUN
ap-1666	266	22	of	of	ADP
ap-1666	266	23	dislocations	dislocation	NOUN
ap-1666	266	24	,	,	PUNCT
ap-1666	266	25	phys	phy	NOUN
ap-1666	266	26	.	.	PUNCT
ap-1666	267	1	rev	rev	PROPN
ap-1666	267	2	.	.	PROPN
ap-1666	268	1	b	b	X
ap-1666	268	2	,	,	PUNCT
ap-1666	268	3	56	56	NUM
ap-1666	268	4	,	,	PUNCT
ap-1666	268	5	1997	1997	NUM
ap-1666	268	6	,	,	PUNCT
ap-1666	268	7	5807	5807	NUM
ap-1666	268	8	.	.	PUNCT
ap-1666	269	1	[	[	X
ap-1666	269	2	15	15	NUM
ap-1666	269	3	]	]	X
ap-1666	269	4	gurtin	gurtin	NOUN
ap-1666	269	5	,	,	PUNCT
ap-1666	269	6	m.e	m.e	PROPN
ap-1666	269	7	.	.	PUNCT
ap-1666	269	8	:	:	PUNCT
ap-1666	269	9	on	on	ADP
ap-1666	269	10	the	the	DET
ap-1666	269	11	plasticity	plasticity	NOUN
ap-1666	269	12	of	of	ADP
ap-1666	269	13	single	single	ADJ
ap-1666	269	14	crystals	crystal	NOUN
ap-1666	269	15	:	:	PUNCT
ap-1666	269	16	free	free	ADJ
ap-1666	269	17	energy	energy	NOUN
ap-1666	269	18	,	,	PUNCT
ap-1666	269	19	microforces	microforce	NOUN
ap-1666	269	20	,	,	PUNCT
ap-1666	269	21	plastic	plastic	NOUN
ap-1666	269	22	-	-	PUNCT
ap-1666	269	23	strain	strain	NOUN
ap-1666	269	24	gradients	gradient	NOUN
ap-1666	269	25	,	,	PUNCT
ap-1666	269	26	j.	j.	PROPN
ap-1666	269	27	mech	mech	PROPN
ap-1666	269	28	.	.	PUNCT
ap-1666	270	1	phys	phy	NOUN
ap-1666	270	2	.	.	PUNCT
ap-1666	271	1	solids	solid	NOUN
ap-1666	271	2	,	,	PUNCT
ap-1666	271	3	48	48	NUM
ap-1666	271	4	,	,	PUNCT
ap-1666	271	5	2000	2000	NUM
ap-1666	271	6	,	,	PUNCT
ap-1666	271	7	989–1036	989–1036	NUM
ap-1666	271	8	.	.	PUNCT
ap-1666	272	1	[	[	X
ap-1666	272	2	16	16	NUM
ap-1666	272	3	]	]	X
ap-1666	272	4	gurtin	gurtin	NOUN
ap-1666	272	5	,	,	PUNCT
ap-1666	272	6	m.e	m.e	PROPN
ap-1666	272	7	.	.	PROPN
ap-1666	272	8	,	,	PUNCT
ap-1666	272	9	anand	anand	PROPN
ap-1666	272	10	,	,	PUNCT
ap-1666	272	11	l.	l.	PROPN
ap-1666	272	12	:	:	PUNCT
ap-1666	272	13	a	a	DET
ap-1666	272	14	theory	theory	NOUN
ap-1666	272	15	of	of	ADP
ap-1666	272	16	straingradient	straingradient	NOUN
ap-1666	272	17	plasticity	plasticity	NOUN
ap-1666	272	18	for	for	ADP
ap-1666	272	19	isotropic	isotropic	NOUN
ap-1666	272	20	,	,	PUNCT
ap-1666	272	21	plastically	plastically	NOUN
ap-1666	272	22	irrotational	irrotational	ADJ
ap-1666	272	23	materials	material	NOUN
ap-1666	272	24	.	.	PUNCT
ap-1666	273	1	i.	i.	PROPN
ap-1666	273	2	small	small	ADJ
ap-1666	273	3	deformations	deformation	NOUN
ap-1666	273	4	,	,	PUNCT
ap-1666	273	5	j.	j.	PROPN
ap-1666	273	6	mech	mech	PROPN
ap-1666	273	7	.	.	PUNCT
ap-1666	274	1	phys	phy	NOUN
ap-1666	274	2	.	.	PUNCT
ap-1666	275	1	solids	solid	NOUN
ap-1666	275	2	,	,	PUNCT
