id	sid	tid	token	lemma	pos
azojete-1	1	1	arid	arid	PROPN
azojete-1	1	2	zone	zone	PROPN
azojete-1	1	3	journal	journal	NOUN
azojete-1	1	4	of	of	ADP
azojete-1	1	5	engineering	engineering	NOUN
azojete-1	1	6	,	,	PUNCT
azojete-1	1	7	technology	technology	NOUN
azojete-1	1	8	&	&	CCONJ
azojete-1	1	9	environment	environment	PROPN
azojete-1	1	10	azojete	azojete	NOUN
azojete-1	1	11	,	,	PUNCT
azojete-1	1	12	september	september	PROPN
azojete-1	1	13	2019	2019	NUM
azojete-1	1	14	.	.	PUNCT
azojete-1	2	1	vol	vol	NOUN
azojete-1	2	2	.	.	PUNCT
azojete-1	3	1	15(3):488	15(3):488	NUM
azojete-1	3	2	-	-	PUNCT
azojete-1	3	3	509	509	NUM
azojete-1	3	4	published	publish	VERB
azojete-1	3	5	by	by	ADP
azojete-1	3	6	the	the	DET
azojete-1	3	7	faculty	faculty	NOUN
azojete-1	3	8	of	of	ADP
azojete-1	3	9	engineering	engineering	NOUN
azojete-1	3	10	,	,	PUNCT
azojete-1	3	11	university	university	NOUN
azojete-1	3	12	of	of	ADP
azojete-1	3	13	maiduguri	maiduguri	PROPN
azojete-1	3	14	,	,	PUNCT
azojete-1	3	15	maiduguri	maiduguri	PROPN
azojete-1	3	16	,	,	PUNCT
azojete-1	3	17	nigeria	nigeria	PROPN
azojete-1	3	18	.	.	PUNCT
azojete-1	4	1	print	print	PROPN
azojete-1	4	2	issn	issn	PROPN
azojete-1	4	3	:	:	PUNCT
azojete-1	4	4	1596	1596	NUM
azojete-1	4	5	-	-	SYM
azojete-1	4	6	2490	2490	NUM
azojete-1	4	7	,	,	PUNCT
azojete-1	4	8	electronic	electronic	ADJ
azojete-1	4	9	issn	issn	NOUN
azojete-1	4	10	:	:	PUNCT
azojete-1	4	11	2545	2545	NUM
azojete-1	4	12	-	-	SYM
azojete-1	4	13	5818	5818	NUM
azojete-1	4	14	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	4	15	488	488	NUM
azojete-1	4	16	original	original	ADJ
azojete-1	4	17	research	research	NOUN
azojete-1	4	18	article	article	NOUN
azojete-1	4	19	analytical	analytical	ADJ
azojete-1	4	20	,	,	PUNCT
azojete-1	4	21	numerical	numerical	ADJ
azojete-1	4	22	and	and	CCONJ
azojete-1	4	23	computational	computational	ADJ
azojete-1	4	24	multiscale	multiscale	NOUN
azojete-1	4	25	modelling	model	VERB
azojete-1	4	26	techniques	technique	NOUN
azojete-1	4	27	for	for	ADP
azojete-1	4	28	heterogenous	heterogenous	ADJ
azojete-1	4	29	materials	material	NOUN
azojete-1	4	30	:	:	PUNCT
azojete-1	5	1	a	a	DET
azojete-1	5	2	review	review	NOUN
azojete-1	5	3	o.	o.	PROPN
azojete-1	5	4	h.	h.	PROPN
azojete-1	5	5	aliyu	aliyu	PROPN
azojete-1	5	6	(	(	PUNCT
azojete-1	5	7	department	department	NOUN
azojete-1	5	8	of	of	ADP
azojete-1	5	9	building	building	NOUN
azojete-1	5	10	,	,	PUNCT
azojete-1	5	11	faculty	faculty	NOUN
azojete-1	5	12	of	of	ADP
azojete-1	5	13	environmental	environmental	ADJ
azojete-1	5	14	sciences	science	NOUN
azojete-1	5	15	,	,	PUNCT
azojete-1	5	16	the	the	DET
azojete-1	5	17	federal	federal	ADJ
azojete-1	5	18	university	university	PROPN
azojete-1	5	19	birnin	birnin	NOUN
azojete-1	5	20	kebbi	kebbi	PROPN
azojete-1	5	21	,	,	PUNCT
azojete-1	5	22	p.m.b	p.m.b	NOUN
azojete-1	5	23	.	.	PROPN
azojete-1	5	24	1157	1157	NUM
azojete-1	5	25	,	,	PUNCT
azojete-1	5	26	birnin	birnin	PROPN
azojete-1	5	27	kebbi	kebbi	PROPN
azojete-1	5	28	,	,	PUNCT
azojete-1	5	29	nigeria	nigeria	PROPN
azojete-1	5	30	)	)	PUNCT
azojete-1	5	31	*	*	PUNCT
azojete-1	6	1	corresponding	correspond	VERB
azojete-1	6	2	author	author	NOUN
azojete-1	6	3	’s	’s	PART
azojete-1	6	4	email	email	NOUN
azojete-1	6	5	address	address	NOUN
azojete-1	6	6	:	:	PUNCT
azojete-1	6	7	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	6	8	article	article	NOUN
azojete-1	6	9	information	information	NOUN
azojete-1	6	10	submitted	submit	VERB
azojete-1	6	11	14	14	NUM
azojete-1	6	12	september	september	PROPN
azojete-1	6	13	,	,	PUNCT
azojete-1	6	14	2018	2018	NUM
azojete-1	6	15	revised	revise	VERB
azojete-1	6	16	16	16	NUM
azojete-1	6	17	march	march	NOUN
azojete-1	6	18	,	,	PUNCT
azojete-1	6	19	2019	2019	NUM
azojete-1	6	20	accepted	accept	VERB
azojete-1	6	21	18	18	NUM
azojete-1	6	22	march	march	NOUN
azojete-1	6	23	,	,	PUNCT
azojete-1	6	24	2019	2019	NUM
azojete-1	6	25	keywords	keyword	NOUN
azojete-1	6	26	:	:	PUNCT
azojete-1	6	27	homogenization	homogenization	NOUN
azojete-1	6	28	heterogeneous	heterogeneous	ADJ
azojete-1	6	29	material	material	NOUN
azojete-1	6	30	representative	representative	NOUN
azojete-1	6	31	volume	volume	NOUN
azojete-1	6	32	element	element	NOUN
azojete-1	6	33	(	(	PUNCT
azojete-1	6	34	rve	rve	PROPN
azojete-1	6	35	)	)	PUNCT
azojete-1	6	36	effective	effective	ADJ
azojete-1	6	37	properties	property	NOUN
azojete-1	6	38	volume	volume	NOUN
azojete-1	6	39	averages	average	NOUN
azojete-1	6	40	computational	computational	ADJ
azojete-1	6	41	homogenization	homogenization	NOUN
azojete-1	6	42	abstract	abstract	NOUN
azojete-1	6	43	this	this	DET
azojete-1	6	44	paper	paper	NOUN
azojete-1	6	45	reviews	review	VERB
azojete-1	6	46	the	the	DET
azojete-1	6	47	analytical	analytical	ADJ
azojete-1	6	48	,	,	PUNCT
azojete-1	6	49	numerical	numerical	ADJ
azojete-1	6	50	as	as	ADV
azojete-1	6	51	well	well	ADV
azojete-1	6	52	as	as	ADP
azojete-1	6	53	the	the	DET
azojete-1	6	54	computational	computational	ADJ
azojete-1	6	55	homogenization	homogenization	NOUN
azojete-1	6	56	multiscale	multiscale	NOUN
azojete-1	6	57	modelling	model	VERB
azojete-1	6	58	schemes	scheme	NOUN
azojete-1	6	59	for	for	ADP
azojete-1	6	60	determining	determine	VERB
azojete-1	6	61	the	the	DET
azojete-1	6	62	effective	effective	ADJ
azojete-1	6	63	material	material	NOUN
azojete-1	6	64	properties	property	NOUN
azojete-1	6	65	for	for	ADP
azojete-1	6	66	heterogeneous	heterogeneous	ADJ
azojete-1	6	67	medium	medium	NOUN
azojete-1	6	68	at	at	ADP
azojete-1	6	69	the	the	DET
azojete-1	6	70	macroscopic	macroscopic	ADJ
azojete-1	6	71	level	level	NOUN
azojete-1	6	72	.	.	PUNCT
azojete-1	7	1	it	it	PRON
azojete-1	7	2	also	also	ADV
azojete-1	7	3	looked	look	VERB
azojete-1	7	4	at	at	ADP
azojete-1	7	5	the	the	DET
azojete-1	7	6	limitations	limitation	NOUN
azojete-1	7	7	of	of	ADP
azojete-1	7	8	the	the	DET
azojete-1	7	9	analytical	analytical	ADJ
azojete-1	7	10	homogenization	homogenization	NOUN
azojete-1	7	11	techniques	technique	NOUN
azojete-1	7	12	in	in	ADP
azojete-1	7	13	simulating	simulate	VERB
azojete-1	7	14	the	the	DET
azojete-1	7	15	effective	effective	ADJ
azojete-1	7	16	non	non	ADJ
azojete-1	7	17	linear	linear	ADJ
azojete-1	7	18	heterogeneous	heterogeneous	ADJ
azojete-1	7	19	material	material	NOUN
azojete-1	7	20	behaviours	behaviour	NOUN
azojete-1	7	21	(	(	PUNCT
azojete-1	7	22	for	for	ADP
azojete-1	7	23	example	example	NOUN
azojete-1	7	24	the	the	DET
azojete-1	7	25	rapid	rapid	ADJ
azojete-1	7	26	localization	localization	NOUN
azojete-1	7	27	of	of	ADP
azojete-1	7	28	damage	damage	NOUN
azojete-1	7	29	and	and	CCONJ
azojete-1	7	30	so	so	ADV
azojete-1	7	31	on	on	ADV
azojete-1	7	32	)	)	PUNCT
azojete-1	7	33	as	as	ADV
azojete-1	7	34	well	well	ADV
azojete-1	7	35	as	as	ADP
azojete-1	7	36	the	the	DET
azojete-1	7	37	advancements	advancement	NOUN
azojete-1	7	38	of	of	ADP
azojete-1	7	39	the	the	DET
azojete-1	7	40	computational	computational	ADJ
azojete-1	7	41	techniques	technique	NOUN
azojete-1	7	42	in	in	ADP
azojete-1	7	43	addressing	address	VERB
azojete-1	7	44	these	these	DET
azojete-1	7	45	limitations	limitation	NOUN
azojete-1	7	46	.	.	PUNCT
azojete-1	8	1	in	in	ADP
azojete-1	8	2	addition	addition	NOUN
azojete-1	8	3	,	,	PUNCT
azojete-1	8	4	the	the	DET
azojete-1	8	5	possible	possible	ADJ
azojete-1	8	6	future	future	ADJ
azojete-1	8	7	trends	trend	NOUN
azojete-1	8	8	for	for	ADP
azojete-1	8	9	the	the	DET
azojete-1	8	10	computational	computational	ADJ
azojete-1	8	11	technique	technique	NOUN
azojete-1	8	12	such	such	ADJ
azojete-1	8	13	as	as	ADP
azojete-1	8	14	the	the	DET
azojete-1	8	15	development	development	NOUN
azojete-1	8	16	of	of	ADP
azojete-1	8	17	a	a	DET
azojete-1	8	18	fully	fully	ADV
azojete-1	8	19	coupled	couple	VERB
azojete-1	8	20	micro	micro	ADJ
azojete-1	8	21	-	-	ADJ
azojete-1	8	22	macro	macro	ADJ
azojete-1	8	23	computational	computational	ADJ
azojete-1	8	24	scheme	scheme	NOUN
azojete-1	8	25	were	be	AUX
azojete-1	8	26	also	also	ADV
azojete-1	8	27	discussed	discuss	VERB
azojete-1	8	28	.	.	PUNCT
azojete-1	9	1	it	it	PRON
azojete-1	9	2	was	be	AUX
azojete-1	9	3	concluded	conclude	VERB
azojete-1	9	4	that	that	SCONJ
azojete-1	9	5	although	although	SCONJ
azojete-1	9	6	,	,	PUNCT
azojete-1	9	7	the	the	DET
azojete-1	9	8	analytical	analytical	ADJ
azojete-1	9	9	technique	technique	NOUN
azojete-1	9	10	was	be	AUX
azojete-1	9	11	quite	quite	ADV
azojete-1	9	12	popular	popular	ADJ
azojete-1	9	13	and	and	CCONJ
azojete-1	9	14	straight	straight	ADV
azojete-1	9	15	forward	forward	ADV
azojete-1	9	16	,	,	PUNCT
azojete-1	9	17	its	its	PRON
azojete-1	9	18	inability	inability	NOUN
azojete-1	9	19	to	to	PART
azojete-1	9	20	capture	capture	VERB
azojete-1	9	21	rapid	rapid	ADJ
azojete-1	9	22	localization	localization	NOUN
azojete-1	9	23	of	of	ADP
azojete-1	9	24	damage	damage	NOUN
azojete-1	9	25	limited	limit	VERB
azojete-1	9	26	its	its	PRON
azojete-1	9	27	application	application	NOUN
azojete-1	9	28	and	and	CCONJ
azojete-1	9	29	that	that	SCONJ
azojete-1	9	30	numerical	numerical	ADJ
azojete-1	9	31	and	and	CCONJ
azojete-1	9	32	computational	computational	ADJ
azojete-1	9	33	schemes	scheme	NOUN
azojete-1	9	34	were	be	AUX
azojete-1	9	35	able	able	ADJ
azojete-1	9	36	to	to	PART
azojete-1	9	37	address	address	VERB
azojete-1	9	38	these	these	DET
azojete-1	9	39	limitations	limitation	NOUN
azojete-1	9	40	as	as	SCONJ
azojete-1	9	41	they	they	PRON
azojete-1	9	42	relied	rely	VERB
azojete-1	9	43	on	on	ADP
azojete-1	9	44	the	the	DET
azojete-1	9	45	establishment	establishment	NOUN
azojete-1	9	46	of	of	ADP
azojete-1	9	47	constitutive	constitutive	ADJ
azojete-1	9	48	relations	relation	NOUN
azojete-1	9	49	for	for	ADP
azojete-1	9	50	the	the	DET
azojete-1	9	51	macroscopic	macroscopic	ADJ
azojete-1	9	52	problems	problem	NOUN
azojete-1	9	53	in	in	ADP
azojete-1	9	54	a	a	DET
azojete-1	9	55	numerical	numerical	ADJ
azojete-1	9	56	form	form	NOUN
azojete-1	9	57	through	through	ADP
azojete-1	9	58	which	which	PRON
azojete-1	9	59	the	the	DET
azojete-1	9	60	macroscopic	macroscopic	ADJ
azojete-1	9	61	problems	problem	NOUN
azojete-1	9	62	were	be	AUX
azojete-1	9	63	constructed	construct	VERB
azojete-1	9	64	and	and	CCONJ
azojete-1	9	65	solved	solve	VERB
azojete-1	9	66	in	in	ADP
azojete-1	9	67	a	a	DET
azojete-1	9	68	nested	nested	ADJ
azojete-1	9	69	manner	manner	NOUN
azojete-1	9	70	.	.	PUNCT
azojete-1	10	1	©	©	ADP
azojete-1	10	2	2019	2019	NUM
azojete-1	10	3	faculty	faculty	NOUN
azojete-1	10	4	of	of	ADP
azojete-1	10	5	engineering	engineering	NOUN
azojete-1	10	6	,	,	PUNCT
azojete-1	10	7	university	university	NOUN
azojete-1	10	8	of	of	ADP
azojete-1	10	9	maiduguri	maiduguri	PROPN
azojete-1	10	10	,	,	PUNCT
azojete-1	10	11	nigeria	nigeria	PROPN
azojete-1	10	12	.	.	PUNCT
azojete-1	11	1	all	all	DET
azojete-1	11	2	rights	right	NOUN
azojete-1	11	3	reserved	reserve	VERB
azojete-1	11	4	.	.	PUNCT
azojete-1	12	1	1.0	1.0	NUM
azojete-1	12	2	introduction	introduction	NOUN
azojete-1	12	3	most	most	ADJ
azojete-1	12	4	engineering	engineering	NOUN
azojete-1	12	5	materials	material	NOUN
azojete-1	12	6	(	(	PUNCT
azojete-1	12	7	steel	steel	NOUN
azojete-1	12	8	,	,	PUNCT
azojete-1	12	9	concrete	concrete	ADJ
azojete-1	12	10	,	,	PUNCT
azojete-1	12	11	polymer	polymer	NOUN
azojete-1	12	12	-	-	PUNCT
azojete-1	12	13	blends	blend	NOUN
azojete-1	12	14	,	,	PUNCT
azojete-1	12	15	functional	functional	ADJ
azojete-1	12	16	materials	material	NOUN
azojete-1	12	17	and	and	CCONJ
azojete-1	12	18	so	so	ADV
azojete-1	12	19	on	on	ADV
azojete-1	12	20	)	)	PUNCT
azojete-1	12	21	are	be	AUX
azojete-1	12	22	inherently	inherently	ADV
azojete-1	12	23	heterogeneous	heterogeneous	ADJ
azojete-1	12	24	in	in	ADP
azojete-1	12	25	nature	nature	NOUN
azojete-1	12	26	(	(	PUNCT
azojete-1	12	27	figure	figure	NOUN
azojete-1	12	28	1	1	NUM
azojete-1	12	29	)	)	PUNCT
azojete-1	12	30	when	when	SCONJ
azojete-1	12	31	viewed	view	VERB
azojete-1	12	32	at	at	ADP
azojete-1	12	33	a	a	DET
azojete-1	12	34	particular	particular	ADJ
azojete-1	12	35	scale	scale	NOUN
azojete-1	12	36	and	and	CCONJ
azojete-1	12	37	are	be	AUX
azojete-1	12	38	mostly	mostly	ADV
azojete-1	12	39	referred	refer	VERB
azojete-1	12	40	to	to	ADP
azojete-1	12	41	as	as	ADP
azojete-1	12	42	composites	composite	NOUN
azojete-1	12	43	(	(	PUNCT
azojete-1	12	44	nguyen	nguyen	NOUN
azojete-1	12	45	et	et	PROPN
azojete-1	12	46	al	al	PROPN
azojete-1	12	47	.	.	PROPN
azojete-1	12	48	,	,	PUNCT
azojete-1	12	49	2012	2012	NUM
azojete-1	12	50	;	;	PUNCT
azojete-1	12	51	matous	matous	PROPN
azojete-1	12	52	et	et	PROPN
azojete-1	12	53	al	al	PROPN
azojete-1	12	54	.	.	PROPN
azojete-1	12	55	,	,	PUNCT
azojete-1	12	56	2017	2017	NUM
azojete-1	12	57	)	)	PUNCT
azojete-1	12	58	.	.	PUNCT
azojete-1	13	1	figure	figure	VERB
azojete-1	13	2	1	1	NUM
azojete-1	13	3	:	:	PUNCT
azojete-1	13	4	natural	natural	ADJ
azojete-1	13	5	random	random	ADJ
azojete-1	13	6	heterogeneous	heterogeneous	ADJ
azojete-1	13	7	material	material	NOUN
azojete-1	13	8	adapted	adapt	VERB
azojete-1	13	9	from	from	ADP
azojete-1	13	10	torquato	torquato	NOUN
azojete-1	13	11	(	(	PUNCT
azojete-1	13	12	2013	2013	NUM
azojete-1	13	13	)	)	PUNCT
azojete-1	13	14	.	.	PUNCT
azojete-1	14	1	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PRON
azojete-1	14	2	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	14	3	arid	arid	NOUN
azojete-1	14	4	zone	zone	PROPN
azojete-1	14	5	journal	journal	NOUN
azojete-1	14	6	of	of	ADP
azojete-1	14	7	engineering	engineering	NOUN
azojete-1	14	8	,	,	PUNCT
azojete-1	14	9	technology	technology	NOUN
azojete-1	14	10	and	and	CCONJ
azojete-1	14	11	environment	environment	NOUN
azojete-1	14	12	,	,	PUNCT
azojete-1	14	13	september	september	PROPN
azojete-1	14	14	,	,	PUNCT
azojete-1	14	15	2019	2019	NUM
azojete-1	14	16	;	;	PUNCT
azojete-1	14	17	vol	vol	NOUN
azojete-1	14	18	.	.	PUNCT
azojete-1	15	1	15(3):488	15(3):488	NUM
azojete-1	15	2	-	-	PUNCT
azojete-1	15	3	509	509	NUM
azojete-1	15	4	.	.	PUNCT
azojete-1	16	1	issn	issn	PROPN
azojete-1	16	2	1596	1596	NUM
azojete-1	16	3	-	-	SYM
azojete-1	16	4	2490	2490	NUM
azojete-1	16	5	;	;	PUNCT
azojete-1	16	6	e	e	X
azojete-1	16	7	-	-	NOUN
azojete-1	16	8	issn	issn	VERB
azojete-1	16	9	2545	2545	NUM
azojete-1	16	10	-	-	SYM
azojete-1	16	11	5818	5818	NUM
azojete-1	16	12	;	;	PUNCT
azojete-1	16	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	16	14	corresponding	correspond	VERB
azojete-1	16	15	author	author	NOUN
azojete-1	16	16	’s	’s	PART
azojete-1	16	17	e	e	NOUN
azojete-1	16	18	-	-	NOUN
azojete-1	16	19	mail	mail	NOUN
azojete-1	16	20	address	address	NOUN
azojete-1	16	21	:	:	PUNCT
azojete-1	16	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	16	23	489	489	NUM
azojete-1	16	24	studies	study	NOUN
azojete-1	16	25	(	(	PUNCT
azojete-1	16	26	llorca	llorca	PROPN
azojete-1	16	27	et	et	PROPN
azojete-1	16	28	al	al	PROPN
azojete-1	16	29	.	.	PROPN
azojete-1	16	30	,	,	PUNCT
azojete-1	16	31	2007	2007	NUM
azojete-1	16	32	;	;	PUNCT
azojete-1	16	33	kouznetsova	kouznetsova	PROPN
azojete-1	16	34	et	et	PROPN
azojete-1	16	35	al	al	PROPN
azojete-1	16	36	.	.	PROPN
azojete-1	16	37	,	,	PUNCT
azojete-1	16	38	2012	2012	NUM
azojete-1	16	39	)	)	PUNCT
azojete-1	16	40	have	have	AUX
azojete-1	16	41	shown	show	VERB
azojete-1	16	42	that	that	SCONJ
azojete-1	16	43	,	,	PUNCT
azojete-1	16	44	the	the	DET
azojete-1	16	45	macroscopic	macroscopic	ADJ