ap-1666	275	3	53	53	NUM
ap-1666	275	4	,	,	PUNCT
ap-1666	275	5	2005	2005	NUM
ap-1666	275	6	,	,	PUNCT
ap-1666	275	7	1624–1649	1624–1649	NUM
ap-1666	275	8	.	.	PUNCT
ap-1666	276	1	[	[	X
ap-1666	276	2	17	17	NUM
ap-1666	276	3	]	]	SYM
ap-1666	276	4	hill	hill	PROPN
ap-1666	276	5	,	,	PUNCT
ap-1666	276	6	r.	r.	PROPN
ap-1666	276	7	:	:	PUNCT
ap-1666	276	8	a	a	DET
ap-1666	276	9	variational	variational	ADJ
ap-1666	276	10	principle	principle	NOUN
ap-1666	276	11	of	of	ADP
ap-1666	276	12	maximum	maximum	ADJ
ap-1666	276	13	plastic	plastic	ADJ
ap-1666	276	14	work	work	NOUN
ap-1666	276	15	in	in	ADP
ap-1666	276	16	classical	classical	ADJ
ap-1666	276	17	plasticity	plasticity	NOUN
ap-1666	276	18	,	,	PUNCT
ap-1666	276	19	q.	q.	PROPN
ap-1666	276	20	j.	j.	PROPN
ap-1666	276	21	mech	mech	PROPN
ap-1666	276	22	.	.	PUNCT
ap-1666	277	1	appl	appl	PROPN
ap-1666	277	2	.	.	PROPN
ap-1666	277	3	math	math	PROPN
ap-1666	277	4	.	.	PUNCT
ap-1666	277	5	,	,	PUNCT
ap-1666	277	6	1	1	NUM
ap-1666	277	7	,	,	PUNCT
ap-1666	277	8	1948	1948	NUM
ap-1666	277	9	,	,	PUNCT
ap-1666	277	10	18–28	18–28	NUM
ap-1666	277	11	.	.	PUNCT
ap-1666	278	1	[	[	X
ap-1666	278	2	18	18	NUM
ap-1666	278	3	]	]	X
ap-1666	278	4	kratochvíl	kratochvíl	PROPN
ap-1666	278	5	,	,	PUNCT
ap-1666	278	6	j.	j.	PROPN
ap-1666	278	7	,	,	PUNCT
ap-1666	278	8	sedláček	sedláček	PROPN
ap-1666	278	9	,	,	PUNCT
ap-1666	278	10	r.	r.	PROPN
ap-1666	278	11	:	:	PUNCT
ap-1666	278	12	statistical	statistical	ADJ
ap-1666	278	13	foundation	foundation	NOUN
ap-1666	278	14	of	of	ADP
ap-1666	278	15	continuum	continuum	ADJ
ap-1666	278	16	dislocation	dislocation	NOUN
ap-1666	278	17	plasticity	plasticity	NOUN
ap-1666	278	18	,	,	PUNCT
ap-1666	278	19	phys	phy	NOUN
ap-1666	278	20	.	.	PUNCT
ap-1666	278	21	rev	rev	PROPN
ap-1666	278	22	.	.	PROPN
ap-1666	279	1	b	b	PROPN
ap-1666	279	2	77	77	NUM
ap-1666	279	3	,	,	PUNCT
ap-1666	279	4	2008	2008	NUM
ap-1666	279	5	,	,	PUNCT
ap-1666	279	6	134102	134102	NUM
ap-1666	279	7	.	.	PUNCT
ap-1666	280	1	[	[	X
ap-1666	280	2	19	19	NUM
ap-1666	280	3	]	]	PUNCT
ap-1666	280	4	kružík	kružík	NOUN
ap-1666	280	5	,	,	PUNCT
ap-1666	280	6	m.	m.	NOUN
ap-1666	280	7	,	,	PUNCT
ap-1666	280	8	zimmer	zimmer	PROPN
ap-1666	280	9	,	,	PUNCT
ap-1666	280	10	j.	j.	PROPN
ap-1666	280	11	:	:	PUNCT
ap-1666	280	12	a	a	DET
ap-1666	280	13	model	model	NOUN
ap-1666	280	14	of	of	ADP
ap-1666	280	15	shape	shape	NOUN
ap-1666	280	16	memory	memory	NOUN
ap-1666	280	17	alloys	alloy	NOUN
ap-1666	280	18	accounting	account	VERB
ap-1666	280	19	for	for	ADP
ap-1666	280	20	plasticity	plasticity	NOUN
ap-1666	280	21	,	,	PUNCT
ap-1666	280	22	i	i	PRON
ap-1666	280	23	m	m	VERB
ap-1666	280	24	a	a	PROPN
ap-1666	280	25	j.	j.	PROPN
ap-1666	280	26	appl	appl	PROPN
ap-1666	280	27	.	.	PROPN
ap-1666	280	28	math	math	PROPN
ap-1666	280	29	.	.	PUNCT
ap-1666	280	30	,	,	PUNCT
ap-1666	280	31	76	76	NUM
ap-1666	280	32	,	,	PUNCT
ap-1666	280	33	2010	2010	NUM
ap-1666	280	34	,	,	PUNCT
ap-1666	280	35	193	193	NUM
ap-1666	280	36	-	-	SYM
ap-1666	280	37	216	216	NUM
ap-1666	280	38	.	.	PUNCT
ap-1666	281	1	[	[	X
ap-1666	281	2	20	20	NUM
ap-1666	281	3	]	]	X
ap-1666	281	4	kuroda	kuroda	PROPN
ap-1666	281	5	,	,	PUNCT
ap-1666	281	6	m.	m.	NOUN
ap-1666	281	7	,	,	PUNCT
ap-1666	281	8	tvergaard	tvergaard	NOUN
ap-1666	281	9	,	,	PUNCT
ap-1666	281	10	v.	v.	ADP
ap-1666	281	11	:	:	PUNCT
ap-1666	281	12	a	a	DET
ap-1666	281	13	finite	finite	ADJ
ap-1666	281	14	deformation	deformation	NOUN
ap-1666	281	15	theory	theory	NOUN
ap-1666	281	16	of	of	ADP
ap-1666	281	17	higher	high	ADJ
ap-1666	281	18	-	-	PUNCT
ap-1666	281	19	order	order	NOUN
ap-1666	281	20	gradient	gradient	NOUN
ap-1666	281	21	crystal	crystal	NOUN
ap-1666	281	22	plasticity	plasticity	NOUN
ap-1666	281	23	,	,	PUNCT
ap-1666	281	24	j.	j.	PROPN
ap-1666	281	25	mech	mech	PROPN
ap-1666	281	26	.	.	PUNCT
ap-1666	282	1	phys	phy	NOUN
ap-1666	282	2	.	.	PUNCT
ap-1666	283	1	solids	solid	NOUN
ap-1666	283	2	,	,	PUNCT
ap-1666	283	3	56	56	NUM
ap-1666	283	4	,	,	PUNCT
ap-1666	283	5	2008	2008	NUM
ap-1666	283	6	,	,	PUNCT
ap-1666	283	7	2573	2573	NUM
ap-1666	283	8	-	-	SYM
ap-1666	283	9	2585	2585	NUM
ap-1666	283	10	.	.	PUNCT
ap-1666	284	1	[	[	X
ap-1666	284	2	21	21	NUM
ap-1666	284	3	]	]	SYM
ap-1666	284	4	mainik	mainik	X
ap-1666	284	5	,	,	PUNCT
ap-1666	284	6	a.	a.	NOUN
ap-1666	284	7	,	,	PUNCT
ap-1666	284	8	mielke	mielke	ADV
ap-1666	284	9	,	,	PUNCT
ap-1666	284	10	a.	a.	NOUN
ap-1666	284	11	:	:	PUNCT
ap-1666	284	12	existence	existence	NOUN
ap-1666	284	13	results	result	VERB
ap-1666	284	14	for	for	ADP
ap-1666	284	15	energetic	energetic	ADJ
ap-1666	284	16	models	model	NOUN
ap-1666	284	17	for	for	ADP
ap-1666	284	18	rate	rate	NOUN
ap-1666	284	19	-	-	PUNCT
ap-1666	284	20	independent	independent	ADJ
ap-1666	284	21	systems	system	NOUN
ap-1666	284	22	.	.	PUNCT
ap-1666	285	1	calc	calc	PROPN
ap-1666	285	2	.	.	PUNCT
ap-1666	286	1	var	var	PROPN
ap-1666	286	2	.	.	PUNCT
ap-1666	287	1	partial	partial	ADJ
ap-1666	287	2	differential	differential	NOUN
ap-1666	287	3	equations	equation	NOUN
ap-1666	287	4	,	,	PUNCT
ap-1666	287	5	22	22	NUM
ap-1666	287	6	,	,	PUNCT
ap-1666	287	7	2005	2005	NUM
ap-1666	287	8	,	,	PUNCT