azojete-1	16	46	behaviour	behaviour	NOUN
azojete-1	16	47	of	of	ADP
azojete-1	16	48	these	these	DET
azojete-1	16	49	composite	composite	ADJ
azojete-1	16	50	materials	material	NOUN
azojete-1	16	51	are	be	AUX
azojete-1	16	52	linked	link	VERB
azojete-1	16	53	to	to	ADP
azojete-1	16	54	their	their	PRON
azojete-1	16	55	mechanical	mechanical	ADJ
azojete-1	16	56	behaviour	behaviour	NOUN
azojete-1	16	57	as	as	ADV
azojete-1	16	58	well	well	ADV
azojete-1	16	59	as	as	ADP
azojete-1	16	60	the	the	DET
azojete-1	16	61	details	detail	NOUN
azojete-1	16	62	of	of	ADP
azojete-1	16	63	their	their	PRON
azojete-1	16	64	microstructure	microstructure	NOUN
azojete-1	16	65	(	(	PUNCT
azojete-1	16	66	that	that	PRON
azojete-1	16	67	is	be	AUX
azojete-1	16	68	volume	volume	NOUN
azojete-1	16	69	fraction	fraction	NOUN
azojete-1	16	70	,	,	PUNCT
azojete-1	16	71	spatial	spatial	ADJ
azojete-1	16	72	distribution	distribution	NOUN
azojete-1	16	73	of	of	ADP
azojete-1	16	74	the	the	DET
azojete-1	16	75	different	different	ADJ
azojete-1	16	76	phases	phase	NOUN
azojete-1	16	77	and	and	CCONJ
azojete-1	16	78	inter	inter	NOUN
azojete-1	16	79	-	-	NOUN
azojete-1	16	80	phases	phase	NOUN
azojete-1	16	81	,	,	PUNCT
azojete-1	16	82	their	their	PRON
azojete-1	16	83	morphological	morphological	ADJ
azojete-1	16	84	properties	property	NOUN
azojete-1	16	85	,	,	PUNCT
azojete-1	16	86	sizes	size	NOUN
azojete-1	16	87	and	and	CCONJ
azojete-1	16	88	shapes	shape	NOUN
azojete-1	16	89	et	et	NOUN
azojete-1	16	90	cetera	cetera	NOUN
azojete-1	16	91	)	)	PUNCT
azojete-1	16	92	.	.	PUNCT
azojete-1	17	1	these	these	DET
azojete-1	17	2	microstructural	microstructural	ADJ
azojete-1	17	3	material	material	NOUN
azojete-1	17	4	details	detail	NOUN
azojete-1	17	5	tend	tend	VERB
azojete-1	17	6	to	to	PART
azojete-1	17	7	evolve	evolve	VERB
azojete-1	17	8	by	by	ADP
azojete-1	17	9	undergoing	undergo	VERB
azojete-1	17	10	phase	phase	NOUN
azojete-1	17	11	transformations	transformation	NOUN
azojete-1	17	12	under	under	ADP
azojete-1	17	13	the	the	DET
azojete-1	17	14	application	application	NOUN
azojete-1	17	15	of	of	ADP
azojete-1	17	16	thermo	thermo	NOUN
azojete-1	17	17	-	-	PUNCT
azojete-1	17	18	mechanical	mechanical	ADJ
azojete-1	17	19	loadings	loading	NOUN
azojete-1	17	20	as	as	ADV
azojete-1	17	21	well	well	ADV
azojete-1	17	22	as	as	ADP
azojete-1	17	23	advanced	advanced	ADJ
azojete-1	17	24	forming	form	VERB
azojete-1	17	25	operations	operation	NOUN
azojete-1	17	26	;	;	PUNCT
azojete-1	17	27	thus	thus	ADV
azojete-1	17	28	,	,	PUNCT
azojete-1	17	29	making	make	VERB
azojete-1	17	30	it	it	PRON
azojete-1	17	31	essential	essential	ADJ
azojete-1	17	32	to	to	PART
azojete-1	17	33	understand	understand	VERB
azojete-1	17	34	the	the	DET
azojete-1	17	35	relationship	relationship	NOUN
azojete-1	17	36	between	between	ADP
azojete-1	17	37	the	the	DET
azojete-1	17	38	microstructure	microstructure	ADJ
azojete-1	17	39	properties	property	NOUN
azojete-1	17	40	and	and	CCONJ
azojete-1	17	41	the	the	DET
azojete-1	17	42	macroscopic	macroscopic	ADJ
azojete-1	17	43	material	material	NOUN
azojete-1	17	44	behaviour	behaviour	NOUN
azojete-1	17	45	(	(	PUNCT
azojete-1	17	46	also	also	ADV
azojete-1	17	47	known	know	VERB
azojete-1	17	48	as	as	ADP
azojete-1	17	49	the	the	DET
azojete-1	17	50	micro	micro	ADJ
azojete-1	17	51	-	-	ADJ
azojete-1	17	52	macro	macro	ADJ
azojete-1	17	53	structure	structure	NOUN
azojete-1	17	54	property	property	NOUN
azojete-1	17	55	relation	relation	NOUN
azojete-1	17	56	)	)	PUNCT
azojete-1	17	57	.	.	PUNCT
azojete-1	18	1	it	it	PRON
azojete-1	18	2	is	be	AUX
azojete-1	18	3	hoped	hope	VERB
azojete-1	18	4	that	that	SCONJ
azojete-1	18	5	by	by	ADP
azojete-1	18	6	taking	take	VERB
azojete-1	18	7	advantage	advantage	NOUN
azojete-1	18	8	of	of	ADP
azojete-1	18	9	this	this	DET
azojete-1	18	10	micro	micro	ADJ
azojete-1	18	11	-	-	ADJ
azojete-1	18	12	macro	macro	ADJ
azojete-1	18	13	structure	structure	NOUN
azojete-1	18	14	-	-	PUNCT
azojete-1	18	15	property	property	NOUN
azojete-1	18	16	relationship	relationship	NOUN
azojete-1	18	17	,	,	PUNCT
azojete-1	18	18	it	it	PRON
azojete-1	18	19	should	should	AUX
azojete-1	18	20	be	be	AUX
azojete-1	18	21	possible	possible	ADJ
azojete-1	18	22	to	to	PART
azojete-1	18	23	manipulate	manipulate	VERB
azojete-1	18	24	the	the	DET
azojete-1	18	25	material	material	NOUN
azojete-1	18	26	microstructure	microstructure	NOUN
azojete-1	18	27	so	so	SCONJ
azojete-1	18	28	as	as	SCONJ
azojete-1	18	29	to	to	PART
azojete-1	18	30	influence	influence	VERB
azojete-1	18	31	the	the	DET
azojete-1	18	32	macroscopic	macroscopic	ADJ
azojete-1	18	33	mechanical	mechanical	ADJ
azojete-1	18	34	behaviour	behaviour	NOUN
azojete-1	18	35	of	of	ADP
azojete-1	18	36	the	the	DET
azojete-1	18	37	composite	composite	ADJ
azojete-1	18	38	material	material	NOUN
azojete-1	18	39	to	to	PART
azojete-1	18	40	obtain	obtain	VERB
azojete-1	18	41	desired	desire	VERB
azojete-1	18	42	results	result	NOUN
azojete-1	18	43	.	.	PUNCT
azojete-1	19	1	for	for	ADP
azojete-1	19	2	example	example	NOUN
azojete-1	19	3	,	,	PUNCT
azojete-1	19	4	“	"	PUNCT
azojete-1	19	5	improved	improved	ADJ
azojete-1	19	6	strength	strength	NOUN
azojete-1	19	7	and	and	CCONJ
azojete-1	19	8	toughness	toughness	NOUN
azojete-1	19	9	,	,	PUNCT
azojete-1	19	10	high	high	ADJ
azojete-1	19	11	stiffness	stiffness	NOUN
azojete-1	19	12	and	and	CCONJ
azojete-1	19	13	high	high	ADJ
azojete-1	19	14	damping	damping	NOUN
azojete-1	19	15	,	,	PUNCT
azojete-1	19	16	improved	improve	VERB
azojete-1	19	17	thermal	thermal	ADJ
azojete-1	19	18	conductivity	conductivity	NOUN
azojete-1	19	19	and	and	CCONJ
azojete-1	19	20	electrical	electrical	ADJ
azojete-1	19	21	permittivity	permittivity	NOUN
azojete-1	19	22	,	,	PUNCT
azojete-1	19	23	improved	improved	ADJ
azojete-1	19	24	permeability	permeability	NOUN
azojete-1	19	25	”	"	PUNCT
azojete-1	19	26	et	et	PROPN
azojete-1	19	27	cetera	cetera	NOUN
azojete-1	19	28	(	(	PUNCT
azojete-1	19	29	kanoute	kanoute	VERB
azojete-1	19	30	et	et	PROPN
azojete-1	19	31	al	al	PROPN
azojete-1	19	32	.	.	PROPN
azojete-1	19	33	,	,	PUNCT
azojete-1	19	34	2009	2009	NUM
azojete-1	19	35	)	)	PUNCT
azojete-1	19	36	;	;	PUNCT
azojete-1	19	37	consequently	consequently	ADV
azojete-1	19	38	,	,	PUNCT
azojete-1	19	39	improving	improve	VERB
azojete-1	19	40	the	the	DET
azojete-1	19	41	materials	material	NOUN
azojete-1	19	42	performance	performance	NOUN
azojete-1	19	43	in	in	ADP
azojete-1	19	44	special	special	ADJ
azojete-1	19	45	industrial	industrial	ADJ
azojete-1	19	46	applications	application	NOUN
azojete-1	19	47	from	from	ADP
azojete-1	19	48	an	an	DET
azojete-1	19	49	engineering	engineering	NOUN
azojete-1	19	50	perspective	perspective	NOUN
azojete-1	19	51	,	,	PUNCT
azojete-1	19	52	provides	provide	VERB
azojete-1	19	53	an	an	DET
azojete-1	19	54	economic	economic	ADJ
azojete-1	19	55	alternative	alternative	NOUN
azojete-1	19	56	to	to	ADP
azojete-1	19	57	the	the	DET
azojete-1	19	58	designing	designing	NOUN
azojete-1	19	59	of	of	ADP
azojete-1	19	60	new	new	ADJ
azojete-1	19	61	materials	material	NOUN
azojete-1	19	62	with	with	ADP
azojete-1	19	63	desirable	desirable	ADJ
azojete-1	19	64	macroscopic	macroscopic	ADJ
azojete-1	19	65	characteristics	characteristic	NOUN
azojete-1	19	66	(	(	PUNCT
azojete-1	19	67	nguyen	nguyen	NOUN
azojete-1	19	68	et	et	PROPN
azojete-1	19	69	al	al	PROPN
azojete-1	19	70	.	.	PROPN
azojete-1	19	71	,	,	PUNCT
azojete-1	19	72	2012	2012	NUM
azojete-1	19	73	;	;	PUNCT
azojete-1	19	74	llorca	llorca	NOUN
azojete-1	19	75	et	et	PROPN
azojete-1	19	76	al	al	PROPN
azojete-1	19	77	.	.	PROPN
azojete-1	19	78	,	,	PUNCT
azojete-1	19	79	2007	2007	NUM
azojete-1	19	80	)	)	PUNCT
azojete-1	19	81	.	.	PUNCT
azojete-1	20	1	establishing	establish	VERB
azojete-1	20	2	this	this	DET
azojete-1	20	3	micro	micro	ADJ
azojete-1	20	4	-	-	ADJ
azojete-1	20	5	macro	macro	ADJ
azojete-1	20	6	structure	structure	NOUN
azojete-1	20	7	-	-	PUNCT
azojete-1	20	8	property	property	NOUN
azojete-1	20	9	relation	relation	NOUN
azojete-1	20	10	has	have	AUX
azojete-1	20	11	been	be	AUX
azojete-1	20	12	a	a	DET
azojete-1	20	13	major	major	ADJ
azojete-1	20	14	challenge	challenge	NOUN
azojete-1	20	15	in	in	ADP
azojete-1	20	16	computational	computational	ADJ
azojete-1	20	17	micromechanics	micromechanic	NOUN
azojete-1	20	18	as	as	ADV
azojete-1	20	19	well	well	ADV
azojete-1	20	20	as	as	ADP
azojete-1	20	21	material	material	NOUN
azojete-1	20	22	science	science	NOUN
azojete-1	20	23	as	as	SCONJ
azojete-1	20	24	it	it	PRON
azojete-1	20	25	is	be	AUX
azojete-1	20	26	not	not	PART
azojete-1	20	27	feasible	feasible	ADJ
azojete-1	20	28	to	to	PART
azojete-1	20	29	carry	carry	VERB
azojete-1	20	30	out	out	ADP
azojete-1	20	31	an	an	DET
azojete-1	20	32	upfront	upfront	ADJ
azojete-1	20	33	experimental	experimental	ADJ
azojete-1	20	34	measurement	measurement	NOUN
azojete-1	20	35	where	where	SCONJ
azojete-1	20	36	all	all	DET
azojete-1	20	37	the	the	DET
azojete-1	20	38	micro	micro	ADJ
azojete-1	20	39	-	-	ADJ
azojete-1	20	40	structural	structural	ADJ
azojete-1	20	41	characteristics	characteristic	NOUN
azojete-1	20	42	are	be	AUX
azojete-1	20	43	explicitly	explicitly	ADV
azojete-1	20	44	considered	consider	VERB
azojete-1	20	45	.	.	PUNCT
azojete-1	21	1	it	it	PRON
azojete-1	21	2	is	be	AUX
azojete-1	21	3	the	the	DET
azojete-1	21	4	need	need	NOUN
azojete-1	21	5	to	to	PART
azojete-1	21	6	provide	provide	VERB
azojete-1	21	7	an	an	DET
azojete-1	21	8	efficient	efficient	ADJ
azojete-1	21	9	modelling	modelling	NOUN
azojete-1	21	10	strategy	strategy	NOUN
azojete-1	21	11	,	,	PUNCT
azojete-1	21	12	to	to	PART
azojete-1	21	13	better	well	ADV
azojete-1	21	14	understand	understand	VERB
azojete-1	21	15	the	the	DET
azojete-1	21	16	relationship	relationship	NOUN
azojete-1	21	17	between	between	ADP
azojete-1	21	18	material	material	NOUN
azojete-1	21	19	micro	micro	NOUN
azojete-1	21	20	-	-	NOUN
azojete-1	21	21	structure	structure	ADJ
azojete-1	21	22	and	and	CCONJ
azojete-1	21	23	macroscopic	macroscopic	ADJ
azojete-1	21	24	properties	property	NOUN
azojete-1	21	25	(	(	PUNCT
azojete-1	21	26	that	that	PRON
azojete-1	21	27	is	be	AUX
azojete-1	21	28	the	the	DET
azojete-1	21	29	micromacro	micromacro	PROPN
azojete-1	21	30	structure	structure	NOUN
azojete-1	21	31	property	property	NOUN
azojete-1	21	32	relation	relation	NOUN
azojete-1	21	33	)	)	PUNCT
azojete-1	21	34	leading	lead	VERB
azojete-1	21	35	to	to	ADP
azojete-1	21	36	the	the	DET
azojete-1	21	37	determination	determination	NOUN
azojete-1	21	38	of	of	ADP
azojete-1	21	39	the	the	DET
azojete-1	21	40	general	general	ADJ
azojete-1	21	41	macroscopic	macroscopic	ADJ
azojete-1	21	42	homogenised	homogenise	VERB
azojete-1	21	43	constant	constant	ADJ
azojete-1	21	44	value	value	NOUN
azojete-1	21	45	for	for	ADP
azojete-1	21	46	the	the	DET
azojete-1	21	47	heterogeneous	heterogeneous	ADJ
azojete-1	21	48	material	material	NOUN
azojete-1	21	49	,	,	PUNCT
azojete-1	21	50	that	that	PRON
azojete-1	21	51	has	have	AUX
azojete-1	21	52	lead	lead	VERB
azojete-1	21	53	to	to	ADP
azojete-1	21	54	the	the	DET
azojete-1	21	55	development	development	NOUN
azojete-1	21	56	of	of	ADP
azojete-1	21	57	the	the	DET
azojete-1	21	58	multiscale	multiscale	ADJ
azojete-1	21	59	models	model	NOUN
azojete-1	21	60	.	.	PUNCT
azojete-1	22	1	this	this	PRON
azojete-1	22	2	is	be	AUX
azojete-1	22	3	because	because	SCONJ
azojete-1	22	4	for	for	ADP
azojete-1	22	5	the	the	DET
azojete-1	22	6	analysis	analysis	NOUN
azojete-1	22	7	of	of	ADP
azojete-1	22	8	composite	composite	ADJ
azojete-1	22	9	materials	material	NOUN
azojete-1	22	10	,	,	PUNCT
azojete-1	22	11	it	it	PRON
azojete-1	22	12	is	be	AUX
azojete-1	22	13	the	the	DET
azojete-1	22	14	effective	effective	ADJ
azojete-1	22	15	or	or	CCONJ
azojete-1	22	16	homogenised	homogenise	VERB
azojete-1	22	17	material	material	NOUN
azojete-1	22	18	property	property	NOUN
azojete-1	22	19	that	that	PRON
azojete-1	22	20	is	be	AUX
azojete-1	22	21	used	use	VERB
azojete-1	22	22	as	as	ADP
azojete-1	22	23	opposed	oppose	VERB
azojete-1	22	24	to	to	ADP
azojete-1	22	25	the	the	DET
azojete-1	22	26	properties	property	NOUN
azojete-1	22	27	of	of	ADP
azojete-1	22	28	the	the	DET
azojete-1	22	29	separate	separate	ADJ
azojete-1	22	30	components	component	NOUN
azojete-1	22	31	that	that	PRON
azojete-1	22	32	make	make	VERB
azojete-1	22	33	up	up	ADP
azojete-1	22	34	the	the	DET
azojete-1	22	35	material	material	NOUN
azojete-1	22	36	(	(	PUNCT
azojete-1	22	37	kanoute	kanoute	VERB
azojete-1	22	38	et	et	PROPN
azojete-1	22	39	al	al	PROPN
azojete-1	22	40	.	.	PROPN
azojete-1	22	41	,	,	PUNCT
azojete-1	22	42	2009	2009	NUM
azojete-1	22	43	;	;	PUNCT
azojete-1	22	44	nguyen	nguyen	PROPN
azojete-1	22	45	et	et	PROPN
azojete-1	22	46	al	al	PROPN
azojete-1	22	47	.	.	PROPN
azojete-1	22	48	,	,	PUNCT
azojete-1	22	49	2012	2012	NUM
azojete-1	22	50	)	)	PUNCT
azojete-1	22	51	.	.	PUNCT
azojete-1	23	1	multiscale	multiscale	PROPN
azojete-1	23	2	modelling	modelling	NOUN
azojete-1	23	3	,	,	PUNCT
azojete-1	23	4	is	be	AUX
azojete-1	23	5	therefore	therefore	ADV
azojete-1	23	6	,	,	PUNCT
azojete-1	23	7	an	an	DET
azojete-1	23	8	area	area	NOUN
azojete-1	23	9	of	of	ADP
azojete-1	23	10	study	study	NOUN
azojete-1	23	11	which	which	PRON
azojete-1	23	12	involves	involve	VERB
azojete-1	23	13	resolving	resolve	VERB
azojete-1	23	14	problems	problem	NOUN
azojete-1	23	15	which	which	PRON
azojete-1	23	16	have	have	VERB
azojete-1	23	17	significant	significant	ADJ
azojete-1	23	18	characteristics	characteristic	NOUN
azojete-1	23	19	at	at	ADP
azojete-1	23	20	multiple	multiple	ADJ
azojete-1	23	21	scales	scale	NOUN
azojete-1	23	22	of	of	ADP
azojete-1	23	23	resolution	resolution	NOUN
azojete-1	23	24	.	.	PUNCT
azojete-1	24	1	it	it	PRON
azojete-1	24	2	usually	usually	ADV
azojete-1	24	3	entails	entail	VERB
azojete-1	24	4	modelling	modelling	NOUN
azojete-1	24	5	from	from	ADP
azojete-1	24	6	the	the	DET
azojete-1	24	7	smallest	small	ADJ
azojete-1	24	8	scale	scale	NOUN
azojete-1	24	9	of	of	ADP
azojete-1	24	10	the	the	DET
azojete-1	24	11	material	material	NOUN
azojete-1	24	12	to	to	ADP
azojete-1	24	13	a	a	DET
azojete-1	24	14	much	much	ADV
azojete-1	24	15	larger	large	ADJ
azojete-1	24	16	scale	scale	NOUN
azojete-1	24	17	(	(	PUNCT
azojete-1	24	18	for	for	ADP
azojete-1	24	19	example	example	NOUN
azojete-1	24	20	,	,	PUNCT
azojete-1	24	21	from	from	ADP
azojete-1	24	22	nanoscale	nanoscale	NOUN
azojete-1	24	23	that	that	PRON
azojete-1	24	24	is	be	AUX
azojete-1	24	25	quantum	quantum	ADJ
azojete-1	24	26	level	level	NOUN
azojete-1	24	27	to	to	ADP
azojete-1	24	28	the	the	DET
azojete-1	24	29	macroscale	macroscale	NOUN
azojete-1	24	30	that	that	PRON
azojete-1	24	31	is	be	AUX
azojete-1	24	32	continuum	continuum	ADJ
azojete-1	24	33	level	level	NOUN
azojete-1	24	34	as	as	SCONJ
azojete-1	24	35	shown	show	VERB
azojete-1	24	36	in	in	ADP
azojete-1	24	37	figure	figure	NOUN
azojete-1	24	38	2	2	NUM
azojete-1	24	39	)	)	PUNCT
azojete-1	24	40	this	this	PRON
azojete-1	24	41	is	be	AUX
azojete-1	24	42	usually	usually	ADV
azojete-1	24	43	achieved	achieve	VERB
azojete-1	24	44	through	through	ADP
azojete-1	24	45	the	the	DET
azojete-1	24	46	use	use	NOUN
azojete-1	24	47	of	of	ADP
azojete-1	24	48	various	various	ADJ
azojete-1	24	49	models	model	NOUN
azojete-1	24	50	at	at	ADP
azojete-1	24	51	the	the	DET
azojete-1	24	52	different	different	ADJ