ap-1666	287	9	73–99	73–99	NUM
ap-1666	287	10	.	.	PUNCT
ap-1666	288	1	[	[	X
ap-1666	288	2	22	22	NUM
ap-1666	288	3	]	]	SYM
ap-1666	288	4	mainik	mainik	X
ap-1666	288	5	,	,	PUNCT
ap-1666	288	6	a.	a.	NOUN
ap-1666	288	7	,	,	PUNCT
ap-1666	288	8	mielke	mielke	ADV
ap-1666	288	9	,	,	PUNCT
ap-1666	288	10	a.	a.	NOUN
ap-1666	288	11	:	:	PUNCT
ap-1666	288	12	global	global	ADJ
ap-1666	288	13	existence	existence	NOUN
ap-1666	288	14	for	for	ADP
ap-1666	288	15	rateindependent	rateindependent	NOUN
ap-1666	288	16	gradient	gradient	NOUN
ap-1666	288	17	plasticity	plasticity	NOUN
ap-1666	288	18	at	at	ADP
ap-1666	288	19	finite	finite	ADJ
ap-1666	288	20	strain	strain	NOUN
ap-1666	288	21	,	,	PUNCT
ap-1666	288	22	j.	j.	PROPN
ap-1666	288	23	nonlinear	nonlinear	PROPN
ap-1666	288	24	sci	sci	PROPN
ap-1666	288	25	.	.	PROPN
ap-1666	288	26	,	,	PUNCT
ap-1666	288	27	19	19	NUM
ap-1666	288	28	,	,	PUNCT
ap-1666	288	29	2009	2009	NUM
ap-1666	288	30	,	,	PUNCT
ap-1666	288	31	221–248	221–248	NUM
ap-1666	288	32	.	.	PUNCT
ap-1666	289	1	[	[	X
ap-1666	289	2	23	23	NUM
ap-1666	289	3	]	]	SYM
ap-1666	289	4	maugin	maugin	NOUN
ap-1666	289	5	,	,	PUNCT
ap-1666	289	6	g.a	g.a	PROPN
ap-1666	289	7	.	.	PROPN
ap-1666	289	8	:	:	PUNCT
ap-1666	290	1	the	the	DET
ap-1666	290	2	thermomechanics	thermomechanic	NOUN
ap-1666	290	3	of	of	ADP
ap-1666	290	4	plasticity	plasticity	NOUN
ap-1666	290	5	and	and	CCONJ
ap-1666	290	6	fracture	fracture	PROPN
ap-1666	290	7	cambridge	cambridge	NOUN
ap-1666	290	8	:	:	PUNCT
ap-1666	290	9	university	university	NOUN
ap-1666	290	10	press	press	NOUN
ap-1666	290	11	,	,	PUNCT
ap-1666	290	12	1992	1992	NUM
ap-1666	290	13	.	.	PUNCT
ap-1666	291	1	[	[	X
ap-1666	291	2	24	24	NUM
ap-1666	291	3	]	]	PUNCT
ap-1666	291	4	mielke	mielke	PROPN
ap-1666	291	5	,	,	PUNCT
ap-1666	291	6	a.	a.	NOUN
ap-1666	291	7	:	:	PUNCT
ap-1666	291	8	energetic	energetic	ADJ
ap-1666	291	9	formulation	formulation	NOUN
ap-1666	291	10	of	of	ADP
ap-1666	291	11	multiplicative	multiplicative	ADJ
ap-1666	291	12	elasto	elasto	NOUN
ap-1666	291	13	-	-	PUNCT
ap-1666	291	14	plasticity	plasticity	NOUN
ap-1666	291	15	using	use	VERB
ap-1666	291	16	dissipation	dissipation	NOUN
ap-1666	291	17	distances	distance	NOUN
ap-1666	291	18	.	.	PUNCT
ap-1666	292	1	cont	cont	NOUN
ap-1666	292	2	.	.	PUNCT
ap-1666	292	3	mech	mech	PROPN
ap-1666	292	4	.	.	PUNCT
ap-1666	293	1	thermodyn	thermodyn	NOUN
ap-1666	293	2	.	.	PUNCT
ap-1666	293	3	,	,	PUNCT
ap-1666	293	4	15	15	NUM
ap-1666	293	5	,	,	PUNCT
ap-1666	293	6	2002	2002	NUM
ap-1666	293	7	,	,	PUNCT
ap-1666	293	8	351–382	351–382	NUM