azojete-1	24	53	scales	scale	NOUN
azojete-1	24	54	of	of	ADP
azojete-1	24	55	resolution	resolution	NOUN
azojete-1	24	56	which	which	PRON
azojete-1	24	57	are	be	AUX
azojete-1	24	58	then	then	ADV
azojete-1	24	59	coupled	couple	VERB
azojete-1	24	60	either	either	CCONJ
azojete-1	24	61	analytically	analytically	ADV
azojete-1	24	62	,	,	PUNCT
azojete-1	24	63	numerically	numerically	ADV
azojete-1	24	64	or	or	CCONJ
azojete-1	24	65	computationally	computationally	ADV
azojete-1	24	66	(	(	PUNCT
azojete-1	24	67	engquist	engquist	NOUN
azojete-1	24	68	et	et	PROPN
azojete-1	24	69	al	al	PROPN
azojete-1	24	70	.	.	PROPN
azojete-1	24	71	,	,	PUNCT
azojete-1	24	72	2007	2007	NUM
azojete-1	24	73	;	;	PUNCT
azojete-1	24	74	weinan	weinan	PROPN
azojete-1	24	75	and	and	CCONJ
azojete-1	24	76	jianfeng	jianfeng	NOUN
azojete-1	24	77	,	,	PUNCT
azojete-1	24	78	2011	2011	NUM
azojete-1	24	79	)	)	PUNCT
azojete-1	24	80	.	.	PUNCT
azojete-1	25	1	figure	figure	VERB
azojete-1	25	2	2	2	NUM
azojete-1	25	3	:	:	PUNCT
azojete-1	25	4	illustration	illustration	NOUN
azojete-1	25	5	of	of	ADP
azojete-1	25	6	the	the	DET
azojete-1	25	7	multi	multi	ADJ
azojete-1	25	8	-	-	NOUN
azojete-1	25	9	scale	scale	ADJ
azojete-1	25	10	modeling	modeling	NOUN
azojete-1	25	11	hierarchy	hierarchy	NOUN
azojete-1	25	12	adapted	adapt	VERB
azojete-1	25	13	from	from	ADP
azojete-1	25	14	weinan	weinan	NOUN
azojete-1	25	15	and	and	CCONJ
azojete-1	25	16	jianfeng	jianfeng	PROPN
azojete-1	25	17	(	(	PUNCT
azojete-1	25	18	2011	2011	NUM
azojete-1	25	19	)	)	PUNCT
azojete-1	25	20	.	.	PUNCT
azojete-1	26	1	file:///c:/users	file:///c:/user	NOUN
azojete-1	26	2	/	/	SYM
azojete-1	26	3	user	user	NOUN
azojete-1	26	4	/	/	SYM
azojete-1	26	5	downloads	download	NOUN
azojete-1	26	6	/	/	SYM
azojete-1	26	7	azojete143	azojete143	PROPN
azojete-1	26	8	/	/	SYM
azojete-1	26	9	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	26	10	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	26	11	ohunene	ohunene	ADJ
azojete-1	26	12	hafsa	hafsa	PROPN
azojete-1	26	13	aliyu	aliyu	PROPN
azojete-1	26	14	:	:	PUNCT
azojete-1	26	15	analytical	analytical	ADJ
azojete-1	26	16	,	,	PUNCT
azojete-1	26	17	numerical	numerical	ADJ
azojete-1	26	18	and	and	CCONJ
azojete-1	26	19	computational	computational	ADJ
azojete-1	26	20	multiscale	multiscale	NOUN
azojete-1	26	21	modelling	model	VERB
azojete-1	26	22	techniques	technique	NOUN
azojete-1	26	23	for	for	ADP
azojete-1	26	24	heterogenous	heterogenous	ADJ
azojete-1	26	25	materials	material	NOUN
azojete-1	26	26	:	:	PUNCT
azojete-1	26	27	a	a	DET
azojete-1	26	28	review	review	NOUN
azojete-1	26	29	.	.	PUNCT
azojete-1	27	1	azojete	azojete	NOUN
azojete-1	27	2	,	,	PUNCT
azojete-1	27	3	15(3):488	15(3):488	PROPN
azojete-1	27	4	-	-	PUNCT
azojete-1	27	5	509	509	NUM
azojete-1	27	6	.	.	PUNCT
azojete-1	28	1	issn	issn	PROPN
azojete-1	28	2	1596	1596	NUM
azojete-1	28	3	-	-	SYM
azojete-1	28	4	2490	2490	NUM
azojete-1	28	5	;	;	PUNCT
azojete-1	28	6	e	e	X
azojete-1	28	7	-	-	NOUN
azojete-1	28	8	issn	issn	VERB
azojete-1	28	9	2545	2545	NUM
azojete-1	28	10	-	-	SYM
azojete-1	28	11	5818	5818	NUM
azojete-1	28	12	,	,	PUNCT
azojete-1	28	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	28	14	corresponding	correspond	VERB
azojete-1	28	15	author	author	NOUN
azojete-1	28	16	’s	’s	PART
azojete-1	28	17	e	e	NOUN
azojete-1	28	18	-	-	NOUN
azojete-1	28	19	mail	mail	NOUN
azojete-1	28	20	address	address	NOUN
azojete-1	28	21	:	:	PUNCT
azojete-1	28	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	28	23	490	490	NUM
azojete-1	28	24	figure	figure	NOUN
azojete-1	28	25	3	3	NUM
azojete-1	28	26	:	:	PUNCT
azojete-1	28	27	a	a	DET
azojete-1	28	28	seamless	seamless	ADJ
azojete-1	28	29	integration	integration	NOUN
azojete-1	28	30	of	of	ADP
azojete-1	28	31	models	model	NOUN
azojete-1	28	32	of	of	ADP
azojete-1	28	33	the	the	DET
azojete-1	28	34	different	different	ADJ
azojete-1	28	35	length	length	NOUN
azojete-1	28	36	scales	scale	NOUN
azojete-1	28	37	into	into	ADP
azojete-1	28	38	one	one	NUM
azojete-1	28	39	coherent	coherent	ADJ
azojete-1	28	40	multiscale	multiscale	NOUN
azojete-1	28	41	modelling	modelling	NOUN
azojete-1	28	42	frame	frame	NOUN
azojete-1	28	43	work	work	NOUN
azojete-1	28	44	.	.	PUNCT
azojete-1	29	1	adapted	adapt	VERB
azojete-1	29	2	from	from	ADP
azojete-1	29	3	icams	icams	PROPN
azojete-1	29	4	webpage	webpage	NOUN
azojete-1	29	5	ruhr	ruhr	PROPN
azojete-1	29	6	university	university	PROPN
azojete-1	29	7	germany	germany	PROPN
azojete-1	29	8	although	although	SCONJ
azojete-1	29	9	,	,	PUNCT
azojete-1	29	10	most	most	ADJ
azojete-1	29	11	engineering	engineering	NOUN
azojete-1	29	12	problems	problem	NOUN
azojete-1	29	13	are	be	AUX
azojete-1	29	14	solved	solve	VERB
azojete-1	29	15	at	at	ADP
azojete-1	29	16	the	the	DET
azojete-1	29	17	macroscopic	macroscopic	ADJ
azojete-1	29	18	scale	scale	NOUN
azojete-1	29	19	,	,	PUNCT
azojete-1	29	20	the	the	DET
azojete-1	29	21	results	result	NOUN
azojete-1	29	22	obtained	obtain	VERB
azojete-1	29	23	from	from	ADP
azojete-1	29	24	such	such	ADJ
azojete-1	29	25	analysis	analysis	NOUN
azojete-1	29	26	are	be	AUX
azojete-1	29	27	not	not	PART
azojete-1	29	28	sufficiently	sufficiently	ADV
azojete-1	29	29	precise	precise	ADJ
azojete-1	29	30	while	while	SCONJ
azojete-1	29	31	the	the	DET
azojete-1	29	32	direct	direct	ADJ
azojete-1	29	33	micro	micro	NOUN
azojete-1	29	34	-	-	NOUN
azojete-1	29	35	scale	scale	ADJ
azojete-1	29	36	modelling	modelling	NOUN
azojete-1	29	37	of	of	ADP
azojete-1	29	38	engineering	engineering	NOUN
azojete-1	29	39	problems	problem	NOUN
azojete-1	29	40	are	be	AUX
azojete-1	29	41	not	not	PART
azojete-1	29	42	cost	cost	VERB
azojete-1	29	43	effective	effective	ADJ
azojete-1	29	44	and	and	CCONJ
azojete-1	29	45	offer	offer	VERB
azojete-1	29	46	too	too	ADV
azojete-1	29	47	much	much	ADJ
azojete-1	29	48	information	information	NOUN
azojete-1	29	49	;	;	PUNCT
azojete-1	29	50	hence	hence	ADV
azojete-1	29	51	the	the	DET
azojete-1	29	52	need	need	NOUN
azojete-1	29	53	for	for	ADP
azojete-1	29	54	multiscale	multiscale	NOUN
azojete-1	29	55	modelling	modelling	NOUN
azojete-1	29	56	(	(	PUNCT
azojete-1	29	57	weinan	weinan	NOUN
azojete-1	29	58	and	and	CCONJ
azojete-1	29	59	jianfeng	jianfeng	PROPN
azojete-1	29	60	,	,	PUNCT
azojete-1	29	61	2011	2011	NUM
azojete-1	29	62	;	;	PUNCT
azojete-1	29	63	kanoute	kanoute	VERB
azojete-1	29	64	et	et	PROPN
azojete-1	29	65	al	al	PROPN
azojete-1	29	66	.	.	PROPN
azojete-1	29	67	,	,	PUNCT
azojete-1	29	68	2009	2009	NUM
azojete-1	29	69	)	)	PUNCT
azojete-1	29	70	.	.	PUNCT
azojete-1	30	1	the	the	DET
azojete-1	30	2	driving	drive	VERB
azojete-1	30	3	force	force	NOUN
azojete-1	30	4	behind	behind	ADP
azojete-1	30	5	carrying	carry	VERB
azojete-1	30	6	out	out	ADP
azojete-1	30	7	multiscale	multiscale	ADJ
azojete-1	30	8	modelling	modelling	NOUN
azojete-1	30	9	is	be	AUX
azojete-1	30	10	to	to	PART
azojete-1	30	11	achieve	achieve	VERB
azojete-1	30	12	a	a	DET
azojete-1	30	13	balance	balance	NOUN
azojete-1	30	14	between	between	ADP
azojete-1	30	15	accuracy	accuracy	NOUN
azojete-1	30	16	and	and	CCONJ
azojete-1	30	17	efficiency	efficiency	NOUN
azojete-1	30	18	by	by	ADP
azojete-1	30	19	coupling	couple	VERB
azojete-1	30	20	together	together	ADV
azojete-1	30	21	both	both	CCONJ
azojete-1	30	22	the	the	DET
azojete-1	30	23	microscopic	microscopic	ADJ
azojete-1	30	24	and	and	CCONJ
azojete-1	30	25	macroscopic	macroscopic	ADJ
azojete-1	30	26	models	model	NOUN
azojete-1	30	27	;	;	PUNCT
azojete-1	30	28	thus	thus	ADV
azojete-1	30	29	,	,	PUNCT
azojete-1	30	30	providing	provide	VERB
azojete-1	30	31	an	an	DET
azojete-1	30	32	accurate	accurate	ADJ
azojete-1	30	33	predictive	predictive	ADJ
azojete-1	30	34	tool	tool	NOUN
azojete-1	30	35	which	which	PRON
azojete-1	30	36	is	be	AUX
azojete-1	30	37	considered	consider	VERB
azojete-1	30	38	crucial	crucial	ADJ
azojete-1	30	39	in	in	ADP
azojete-1	30	40	engineering	engineering	NOUN
azojete-1	30	41	and	and	CCONJ
azojete-1	30	42	material	material	NOUN
azojete-1	30	43	science	science	NOUN
azojete-1	30	44	(	(	PUNCT
azojete-1	30	45	engquist	engquist	NOUN
azojete-1	30	46	et	et	PROPN
azojete-1	30	47	al	al	PROPN
azojete-1	30	48	.	.	PROPN
azojete-1	30	49	,	,	PUNCT
azojete-1	30	50	2007	2007	NUM
azojete-1	30	51	)	)	PUNCT
azojete-1	30	52	.	.	PUNCT
azojete-1	31	1	this	this	DET
azojete-1	31	2	paper	paper	NOUN
azojete-1	31	3	reviews	review	VERB
azojete-1	31	4	the	the	DET
azojete-1	31	5	advancements	advancement	NOUN
azojete-1	31	6	in	in	ADP
azojete-1	31	7	multiscale	multiscale	NOUN
azojete-1	31	8	modelling	modelling	NOUN
azojete-1	31	9	of	of	ADP
azojete-1	31	10	composite	composite	ADJ
azojete-1	31	11	material	material	NOUN
azojete-1	31	12	(	(	PUNCT
azojete-1	31	13	such	such	ADJ
azojete-1	31	14	as	as	ADP
azojete-1	31	15	steel	steel	NOUN
azojete-1	31	16	,	,	PUNCT
azojete-1	31	17	concrete	concrete	ADJ
azojete-1	31	18	,	,	PUNCT
azojete-1	31	19	polymer	polymer	NOUN
azojete-1	31	20	-	-	PUNCT
azojete-1	31	21	blends	blend	NOUN
azojete-1	31	22	,	,	PUNCT
azojete-1	31	23	and	and	CCONJ
azojete-1	31	24	so	so	ADV
azojete-1	31	25	on	on	ADP
azojete-1	31	26	)	)	PUNCT
azojete-1	31	27	which	which	PRON
azojete-1	31	28	are	be	AUX
azojete-1	31	29	used	use	VERB
azojete-1	31	30	for	for	ADP
azojete-1	31	31	various	various	ADJ
azojete-1	31	32	industrial	industrial	ADJ
azojete-1	31	33	applications	application	NOUN
azojete-1	31	34	to	to	PART
azojete-1	31	35	determine	determine	VERB
azojete-1	31	36	their	their	PRON
azojete-1	31	37	macroscopic	macroscopic	ADJ
azojete-1	31	38	material	material	NOUN
azojete-1	31	39	properties	property	NOUN
azojete-1	31	40	such	such	ADJ
azojete-1	31	41	as	as	ADP
azojete-1	31	42	stress	stress	NOUN
azojete-1	31	43	and	and	CCONJ
azojete-1	31	44	stain	stain	NOUN
azojete-1	31	45	fields	field	NOUN
azojete-1	31	46	in	in	ADP
azojete-1	31	47	addition	addition	NOUN
azojete-1	31	48	to	to	ADP
azojete-1	31	49	their	their	PRON
azojete-1	31	50	macroscopic	macroscopic	ADJ
azojete-1	31	51	material	material	NOUN
azojete-1	31	52	behaviour	behaviour	NOUN
azojete-1	31	53	such	such	ADJ
azojete-1	31	54	as	as	ADP
azojete-1	31	55	their	their	PRON
azojete-1	31	56	energy	energy	NOUN
azojete-1	31	57	absorption	absorption	NOUN
azojete-1	31	58	at	at	ADP
azojete-1	31	59	high	high	ADJ
azojete-1	31	60	strain	strain	NOUN
azojete-1	31	61	rates	rate	NOUN
azojete-1	31	62	,	,	PUNCT
azojete-1	31	63	cracking	cracking	NOUN
azojete-1	31	64	,	,	PUNCT
azojete-1	31	65	creep	creep	PROPN
azojete-1	31	66	,	,	PUNCT
azojete-1	31	67	et	et	NOUN
azojete-1	31	68	cetera	cetera	NOUN
azojete-1	31	69	by	by	ADP
azojete-1	31	70	using	use	VERB
azojete-1	31	71	the	the	DET
azojete-1	31	72	various	various	ADJ
azojete-1	31	73	homogenization	homogenization	NOUN
azojete-1	31	74	methods	method	NOUN
azojete-1	31	75	(	(	PUNCT
azojete-1	31	76	nguyen	nguyen	NOUN
azojete-1	31	77	et	et	PROPN
azojete-1	31	78	al	al	PROPN
azojete-1	31	79	.	.	PROPN
azojete-1	31	80	,	,	PUNCT
azojete-1	31	81	2012	2012	NUM
azojete-1	31	82	;	;	PUNCT
azojete-1	31	83	aliyu	aliyu	NOUN
azojete-1	31	84	,	,	PUNCT
azojete-1	31	85	2019	2019	NUM
azojete-1	31	86	)	)	PUNCT
azojete-1	31	87	.	.	PUNCT
azojete-1	32	1	2	2	X
azojete-1	32	2	.	.	X
azojete-1	32	3	homogenisation	homogenisation	NOUN
azojete-1	32	4	techniques	technique	NOUN
azojete-1	32	5	as	as	ADP
azojete-1	32	6	previously	previously	ADV
azojete-1	32	7	mentioned	mention	VERB
azojete-1	32	8	,	,	PUNCT
azojete-1	32	9	the	the	DET
azojete-1	32	10	significance	significance	NOUN
azojete-1	32	11	of	of	ADP
azojete-1	32	12	modelling	modelling	NOUN
azojete-1	32	13	across	across	ADP
azojete-1	32	14	multiple	multiple	ADJ
azojete-1	32	15	-	-	PUNCT
azojete-1	32	16	scales	scale	NOUN
azojete-1	32	17	is	be	AUX
azojete-1	32	18	that	that	SCONJ
azojete-1	32	19	the	the	DET
azojete-1	32	20	predictions	prediction	NOUN
azojete-1	32	21	obtained	obtain	VERB
azojete-1	32	22	from	from	ADP
azojete-1	32	23	such	such	ADJ
azojete-1	32	24	modelling	modelling	NOUN
azojete-1	32	25	techniques	technique	NOUN
azojete-1	32	26	are	be	AUX
azojete-1	32	27	more	more	ADV
azojete-1	32	28	precise	precise	ADJ
azojete-1	32	29	and	and	CCONJ
azojete-1	32	30	accurate	accurate	ADJ
azojete-1	32	31	(	(	PUNCT
azojete-1	32	32	weinan	weinan	NOUN
azojete-1	32	33	and	and	CCONJ
azojete-1	32	34	jianfeng	jianfeng	NOUN
azojete-1	32	35	,	,	PUNCT
azojete-1	32	36	2011	2011	NUM
azojete-1	32	37	)	)	PUNCT
azojete-1	32	38	.	.	PUNCT
azojete-1	33	1	the	the	DET
azojete-1	33	2	conventional	conventional	ADJ
azojete-1	33	3	multi	multi	ADJ
azojete-1	33	4	-	-	NOUN
azojete-1	33	5	scale	scale	ADJ
azojete-1	33	6	modelling	modelling	NOUN
azojete-1	33	7	of	of	ADP
azojete-1	33	8	composites	composite	NOUN
azojete-1	33	9	is	be	AUX
azojete-1	33	10	either	either	CCONJ
azojete-1	33	11	carried	carry	VERB
azojete-1	33	12	out	out	ADP
azojete-1	33	13	within	within	ADP
azojete-1	33	14	the	the	DET
azojete-1	33	15	framework	framework	NOUN
azojete-1	33	16	of	of	ADP
azojete-1	33	17	homogenisation	homogenisation	NOUN
azojete-1	33	18	methods	method	NOUN
azojete-1	33	19	or	or	CCONJ
azojete-1	33	20	the	the	DET
azojete-1	33	21	concurrent	concurrent	ADJ
azojete-1	33	22	method	method	NOUN
azojete-1	33	23	depending	depend	VERB
azojete-1	33	24	on	on	ADP
azojete-1	33	25	whether	whether	SCONJ
azojete-1	33	26	the	the	DET
azojete-1	33	27	scales	scale	NOUN
azojete-1	33	28	are	be	AUX
azojete-1	33	29	distinctively	distinctively	ADV
azojete-1	33	30	separated	separate	VERB
azojete-1	33	31	or	or	CCONJ
azojete-1	33	32	coupled	couple	VERB
azojete-1	33	33	(	(	PUNCT
azojete-1	33	34	nguyen	nguyen	NOUN
azojete-1	33	35	et	et	PROPN
azojete-1	33	36	al	al	PROPN
azojete-1	33	37	.	.	PROPN
azojete-1	33	38	,	,	PUNCT
azojete-1	33	39	2012	2012	NUM
azojete-1	33	40	)	)	PUNCT
azojete-1	33	41	.	.	PUNCT
azojete-1	34	1	the	the	DET
azojete-1	34	2	fundamental	fundamental	ADJ
azojete-1	34	3	aim	aim	NOUN
azojete-1	34	4	of	of	ADP
azojete-1	34	5	homogenisation	homogenisation	NOUN
azojete-1	34	6	techniques	technique	NOUN
azojete-1	34	7	is	be	AUX
azojete-1	34	8	to	to	PART
azojete-1	34	9	determine	determine	VERB
azojete-1	34	10	the	the	DET
azojete-1	34	11	effective	effective	ADJ
azojete-1	34	12	properties	property	NOUN
azojete-1	34	13	for	for	ADP
azojete-1	34	14	heterogeneous	heterogeneous	ADJ
azojete-1	34	15	materials	material	NOUN
azojete-1	34	16	from	from	ADP
azojete-1	34	17	the	the	DET
azojete-1	34	18	mechanical	mechanical	ADJ
azojete-1	34	19	behaviour	behaviour	NOUN
azojete-1	34	20	of	of	ADP
azojete-1	34	21	the	the	DET
azojete-1	34	22	materials	material	NOUN
azojete-1	34	23	constituents	constituent	NOUN
azojete-1	34	24	’	'	PUNCT
azojete-1	34	25	microstructure	microstructure	NOUN
azojete-1	34	26	;	;	PUNCT
azojete-1	34	27	thus	thus	ADV
azojete-1	34	28	,	,	PUNCT
azojete-1	34	29	providing	provide	VERB
azojete-1	34	30	a	a	DET
azojete-1	34	31	means	mean	NOUN
azojete-1	34	32	for	for	ADP
azojete-1	34	33	replacing	replace	VERB
azojete-1	34	34	the	the	DET
azojete-1	34	35	heterogeneous	heterogeneous	ADJ
azojete-1	34	36	material	material	NOUN
azojete-1	34	37	with	with	ADP
azojete-1	34	38	a	a	DET
azojete-1	34	39	homogenous	homogenous	ADJ
azojete-1	34	40	one	one	NOUN
azojete-1	34	41	.	.	PUNCT
azojete-1	35	1	for	for	ADP
azojete-1	35	2	many	many	ADJ
azojete-1	35	3	decades	decade	NOUN
azojete-1	35	4	now	now	ADV
azojete-1	35	5	,	,	PUNCT