ap-1666	293	9	.	.	PUNCT
ap-1666	294	1	[	[	X
ap-1666	294	2	25	25	NUM
ap-1666	294	3	]	]	PUNCT
ap-1666	294	4	mielke	mielke	PROPN
ap-1666	294	5	,	,	PUNCT
ap-1666	294	6	a.	a.	NOUN
ap-1666	294	7	:	:	PUNCT
ap-1666	294	8	evolution	evolution	NOUN
ap-1666	294	9	of	of	ADP
ap-1666	294	10	rate	rate	NOUN
ap-1666	294	11	-	-	PUNCT
ap-1666	294	12	independent	independent	ADJ
ap-1666	294	13	systems	system	NOUN
ap-1666	294	14	.	.	PUNCT
ap-1666	295	1	in	in	ADP
ap-1666	295	2	:	:	PUNCT
ap-1666	295	3	evolutionary	evolutionary	ADJ
ap-1666	295	4	equations	equation	NOUN
ap-1666	295	5	.	.	PUNCT
ap-1666	296	1	ii	ii	PROPN
ap-1666	296	2	,	,	PUNCT
ap-1666	296	3	handb	handb	PROPN
ap-1666	296	4	.	.	PUNCT
ap-1666	296	5	differ	differ	VERB
ap-1666	296	6	.	.	PUNCT
ap-1666	297	1	equ	equ	PROPN
ap-1666	297	2	.	.	PROPN
ap-1666	297	3	,	,	PUNCT
ap-1666	297	4	pp	pp	PROPN
ap-1666	297	5	.	.	PUNCT
ap-1666	298	1	461–559	461–559	NUM
ap-1666	298	2	,	,	PUNCT
ap-1666	298	3	amsterdam	amsterdam	PROPN
ap-1666	298	4	:	:	PUNCT
ap-1666	298	5	elsevier	elsevier	NOUN
ap-1666	298	6	/	/	SYM
ap-1666	298	7	north	north	PROPN
ap-1666	298	8	-	-	PUNCT
ap-1666	298	9	holland	holland	NOUN
ap-1666	298	10	,	,	PUNCT
ap-1666	298	11	2005	2005	NUM
ap-1666	298	12	.	.	PUNCT
ap-1666	299	1	[	[	X
ap-1666	299	2	26	26	NUM
ap-1666	299	3	]	]	PUNCT
ap-1666	299	4	mielke	mielke	PROPN
ap-1666	299	5	,	,	PUNCT
ap-1666	299	6	a.	a.	NOUN
ap-1666	299	7	,	,	PUNCT
ap-1666	299	8	roubíček	roubíček	NOUN
ap-1666	299	9	,	,	PUNCT
ap-1666	299	10	t.	t.	PROPN
ap-1666	299	11	:	:	PUNCT
ap-1666	299	12	a	a	DET
ap-1666	299	13	rate	rate	NOUN
ap-1666	299	14	-	-	PUNCT
ap-1666	299	15	independent	independent	ADJ
ap-1666	299	16	model	model	NOUN
ap-1666	299	17	for	for	ADP
ap-1666	299	18	inelastic	inelastic	ADJ
ap-1666	299	19	behavior	behavior	NOUN
ap-1666	299	20	of	of	ADP
ap-1666	299	21	shape	shape	NOUN
ap-1666	299	22	-	-	PUNCT
ap-1666	299	23	memory	memory	NOUN
ap-1666	299	24	alloys	alloy	NOUN
ap-1666	299	25	,	,	PUNCT
ap-1666	299	26	multiscale	multiscale	NOUN
ap-1666	299	27	model	model	NOUN
ap-1666	299	28	.	.	PUNCT
ap-1666	300	1	simul	simul	PROPN
ap-1666	300	2	.	.	PROPN
ap-1666	300	3	,	,	PUNCT
ap-1666	300	4	1	1	NUM
ap-1666	300	5	,	,	PUNCT
ap-1666	300	6	2003	2003	NUM
ap-1666	300	7	,	,	PUNCT
ap-1666	300	8	571	571	NUM
ap-1666	300	9	–	–	PUNCT
ap-1666	300	10	597	597	NUM
ap-1666	300	11	.	.	PUNCT
ap-1666	301	1	[	[	X
ap-1666	301	2	27	27	NUM
ap-1666	301	3	]	]	X
ap-1666	301	4	mielke	mielke	PROPN
ap-1666	301	5	,	,	PUNCT
ap-1666	301	6	a.	a.	PROPN
ap-1666	301	7	,	,	PUNCT
ap-1666	301	8	theil	theil	PROPN
ap-1666	301	9	,	,	PUNCT
ap-1666	301	10	f.	f.	PROPN
ap-1666	301	11	:	:	PUNCT
ap-1666	301	12	a	a	DET
ap-1666	301	13	mathematical	mathematical	ADJ
ap-1666	301	14	model	model	NOUN
ap-1666	301	15	for	for	ADP
ap-1666	301	16	rate	rate	NOUN
ap-1666	301	17	-	-	PUNCT
ap-1666	301	18	independent	independent	ADJ
ap-1666	301	19	phase	phase	NOUN
ap-1666	301	20	transformations	transformation	NOUN
ap-1666	301	21	with	with	ADP
ap-1666	301	22	hysteresis	hysteresis	NOUN
ap-1666	301	23	.	.	PUNCT
ap-1666	302	1	in	in	ADP
ap-1666	302	2	:	:	PUNCT
ap-1666	302	3	models	model	NOUN
ap-1666	302	4	of	of	ADP
ap-1666	302	5	continuum	continuum	ADJ
ap-1666	302	6	mechanics	mechanic	NOUN
ap-1666	302	7	in	in	ADP
ap-1666	302	8	analysis	analysis	NOUN
ap-1666	302	9	and	and	CCONJ
ap-1666	302	10	engineering	engineering	NOUN
ap-1666	302	11	.	.	PUNCT
ap-1666	303	1	(	(	PUNCT
ap-1666	303	2	eds	ed	NOUN
ap-1666	303	3	.	.	PUNCT
ap-1666	303	4	:	:	PUNCT
ap-1666	303	5	h.-d.alder	h.-d.alder	NOUN
ap-1666	303	6	,	,	PUNCT
ap-1666	303	7	r.balean	r.balean	ADJ
ap-1666	303	8	,	,	PUNCT
ap-1666	303	9	r.farwig	r.farwig	NOUN
ap-1666	303	10	)	)	PUNCT
ap-1666	303	11	,	,	PUNCT
ap-1666	303	12	aachen	aachen	PROPN
ap-1666	303	13	:	:	PUNCT
ap-1666	303	14	shaker	shaker	NOUN
ap-1666	303	15	verlag	verlag	PROPN
ap-1666	303	16	,	,	PUNCT
ap-1666	303	17	1999	1999	NUM
ap-1666	303	18	,	,	PUNCT
ap-1666	303	19	pp.117	pp.117	PROPN
ap-1666	303	20	-	-	PUNCT
ap-1666	303	21	129	129	NUM
ap-1666	303	22	.	.	PUNCT
ap-1666	304	1	[	[	X
ap-1666	304	2	28	28	NUM
ap-1666	304	3	]	]	X
ap-1666	304	4	mielke	mielke	PROPN
ap-1666	304	5	,	,	PUNCT
ap-1666	304	6	a.	a.	PROPN
ap-1666	304	7	,	,	PUNCT
ap-1666	304	8	theil	theil	PROPN
ap-1666	304	9	,	,	PUNCT
ap-1666	304	10	f.	f.	PROPN
ap-1666	304	11	,	,	PUNCT
ap-1666	304	12	levitas	levita	NOUN
ap-1666	304	13	,	,	PUNCT
ap-1666	304	14	v.i	v.i	PROPN
ap-1666	304	15	.	.	PROPN
ap-1666	304	16	:	:	PUNCT
ap-1666	305	1	a	a	DET
ap-1666	305	2	variational	variational	ADJ
ap-1666	305	3	formulation	formulation	NOUN
ap-1666	305	4	of	of	ADP
ap-1666	305	5	rate	rate	NOUN
ap-1666	305	6	-	-	PUNCT
ap-1666	305	7	independent	independent	ADJ
ap-1666	305	8	phase	phase	NOUN
ap-1666	305	9	transformations	transformation	NOUN
ap-1666	305	10	using	use	VERB
ap-1666	305	11	an	an	DET
ap-1666	305	12	extremum	extremum	ADJ
ap-1666	305	13	principle	principle	NOUN
ap-1666	305	14	,	,	PUNCT
ap-1666	305	15	arch	arch	NOUN
ap-1666	305	16	.	.	PUNCT
ap-1666	306	1	ration	ration	NOUN
ap-1666	306	2	.	.	PUNCT
ap-1666	307	1	mech	mech	PROPN
ap-1666	307	2	.	.	PUNCT