azojete-1	35	6	quite	quite	DET
azojete-1	35	7	a	a	DET
azojete-1	35	8	number	number	NOUN
azojete-1	35	9	of	of	ADP
azojete-1	35	10	micromechanical	micromechanical	ADJ
azojete-1	35	11	modelling	modelling	NOUN
azojete-1	35	12	techniques	technique	NOUN
azojete-1	35	13	dealing	deal	VERB
azojete-1	35	14	with	with	ADP
azojete-1	35	15	heterogeneous	heterogeneous	ADJ
azojete-1	35	16	materials	material	NOUN
azojete-1	35	17	have	have	AUX
azojete-1	35	18	been	be	AUX
azojete-1	35	19	developed	develop	VERB
azojete-1	35	20	(	(	PUNCT
azojete-1	35	21	kanoute	kanoute	VERB
azojete-1	35	22	et	et	PROPN
azojete-1	35	23	al	al	PROPN
azojete-1	35	24	.	.	PROPN
azojete-1	35	25	,	,	PUNCT
azojete-1	35	26	2009	2009	NUM
azojete-1	35	27	)	)	PUNCT
azojete-1	35	28	.	.	PUNCT
azojete-1	36	1	the	the	DET
azojete-1	36	2	micromechanical	micromechanical	ADJ
azojete-1	36	3	modelling	modelling	NOUN
azojete-1	36	4	technique	technique	NOUN
azojete-1	36	5	to	to	PART
azojete-1	36	6	be	be	AUX
azojete-1	36	7	adopted	adopt	VERB
azojete-1	36	8	in	in	ADP
azojete-1	36	9	achieving	achieve	VERB
azojete-1	36	10	a	a	DET
azojete-1	36	11	homogenised	homogenised	ADJ
azojete-1	36	12	constant	constant	ADJ
azojete-1	36	13	material	material	NOUN
azojete-1	36	14	value	value	NOUN
azojete-1	36	15	for	for	ADP
azojete-1	36	16	a	a	DET
azojete-1	36	17	heterogeneous	heterogeneous	ADJ
azojete-1	36	18	or	or	CCONJ
azojete-1	36	19	composite	composite	ADJ
azojete-1	36	20	material	material	NOUN
azojete-1	36	21	falls	fall	VERB
azojete-1	36	22	into	into	ADP
azojete-1	36	23	one	one	NUM
azojete-1	36	24	of	of	ADP
azojete-1	36	25	three	three	NUM
azojete-1	36	26	main	main	ADJ
azojete-1	36	27	categories	category	NOUN
azojete-1	36	28	.	.	PUNCT
azojete-1	37	1	in	in	ADP
azojete-1	37	2	the	the	DET
azojete-1	37	3	first	first	ADJ
azojete-1	37	4	category	category	NOUN
azojete-1	37	5	,	,	PUNCT
azojete-1	37	6	schemes	scheme	NOUN
azojete-1	37	7	employed	employ	VERB
azojete-1	37	8	used	use	VERB
azojete-1	37	9	high	high	ADJ
azojete-1	37	10	resolutions	resolution	NOUN
azojete-1	37	11	at	at	ADP
azojete-1	37	12	certain	certain	ADJ
azojete-1	37	13	sections	section	NOUN
azojete-1	37	14	of	of	ADP
azojete-1	37	15	the	the	DET
azojete-1	37	16	domain	domain	NOUN
azojete-1	37	17	where	where	SCONJ
azojete-1	37	18	fine	fine	ADJ
azojete-1	37	19	(	(	PUNCT
azojete-1	37	20	microscopic	microscopic	ADJ
azojete-1	37	21	)	)	PUNCT
azojete-1	37	22	scale	scale	NOUN
azojete-1	37	23	detail	detail	NOUN
azojete-1	37	24	of	of	ADP
azojete-1	37	25	the	the	DET
azojete-1	37	26	microstructure	microstructure	ADJ
azojete-1	37	27	morphology	morphology	NOUN
azojete-1	37	28	(	(	PUNCT
azojete-1	37	29	i.e.	i.e.	X
azojete-1	37	30	at	at	ADP
azojete-1	37	31	cracked	crack	VERB
azojete-1	37	32	tips	tip	NOUN
azojete-1	37	33	,	,	PUNCT
azojete-1	37	34	and	and	CCONJ
azojete-1	37	35	interfaces	interface	NOUN
azojete-1	37	36	)	)	PUNCT
azojete-1	37	37	needs	need	VERB
azojete-1	37	38	to	to	PART
azojete-1	37	39	be	be	AUX
azojete-1	37	40	determined	determine	VERB
azojete-1	37	41	.	.	PUNCT
azojete-1	38	1	for	for	ADP
azojete-1	38	2	the	the	DET
azojete-1	38	3	second	second	ADJ
azojete-1	38	4	category	category	NOUN
azojete-1	38	5	,	,	PUNCT
azojete-1	38	6	the	the	DET
azojete-1	38	7	schemes	scheme	NOUN
azojete-1	38	8	rely	rely	VERB
azojete-1	38	9	on	on	ADP
azojete-1	38	10	the	the	DET
azojete-1	38	11	description	description	NOUN
azojete-1	38	12	of	of	ADP
azojete-1	38	13	the	the	DET
azojete-1	38	14	http://www.azojete.com.ng	http://www.azojete.com.ng	ADJ
azojete-1	38	15	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	38	16	arid	arid	NOUN
azojete-1	38	17	zone	zone	NOUN
azojete-1	38	18	journal	journal	NOUN
azojete-1	38	19	of	of	ADP
azojete-1	38	20	engineering	engineering	NOUN
azojete-1	38	21	,	,	PUNCT
azojete-1	38	22	technology	technology	NOUN
azojete-1	38	23	and	and	CCONJ
azojete-1	38	24	environment	environment	NOUN
azojete-1	38	25	,	,	PUNCT
azojete-1	38	26	september	september	PROPN
azojete-1	38	27	,	,	PUNCT
azojete-1	38	28	2019	2019	NUM
azojete-1	38	29	;	;	PUNCT
azojete-1	38	30	vol	vol	NOUN
azojete-1	38	31	.	.	PUNCT
azojete-1	39	1	15(3):488	15(3):488	NUM
azojete-1	39	2	-	-	PUNCT
azojete-1	39	3	509	509	NUM
azojete-1	39	4	.	.	PUNCT
azojete-1	40	1	issn	issn	PROPN
azojete-1	40	2	1596	1596	NUM
azojete-1	40	3	-	-	SYM
azojete-1	40	4	2490	2490	NUM
azojete-1	40	5	;	;	PUNCT
azojete-1	40	6	e	e	X
azojete-1	40	7	-	-	NOUN
azojete-1	40	8	issn	issn	VERB
azojete-1	40	9	2545	2545	NUM
azojete-1	40	10	-	-	SYM
azojete-1	40	11	5818	5818	NUM
azojete-1	40	12	;	;	PUNCT
azojete-1	40	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	40	14	corresponding	correspond	VERB
azojete-1	40	15	author	author	NOUN
azojete-1	40	16	’s	’s	PART
azojete-1	40	17	e	e	NOUN
azojete-1	40	18	-	-	NOUN
azojete-1	40	19	mail	mail	NOUN
azojete-1	40	20	address	address	NOUN
azojete-1	40	21	:	:	PUNCT
azojete-1	40	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	40	23	491	491	NUM
azojete-1	40	24	macrostructure	macrostructure	NOUN
azojete-1	40	25	from	from	ADP
azojete-1	40	26	the	the	DET
azojete-1	40	27	analysis	analysis	NOUN
azojete-1	40	28	of	of	ADP
azojete-1	40	29	the	the	DET
azojete-1	40	30	underlying	underlie	VERB
azojete-1	40	31	fine	fine	NOUN
azojete-1	40	32	(	(	PUNCT
azojete-1	40	33	microscopic	microscopic	ADJ
azojete-1	40	34	)	)	PUNCT
azojete-1	40	35	scale	scale	NOUN
azojete-1	40	36	problem	problem	NOUN
azojete-1	40	37	while	while	SCONJ
azojete-1	40	38	the	the	DET
azojete-1	40	39	third	third	ADJ
azojete-1	40	40	category	category	NOUN
azojete-1	40	41	uses	use	VERB
azojete-1	40	42	schemes	scheme	NOUN
azojete-1	40	43	which	which	PRON
azojete-1	40	44	allows	allow	VERB
azojete-1	40	45	for	for	ADP
azojete-1	40	46	some	some	DET
azojete-1	40	47	sections	section	NOUN
azojete-1	40	48	of	of	ADP
azojete-1	40	49	the	the	DET
azojete-1	40	50	domain	domain	NOUN
azojete-1	40	51	to	to	PART
azojete-1	40	52	be	be	AUX
azojete-1	40	53	completely	completely	ADV
azojete-1	40	54	resolved	resolve	VERB
azojete-1	40	55	at	at	ADP
azojete-1	40	56	the	the	DET
azojete-1	40	57	fine	fine	ADJ
azojete-1	40	58	microscopic	microscopic	ADJ
azojete-1	40	59	scale	scale	NOUN
azojete-1	40	60	and	and	CCONJ
azojete-1	40	61	the	the	DET
azojete-1	40	62	other	other	ADJ
azojete-1	40	63	sections	section	NOUN
azojete-1	40	64	resolved	resolve	VERB
azojete-1	40	65	by	by	ADP
azojete-1	40	66	using	use	VERB
azojete-1	40	67	the	the	DET
azojete-1	40	68	effective	effective	ADJ
azojete-1	40	69	macroscopic	macroscopic	ADJ
azojete-1	40	70	response	response	NOUN
azojete-1	40	71	(	(	PUNCT
azojete-1	40	72	nemat	nemat	NOUN
azojete-1	40	73	-	-	PUNCT
azojete-1	40	74	nasser	nasser	PROPN
azojete-1	40	75	and	and	CCONJ
azojete-1	40	76	hori	hori	PROPN
azojete-1	40	77	1999	1999	NUM
azojete-1	40	78	;	;	PUNCT
azojete-1	40	79	sluis	sluis	PROPN
azojete-1	40	80	et	et	PROPN
azojete-1	40	81	al	al	PROPN
azojete-1	40	82	.	.	PROPN
azojete-1	40	83	,	,	PUNCT
azojete-1	40	84	2000	2000	NUM
azojete-1	40	85	;	;	PUNCT
azojete-1	40	86	kouznetsova	kouznetsova	PROPN
azojete-1	40	87	et	et	PROPN
azojete-1	40	88	al	al	PROPN
azojete-1	40	89	.	.	PROPN
azojete-1	40	90	,	,	PUNCT
azojete-1	40	91	2012	2012	NUM
azojete-1	40	92	;	;	PUNCT
azojete-1	40	93	torquatom	torquatom	PROPN
azojete-1	40	94	,	,	PUNCT
azojete-1	40	95	2013	2013	NUM
azojete-1	40	96	;	;	PUNCT
azojete-1	40	97	matous	matous	PROPN
azojete-1	40	98	et	et	PROPN
azojete-1	40	99	al	al	PROPN
azojete-1	40	100	.	.	PROPN
azojete-1	40	101	,	,	PUNCT
azojete-1	40	102	2017	2017	NUM
azojete-1	40	103	)	)	PUNCT
azojete-1	40	104	.	.	PUNCT
azojete-1	41	1	schemes	scheme	NOUN
azojete-1	41	2	under	under	ADP
azojete-1	41	3	the	the	DET
azojete-1	41	4	above	above	ADJ
azojete-1	41	5	three	three	NUM
azojete-1	41	6	categories	category	NOUN
azojete-1	41	7	will	will	AUX
azojete-1	41	8	be	be	AUX
azojete-1	41	9	discussed	discuss	VERB
azojete-1	41	10	in	in	ADP
azojete-1	41	11	the	the	DET
azojete-1	41	12	following	follow	VERB
azojete-1	41	13	sections	section	NOUN
azojete-1	41	14	analytical	analytical	ADJ
azojete-1	41	15	/	/	SYM
azojete-1	41	16	mathematical	mathematical	ADJ
azojete-1	41	17	homogenisation	homogenisation	NOUN
azojete-1	41	18	,	,	PUNCT
azojete-1	41	19	numerical	numerical	ADJ
azojete-1	41	20	homogenisation	homogenisation	NOUN
azojete-1	41	21	as	as	ADV
azojete-1	41	22	well	well	ADV
azojete-1	41	23	as	as	ADP
azojete-1	41	24	computational	computational	ADJ
azojete-1	41	25	homogenisation	homogenisation	NOUN
azojete-1	41	26	.	.	PUNCT
azojete-1	42	1	2.1	2.1	NUM
azojete-1	42	2	analytical	analytical	ADJ
azojete-1	42	3	/	/	SYM
azojete-1	42	4	mathematical	mathematical	ADJ
azojete-1	42	5	homogenisation	homogenisation	NOUN
azojete-1	42	6	initial	initial	ADJ
azojete-1	42	7	research	research	NOUN
azojete-1	42	8	on	on	ADP
azojete-1	42	9	homogenization	homogenization	NOUN
azojete-1	42	10	techniques	technique	NOUN
azojete-1	42	11	can	can	AUX
azojete-1	42	12	be	be	AUX
azojete-1	42	13	attributed	attribute	VERB
azojete-1	42	14	to	to	ADP
azojete-1	42	15	the	the	DET
azojete-1	42	16	works	work	NOUN
azojete-1	42	17	of	of	ADP
azojete-1	42	18	voigt	voigt	PROPN
azojete-1	42	19	(	(	PUNCT
azojete-1	42	20	1889	1889	NUM
azojete-1	42	21	)	)	PUNCT
azojete-1	42	22	and	and	CCONJ
azojete-1	42	23	reuss	reuss	NOUN
azojete-1	42	24	(	(	PUNCT
azojete-1	42	25	1929	1929	NUM
azojete-1	42	26	)	)	PUNCT
azojete-1	42	27	.	.	PUNCT
azojete-1	43	1	they	they	PRON
azojete-1	43	2	were	be	AUX
azojete-1	43	3	both	both	ADV
azojete-1	43	4	able	able	ADJ
azojete-1	43	5	to	to	PART
azojete-1	43	6	develop	develop	VERB
azojete-1	43	7	models	model	NOUN
azojete-1	43	8	which	which	PRON
azojete-1	43	9	gave	give	VERB
azojete-1	43	10	rough	rough	ADJ
azojete-1	43	11	estimates	estimate	NOUN
azojete-1	43	12	of	of	ADP
azojete-1	43	13	the	the	DET
azojete-1	43	14	upper	upper	ADJ
azojete-1	43	15	and	and	CCONJ
azojete-1	43	16	lower	low	ADJ
azojete-1	43	17	bound	bound	ADJ
azojete-1	43	18	values	value	NOUN
azojete-1	43	19	of	of	ADP
azojete-1	43	20	the	the	DET
azojete-1	43	21	effective	effective	ADJ
azojete-1	43	22	moduli	modulus	NOUN
azojete-1	43	23	of	of	ADP
azojete-1	43	24	heterogeneous	heterogeneous	ADJ
azojete-1	43	25	materials	material	NOUN
azojete-1	43	26	.	.	PUNCT
azojete-1	44	1	both	both	DET
azojete-1	44	2	models	model	NOUN
azojete-1	44	3	only	only	ADV
azojete-1	44	4	took	take	VERB
azojete-1	44	5	into	into	ADP
azojete-1	44	6	account	account	NOUN
azojete-1	44	7	the	the	DET
azojete-1	44	8	volume	volume	NOUN
azojete-1	44	9	fraction	fraction	NOUN
azojete-1	44	10	.	.	PUNCT
azojete-1	45	1	this	this	PRON
azojete-1	45	2	limited	limit	VERB
azojete-1	45	3	its	its	PRON
azojete-1	45	4	application	application	NOUN
azojete-1	45	5	as	as	SCONJ
azojete-1	45	6	the	the	DET
azojete-1	45	7	influence	influence	NOUN
azojete-1	45	8	of	of	ADP
azojete-1	45	9	other	other	ADJ
azojete-1	45	10	characteristic	characteristic	ADJ
azojete-1	45	11	properties	property	NOUN
azojete-1	45	12	of	of	ADP
azojete-1	45	13	the	the	DET
azojete-1	45	14	microstructure	microstructure	NOUN
azojete-1	45	15	was	be	AUX
azojete-1	45	16	not	not	PART
azojete-1	45	17	taken	take	VERB
azojete-1	45	18	into	into	ADP
azojete-1	45	19	consideration	consideration	NOUN
azojete-1	45	20	.	.	PUNCT
azojete-1	46	1	2.1.1	2.1.1	NUM
azojete-1	46	2	general	general	ADJ
azojete-1	46	3	procedure	procedure	NOUN
azojete-1	46	4	as	as	ADP
azojete-1	46	5	the	the	DET
azojete-1	46	6	principle	principle	ADJ
azojete-1	46	7	objective	objective	NOUN
azojete-1	46	8	of	of	ADP
azojete-1	46	9	homogenization	homogenization	NOUN
azojete-1	46	10	is	be	AUX
azojete-1	46	11	to	to	PART
azojete-1	46	12	describe	describe	VERB
azojete-1	46	13	the	the	DET
azojete-1	46	14	effective	effective	ADJ
azojete-1	46	15	properties	property	NOUN
azojete-1	46	16	of	of	ADP
azojete-1	46	17	the	the	DET
azojete-1	46	18	composite	composite	ADJ
azojete-1	46	19	material	material	NOUN
azojete-1	46	20	from	from	ADP
azojete-1	46	21	the	the	DET
azojete-1	46	22	mechanical	mechanical	ADJ
azojete-1	46	23	behaviour	behaviour	NOUN
azojete-1	46	24	of	of	ADP
azojete-1	46	25	the	the	DET
azojete-1	46	26	materials	material	NOUN
azojete-1	46	27	constituents	constituent	NOUN
azojete-1	46	28	’	'	PUNCT
azojete-1	46	29	microstructure	microstructure	NOUN
azojete-1	46	30	as	as	SCONJ
azojete-1	46	31	shown	show	VERB
azojete-1	46	32	in	in	ADP
azojete-1	46	33	figure	figure	NOUN
azojete-1	46	34	4	4	NUM
azojete-1	46	35	.	.	PUNCT
azojete-1	46	36	figure	figure	VERB
azojete-1	46	37	4	4	NUM
azojete-1	46	38	:	:	PUNCT
azojete-1	46	39	schematic	schematic	ADJ
azojete-1	46	40	representation	representation	NOUN
azojete-1	46	41	of	of	ADP
azojete-1	46	42	homogenization	homogenization	NOUN
azojete-1	46	43	of	of	ADP
azojete-1	46	44	material	material	NOUN
azojete-1	46	45	(	(	PUNCT
azojete-1	46	46	temizer	temizer	NOUN
azojete-1	46	47	and	and	CCONJ
azojete-1	46	48	zohid	zohid	PROPN
azojete-1	46	49	2006	2006	NUM
azojete-1	46	50	;	;	PUNCT
azojete-1	46	51	cited	cite	VERB
azojete-1	46	52	in	in	ADP
azojete-1	46	53	nyguyen	nyguyen	NOUN
azojete-1	46	54	et	et	PROPN
azojete-1	46	55	al	al	PROPN
azojete-1	46	56	.	.	PROPN
azojete-1	46	57	2012	2012	NUM
azojete-1	46	58	)	)	PUNCT
azojete-1	46	59	.	.	PUNCT
azojete-1	47	1	the	the	DET
azojete-1	47	2	bridging	bridging	NOUN
azojete-1	47	3	of	of	ADP
azojete-1	47	4	length	length	NOUN
azojete-1	47	5	scales	scale	NOUN
azojete-1	47	6	is	be	AUX
azojete-1	47	7	necessary	necessary	ADJ
azojete-1	47	8	and	and	CCONJ
azojete-1	47	9	this	this	PRON
azojete-1	47	10	is	be	AUX
azojete-1	47	11	carried	carry	VERB
azojete-1	47	12	out	out	ADP
azojete-1	47	13	by	by	ADP
azojete-1	47	14	volume	volume	NOUN
azojete-1	47	15	averaging	averaging	NOUN
azojete-1	47	16	and	and	CCONJ
azojete-1	47	17	is	be	AUX
azojete-1	47	18	denominated	denominate	VERB
azojete-1	47	19	homogenization	homogenization	NOUN
azojete-1	47	20	(	(	PUNCT
azojete-1	47	21	llorca	llorca	NOUN
azojete-1	47	22	et	et	PROPN
azojete-1	47	23	al	al	PROPN
azojete-1	47	24	.	.	PROPN
azojete-1	47	25	,	,	PUNCT
azojete-1	47	26	2007	2007	NUM
azojete-1	47	27	)	)	PUNCT
azojete-1	47	28	.	.	PUNCT
azojete-1	48	1	∈	∈	PROPN
azojete-1	48	2	�	�	PROPN
azojete-1	48	3	=	=	SYM
azojete-1	48	4	1	1	NUM
azojete-1	48	5	ω	ω	NUM
azojete-1	48	6	ω	ω	NUM
azojete-1	48	7	∈	∈	PROPN
azojete-1	48	8	�	�	PROPN
azojete-1	48	9	(	(	PUNCT
azojete-1	48	10	x)dω	x)dω	PROPN
azojete-1	48	11	and	and	CCONJ
azojete-1	48	12	σ	σ	PROPN
azojete-1	48	13	�	�	PROPN
azojete-1	48	14	=	=	SYM
azojete-1	48	15	1	1	NUM
azojete-1	48	16	ω	ω	NUM
azojete-1	48	17	ω	ω	PROPN
azojete-1	48	18	σ	σ	PROPN
azojete-1	48	19	�	�	PROPN
azojete-1	48	20	(	(	PUNCT
azojete-1	48	21	x)dω	x)dω	PROPN
azojete-1	48	22	(	(	PUNCT
azojete-1	48	23	1	1	NUM
azojete-1	48	24	)	)	PUNCT
azojete-1	48	25	where	where	SCONJ
azojete-1	48	26	:	:	PUNCT
azojete-1	48	27	ω	ω	X
azojete-1	48	28	is	be	AUX
azojete-1	48	29	the	the	DET
azojete-1	48	30	microscopic	microscopic	ADJ
azojete-1	48	31	sample	sample	NOUN
azojete-1	48	32	;	;	PUNCT
azojete-1	48	33	�	�	PROPN
azojete-1	48	34	(	(	PUNCT
azojete-1	48	35	�	�	PROPN
azojete-1	48	36	)	)	PUNCT
azojete-1	48	37	microscopic	microscopic	ADJ
azojete-1	48	38	stress	stress	NOUN
azojete-1	48	39	;	;	PUNCT
azojete-1	48	40	�	�	PROPN
azojete-1	48	41	(	(	PUNCT
azojete-1	48	42	�	�	PROPN
azojete-1	48	43	)	)	PUNCT
azojete-1	48	44	microscopic	microscopic	ADJ
azojete-1	48	45	strain	strain	NOUN
azojete-1	48	46	;	;	PUNCT
azojete-1	48	47	position	position	NOUN
azojete-1	48	48	vector	vector	NOUN
azojete-1	48	49	;	;	PUNCT
azojete-1	48	50	(	(	PUNCT
azojete-1	48	51	�	�	NOUN
azojete-1	48	52	�	�	NOUN
azojete-1	48	53	)	)	PUNCT
azojete-1	48	54	macroscopic	macroscopic	ADJ
azojete-1	48	55	strain	strain	NOUN
azojete-1	48	56	and	and	CCONJ
azojete-1	48	57	(	(	PUNCT
azojete-1	48	58	�	�	PROPN
azojete-1	48	59	�	�	NOUN
azojete-1	48	60	)	)	PUNCT
azojete-1	48	61	macroscopic	macroscopic	ADJ
azojete-1	48	62	stress	stress	NOUN
azojete-1	48	63	.	.	PUNCT
azojete-1	49	1	while	while	SCONJ
azojete-1	49	2	the	the	DET
azojete-1	49	3	expression	expression	NOUN
azojete-1	49	4	which	which	PRON
azojete-1	49	5	gives	give	VERB
azojete-1	49	6	the	the	DET
azojete-1	49	7	denominated	denominate	VERB
azojete-1	49	8	localization	localization	NOUN
azojete-1	49	9	is	be	AUX
azojete-1	49	10	given	give	VERB
azojete-1	49	11	by	by	ADP
azojete-1	49	12	:	:	PUNCT
azojete-1	49	13	∈	∈	PROPN
azojete-1	49	14	(	(	PUNCT
azojete-1	49	15	x	x	NOUN
azojete-1	49	16	)	)	PUNCT
azojete-1	49	17	=	=	SYM
azojete-1	49	18	a(x):∈	a(x):∈	NOUN
azojete-1	49	19	�	�	PROPN
azojete-1	49	20	and	and	CCONJ
azojete-1	49	21	σ(x	σ(x	NOUN
azojete-1	49	22	)	)	PUNCT
azojete-1	49	23	=	=	PUNCT
azojete-1	50	1	b(x):σ	b(x):σ	NOUN
azojete-1	50	2	�	�	X
azojete-1	50	3	(	(	PUNCT
azojete-1	50	4	2	2	NUM
azojete-1	50	5	)	)	PUNCT
azojete-1	50	6	where	where	SCONJ
azojete-1	50	7	:	:	PUNCT
azojete-1	50	8	�	�	PROPN
azojete-1	50	9	(	(	PUNCT
azojete-1	50	10	�	�	PROPN
azojete-1	50	11	)	)	PUNCT
azojete-1	50	12	and	and	CCONJ
azojete-1	50	13	�	�	PROPN
azojete-1	50	14	(	(	PUNCT
azojete-1	50	15	�	�	PROPN
azojete-1	50	16	)	)	PUNCT
azojete-1	50	17	are	be	AUX
azojete-1	50	18	the	the	DET
azojete-1	50	19	stain	stain	NOUN
azojete-1	50	20	and	and	CCONJ
azojete-1	50	21	stress	stress	NOUN
azojete-1	50	22	concentration	concentration	NOUN
azojete-1	50	23	tensors	tensor	NOUN
azojete-1	50	24	.	.	PUNCT
azojete-1	51	1	the	the	DET
azojete-1	51	2	increasing	increase	VERB
azojete-1	51	3	complexity	complexity	NOUN
azojete-1	51	4	of	of	ADP
azojete-1	51	5	the	the	DET
azojete-1	51	6	microscopic	microscopic	ADJ
azojete-1	51	7	mechanical	mechanical	ADJ
azojete-1	51	8	behaviour	behaviour	NOUN
azojete-1	51	9	and	and	CCONJ
azojete-1	51	10	geometries	geometry	NOUN
azojete-1	51	11	hinders	hinder	VERB
azojete-1	51	12	the	the	DET
azojete-1	51	13	underlying	underlie	VERB
azojete-1	51	14	objective	objective	NOUN
azojete-1	51	15	of	of	ADP
azojete-1	51	16	the	the	DET
azojete-1	51	17	above	above	ADJ
azojete-1	51	18	technique	technique	NOUN
azojete-1	51	19	.	.	PUNCT
azojete-1	52	1	hence	hence	ADV
azojete-1	52	2	,	,	PUNCT
azojete-1	52	3	the	the	DET
azojete-1	52	4	simplifications	simplification	NOUN
azojete-1	52	5	of	of	ADP
azojete-1	52	6	the	the	DET
azojete-1	52	7	above	above	ADJ
azojete-1	52	8	file:///c:/users	file:///c:/user	NOUN
azojete-1	52	9	/	/	SYM
azojete-1	52	10	user	user	NOUN
azojete-1	52	11	/	/	SYM
azojete-1	52	12	downloads	download	NOUN
azojete-1	52	13	/	/	SYM
azojete-1	52	14	azojete143	azojete143	PROPN
azojete-1	52	15	/	/	SYM
azojete-1	52	16	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	52	17	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	52	18	ohunene	ohunene	ADJ
azojete-1	52	19	hafsa	hafsa	PROPN
azojete-1	52	20	aliyu	aliyu	PROPN
azojete-1	52	21	:	:	PUNCT
azojete-1	52	22	analytical	analytical	ADJ
azojete-1	52	23	,	,	PUNCT
azojete-1	52	24	numerical	numerical	ADJ
azojete-1	52	25	and	and	CCONJ
azojete-1	52	26	computational	computational	ADJ
azojete-1	52	27	multiscale	multiscale	NOUN
azojete-1	52	28	modelling	model	VERB
azojete-1	52	29	techniques	technique	NOUN
azojete-1	52	30	for	for	ADP
azojete-1	52	31	heterogenous	heterogenous	ADJ
azojete-1	52	32	materials	material	NOUN
azojete-1	52	33	:	:	PUNCT
azojete-1	52	34	a	a	DET
azojete-1	52	35	review	review	NOUN
azojete-1	52	36	.	.	PUNCT
azojete-1	53	1	azojete	azojete	NOUN
azojete-1	53	2	,	,	PUNCT
azojete-1	53	3	15(3):488	15(3):488	PROPN
azojete-1	53	4	-	-	PUNCT
azojete-1	53	5	509	509	NUM
azojete-1	53	6	.	.	PUNCT
azojete-1	54	1	issn	issn	PROPN
azojete-1	54	2	1596	1596	NUM
azojete-1	54	3	-	-	SYM
azojete-1	54	4	2490	2490	NUM
azojete-1	54	5	;	;	PUNCT
azojete-1	54	6	e	e	X
azojete-1	54	7	-	-	NOUN
azojete-1	54	8	issn	issn	VERB
azojete-1	54	9	2545	2545	NUM
azojete-1	54	10	-	-	SYM
azojete-1	54	11	5818	5818	NUM
azojete-1	54	12	,	,	PUNCT
azojete-1	54	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	54	14	corresponding	correspond	VERB
azojete-1	54	15	author	author	NOUN
azojete-1	54	16	’s	’s	PART
azojete-1	54	17	e	e	NOUN
azojete-1	54	18	-	-	NOUN
azojete-1	54	19	mail	mail	NOUN
azojete-1	54	20	address	address	NOUN
azojete-1	54	21	:	:	PUNCT
azojete-1	54	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	54	23	492	492	NUM
azojete-1	54	24	assumptions	assumption	NOUN
azojete-1	54	25	are	be	AUX
azojete-1	54	26	necessary	necessary	ADJ
azojete-1	54	27	which	which	PRON
azojete-1	54	28	leads	lead	VERB
azojete-1	54	29	to	to	ADP
azojete-1	54	30	a	a	DET
azojete-1	54	31	number	number	NOUN
azojete-1	54	32	of	of	ADP
azojete-1	54	33	homogenization	homogenization	NOUN
azojete-1	54	34	models	model	NOUN
azojete-1	54	35	with	with	ADP
azojete-1	54	36	the	the	DET
azojete-1	54	37	most	most	ADV
azojete-1	54	38	significant	significant	ADJ
azojete-1	54	39	simplification	simplification	NOUN
azojete-1	54	40	being	be	AUX
azojete-1	54	41	the	the	DET
azojete-1	54	42	“	"	PUNCT
azojete-1	54	43	mean	mean	ADJ
azojete-1	54	44	-	-	PUNCT
azojete-1	54	45	field	field	NOUN
azojete-1	54	46	approach	approach	NOUN
azojete-1	54	47	which	which	PRON
azojete-1	54	48	approximates	approximate	VERB
azojete-1	54	49	the	the	DET
azojete-1	54	50	strain	strain	NOUN
azojete-1	54	51	and	and	CCONJ
azojete-1	54	52	stress	stress	NOUN
azojete-1	54	53	fields	field	NOUN
azojete-1	54	54	by	by	ADP
azojete-1	54	55	phase	phase	NOUN
azojete-1	54	56	-	-	PUNCT
azojete-1	54	57	wise	wise	ADJ
azojete-1	54	58	constant	constant	ADJ
azojete-1	54	59	fields	field	NOUN
azojete-1	54	60	”	"	PUNCT
azojete-1	54	61	�	�	PROPN
azojete-1	54	62	�	�	PROPN
azojete-1	54	63	and	and	CCONJ
azojete-1	54	64	�	�	PROPN
azojete-1	54	65	�	�	PROPN
azojete-1	54	66	given	give	VERB
azojete-1	54	67	in	in	ADP
azojete-1	54	68	equation	equation	NOUN
azojete-1	54	69	3	3	NUM
azojete-1	54	70	.	.	PUNCT
azojete-1	54	71	ϵi	ϵi	NOUN
azojete-1	55	1	=	=	NOUN
azojete-1	55	2	ai	ai	VERB
azojete-1	55	3	:	:	PUNCT
azojete-1	55	4	ϵ	ϵ	X
azojete-1	55	5	�	�	PROPN
azojete-1	55	6	and	and	CCONJ
azojete-1	55	7	σi	σi	NOUN
azojete-1	55	8	=	=	NOUN
azojete-1	55	9	bi	bi	NOUN
azojete-1	55	10	:	:	PUNCT
azojete-1	55	11	σ	σ	PROPN
azojete-1	55	12	�	�	PROPN
azojete-1	55	13	(	(	PUNCT
azojete-1	55	14	3	3	NUM
azojete-1	55	15	)	)	PUNCT
azojete-1	55	16	where	where	SCONJ
azojete-1	55	17	:	:	PUNCT
azojete-1	55	18	�	�	PROPN
azojete-1	55	19	�	�	PROPN
azojete-1	55	20	�	�	PROPN
azojete-1	55	21	strain	strain	VERB
azojete-1	55	22	concentration	concentration	NOUN
azojete-1	55	23	tensor	tensor	NOUN
azojete-1	55	24	for	for	ADP
azojete-1	55	25	the	the	DET
azojete-1	55	26	phase	phase	NOUN
azojete-1	55	27	i	i	PRON
azojete-1	55	28	�	�	VERB
azojete-1	55	29	�	�	PROPN
azojete-1	55	30	stress	stress	NOUN
azojete-1	55	31	concentration	concentration	NOUN
azojete-1	55	32	tensor	tensor	NOUN
azojete-1	55	33	for	for	ADP
azojete-1	55	34	the	the	DET
azojete-1	55	35	phase	phase	NOUN
azojete-1	55	36	i	i	PRON
azojete-1	55	37	(	(	PUNCT
azojete-1	55	38	llorca	llorca	PROPN
azojete-1	55	39	et	et	PROPN
azojete-1	55	40	al	al	PROPN
azojete-1	55	41	.	.	PROPN
azojete-1	55	42	,	,	PUNCT
azojete-1	55	43	2007	2007	NUM
azojete-1	55	44	)	)	PUNCT
azojete-1	55	45	in	in	ADP
azojete-1	55	46	adopting	adopt	VERB
azojete-1	55	47	this	this	DET
azojete-1	55	48	principle	principle	NOUN
azojete-1	55	49	,	,	PUNCT
azojete-1	55	50	eshelby	eshelby	X
azojete-1	55	51	(	(	PUNCT
azojete-1	55	52	1957	1957	NUM
azojete-1	55	53	)	)	PUNCT
azojete-1	55	54	,	,	PUNCT
azojete-1	55	55	came	come	VERB
azojete-1	55	56	up	up	ADP
azojete-1	55	57	with	with	ADP
azojete-1	55	58	an	an	DET
azojete-1	55	59	effective	effective	ADJ
azojete-1	55	60	medium	medium	ADJ
azojete-1	55	61	approximation	approximation	NOUN
azojete-1	55	62	in	in	ADP
azojete-1	55	63	obtaining	obtain	VERB
azojete-1	55	64	the	the	DET
azojete-1	55	65	overall	overall	ADJ
azojete-1	55	66	effective	effective	ADJ
azojete-1	55	67	properties	property	NOUN
azojete-1	55	68	of	of	ADP
azojete-1	55	69	the	the	DET
azojete-1	55	70	heterogeneous	heterogeneous	ADJ
azojete-1	55	71	medium	medium	NOUN
azojete-1	55	72	where	where	SCONJ
azojete-1	55	73	the	the	DET
azojete-1	55	74	microstructure	microstructure	NOUN
azojete-1	55	75	is	be	AUX
azojete-1	55	76	composed	compose	VERB
azojete-1	55	77	of	of	ADP
azojete-1	55	78	a	a	DET
azojete-1	55	79	matrix	matrix	NOUN
azojete-1	55	80	and	and	CCONJ
azojete-1	55	81	a	a	DET
azojete-1	55	82	spherical	spherical	ADJ
azojete-1	55	83	or	or	CCONJ
azojete-1	55	84	ellipsoidal	ellipsoidal	ADJ
azojete-1	55	85	inclusion	inclusion	NOUN
azojete-1	55	86	.	.	PUNCT
azojete-1	56	1	he	he	PRON
azojete-1	56	2	also	also	ADV
azojete-1	56	3	noted	note	VERB
azojete-1	56	4	that	that	SCONJ
azojete-1	56	5	the	the	DET
azojete-1	56	6	strain	strain	NOUN
azojete-1	56	7	field	field	NOUN
azojete-1	56	8	within	within	ADP
azojete-1	56	9	the	the	DET
azojete-1	56	10	inclusion	inclusion	NOUN
azojete-1	56	11	was	be	AUX
azojete-1	56	12	constant	constant	ADJ
azojete-1	56	13	.	.	PUNCT
azojete-1	57	1	so	so	ADV
azojete-1	57	2	that	that	SCONJ
azojete-1	57	3	for	for	ADP
azojete-1	57	4	a	a	DET
azojete-1	57	5	linear	linear	ADJ
azojete-1	57	6	constitutive	constitutive	ADJ
azojete-1	57	7	equation	equation	NOUN
azojete-1	57	8	:	:	PUNCT
azojete-1	57	9	σi	σi	PROPN
azojete-1	57	10	=	=	SYM
azojete-1	57	11	li	li	PROPN
azojete-1	57	12	:	:	PUNCT
azojete-1	57	13	εi	εi	VERB
azojete-1	57	14	;	;	PUNCT
azojete-1	57	15	(	(	PUNCT
azojete-1	57	16	4)l	4)l	NUM
azojete-1	57	17	=	=	NOUN
azojete-1	58	1	i	i	PRON
azojete-1	58	2	n	n	PRON
azojete-1	58	3	fili	fili	PROPN
azojete-1	58	4	:	:	PUNCT
azojete-1	58	5	�	�	PROPN
azojete-1	58	6	ai	ai	PROPN
azojete-1	58	7	(	(	PUNCT
azojete-1	58	8	5	5	NUM
azojete-1	58	9	)	)	PUNCT
azojete-1	58	10	i	i	PRON
azojete-1	59	1	=	=	VERB
azojete-1	59	2	i	i	PRON
azojete-1	59	3	n	n	PRON
azojete-1	59	4	fi	fi	NOUN
azojete-1	59	5	�	�	PROPN
azojete-1	59	6	ai	ai	VERB
azojete-1	59	7	=	=	VERB
azojete-1	60	1	i	i	PRON
azojete-1	60	2	n	n	NUM
azojete-1	60	3	fi	fi	NOUN
azojete-1	60	4	�	�	PROPN
azojete-1	60	5	bi	bi	NOUN
azojete-1	60	6	(	(	PUNCT
azojete-1	60	7	6	6	NUM
azojete-1	60	8	)	)	PUNCT
azojete-1	60	9	ϵi	ϵi	NOUN
azojete-1	61	1	=	=	PUNCT
azojete-1	61	2	aidil:ϵ	aidil:ϵ	PROPN
azojete-1	61	3	�	�	PROPN
azojete-1	61	4	(	(	PUNCT
azojete-1	61	5	7	7	NUM
azojete-1	61	6	)	)	PUNCT
azojete-1	61	7	where	where	SCONJ
azojete-1	61	8	aidil	aidil	NOUN
azojete-1	61	9	=	=	PUNCT
azojete-1	61	10	i	i	PRON
azojete-1	61	11	+	+	NOUN
azojete-1	61	12	si	si	ADJ
azojete-1	61	13	:	:	PUNCT
azojete-1	61	14	lm	lm	X
azojete-1	61	15	�	�	PROPN
azojete-1	61	16	1	1	NUM
azojete-1	61	17	:	:	PUNCT
azojete-1	61	18	li	li	PROPN
azojete-1	61	19	�	�	PROPN
azojete-1	61	20	lm	lm	SYM
azojete-1	61	21	�	�	PROPN
azojete-1	61	22	1	1	NUM
azojete-1	61	23	(	(	PUNCT
azojete-1	61	24	8)	8)	NUM
azojete-1	61	25	the	the	DET
azojete-1	61	26	elastic	elastic	ADJ
azojete-1	61	27	stiffness	stiffness	NOUN
azojete-1	61	28	tensor	tensor	NOUN
azojete-1	61	29	of	of	ADP
azojete-1	61	30	the	the	DET
azojete-1	61	31	effective	effective	ADJ
azojete-1	61	32	material	material	NOUN
azojete-1	61	33	can	can	AUX
azojete-1	61	34	then	then	ADV
azojete-1	61	35	be	be	AUX
azojete-1	61	36	evaluated	evaluate	VERB
azojete-1	61	37	from	from	ADP
azojete-1	61	38	equations	equation	NOUN
azojete-1	61	39	(	(	PUNCT
azojete-1	61	40	1	1	NUM
azojete-1	61	41	)	)	PUNCT
azojete-1	61	42	,	,	PUNCT
azojete-1	61	43	(	(	PUNCT
azojete-1	61	44	6	6	NUM
azojete-1	61	45	)	)	PUNCT
azojete-1	61	46	and	and	CCONJ
azojete-1	61	47	(	(	PUNCT
azojete-1	61	48	8)	8)	NUM
azojete-1	61	49	as	as	ADP
azojete-1	61	50	:	:	PUNCT
azojete-1	61	51	l	l	X
azojete-1	61	52	=	=	PUNCT
azojete-1	62	1	lm	lm	INTJ
azojete-1	63	1	+	+	NUM
azojete-1	63	2	fi	fi	NOUN
azojete-1	63	3	li	li	PROPN
azojete-1	63	4	�	�	PROPN
azojete-1	63	5	lm	lm	PROPN
azojete-1	63	6	:	:	PUNCT
azojete-1	63	7	aidil	aidil	PROPN
azojete-1	63	8	(	(	PUNCT
azojete-1	63	9	9	9	NUM
azojete-1	63	10	)	)	PUNCT
azojete-1	63	11	where	where	SCONJ
azojete-1	63	12	:	:	PUNCT
azojete-1	63	13	�	�	NOUN
azojete-1	63	14	�	�	PROPN
azojete-1	63	15	stiffness	stiffness	NOUN
azojete-1	63	16	tensor	tensor	NOUN
azojete-1	63	17	for	for	ADP
azojete-1	63	18	the	the	DET
azojete-1	63	19	matrix	matrix	NOUN
azojete-1	63	20	�	�	SYM
azojete-1	63	21	�	�	NOUN
azojete-1	63	22	elastic	elastic	ADJ
azojete-1	63	23	stiffness	stiffness	NOUN
azojete-1	63	24	tensor	tensor	NOUN
azojete-1	63	25	for	for	ADP
azojete-1	63	26	the	the	DET
azojete-1	63	27	inclusion	inclusion	NOUN
azojete-1	63	28	�	�	NOUN
azojete-1	63	29	effective	effective	ADJ
azojete-1	63	30	elastic	elastic	ADJ
azojete-1	63	31	stiffness	stiffness	NOUN
azojete-1	63	32	tensor	tensor	NOUN
azojete-1	63	33	nnumber	nnumber	NOUN
azojete-1	63	34	of	of	ADP
azojete-1	63	35	phases	phase	NOUN
azojete-1	63	36	i	i	NOUN
azojete-1	63	37	-	-	PUNCT
azojete-1	63	38	identity	identity	NOUN
azojete-1	63	39	tensor	tensor	NOUN
azojete-1	63	40	�	�	PROPN
azojete-1	63	41	�	�	PROPN
azojete-1	63	42	eshelby	eshelby	PROPN
azojete-1	63	43	’s	’s	PART
azojete-1	63	44	tensor	tensor	NOUN
azojete-1	63	45	for	for	ADP
azojete-1	63	46	the	the	DET
azojete-1	63	47	inclusion	inclusion	NOUN
azojete-1	63	48	.	.	PUNCT
azojete-1	64	1	�	�	PROPN
azojete-1	64	2	�	�	PROPN
azojete-1	64	3	�	�	PROPN
azojete-1	64	4	�	�	PROPN
azojete-1	64	5	�	�	PROPN
azojete-1	64	6	strain	strain	NOUN
azojete-1	64	7	concentration	concentration	NOUN
azojete-1	64	8	tensor	tensor	NOUN
azojete-1	64	9	for	for	ADP
azojete-1	64	10	the	the	DET
azojete-1	64	11	dilute	dilute	NOUN
azojete-1	64	12	condition	condition	NOUN
azojete-1	64	13	�	�	PROPN
azojete-1	64	14	�	�	PROPN
azojete-1	64	15	�	�	PROPN
azojete-1	64	16	dilute	dilute	NOUN
azojete-1	64	17	�	�	PROPN
azojete-1	64	18	�	�	PROPN
azojete-1	64	19	volume	volume	NOUN
azojete-1	64	20	fraction	fraction	NOUN
azojete-1	64	21	this	this	DET
azojete-1	64	22	eshelby	eshelby	ADJ
azojete-1	64	23	effective	effective	ADJ
azojete-1	64	24	medium	medium	ADJ
azojete-1	64	25	approximation	approximation	NOUN
azojete-1	64	26	was	be	AUX
azojete-1	64	27	further	far	ADV
azojete-1	64	28	extended	extend	VERB
azojete-1	64	29	by	by	ADP
azojete-1	64	30	hill	hill	NOUN
azojete-1	64	31	(	(	PUNCT
azojete-1	64	32	1965	1965	NUM
azojete-1	64	33	)	)	PUNCT
azojete-1	64	34	along	along	ADP
azojete-1	64	35	the	the	DET
azojete-1	64	36	lines	line	NOUN
azojete-1	64	37	of	of	ADP
azojete-1	64	38	this	this	DET
azojete-1	64	39	mean	mean	ADJ
azojete-1	64	40	field	field	NOUN
azojete-1	64	41	approximations	approximation	NOUN
azojete-1	64	42	,	,	PUNCT
azojete-1	64	43	kr	kr	PROPN
azojete-1	64	44	�	�	PROPN
azojete-1	64	45	�	�	PROPN
azojete-1	64	46	ner	ner	NOUN
azojete-1	64	47	(	(	PUNCT
azojete-1	64	48	1958	1958	NUM
azojete-1	64	49	)	)	PUNCT
azojete-1	64	50	came	come	VERB
azojete-1	64	51	up	up	ADP
azojete-1	64	52	with	with	ADP
azojete-1	64	53	a	a	DET