ap-1666	308	1	anal	anal	PROPN
ap-1666	308	2	.	.	PUNCT
ap-1666	309	1	162	162	NUM
ap-1666	309	2	,	,	PUNCT
ap-1666	309	3	2002	2002	NUM
ap-1666	309	4	,	,	PUNCT
ap-1666	309	5	137–177	137–177	NUM
ap-1666	309	6	.	.	PUNCT
ap-1666	310	1	[	[	X
ap-1666	310	2	29	29	NUM
ap-1666	310	3	]	]	X
ap-1666	310	4	mühlhaus	mühlhaus	NOUN
ap-1666	310	5	,	,	PUNCT
ap-1666	310	6	h	h	PROPN
ap-1666	310	7	-	-	PUNCT
ap-1666	310	8	b.	b.	PROPN
ap-1666	310	9	,	,	PUNCT
ap-1666	310	10	aifantis	aifantis	PROPN
ap-1666	310	11	,	,	PUNCT
ap-1666	310	12	e.c	e.c	PROPN
ap-1666	310	13	.	.	PROPN
ap-1666	310	14	:	:	PUNCT
ap-1666	310	15	a	a	DET
ap-1666	310	16	variational	variational	ADJ
ap-1666	310	17	principle	principle	NOUN
ap-1666	310	18	for	for	ADP
ap-1666	310	19	gradient	gradient	ADJ
ap-1666	310	20	plasticity	plasticity	NOUN
ap-1666	310	21	,	,	PUNCT
ap-1666	310	22	int	int	NOUN
ap-1666	310	23	.	.	PUNCT
ap-1666	311	1	j.	j.	PROPN
ap-1666	311	2	solid	solid	PROPN
ap-1666	311	3	.	.	PUNCT
ap-1666	311	4	structures	structure	NOUN
ap-1666	311	5	28	28	NUM
ap-1666	311	6	,	,	PUNCT
ap-1666	311	7	1991	1991	NUM
ap-1666	311	8	,	,	PUNCT
ap-1666	311	9	845–857	845–857	NUM
ap-1666	311	10	.	.	PUNCT
ap-1666	312	1	[	[	X
ap-1666	312	2	30	30	NUM
ap-1666	312	3	]	]	X
ap-1666	312	4	ortiz	ortiz	PROPN
ap-1666	312	5	,	,	PUNCT
ap-1666	312	6	m.	m.	NOUN
ap-1666	312	7	,	,	PUNCT
ap-1666	312	8	repetto	repetto	PROPN
ap-1666	312	9	,	,	PUNCT
ap-1666	312	10	e.a	e.a	PROPN
ap-1666	312	11	.	.	PROPN
ap-1666	312	12	:	:	PUNCT
ap-1666	312	13	nonconvex	nonconvex	NOUN
ap-1666	312	14	energy	energy	NOUN
ap-1666	312	15	minimization	minimization	NOUN
ap-1666	312	16	and	and	CCONJ
ap-1666	312	17	dislocation	dislocation	NOUN
ap-1666	312	18	structures	structure	NOUN
ap-1666	312	19	in	in	ADP
ap-1666	312	20	ductile	ductile	ADJ
ap-1666	312	21	single	single	ADJ
ap-1666	312	22	crystals	crystal	NOUN
ap-1666	312	23	.	.	PUNCT
ap-1666	313	1	j.	j.	PROPN
ap-1666	313	2	mech	mech	PROPN
ap-1666	313	3	.	.	PUNCT
ap-1666	314	1	phys	phy	NOUN
ap-1666	314	2	.	.	PUNCT
ap-1666	315	1	solids	solid	NOUN
ap-1666	315	2	,	,	PUNCT
ap-1666	315	3	47	47	NUM
ap-1666	315	4	,	,	PUNCT
ap-1666	315	5	1999	1999	NUM
ap-1666	315	6	,	,	PUNCT
ap-1666	315	7	397–462	397–462	NUM
ap-1666	315	8	.	.	PUNCT
ap-1666	316	1	[	[	X
ap-1666	316	2	31	31	NUM
ap-1666	316	3	]	]	X
ap-1666	316	4	simo	simo	PROPN
ap-1666	316	5	,	,	PUNCT
ap-1666	316	6	j.	j.	PROPN
ap-1666	316	7	:	:	PUNCT
ap-1666	316	8	a	a	DET
ap-1666	316	9	framework	framework	NOUN
ap-1666	316	10	for	for	ADP
ap-1666	316	11	finite	finite	ADJ
ap-1666	316	12	strain	strain	NOUN