azojete-1	64	54	self	self	NOUN
azojete-1	64	55	consistent	consistent	ADJ
azojete-1	64	56	approach	approach	NOUN
azojete-1	64	57	for	for	ADP
azojete-1	64	58	obtaining	obtain	VERB
azojete-1	64	59	the	the	DET
azojete-1	64	60	effective	effective	ADJ
azojete-1	64	61	material	material	NOUN
azojete-1	64	62	property	property	NOUN
azojete-1	64	63	for	for	ADP
azojete-1	64	64	a	a	DET
azojete-1	64	65	matrix	matrix	NOUN
azojete-1	64	66	and	and	CCONJ
azojete-1	64	67	spherical	spherical	ADJ
azojete-1	64	68	or	or	CCONJ
azojete-1	64	69	ellipsoidal	ellipsoidal	ADJ
azojete-1	64	70	inclusions	inclusion	NOUN
azojete-1	64	71	in	in	ADP
azojete-1	64	72	the	the	DET
azojete-1	64	73	elastic	elastic	ADJ
azojete-1	64	74	regime	regime	NOUN
azojete-1	64	75	.	.	PUNCT
azojete-1	65	1	the	the	DET
azojete-1	65	2	main	main	ADJ
azojete-1	65	3	idea	idea	NOUN
azojete-1	65	4	behind	behind	ADP
azojete-1	65	5	this	this	DET
azojete-1	65	6	approach	approach	NOUN
azojete-1	65	7	is	be	AUX
azojete-1	65	8	that	that	SCONJ
azojete-1	65	9	for	for	ADP
azojete-1	65	10	a	a	DET
azojete-1	65	11	composite	composite	NOUN
azojete-1	65	12	composed	compose	VERB
azojete-1	65	13	of	of	ADP
azojete-1	65	14	scattered	scatter	VERB
azojete-1	65	15	particles	particle	NOUN
azojete-1	65	16	,	,	PUNCT
azojete-1	65	17	it	it	PRON
azojete-1	65	18	is	be	AUX
azojete-1	65	19	possible	possible	ADJ
azojete-1	65	20	to	to	PART
azojete-1	65	21	assume	assume	VERB
azojete-1	65	22	that	that	SCONJ
azojete-1	65	23	the	the	DET
azojete-1	65	24	composite	composite	NOUN
azojete-1	65	25	is	be	AUX
azojete-1	65	26	composed	compose	VERB
azojete-1	65	27	of	of	ADP
azojete-1	65	28	a	a	DET
azojete-1	65	29	particle	particle	NOUN
azojete-1	65	30	of	of	ADP
azojete-1	65	31	one	one	NUM
azojete-1	65	32	phase	phase	NOUN
azojete-1	65	33	embedded	embed	VERB
azojete-1	65	34	in	in	ADP
azojete-1	65	35	an	an	DET
azojete-1	65	36	effective	effective	ADJ
azojete-1	65	37	medium	medium	NOUN
azojete-1	65	38	.	.	PUNCT
azojete-1	66	1	in	in	ADP
azojete-1	66	2	his	his	PRON
azojete-1	66	3	work	work	NOUN
azojete-1	66	4	,	,	PUNCT
azojete-1	66	5	the	the	DET
azojete-1	66	6	strain	strain	NOUN
azojete-1	66	7	concentration	concentration	NOUN
azojete-1	66	8	tensor	tensor	NOUN
azojete-1	66	9	aisc	aisc	PROPN
azojete-1	66	10	was	be	AUX
azojete-1	66	11	obtained	obtain	VERB
azojete-1	66	12	from	from	ADP
azojete-1	66	13	the	the	DET
azojete-1	66	14	eshelby	eshelby	PROPN
azojete-1	66	15	dilute	dilute	NOUN
azojete-1	66	16	solution	solution	NOUN
azojete-1	66	17	in	in	ADP
azojete-1	66	18	eqn	eqn	NOUN
azojete-1	66	19	.	.	PUNCT
azojete-1	67	1	(	(	PUNCT
azojete-1	67	2	8)	8)	NUM
azojete-1	67	3	above	above	ADV
azojete-1	67	4	by	by	ADP
azojete-1	67	5	replacing	replace	VERB
azojete-1	67	6	the	the	DET
azojete-1	67	7	matrix	matrix	NOUN
azojete-1	67	8	elastic	elastic	ADJ
azojete-1	67	9	constant	constant	ADJ
azojete-1	67	10	(	(	PUNCT
azojete-1	67	11	lm	lm	INTJ
azojete-1	67	12	)	)	PUNCT
azojete-1	67	13	in	in	ADP
azojete-1	67	14	eqn	eqn	NOUN
azojete-1	67	15	.	.	PUNCT
azojete-1	68	1	(	(	PUNCT
azojete-1	68	2	8)	8)	NUM
azojete-1	68	3	with	with	ADP
azojete-1	68	4	those	those	PRON
azojete-1	68	5	of	of	ADP
azojete-1	68	6	the	the	DET
azojete-1	68	7	effective	effective	ADJ
azojete-1	68	8	medium	medium	NOUN
azojete-1	68	9	(	(	PUNCT
azojete-1	68	10	)	)	PUNCT
azojete-1	68	11	to	to	PART
azojete-1	68	12	give	give	VERB
azojete-1	68	13	the	the	DET
azojete-1	68	14	resulting	result	VERB
azojete-1	68	15	expression	expression	NOUN
azojete-1	68	16	in	in	ADP
azojete-1	68	17	equation	equation	NOUN
azojete-1	68	18	(	(	PUNCT
azojete-1	68	19	10	10	NUM
azojete-1	68	20	)	)	PUNCT
azojete-1	68	21	�	�	PROPN
azojete-1	68	22	�	�	PROPN
azojete-1	68	23	�	�	PROPN
azojete-1	68	24	�	�	PROPN
azojete-1	68	25	=	=	SYM
azojete-1	68	26	�	�	PROPN
azojete-1	68	27	+	+	SYM
azojete-1	68	28	�	�	PROPN
azojete-1	68	29	�	�	PROPN
azojete-1	68	30	:	:	PUNCT
azojete-1	68	31	�	�	PROPN
azojete-1	68	32	�	�	PROPN
azojete-1	68	33	�	�	PROPN
azojete-1	68	34	:	:	PUNCT
azojete-1	68	35	�	�	PROPN
azojete-1	68	36	�	�	PROPN
azojete-1	68	37	�	�	PROPN
azojete-1	68	38	�	�	PROPN
azojete-1	68	39	�	�	PROPN
azojete-1	68	40	�	�	PROPN
azojete-1	68	41	(	(	PUNCT
azojete-1	68	42	1	1	NUM
azojete-1	68	43	�	�	PROPN
azojete-1	68	44	)	)	PUNCT
azojete-1	68	45	the	the	DET
azojete-1	68	46	effective	effective	ADJ
azojete-1	68	47	material	material	NOUN
azojete-1	68	48	property	property	NOUN
azojete-1	68	49	(	(	PUNCT
azojete-1	68	50	�	�	PROPN
azojete-1	68	51	)	)	PUNCT
azojete-1	68	52	was	be	AUX
azojete-1	68	53	then	then	ADV
azojete-1	68	54	be	be	AUX
azojete-1	68	55	evaluated	evaluate	VERB
azojete-1	68	56	by	by	ADP
azojete-1	68	57	substituting	substitute	VERB
azojete-1	68	58	eqns	eqns	PROPN
azojete-1	68	59	.	.	PUNCT
azojete-1	69	1	(	(	PUNCT
azojete-1	69	2	10	10	NUM
azojete-1	69	3	)	)	PUNCT
azojete-1	69	4	in	in	ADP
azojete-1	69	5	(	(	PUNCT
azojete-1	69	6	5	5	NUM
azojete-1	69	7	)	)	PUNCT
azojete-1	69	8	to	to	PART
azojete-1	69	9	obtain	obtain	VERB
azojete-1	69	10	eqn	eqn	NOUN
azojete-1	69	11	.	.	PUNCT
azojete-1	70	1	(	(	PUNCT
azojete-1	70	2	11	11	NUM
azojete-1	70	3	)	)	PUNCT
azojete-1	70	4	.	.	PUNCT
azojete-1	71	1	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	71	2	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	71	3	arid	arid	NOUN
azojete-1	71	4	zone	zone	NOUN
azojete-1	71	5	journal	journal	NOUN
azojete-1	71	6	of	of	ADP
azojete-1	71	7	engineering	engineering	NOUN
azojete-1	71	8	,	,	PUNCT
azojete-1	71	9	technology	technology	NOUN
azojete-1	71	10	and	and	CCONJ
azojete-1	71	11	environment	environment	NOUN
azojete-1	71	12	,	,	PUNCT
azojete-1	71	13	september	september	PROPN
azojete-1	71	14	,	,	PUNCT
azojete-1	71	15	2019	2019	NUM
azojete-1	71	16	;	;	PUNCT
azojete-1	71	17	vol	vol	NOUN
azojete-1	71	18	.	.	PUNCT
azojete-1	72	1	15(3):488	15(3):488	NUM
azojete-1	72	2	-	-	PUNCT
azojete-1	72	3	509	509	NUM
azojete-1	72	4	.	.	PUNCT
azojete-1	73	1	issn	issn	PROPN
azojete-1	73	2	1596	1596	NUM
azojete-1	73	3	-	-	SYM
azojete-1	73	4	2490	2490	NUM
azojete-1	73	5	;	;	PUNCT
azojete-1	73	6	e	e	X
azojete-1	73	7	-	-	NOUN
azojete-1	73	8	issn	issn	VERB
azojete-1	73	9	2545	2545	NUM
azojete-1	73	10	-	-	SYM
azojete-1	73	11	5818	5818	NUM
azojete-1	73	12	;	;	PUNCT
azojete-1	73	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	73	14	corresponding	correspond	VERB
azojete-1	73	15	author	author	NOUN
azojete-1	73	16	’s	’s	PART
azojete-1	73	17	e	e	NOUN
azojete-1	73	18	-	-	NOUN
azojete-1	73	19	mail	mail	NOUN
azojete-1	73	20	address	address	NOUN
azojete-1	73	21	:	:	PUNCT
azojete-1	73	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	74	1	493	493	NUM
azojete-1	74	2	l	l	NOUN
azojete-1	74	3	=	=	PUNCT
azojete-1	75	1	i	i	PRON
azojete-1	75	2	n	n	PRON
azojete-1	75	3	fili	fili	PROPN
azojete-1	75	4	:	:	PUNCT
azojete-1	75	5	�	�	PROPN
azojete-1	75	6	i	i	NOUN
azojete-1	75	7	+	+	NOUN
azojete-1	75	8	si	si	ADJ
azojete-1	75	9	:	:	ADJ
azojete-1	75	10	l	l	NOUN
azojete-1	75	11	�	�	PROPN
azojete-1	75	12	1	1	NUM
azojete-1	75	13	:	:	PUNCT
azojete-1	75	14	li	li	PROPN
azojete-1	75	15	�	�	PROPN
azojete-1	75	16	l	l	PROPN
azojete-1	75	17	�	�	PROPN
azojete-1	75	18	1	1	NUM
azojete-1	75	19	(	(	PUNCT
azojete-1	75	20	11	11	NUM
azojete-1	75	21	)	)	PUNCT
azojete-1	75	22	this	this	DET
azojete-1	75	23	self	self	NOUN
azojete-1	75	24	consistent	consistent	ADJ
azojete-1	75	25	approach	approach	NOUN
azojete-1	75	26	was	be	AUX
azojete-1	75	27	further	far	ADV
azojete-1	75	28	extended	extend	VERB
azojete-1	75	29	to	to	ADP
azojete-1	75	30	non	non	ADJ
azojete-1	75	31	-	-	ADJ
azojete-1	75	32	linear	linear	ADJ
azojete-1	75	33	cases	case	NOUN
azojete-1	75	34	in	in	ADP
azojete-1	75	35	the	the	DET
azojete-1	75	36	studies	study	NOUN
azojete-1	75	37	carried	carry	VERB
azojete-1	75	38	out	out	ADP
azojete-1	75	39	by	by	ADP
azojete-1	75	40	hill	hill	NOUN
azojete-1	75	41	(	(	PUNCT
azojete-1	75	42	1965	1965	NUM
azojete-1	75	43	)	)	PUNCT
azojete-1	75	44	,	,	PUNCT
azojete-1	75	45	hutchinson	hutchinson	PROPN
azojete-1	75	46	(	(	PUNCT
azojete-1	75	47	1976	1976	NUM
azojete-1	75	48	)	)	PUNCT
azojete-1	75	49	and	and	CCONJ
azojete-1	75	50	bereviller	bereviller	NOUN
azojete-1	75	51	(	(	PUNCT
azojete-1	75	52	1979	1979	NUM
azojete-1	75	53	)	)	PUNCT
azojete-1	75	54	.	.	PUNCT
azojete-1	76	1	the	the	DET
azojete-1	76	2	effective	effective	ADJ
azojete-1	76	3	properties	property	NOUN
azojete-1	76	4	of	of	ADP
azojete-1	76	5	the	the	DET
azojete-1	76	6	heterogeneous	heterogeneous	ADJ
azojete-1	76	7	medium	medium	NOUN
azojete-1	76	8	in	in	ADP
azojete-1	76	9	an	an	DET
azojete-1	76	10	elastic	elastic	ADJ
azojete-1	76	11	regime	regime	NOUN
azojete-1	76	12	can	can	AUX
azojete-1	76	13	also	also	ADV
azojete-1	76	14	be	be	AUX
azojete-1	76	15	evaluated	evaluate	VERB
azojete-1	76	16	using	use	VERB
azojete-1	76	17	the	the	DET
azojete-1	76	18	variation	variation	NOUN
azojete-1	76	19	principles	principle	NOUN
azojete-1	76	20	.	.	PUNCT
azojete-1	77	1	employing	employ	VERB
azojete-1	77	2	this	this	DET
azojete-1	77	3	technique	technique	NOUN
azojete-1	77	4	gives	give	VERB
azojete-1	77	5	an	an	DET
azojete-1	77	6	upper	upper	NOUN
azojete-1	77	7	and	and	CCONJ
azojete-1	77	8	a	a	DET
azojete-1	77	9	lower	lower	ADV
azojete-1	77	10	bound	bind	VERB
azojete-1	77	11	value	value	NOUN
azojete-1	77	12	for	for	ADP
azojete-1	77	13	the	the	DET
azojete-1	77	14	effective	effective	ADJ
azojete-1	77	15	property	property	NOUN
azojete-1	77	16	.	.	PUNCT
azojete-1	78	1	the	the	DET
azojete-1	78	2	simplest	simple	ADJ
azojete-1	78	3	works	work	VERB
azojete-1	78	4	on	on	ADP
azojete-1	78	5	this	this	DET
azojete-1	78	6	variation	variation	NOUN
azojete-1	78	7	principle	principle	NOUN
azojete-1	78	8	were	be	AUX
azojete-1	78	9	those	those	PRON
azojete-1	78	10	of	of	ADP
azojete-1	78	11	voigit	voigit	NOUN
azojete-1	78	12	and	and	CCONJ
azojete-1	78	13	ruess	ruess	PROPN
azojete-1	78	14	(	(	PUNCT
azojete-1	78	15	hill	hill	PROPN
azojete-1	78	16	,	,	PUNCT
azojete-1	78	17	1963	1963	NUM
azojete-1	78	18	)	)	PUNCT
azojete-1	78	19	.	.	PUNCT
azojete-1	79	1	in	in	ADP
azojete-1	79	2	their	their	PRON
azojete-1	79	3	models	model	NOUN
azojete-1	79	4	the	the	DET
azojete-1	79	5	strain	strain	ADJ
azojete-1	79	6	energy	energy	NOUN
azojete-1	79	7	density	density	NOUN
azojete-1	79	8	function	function	NOUN
azojete-1	79	9	(	(	PUNCT
azojete-1	79	10	x	x	NOUN
azojete-1	79	11	,	,	PUNCT
azojete-1	79	12	)	)	PUNCT
azojete-1	79	13	and	and	CCONJ
azojete-1	79	14	the	the	DET
azojete-1	79	15	complementary	complementary	ADJ
azojete-1	79	16	energy	energy	NOUN
azojete-1	79	17	density	density	NOUN
azojete-1	79	18	function	function	NOUN
azojete-1	79	19	(	(	PUNCT
azojete-1	79	20	x	x	NOUN
azojete-1	79	21	,	,	PUNCT
azojete-1	79	22	)	)	PUNCT
azojete-1	79	23	were	be	AUX
azojete-1	79	24	expressed	express	VERB
azojete-1	79	25	in	in	ADP
azojete-1	79	26	terms	term	NOUN
azojete-1	79	27	of	of	ADP
azojete-1	79	28	a	a	DET
azojete-1	79	29	homogenous	homogenous	ADJ
azojete-1	79	30	phase	phase	NOUN
azojete-1	79	31	potential	potential	NOUN
azojete-1	79	32	as	as	ADP
azojete-1	79	33	:	:	PUNCT
azojete-1	79	34	ω(x	ω(x	NUM
azojete-1	79	35	,	,	PUNCT
azojete-1	79	36	ε	ε	PROPN
azojete-1	79	37	)	)	PUNCT
azojete-1	79	38	=	=	PUNCT
azojete-1	79	39	r=1	r=1	NOUN
azojete-1	79	40	n	n	X
azojete-1	79	41	χ(r)(x	χ(r)(x	NOUN
azojete-1	79	42	)	)	PUNCT
azojete-1	79	43	ω(r)(ε	ω(r)(ε	NUM
azojete-1	79	44	)	)	PUNCT
azojete-1	79	45	�	�	PROPN
azojete-1	79	46	(	(	PUNCT
azojete-1	79	47	12	12	NUM
azojete-1	79	48	)	)	PUNCT
azojete-1	79	49	u(x	u(x	NOUN
azojete-1	79	50	,	,	PUNCT
azojete-1	79	51	σ	σ	NOUN
azojete-1	79	52	)	)	PUNCT
azojete-1	79	53	=	=	PUNCT
azojete-1	79	54	r=1	r=1	NOUN
azojete-1	79	55	n	n	X
azojete-1	79	56	χ(r)(x	χ(r)(x	NOUN
azojete-1	79	57	)	)	PUNCT
azojete-1	79	58	u(r)(σ	u(r)(σ	NOUN
azojete-1	79	59	)	)	PUNCT
azojete-1	79	60	�	�	PROPN
azojete-1	79	61	(	(	PUNCT
azojete-1	79	62	13	13	NUM
azojete-1	79	63	)	)	PUNCT
azojete-1	79	64	where	where	SCONJ
azojete-1	79	65	:	:	PUNCT
azojete-1	79	66	ω(r)(ε	ω(r)(ε	NUM
azojete-1	79	67	)	)	PUNCT
azojete-1	79	68	and	and	CCONJ
azojete-1	79	69	u(r)(σ	u(r)(σ	NOUN
azojete-1	79	70	)	)	PUNCT
azojete-1	79	71	–	–	PUNCT
azojete-1	79	72	are	be	AUX
azojete-1	79	73	the	the	DET
azojete-1	79	74	homogeneous	homogeneous	ADJ
azojete-1	79	75	phase	phase	NOUN
azojete-1	79	76	potentials	potential	VERB
azojete-1	79	77	and	and	CCONJ
azojete-1	79	78	χ(r)(x)=1	χ(r)(x)=1	PROPN
azojete-1	79	79	if	if	SCONJ
azojete-1	79	80	x	x	PROPN
azojete-1	79	81	�	�	PROPN
azojete-1	79	82	ω	ω	PROPN
azojete-1	79	83	(	(	PUNCT
azojete-1	79	84	㌠	㌠	NOUN
azojete-1	79	85	)	)	PUNCT
azojete-1	79	86	or	or	CCONJ
azojete-1	79	87	zero	zero	NUM
azojete-1	79	88	.	.	PUNCT
azojete-1	80	1	firstly	firstly	ADV
azojete-1	80	2	,	,	PUNCT
azojete-1	80	3	the	the	DET
azojete-1	80	4	effective	effective	ADJ
azojete-1	80	5	strain	strain	NOUN
azojete-1	80	6	and	and	CCONJ
azojete-1	80	7	complementary	complementary	ADJ
azojete-1	80	8	potentials	potential	NOUN
azojete-1	80	9	(	(	PUNCT
azojete-1	80	10	w	w	NOUN
azojete-1	80	11	�	�	PROPN
azojete-1	80	12	(	(	PUNCT
azojete-1	80	13	ε	ε	PROPN
azojete-1	80	14	�	�	PROPN
azojete-1	80	15	)	)	PUNCT
azojete-1	80	16	andu	andu	NOUN
azojete-1	80	17	�	�	PROPN
azojete-1	80	18	(σ	(σ	PROPN
azojete-1	80	19	�	�	PROPN
azojete-1	80	20	)	)	PUNCT
azojete-1	80	21	)	)	PUNCT
azojete-1	80	22	for	for	ADP
azojete-1	80	23	the	the	DET
azojete-1	80	24	heterogeneous	heterogeneous	ADJ
azojete-1	80	25	medium	medium	NOUN
azojete-1	80	26	is	be	AUX
azojete-1	80	27	achieved	achieve	VERB
azojete-1	80	28	by	by	ADP
azojete-1	80	29	averaging	average	VERB
azojete-1	80	30	their	their	PRON
azojete-1	80	31	minimum	minimum	ADJ
azojete-1	80	32	potential	potential	ADJ
azojete-1	80	33	energies	energy	NOUN
azojete-1	80	34	given	give	VERB
azojete-1	80	35	as	as	ADP
azojete-1	80	36	:	:	PUNCT
azojete-1	80	37	w	w	PROPN
azojete-1	80	38	�	�	PROPN
azojete-1	80	39	(	(	PUNCT
azojete-1	80	40	ε	ε	PROPN
azojete-1	80	41	�	�	PROPN
azojete-1	80	42	)	)	PUNCT
azojete-1	80	43	=	=	SYM
azojete-1	80	44	min	min	PROPN
azojete-1	80	45	ω(x	ω(x	PROPN
azojete-1	80	46	,	,	PUNCT
azojete-1	80	47	ε	ε	PROPN
azojete-1	80	48	)	)	PUNCT
azojete-1	80	49	(	(	PUNCT
azojete-1	80	50	14	14	NUM
azojete-1	80	51	)	)	PUNCT
azojete-1	80	52	�	�	PROPN
azojete-1	80	53	(	(	PUNCT
azojete-1	80	54	x)∈k	x)∈k	PROPN
azojete-1	80	55	u	u	NOUN
azojete-1	80	56	�	�	PROPN
azojete-1	80	57	(σ	(σ	PROPN
azojete-1	80	58	�	�	PROPN
azojete-1	80	59	)	)	PUNCT
azojete-1	81	1	=	=	SYM
azojete-1	81	2	min	min	NOUN
azojete-1	81	3	u(x	u(x	PROPN
azojete-1	81	4	,	,	PUNCT
azojete-1	81	5	σ	σ	PROPN
azojete-1	81	6	)	)	PUNCT
azojete-1	81	7	(	(	PUNCT
azojete-1	81	8	15	15	NUM
azojete-1	81	9	)	)	PUNCT
azojete-1	81	10	�	�	PROPN
azojete-1	81	11	(	(	PUNCT
azojete-1	81	12	x)∈s	x)∈s	X
azojete-1	81	13	(	(	PUNCT
azojete-1	81	14	kanoute	kanoute	VERB
azojete-1	81	15	et	et	PROPN
azojete-1	81	16	al	al	PROPN
azojete-1	81	17	.	.	PROPN
azojete-1	81	18	,	,	PUNCT
azojete-1	81	19	2009	2009	NUM
azojete-1	81	20	)	)	PUNCT
azojete-1	82	1	where	where	SCONJ
azojete-1	82	2	:	:	PUNCT
azojete-1	82	3	�	�	PROPN
azojete-1	82	4	�	�	PROPN
azojete-1	82	5	(	(	PUNCT
azojete-1	82	6	�	�	PROPN
azojete-1	82	7	�	�	PROPN
azojete-1	82	8	)	)	PUNCT
azojete-1	82	9	–	–	PUNCT
azojete-1	82	10	average	average	ADJ
azojete-1	82	11	minimum	minimum	ADJ
azojete-1	82	12	complimentary	complimentary	ADJ
azojete-1	82	13	potential	potential	NOUN
azojete-1	82	14	(	(	PUNCT
azojete-1	82	15	�	�	NOUN
azojete-1	82	16	�	�	PROPN
azojete-1	82	17	)	)	PUNCT
azojete-1	82	18	average	average	NOUN
azojete-1	82	19	of	of	ADP
azojete-1	82	20	the	the	DET
azojete-1	82	21	actual	actual	ADJ
azojete-1	82	22	strain	strain	NOUN
azojete-1	82	23	field	field	NOUN
azojete-1	82	24	�	�	PROPN
azojete-1	82	25	�	�	PROPN
azojete-1	82	26	�	�	PROPN
azojete-1	82	27	(	(	PUNCT
azojete-1	82	28	�	�	PROPN
azojete-1	82	29	�	�	NOUN
azojete-1	82	30	)	)	PUNCT
azojete-1	82	31	-average	-average	NOUN
azojete-1	82	32	minimum	minimum	ADJ
azojete-1	82	33	complimentary	complimentary	ADJ
azojete-1	82	34	strain	strain	NOUN
azojete-1	82	35	(	(	PUNCT
azojete-1	82	36	�	�	NOUN
azojete-1	82	37	�	�	PROPN
azojete-1	82	38	)	)	PUNCT
azojete-1	82	39	average	average	NOUN
azojete-1	82	40	of	of	ADP
azojete-1	82	41	the	the	DET
azojete-1	82	42	actual	actual	ADJ
azojete-1	82	43	strain	strain	NOUN
azojete-1	82	44	field	field	NOUN
azojete-1	82	45	�	�	PROPN
azojete-1	82	46	while	while	SCONJ
azojete-1	82	47	the	the	DET
azojete-1	82	48	strain	strain	NOUN
azojete-1	82	49	energy	energy	NOUN
azojete-1	82	50	and	and	CCONJ
azojete-1	82	51	complementary	complementary	ADJ
azojete-1	82	52	density	density	NOUN
azojete-1	82	53	functions	function	NOUN
azojete-1	82	54	as	as	SCONJ
azojete-1	82	55	given	give	VERB
azojete-1	82	56	in	in	ADP
azojete-1	82	57	the	the	DET
azojete-1	82	58	mccauley	mccauley	NOUN
azojete-1	82	59	brackets	bracket	NOUN
azojete-1	82	60	(	(	PUNCT
azojete-1	82	61	that	that	PRON
azojete-1	82	62	is	be	AUX
azojete-1	82	63	equation	equation	NOUN
azojete-1	82	64	(	(	PUNCT
azojete-1	82	65	14	14	NUM
azojete-1	82	66	)	)	PUNCT
azojete-1	82	67	and	and	CCONJ
azojete-1	82	68	(	(	PUNCT
azojete-1	82	69	15	15	NUM
azojete-1	82	70	)	)	PUNCT
azojete-1	82	71	)	)	PUNCT
azojete-1	82	72	gives	give	VERB
azojete-1	82	73	the	the	DET
azojete-1	82	74	volume	volume	NOUN
azojete-1	82	75	averages	average	NOUN
azojete-1	82	76	in	in	ADP
azojete-1	82	77	the	the	DET
azojete-1	82	78	domain	domain	NOUN
azojete-1	82	79	ω	ω	NOUN
azojete-1	82	80	.	.	PUNCT
azojete-1	82	81	;	;	PUNCT
azojete-1	82	82	�	�	PROPN
azojete-1	82	83	�	�	PROPN
azojete-1	82	84	and	and	CCONJ
azojete-1	82	85	�	�	PROPN
azojete-1	82	86	�	�	PROPN
azojete-1	82	87	are	be	AUX
azojete-1	82	88	the	the	DET
azojete-1	82	89	average	average	ADJ
azojete-1	82	90	strain	strain	NOUN
azojete-1	82	91	and	and	CCONJ
azojete-1	82	92	stress	stress	NOUN
azojete-1	82	93	fields	field	NOUN
azojete-1	82	94	while	while	SCONJ
azojete-1	82	95	k	k	PROPN
azojete-1	82	96	is	be	AUX
azojete-1	82	97	the	the	DET
azojete-1	82	98	set	set	NOUN
azojete-1	82	99	of	of	ADP
azojete-1	82	100	kinematically	kinematically	ADV
azojete-1	82	101	admissible	admissible	ADJ
azojete-1	82	102	strains	strain	NOUN
azojete-1	82	103	and	and	CCONJ
azojete-1	82	104	s	s	VERB
azojete-1	82	105	is	be	AUX
azojete-1	82	106	the	the	DET
azojete-1	82	107	set	set	NOUN
azojete-1	82	108	of	of	ADP
azojete-1	82	109	statically	statically	ADV
azojete-1	82	110	admissible	admissible	ADJ
azojete-1	82	111	stresses	stress	NOUN
azojete-1	82	112	.	.	PUNCT
azojete-1	83	1	the	the	DET
azojete-1	83	2	effective	effective	ADJ
azojete-1	83	3	strain	strain	NOUN
azojete-1	83	4	and	and	CCONJ
azojete-1	83	5	stress	stress	NOUN
azojete-1	83	6	potential	potential	NOUN
azojete-1	83	7	for	for	ADP
azojete-1	83	8	the	the	DET
azojete-1	83	9	elastic	elastic	ADJ
azojete-1	83	10	heterogeneous	heterogeneous	ADJ
azojete-1	83	11	medium	medium	NOUN
azojete-1	83	12	at	at	ADP
azojete-1	83	13	the	the	DET
azojete-1	83	14	macroscale	macroscale	NOUN
azojete-1	83	15	is	be	AUX
azojete-1	83	16	therefore	therefore	ADV
azojete-1	83	17	given	give	VERB
azojete-1	83	18	by	by	ADP
azojete-1	83	19	the	the	DET
azojete-1	83	20	voigt	voigt	PROPN
azojete-1	83	21	and	and	CCONJ
azojete-1	83	22	ruess	ruess	PROPN
azojete-1	83	23	model	model	NOUN
azojete-1	83	24	as	as	SCONJ
azojete-1	83	25	shown	show	VERB
azojete-1	83	26	in	in	ADP
azojete-1	83	27	eqns	eqns	PROPN
azojete-1	83	28	.	.	PUNCT
azojete-1	84	1	(	(	PUNCT
azojete-1	84	2	18	18	NUM
azojete-1	84	3	)	)	PUNCT
azojete-1	84	4	and	and	CCONJ
azojete-1	84	5	(	(	PUNCT
azojete-1	84	6	19	19	NUM
azojete-1	84	7	):	):	PUNCT
azojete-1	84	8	file:///c:/users	file:///c:/user	NOUN
azojete-1	84	9	/	/	SYM
azojete-1	84	10	user	user	NOUN
azojete-1	84	11	/	/	SYM
azojete-1	84	12	downloads	download	NOUN
azojete-1	84	13	/	/	SYM
azojete-1	84	14	azojete143	azojete143	PROPN
azojete-1	84	15	/	/	SYM
azojete-1	84	16	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	84	17	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	84	18	ohunene	ohunene	ADJ
azojete-1	84	19	hafsa	hafsa	PROPN
azojete-1	84	20	aliyu	aliyu	PROPN
azojete-1	84	21	:	:	PUNCT
azojete-1	85	1	analytical	analytical	ADJ
azojete-1	85	2	,	,	PUNCT
azojete-1	85	3	numerical	numerical	ADJ
azojete-1	85	4	and	and	CCONJ
azojete-1	85	5	computational	computational	ADJ
azojete-1	85	6	multiscale	multiscale	NOUN
azojete-1	85	7	modelling	model	VERB
azojete-1	85	8	techniques	technique	NOUN
azojete-1	85	9	for	for	ADP
azojete-1	85	10	heterogenous	heterogenous	ADJ
azojete-1	85	11	materials	material	NOUN
azojete-1	85	12	:	:	PUNCT
azojete-1	85	13	a	a	DET
azojete-1	85	14	review	review	NOUN
azojete-1	85	15	.	.	PUNCT
azojete-1	86	1	azojete	azojete	NOUN
azojete-1	86	2	,	,	PUNCT
azojete-1	86	3	15(3):488	15(3):488	PROPN
azojete-1	86	4	-	-	PUNCT
azojete-1	86	5	509	509	NUM
azojete-1	86	6	.	.	PUNCT
azojete-1	87	1	issn	issn	PROPN
azojete-1	87	2	1596	1596	NUM
azojete-1	87	3	-	-	SYM
azojete-1	87	4	2490	2490	NUM
azojete-1	87	5	;	;	PUNCT
azojete-1	87	6	e	e	X
azojete-1	87	7	-	-	NOUN
azojete-1	87	8	issn	issn	VERB
azojete-1	87	9	2545	2545	NUM
azojete-1	87	10	-	-	SYM
azojete-1	87	11	5818	5818	NUM
azojete-1	87	12	,	,	PUNCT
azojete-1	87	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	87	14	corresponding	correspond	VERB
azojete-1	87	15	author	author	NOUN
azojete-1	87	16	’s	’s	PART
azojete-1	87	17	e	e	NOUN
azojete-1	87	18	-	-	NOUN
azojete-1	87	19	mail	mail	NOUN
azojete-1	87	20	address	address	NOUN
azojete-1	87	21	:	:	PUNCT
azojete-1	87	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	87	23	494	494	NUM
azojete-1	87	24	(	(	PUNCT
azojete-1	87	25	a	a	NOUN
azojete-1	87	26	)	)	PUNCT
azojete-1	87	27	voigt	voigt	PROPN
azojete-1	87	28	model	model	PROPN
azojete-1	87	29	w	w	PROPN
azojete-1	87	30	�	�	PROPN
azojete-1	87	31	(	(	PUNCT
azojete-1	87	32	ε	ε	PROPN
azojete-1	87	33	�	�	PROPN
azojete-1	87	34	)	)	PUNCT
azojete-1	87	35	=	=	SYM
azojete-1	87	36	1	1	NUM
azojete-1	87	37	2	2	NUM
azojete-1	87	38	ε	ε	PROPN
azojete-1	87	39	�	�	PROPN
azojete-1	87	40	:	:	PUNCT
azojete-1	87	41	l	l	NOUN
azojete-1	87	42	�	�	PROPN
azojete-1	87	43	:	:	PUNCT
azojete-1	87	44	ε	ε	PROPN
azojete-1	87	45	�	�	PROPN
azojete-1	87	46	(	(	PUNCT
azojete-1	87	47	16	16	NUM
azojete-1	87	48	)	)	PUNCT
azojete-1	87	49	l	l	NOUN
azojete-1	87	50	�	�	NOUN
azojete-1	87	51	=	=	SYM
azojete-1	87	52	r=1	r=1	NOUN
azojete-1	87	53	n	n	PRON
azojete-1	87	54	c(r	c(r	NOUN
azojete-1	87	55	)	)	PUNCT
azojete-1	87	56	l(r	l(r	PROPN
azojete-1	87	57	)	)	PUNCT
azojete-1	87	58	(	(	PUNCT
azojete-1	87	59	17	17	NUM
azojete-1	87	60	)	)	PUNCT
azojete-1	87	61	�	�	PROPN
azojete-1	87	62	to	to	PART
azojete-1	87	63	arrive	arrive	VERB
azojete-1	87	64	at	at	ADP
azojete-1	87	65	the	the	DET
azojete-1	87	66	above	above	ADJ
azojete-1	87	67	expressions	expression	NOUN
azojete-1	87	68	,	,	PUNCT
azojete-1	87	69	voigt	voigt	PROPN
azojete-1	87	70	assumed	assume	VERB
azojete-1	87	71	that	that	SCONJ
azojete-1	87	72	the	the	DET
azojete-1	87	73	strain	strain	NOUN
azojete-1	87	74	field	field	NOUN
azojete-1	87	75	within	within	ADP
azojete-1	87	76	the	the	DET
azojete-1	87	77	heterogeneous	heterogeneous	ADJ
azojete-1	87	78	medium	medium	NOUN
azojete-1	87	79	was	be	AUX
azojete-1	87	80	constant	constant	ADJ
azojete-1	87	81	.	.	PUNCT
azojete-1	88	1	u	u	PROPN
azojete-1	88	2	�	�	PROPN
azojete-1	88	3	(σ	(σ	PROPN
azojete-1	88	4	�	�	PROPN
azojete-1	88	5	)	)	PUNCT
azojete-1	88	6	=	=	SYM
azojete-1	88	7	1	1	NUM
azojete-1	88	8	2	2	NUM
azojete-1	88	9	σ	σ	PROPN
azojete-1	88	10	�	�	PROPN
azojete-1	88	11	:	:	PUNCT
azojete-1	88	12	m	m	VERB
azojete-1	88	13	�	�	PROPN
azojete-1	88	14	:	:	PUNCT
azojete-1	88	15	σ	σ	PROPN
azojete-1	88	16	�	�	PROPN
azojete-1	88	17	(	(	PUNCT
azojete-1	88	18	18	18	NUM
azojete-1	88	19	)	)	PUNCT
azojete-1	88	20	(	(	PUNCT
azojete-1	88	21	b	b	X
azojete-1	88	22	)	)	PUNCT
azojete-1	88	23	ruess	ruess	NOUN
azojete-1	88	24	model	model	NOUN
azojete-1	88	25	l	l	PROPN
azojete-1	88	26	�	�	PROPN
azojete-1	88	27	�	�	PROPN
azojete-1	88	28	1	1	NUM
azojete-1	88	29	�	�	NOUN
azojete-1	88	30	1	1	NUM
azojete-1	88	31	=	=	SYM
azojete-1	88	32	r=1	r=1	NOUN
azojete-1	88	33	n	n	X
azojete-1	88	34	c(r	c(r	NOUN
azojete-1	88	35	)	)	PUNCT
azojete-1	88	36	(	(	PUNCT
azojete-1	88	37	l(r))	l(r))	X
azojete-1	88	38	�	�	PROPN
azojete-1	88	39	1	1	NUM
azojete-1	88	40	(	(	PUNCT
azojete-1	88	41	19	19	NUM
azojete-1	88	42	)	)	PUNCT
azojete-1	88	43	�	�	PROPN
azojete-1	88	44	the	the	DET
azojete-1	88	45	assumption	assumption	NOUN
azojete-1	88	46	in	in	ADP
azojete-1	88	47	ruess	ruess	PROPN
azojete-1	88	48	model	model	NOUN
azojete-1	88	49	is	be	AUX
azojete-1	88	50	that	that	SCONJ
azojete-1	88	51	a	a	DET
azojete-1	88	52	uniform	uniform	ADJ
azojete-1	88	53	stress	stress	NOUN
azojete-1	88	54	was	be	AUX
azojete-1	88	55	applied	apply	VERB
azojete-1	88	56	to	to	ADP
azojete-1	88	57	the	the	DET
azojete-1	88	58	polycrystals	polycrystal	NOUN
azojete-1	88	59	with	with	ADP
azojete-1	88	60	resulting	result	VERB
azojete-1	88	61	comparable	comparable	ADJ
azojete-1	88	62	stresses	stress	NOUN
azojete-1	88	63	in	in	ADP
azojete-1	88	64	the	the	DET
azojete-1	88	65	constituent	constituent	NOUN
azojete-1	88	66	crystallite	crystallite	NOUN
azojete-1	88	67	.	.	PUNCT
azojete-1	89	1	where	where	SCONJ
azojete-1	89	2	:	:	PUNCT
azojete-1	89	3	lis	li	VERB
azojete-1	89	4	the	the	DET
azojete-1	89	5	effective	effective	ADJ
azojete-1	89	6	elastic	elastic	ADJ
azojete-1	89	7	tensor	tensor	NOUN
azojete-1	89	8	mcompliance	mcompliance	NOUN
azojete-1	89	9	tensor	tensor	NOUN
azojete-1	89	10	the	the	DET
azojete-1	89	11	volume	volume	NOUN
azojete-1	89	12	fraction	fraction	NOUN
azojete-1	89	13	for	for	ADP
azojete-1	89	14	the	the	DET
azojete-1	89	15	phase	phase	NOUN
azojete-1	89	16	r	r	NOUN
azojete-1	89	17	�	�	PROPN
azojete-1	89	18	(	(	PUNCT
azojete-1	89	19	㌠	㌠	NOUN
azojete-1	89	20	)	)	PUNCT
azojete-1	89	21	the	the	DET
azojete-1	89	22	elasticity	elasticity	NOUN
azojete-1	89	23	tensor	tensor	NOUN
azojete-1	89	24	for	for	ADP
azojete-1	89	25	the	the	DET
azojete-1	89	26	phase	phase	NOUN
azojete-1	89	27	r	r	PROPN
azojete-1	89	28	hill	hill	NOUN
azojete-1	89	29	(	(	PUNCT
azojete-1	89	30	1952	1952	NUM
azojete-1	89	31	)	)	PUNCT
azojete-1	89	32	,	,	PUNCT
azojete-1	89	33	noted	note	VERB
azojete-1	89	34	that	that	SCONJ
azojete-1	89	35	because	because	SCONJ
azojete-1	89	36	of	of	ADP
azojete-1	89	37	the	the	DET
azojete-1	89	38	assumptions	assumption	NOUN
azojete-1	89	39	of	of	ADP
azojete-1	89	40	a	a	DET
azojete-1	89	41	constant	constant	ADJ
azojete-1	89	42	strain	strain	NOUN
azojete-1	89	43	field	field	NOUN
azojete-1	89	44	in	in	ADP
azojete-1	89	45	eqn	eqn	NOUN
azojete-1	89	46	.	.	PUNCT
azojete-1	90	1	(	(	PUNCT
azojete-1	90	2	14	14	NUM
azojete-1	90	3	)	)	PUNCT
azojete-1	90	4	and	and	CCONJ
azojete-1	90	5	a	a	DET
azojete-1	90	6	constant	constant	ADJ
azojete-1	90	7	stress	stress	NOUN
azojete-1	90	8	field	field	NOUN
azojete-1	90	9	in	in	ADP
azojete-1	90	10	eqn	eqn	NOUN
azojete-1	90	11	.	.	PUNCT
azojete-1	91	1	(	(	PUNCT
azojete-1	91	2	15	15	NUM
azojete-1	91	3	)	)	PUNCT
azojete-1	91	4	,	,	PUNCT
azojete-1	91	5	voigt	voigt	PROPN
azojete-1	91	6	model	model	NOUN
azojete-1	91	7	gives	give	VERB
azojete-1	91	8	an	an	DET
azojete-1	91	9	upper	upper	ADJ
azojete-1	91	10	bound	bind	VERB
azojete-1	91	11	estimate	estimate	NOUN
azojete-1	91	12	as	as	SCONJ
azojete-1	91	13	shown	show	VERB
azojete-1	91	14	in	in	ADP
azojete-1	91	15	eqn	eqn	NOUN
azojete-1	91	16	.	.	PUNCT
azojete-1	92	1	(	(	PUNCT
azojete-1	92	2	16	16	NUM
azojete-1	92	3	)	)	PUNCT
azojete-1	92	4	while	while	SCONJ
azojete-1	92	5	ruess	ruess	NOUN
azojete-1	92	6	model	model	NOUN
azojete-1	92	7	gives	give	VERB
azojete-1	92	8	a	a	DET
azojete-1	92	9	lower	lower	ADV
azojete-1	92	10	bound	bind	VERB
azojete-1	92	11	estimate	estimate	NOUN
azojete-1	92	12	as	as	SCONJ
azojete-1	92	13	shown	show	VERB
azojete-1	92	14	in	in	ADP
azojete-1	92	15	eqn	eqn	NOUN
azojete-1	92	16	.	.	PUNCT
azojete-1	93	1	(	(	PUNCT
azojete-1	93	2	17	17	NUM
azojete-1	93	3	)	)	PUNCT
azojete-1	93	4	w	w	PROPN
azojete-1	93	5	�	�	PROPN
azojete-1	93	6	(	(	PUNCT
azojete-1	93	7	ε	ε	PROPN
azojete-1	93	8	�	�	PROPN
azojete-1	93	9	)	)	PUNCT
azojete-1	93	10	<	<	X
azojete-1	93	11	1	1	NUM
azojete-1	93	12	2	2	NUM
azojete-1	93	13	ε	ε	PROPN
azojete-1	93	14	�	�	PROPN
azojete-1	93	15	:	:	PUNCT
azojete-1	93	16	l	l	NOUN
azojete-1	93	17	�	�	PROPN
azojete-1	93	18	:	:	PUNCT
azojete-1	93	19	ε	ε	PROPN
azojete-1	93	20	�	�	PROPN
azojete-1	93	21	(	(	PUNCT
azojete-1	93	22	2	2	NUM
azojete-1	93	23	�	�	NOUN
azojete-1	93	24	)	)	PUNCT
azojete-1	93	25	u	u	NOUN
azojete-1	93	26	�	�	PROPN
azojete-1	93	27	(σ	(σ	PROPN
azojete-1	93	28	�	�	PROPN
azojete-1	93	29	)	)	PUNCT
azojete-1	93	30	≤	≤	NUM
azojete-1	93	31	1	1	NUM
azojete-1	93	32	2	2	NUM
azojete-1	93	33	σ	σ	PROPN
azojete-1	93	34	�	�	PROPN
azojete-1	93	35	:	:	PUNCT
azojete-1	93	36	m	m	VERB
azojete-1	93	37	�	�	PROPN
azojete-1	93	38	:	:	PUNCT
azojete-1	93	39	σ	σ	PROPN
azojete-1	93	40	�	�	PROPN
azojete-1	93	41	(	(	PUNCT
azojete-1	93	42	21	21	NUM
azojete-1	93	43	)	)	PUNCT
azojete-1	93	44	in	in	ADP
azojete-1	93	45	adopting	adopt	VERB
azojete-1	93	46	the	the	DET
azojete-1	93	47	variation	variation	NOUN
azojete-1	93	48	principle	principle	NOUN
azojete-1	93	49	,	,	PUNCT
azojete-1	93	50	voigt	voigt	PROPN
azojete-1	93	51	and	and	CCONJ
azojete-1	93	52	ruess	ruess	PROPN
azojete-1	93	53	have	have	AUX
azojete-1	93	54	only	only	ADV
azojete-1	93	55	taken	take	VERB
azojete-1	93	56	into	into	ADP
azojete-1	93	57	account	account	NOUN
azojete-1	93	58	the	the	DET
azojete-1	93	59	volume	volume	NOUN
azojete-1	93	60	fraction	fraction	NOUN
azojete-1	93	61	of	of	ADP
azojete-1	93	62	each	each	DET
azojete-1	93	63	phase	phase	NOUN
azojete-1	93	64	(	(	PUNCT
azojete-1	93	65	one	one	NUM
azojete-1	93	66	-	-	PUNCT
azojete-1	93	67	point	point	NOUN
azojete-1	93	68	limit	limit	NOUN
azojete-1	93	69	)	)	PUNCT
azojete-1	93	70	which	which	PRON
azojete-1	93	71	limited	limit	VERB
azojete-1	93	72	the	the	DET
azojete-1	93	73	application	application	NOUN
azojete-1	93	74	of	of	ADP
azojete-1	93	75	their	their	PRON
azojete-1	93	76	model	model	NOUN
azojete-1	93	77	as	as	SCONJ
azojete-1	93	78	the	the	DET
azojete-1	93	79	influence	influence	NOUN
azojete-1	93	80	of	of	ADP
azojete-1	93	81	other	other	ADJ
azojete-1	93	82	characteristic	characteristic	ADJ
azojete-1	93	83	properties	property	NOUN
azojete-1	93	84	of	of	ADP
azojete-1	93	85	the	the	DET
azojete-1	93	86	microstructure	microstructure	NOUN
azojete-1	93	87	on	on	ADP
azojete-1	93	88	the	the	DET
azojete-1	93	89	effective	effective	ADJ
azojete-1	93	90	properties	property	NOUN
azojete-1	93	91	of	of	ADP
azojete-1	93	92	the	the	DET
azojete-1	93	93	heterogeneous	heterogeneous	ADJ