ap-1666	316	13	elastoplasticity	elastoplasticity	NOUN
ap-1666	316	14	based	base	VERB
ap-1666	316	15	on	on	ADP
ap-1666	316	16	maximum	maximum	ADJ
ap-1666	316	17	plastic	plastic	ADJ
ap-1666	316	18	dissipation	dissipation	NOUN
ap-1666	316	19	and	and	CCONJ
ap-1666	316	20	multiplicative	multiplicative	ADJ
ap-1666	316	21	decomposition	decomposition	NOUN
ap-1666	316	22	.	.	PUNCT
ap-1666	317	1	part	part	NOUN
ap-1666	317	2	i.	i.	PROPN
ap-1666	317	3	continuum	continuum	PROPN
ap-1666	317	4	formulation	formulation	PROPN
ap-1666	317	5	,	,	PUNCT
ap-1666	317	6	comp	comp	NOUN
ap-1666	317	7	.	.	PUNCT
ap-1666	317	8	meth	meth	NOUN
ap-1666	317	9	.	.	PUNCT
ap-1666	318	1	appl	appl	PROPN
ap-1666	318	2	.	.	PROPN
ap-1666	318	3	mech	mech	PROPN
ap-1666	318	4	.	.	PUNCT
ap-1666	319	1	engrg	engrg	PROPN
ap-1666	319	2	.	.	PROPN
ap-1666	319	3	,	,	PUNCT
ap-1666	319	4	66	66	NUM
ap-1666	319	5	,	,	PUNCT
ap-1666	319	6	1988	1988	NUM
ap-1666	319	7	,	,	PUNCT
ap-1666	319	8	199–219	199–219	NUM
ap-1666	319	9	.	.	PUNCT
ap-1666	320	1	part	part	PROPN
ap-1666	320	2	ii	ii	PROPN
ap-1666	320	3	.	.	PUNCT
ap-1666	320	4	computational	computational	ADJ
ap-1666	320	5	aspects	aspect	NOUN
ap-1666	320	6	,	,	PUNCT
ap-1666	320	7	comp	comp	NOUN
ap-1666	320	8	.	.	PUNCT
ap-1666	320	9	meth	meth	NOUN
ap-1666	320	10	.	.	PUNCT
ap-1666	321	1	appl	appl	PROPN
ap-1666	321	2	.	.	PROPN
ap-1666	321	3	mech	mech	PROPN
ap-1666	321	4	.	.	PUNCT
ap-1666	322	1	engrg	engrg	PROPN
ap-1666	322	2	.	.	PROPN
ap-1666	323	1	68	68	NUM
ap-1666	323	2	,	,	PUNCT
ap-1666	323	3	1988	1988	NUM
ap-1666	323	4	,	,	PUNCT
ap-1666	323	5	1–31	1–31	PROPN
ap-1666	323	6	.	.	PUNCT
ap-1666	324	1	[	[	X
ap-1666	324	2	32	32	NUM
ap-1666	324	3	]	]	PUNCT
ap-1666	324	4	tsagrakis	tsagraki	NOUN
ap-1666	324	5	,	,	PUNCT
ap-1666	324	6	i.	i.	PROPN
ap-1666	324	7	,	,	PUNCT
ap-1666	324	8	aifantis	aifantis	PROPN
ap-1666	324	9	,	,	PUNCT
ap-1666	324	10	e.c	e.c	PROPN
ap-1666	324	11	.	.	PROPN
ap-1666	324	12	:	:	PUNCT
ap-1666	324	13	recent	recent	ADJ
ap-1666	324	14	developments	development	NOUN
ap-1666	324	15	in	in	ADP
ap-1666	324	16	gradient	gradient	ADJ
ap-1666	324	17	plasticity	plasticity	NOUN
ap-1666	324	18	.	.	PUNCT
ap-1666	325	1	j.	j.	PROPN
ap-1666	325	2	engrg	engrg	PROPN
ap-1666	325	3	.	.	PUNCT
ap-1666	326	1	mater	mater	NOUN
ap-1666	326	2	.	.	PUNCT
ap-1666	327	1	tech	tech	NOUN
ap-1666	327	2	.	.	PUNCT
ap-1666	328	1	124	124	NUM
ap-1666	328	2	,	,	PUNCT
ap-1666	328	3	2002	2002	NUM
ap-1666	328	4	,	,	PUNCT
ap-1666	328	5	352–357	352–357	NUM
ap-1666	328	6	.	.	PUNCT
ap-1666	329	1	14	14	NUM