azojete-1	93	94	medium	medium	NOUN
azojete-1	93	95	have	have	AUX
azojete-1	93	96	not	not	PART
azojete-1	93	97	been	be	AUX
azojete-1	93	98	taken	take	VERB
azojete-1	93	99	into	into	ADP
azojete-1	93	100	consideration	consideration	NOUN
azojete-1	93	101	.	.	PUNCT
azojete-1	94	1	hashin	hashin	NOUN
azojete-1	94	2	and	and	CCONJ
azojete-1	94	3	shtrikman	shtrikman	NOUN
azojete-1	94	4	(	(	PUNCT
azojete-1	94	5	1962a	1962a	NUM
azojete-1	94	6	,	,	PUNCT
azojete-1	94	7	1962b	1962b	NUM
azojete-1	94	8	and	and	CCONJ
azojete-1	94	9	1963	1963	NUM
azojete-1	94	10	)	)	PUNCT
azojete-1	94	11	,	,	PUNCT
azojete-1	94	12	also	also	ADV
azojete-1	94	13	employed	employ	VERB
azojete-1	94	14	the	the	DET
azojete-1	94	15	variation	variation	NOUN
azojete-1	94	16	principles	principle	NOUN
azojete-1	94	17	but	but	CCONJ
azojete-1	94	18	took	take	VERB
azojete-1	94	19	into	into	ADP
azojete-1	94	20	account	account	NOUN
azojete-1	94	21	the	the	DET
azojete-1	94	22	polarization	polarization	NOUN
azojete-1	94	23	fields	field	NOUN
azojete-1	94	24	and	and	CCONJ
azojete-1	94	25	were	be	AUX
azojete-1	94	26	able	able	ADJ
azojete-1	94	27	to	to	PART
azojete-1	94	28	derive	derive	VERB
azojete-1	94	29	much	much	ADV
azojete-1	94	30	tighter	tight	ADJ
azojete-1	94	31	bounds	bound	NOUN
azojete-1	94	32	for	for	ADP
azojete-1	94	33	the	the	DET
azojete-1	94	34	effective	effective	ADJ
azojete-1	94	35	properties	property	NOUN
azojete-1	94	36	of	of	ADP
azojete-1	94	37	heterogeneous	heterogeneous	ADJ
azojete-1	94	38	materials	material	NOUN
azojete-1	94	39	(	(	PUNCT
azojete-1	94	40	two	two	NUM
azojete-1	94	41	-	-	PUNCT
azojete-1	94	42	point	point	NOUN
azojete-1	94	43	bounds	bound	NOUN
azojete-1	94	44	)	)	PUNCT
azojete-1	94	45	in	in	ADP
azojete-1	94	46	comparison	comparison	NOUN
azojete-1	94	47	to	to	ADP
azojete-1	94	48	that	that	PRON
azojete-1	94	49	obtained	obtain	VERB
azojete-1	94	50	from	from	ADP
azojete-1	94	51	the	the	DET
azojete-1	94	52	voigt	voigt	PROPN
azojete-1	94	53	and	and	CCONJ
azojete-1	94	54	ruess	ruess	PROPN
azojete-1	94	55	model	model	NOUN
azojete-1	94	56	(	(	PUNCT
azojete-1	94	57	one	one	NUM
azojete-1	94	58	-	-	PUNCT
azojete-1	94	59	point	point	NOUN
azojete-1	94	60	limit	limit	NOUN
azojete-1	94	61	)	)	PUNCT
azojete-1	94	62	.	.	PUNCT
azojete-1	95	1	k1	k1	NOUN
azojete-1	95	2	+	+	CCONJ
azojete-1	95	3	v2	v2	PROPN
azojete-1	95	4	1	1	NUM
azojete-1	95	5	k2	k2	PROPN
azojete-1	95	6	�	�	PROPN
azojete-1	95	7	k1	k1	PROPN
azojete-1	95	8	+	+	CCONJ
azojete-1	95	9	3	3	NUM
azojete-1	95	10	1	1	NUM
azojete-1	95	11	�	�	PROPN
azojete-1	95	12	v2	v2	PROPN
azojete-1	95	13	3k1	3k1	NUM
azojete-1	95	14	+	+	CCONJ
azojete-1	95	15	4μ1	4μ1	NUM
azojete-1	95	16	≤	≤	NUM
azojete-1	95	17	k∗	k∗	VERB
azojete-1	95	18	≤	≤	ADJ
azojete-1	95	19	k2	k2	PROPN
azojete-1	95	20	+	+	CCONJ
azojete-1	95	21	1	1	NUM
azojete-1	95	22	�	�	PROPN
azojete-1	95	23	v2	v2	NOUN
azojete-1	95	24	1	1	NUM
azojete-1	95	25	k1	k1	PROPN
azojete-1	95	26	�	�	PROPN
azojete-1	95	27	k2	k2	PROPN
azojete-1	95	28	+	+	CCONJ
azojete-1	95	29	3v2	3v2	NUM
azojete-1	95	30	3k2	3k2	NUM
azojete-1	96	1	+	+	X
azojete-1	96	2	4μ2	4μ2	NUM
azojete-1	96	3	(	(	PUNCT
azojete-1	96	4	22	22	NUM
azojete-1	96	5	)	)	PUNCT
azojete-1	96	6	μ1	μ1	NOUN
azojete-1	96	7	+	+	CCONJ
azojete-1	96	8	v2	v2	PROPN
azojete-1	96	9	1	1	NUM
azojete-1	96	10	μ2	μ2	NOUN
azojete-1	96	11	�	�	PROPN
azojete-1	96	12	μ1	μ1	PROPN
azojete-1	96	13	+	+	CCONJ
azojete-1	96	14	6	6	NUM
azojete-1	96	15	1	1	NUM
azojete-1	96	16	�	�	PROPN
azojete-1	96	17	v2	v2	PROPN
azojete-1	96	18	(	(	PUNCT
azojete-1	96	19	k1	k1	NOUN
azojete-1	96	20	+	+	CCONJ
azojete-1	96	21	2μ1	2μ1	NOUN
azojete-1	96	22	)	)	PUNCT
azojete-1	96	23	5μ1(3k1	5μ1(3k1	NOUN
azojete-1	96	24	+	+	NUM
azojete-1	96	25	4μ1	4μ1	NOUN
azojete-1	96	26	)	)	PUNCT
azojete-1	96	27	≤	≤	NUM
azojete-1	96	28	μ∗	μ∗	ADJ
azojete-1	96	29	≤	≤	NOUN
azojete-1	96	30	μ2	μ2	NOUN
azojete-1	96	31	+	+	CCONJ
azojete-1	96	32	1	1	NUM
azojete-1	96	33	�	�	NOUN
azojete-1	96	34	v2	v2	NOUN
azojete-1	96	35	1	1	NUM
azojete-1	96	36	μ1	μ1	PROPN
azojete-1	96	37	�	�	PROPN
azojete-1	96	38	μ2	μ2	NOUN
azojete-1	96	39	+	+	ADP
azojete-1	96	40	6v2(k2	6v2(k2	NUM
azojete-1	96	41	+	+	CCONJ
azojete-1	96	42	2μ2	2μ2	NUM
azojete-1	96	43	)	)	PUNCT
azojete-1	96	44	5μ2(3k2	5μ2(3k2	NOUN
azojete-1	97	1	+	+	NUM
azojete-1	97	2	4μ2	4μ2	NUM
azojete-1	97	3	)	)	PUNCT
azojete-1	97	4	(	(	PUNCT
azojete-1	97	5	23	23	NUM
azojete-1	97	6	)	)	PUNCT
azojete-1	98	1	where	where	SCONJ
azojete-1	98	2	:	:	PUNCT
azojete-1	98	3	�	�	PROPN
azojete-1	98	4	1,	1,	NUM
azojete-1	98	5	�	�	NOUN
azojete-1	98	6	1	1	NUM
azojete-1	98	7	–	–	PUNCT
azojete-1	98	8	bulk	bulk	ADJ
azojete-1	98	9	moduli	modulus	NOUN
azojete-1	98	10	in	in	ADP
azojete-1	98	11	the	the	DET
azojete-1	98	12	first	first	ADJ
azojete-1	98	13	phase	phase	NOUN
azojete-1	98	14	of	of	ADP
azojete-1	98	15	the	the	DET
azojete-1	98	16	microstructure	microstructure	ADJ
azojete-1	98	17	�	�	NOUN
azojete-1	98	18	2,	2,	NOUN
azojete-1	98	19	�	�	NOUN
azojete-1	98	20	2	2	NUM
azojete-1	98	21	–	–	PUNCT
azojete-1	98	22	shear	shear	NOUN
azojete-1	98	23	moduli	modulus	NOUN
azojete-1	98	24	in	in	ADP
azojete-1	98	25	the	the	DET
azojete-1	98	26	second	second	ADJ
azojete-1	98	27	phase	phase	NOUN
azojete-1	98	28	of	of	ADP
azojete-1	98	29	the	the	DET
azojete-1	98	30	microstructure	microstructure	ADJ
azojete-1	98	31	�	�	NOUN
azojete-1	98	32	2	2	NUM
azojete-1	98	33	–	–	PUNCT
azojete-1	98	34	volume	volume	NOUN
azojete-1	98	35	fraction	fraction	NOUN
azojete-1	98	36	in	in	ADP
azojete-1	98	37	the	the	DET
azojete-1	98	38	second	second	ADJ
azojete-1	98	39	phase	phase	NOUN
azojete-1	98	40	(	(	PUNCT
azojete-1	98	41	konoute	konoute	VERB
azojete-1	98	42	et	et	PROPN
azojete-1	98	43	al	al	PROPN
azojete-1	98	44	.	.	PROPN
azojete-1	98	45	,	,	PUNCT
azojete-1	98	46	2009	2009	NUM
azojete-1	98	47	)	)	PUNCT
azojete-1	98	48	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	98	49	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	98	50	arid	arid	NOUN
azojete-1	98	51	zone	zone	NOUN
azojete-1	98	52	journal	journal	NOUN
azojete-1	98	53	of	of	ADP
azojete-1	98	54	engineering	engineering	NOUN
azojete-1	98	55	,	,	PUNCT
azojete-1	98	56	technology	technology	NOUN
azojete-1	98	57	and	and	CCONJ
azojete-1	98	58	environment	environment	NOUN
azojete-1	98	59	,	,	PUNCT
azojete-1	98	60	september	september	PROPN
azojete-1	98	61	,	,	PUNCT
azojete-1	98	62	2019	2019	NUM
azojete-1	98	63	;	;	PUNCT
azojete-1	98	64	vol	vol	NOUN
azojete-1	98	65	.	.	PUNCT
azojete-1	99	1	15(3):488	15(3):488	NUM
azojete-1	99	2	-	-	PUNCT
azojete-1	99	3	509	509	NUM
azojete-1	99	4	.	.	PUNCT
azojete-1	100	1	issn	issn	PROPN
azojete-1	100	2	1596	1596	NUM
azojete-1	100	3	-	-	SYM
azojete-1	100	4	2490	2490	NUM
azojete-1	100	5	;	;	PUNCT
azojete-1	100	6	e	e	X
azojete-1	100	7	-	-	NOUN
azojete-1	100	8	issn	issn	VERB
azojete-1	100	9	2545	2545	NUM
azojete-1	100	10	-	-	SYM
azojete-1	100	11	5818	5818	NUM
azojete-1	100	12	;	;	PUNCT
azojete-1	100	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	100	14	corresponding	correspond	VERB
azojete-1	100	15	author	author	NOUN
azojete-1	100	16	’s	’s	PART
azojete-1	100	17	e	e	NOUN
azojete-1	100	18	-	-	NOUN
azojete-1	100	19	mail	mail	NOUN
azojete-1	100	20	address	address	NOUN
azojete-1	100	21	:	:	PUNCT
azojete-1	100	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	100	23	495	495	NUM
azojete-1	100	24	this	this	DET
azojete-1	100	25	technique	technique	NOUN
azojete-1	100	26	was	be	AUX
azojete-1	100	27	later	later	ADV
azojete-1	100	28	expanded	expand	VERB
azojete-1	100	29	by	by	ADP
azojete-1	100	30	torquato	torquato	NOUN
azojete-1	100	31	(	(	PUNCT
azojete-1	100	32	2001	2001	NUM
azojete-1	100	33	)	)	PUNCT
azojete-1	100	34	by	by	ADP
azojete-1	100	35	including	include	VERB
azojete-1	100	36	the	the	DET
azojete-1	100	37	details	detail	NOUN
azojete-1	100	38	of	of	ADP
azojete-1	100	39	the	the	DET
azojete-1	100	40	phase	phase	NOUN
azojete-1	100	41	arrangement	arrangement	NOUN
azojete-1	100	42	in	in	ADP
azojete-1	100	43	his	his	PRON
azojete-1	100	44	model	model	NOUN
azojete-1	100	45	(	(	PUNCT
azojete-1	100	46	three	three	NUM
azojete-1	100	47	-	-	PUNCT
azojete-1	100	48	point	point	NOUN
azojete-1	100	49	bounds	bound	NOUN
azojete-1	100	50	)	)	PUNCT
azojete-1	100	51	.	.	PUNCT
azojete-1	101	1	the	the	DET
azojete-1	101	2	variation	variation	NOUN
azojete-1	101	3	technique	technique	NOUN
azojete-1	101	4	was	be	AUX
azojete-1	101	5	further	far	ADV
azojete-1	101	6	extended	extend	VERB
azojete-1	101	7	to	to	ADP
azojete-1	101	8	non	non	ADJ
azojete-1	101	9	-	-	ADJ
azojete-1	101	10	linear	linear	ADJ
azojete-1	101	11	cases	case	NOUN
azojete-1	101	12	in	in	ADP
azojete-1	101	13	the	the	DET
azojete-1	101	14	work	work	NOUN
azojete-1	101	15	carried	carry	VERB
azojete-1	101	16	out	out	ADP
azojete-1	101	17	by	by	ADP
azojete-1	101	18	talbot	talbot	PROPN
azojete-1	101	19	and	and	CCONJ
azojete-1	101	20	willis	willis	PROPN
azojete-1	101	21	1985	1985	NUM
azojete-1	101	22	and	and	CCONJ
azojete-1	101	23	willis	willis	PROPN
azojete-1	101	24	1986	1986	NUM
azojete-1	101	25	.	.	PUNCT
azojete-1	102	1	further	further	ADJ
azojete-1	102	2	advancement	advancement	NOUN
azojete-1	102	3	in	in	ADP
azojete-1	102	4	variation	variation	NOUN
azojete-1	102	5	principles	principle	NOUN
azojete-1	102	6	has	have	AUX
azojete-1	102	7	lead	lead	VERB
azojete-1	102	8	to	to	ADP
azojete-1	102	9	the	the	DET
azojete-1	102	10	ponte	ponte	NOUN
azojete-1	102	11	castaneda	castaneda	PROPN
azojete-1	102	12	(	(	PUNCT
azojete-1	102	13	1991	1991	NUM
azojete-1	102	14	,	,	PUNCT
azojete-1	102	15	1992	1992	NUM
azojete-1	102	16	)	)	PUNCT
azojete-1	102	17	and	and	CCONJ
azojete-1	102	18	talbot	talbot	PROPN
azojete-1	102	19	and	and	CCONJ
azojete-1	102	20	willis	willis	PROPN
azojete-1	102	21	(	(	PUNCT
azojete-1	102	22	1992	1992	NUM
azojete-1	102	23	)	)	PUNCT
azojete-1	102	24	variation	variation	NOUN
azojete-1	102	25	principles	principle	NOUN
azojete-1	102	26	in	in	ADP
azojete-1	102	27	estimating	estimate	VERB
azojete-1	102	28	the	the	DET
azojete-1	102	29	effective	effective	ADJ
azojete-1	102	30	properties	property	NOUN
azojete-1	102	31	of	of	ADP
azojete-1	102	32	non	non	ADJ
azojete-1	102	33	-	-	ADJ
azojete-1	102	34	linear	linear	ADJ
azojete-1	102	35	composites	composite	NOUN
azojete-1	102	36	(	(	PUNCT
azojete-1	102	37	such	such	ADJ
azojete-1	102	38	as	as	ADP
azojete-1	102	39	,	,	PUNCT
azojete-1	102	40	the	the	DET
azojete-1	102	41	rapid	rapid	ADJ
azojete-1	102	42	localization	localization	NOUN
azojete-1	102	43	of	of	ADP
azojete-1	102	44	damage	damage	NOUN
azojete-1	102	45	,	,	PUNCT
azojete-1	102	46	energy	energy	NOUN
azojete-1	102	47	absorption	absorption	NOUN
azojete-1	102	48	at	at	ADP
azojete-1	102	49	high	high	ADJ
azojete-1	102	50	strain	strain	NOUN
azojete-1	102	51	rates	rate	NOUN
azojete-1	102	52	that	that	PRON
azojete-1	102	53	is	be	AUX
azojete-1	102	54	large	large	ADJ
azojete-1	102	55	plastic	plastic	NOUN
azojete-1	102	56	deformations	deformation	NOUN
azojete-1	102	57	and	and	CCONJ
azojete-1	102	58	so	so	ADV
azojete-1	102	59	on	on	ADV
azojete-1	102	60	)	)	PUNCT
azojete-1	102	61	as	as	ADV
azojete-1	102	62	well	well	ADV
azojete-1	102	63	as	as	ADP
azojete-1	102	64	the	the	DET
azojete-1	102	65	suquet	suquet	NOUN
azojete-1	102	66	variation	variation	NOUN
azojete-1	102	67	principles	principle	NOUN
azojete-1	102	68	for	for	ADP
azojete-1	102	69	power	power	NOUN
azojete-1	102	70	law	law	NOUN
azojete-1	102	71	composites	composite	NOUN
azojete-1	102	72	.	.	PUNCT
azojete-1	103	1	as	as	ADP
azojete-1	103	2	an	an	DET
azojete-1	103	3	improvement	improvement	NOUN
azojete-1	103	4	on	on	ADP
azojete-1	103	5	voigt	voigt	PROPN
azojete-1	103	6	upper	upper	PROPN
azojete-1	103	7	bound	bind	VERB
azojete-1	103	8	estimate	estimate	NOUN
azojete-1	103	9	of	of	ADP
azojete-1	103	10	the	the	DET
azojete-1	103	11	effective	effective	ADJ
azojete-1	103	12	macroscopic	macroscopic	ADJ
azojete-1	103	13	properties	property	NOUN
azojete-1	103	14	for	for	ADP
azojete-1	103	15	rigid	rigid	ADJ
azojete-1	103	16	plastic	plastic	NOUN
azojete-1	103	17	material	material	NOUN
azojete-1	103	18	,	,	PUNCT
azojete-1	103	19	olson	olson	NOUN
azojete-1	103	20	(	(	PUNCT
azojete-1	103	21	1994	1994	NUM
azojete-1	103	22	)	)	PUNCT
azojete-1	103	23	came	come	VERB
azojete-1	103	24	up	up	ADP
azojete-1	103	25	with	with	ADP
azojete-1	103	26	his	his	PRON
azojete-1	103	27	own	own	ADJ
azojete-1	103	28	variation	variation	NOUN
azojete-1	103	29	principles	principle	NOUN
azojete-1	103	30	for	for	ADP
azojete-1	103	31	perfectly	perfectly	ADV
azojete-1	103	32	plastic	plastic	ADJ
azojete-1	103	33	composites	composite	NOUN
azojete-1	103	34	.	.	PUNCT
azojete-1	104	1	lately	lately	ADV
azojete-1	104	2	,	,	PUNCT
azojete-1	104	3	homogenization	homogenization	NOUN
azojete-1	104	4	schemes	scheme	NOUN
azojete-1	104	5	employed	employ	VERB
azojete-1	104	6	in	in	ADP
azojete-1	104	7	the	the	DET
azojete-1	104	8	analysis	analysis	NOUN
azojete-1	104	9	of	of	ADP
azojete-1	104	10	elasto	elasto	NOUN
azojete-1	104	11	-	-	PUNCT
azojete-1	104	12	plastic	plastic	NOUN
azojete-1	104	13	composite	composite	ADJ
azojete-1	104	14	materials	material	NOUN
azojete-1	104	15	has	have	AUX
azojete-1	104	16	been	be	AUX
azojete-1	104	17	reviewed	review	VERB
azojete-1	104	18	by	by	ADP
azojete-1	104	19	scholars	scholar	NOUN
azojete-1	104	20	such	such	ADJ
azojete-1	104	21	as	as	ADP
azojete-1	104	22	:	:	PUNCT
azojete-1	104	23	ponte	ponte	PROPN
azojete-1	104	24	castaneda	castaneda	PROPN
azojete-1	104	25	and	and	CCONJ
azojete-1	104	26	suquet	suquet	PROPN
azojete-1	104	27	(	(	PUNCT
azojete-1	104	28	1998	1998	NUM
azojete-1	104	29	)	)	PUNCT
azojete-1	104	30	as	as	ADV
azojete-1	104	31	well	well	ADV
azojete-1	104	32	as	as	ADP
azojete-1	104	33	chaboche	chaboche	PROPN
azojete-1	104	34	et	et	PROPN
azojete-1	104	35	al	al	PROPN
azojete-1	104	36	.	.	PROPN
azojete-1	105	1	(	(	PUNCT
azojete-1	105	2	2005	2005	NUM
azojete-1	105	3	)	)	PUNCT
azojete-1	105	4	.	.	PUNCT
azojete-1	106	1	in	in	ADP
azojete-1	106	2	their	their	PRON
azojete-1	106	3	opinion	opinion	NOUN
azojete-1	106	4	the	the	DET
azojete-1	106	5	schemes	scheme	NOUN
azojete-1	106	6	can	can	AUX
azojete-1	106	7	be	be	AUX
azojete-1	106	8	categorised	categorise	VERB
azojete-1	106	9	into	into	ADP
azojete-1	106	10	two	two	NUM
azojete-1	106	11	groups	group	NOUN
azojete-1	106	12	,	,	PUNCT
azojete-1	106	13	namely	namely	ADV
azojete-1	106	14	,	,	PUNCT
azojete-1	106	15	those	those	PRON
azojete-1	106	16	based	base	VERB
azojete-1	106	17	on	on	ADP
azojete-1	106	18	the	the	DET
azojete-1	106	19	use	use	NOUN
azojete-1	106	20	of	of	ADP
azojete-1	106	21	secant	secant	ADJ
azojete-1	106	22	stiffness	stiffness	NOUN
azojete-1	106	23	tensor	tensor	NOUN
azojete-1	106	24	and	and	CCONJ
azojete-1	106	25	those	those	PRON
azojete-1	106	26	based	base	VERB
azojete-1	106	27	on	on	ADP
azojete-1	106	28	the	the	DET
azojete-1	106	29	use	use	NOUN
azojete-1	106	30	of	of	ADP
azojete-1	106	31	tangent	tangent	ADJ
azojete-1	106	32	stiffness	stiffness	ADJ
azojete-1	106	33	tensor	tensor	NOUN
azojete-1	106	34	.	.	PUNCT
azojete-1	107	1	schemes	scheme	NOUN
azojete-1	107	2	based	base	VERB
azojete-1	107	3	on	on	ADP
azojete-1	107	4	the	the	DET
azojete-1	107	5	secant	secant	ADJ
azojete-1	107	6	formulations	formulation	NOUN
azojete-1	107	7	dealt	deal	VERB
azojete-1	107	8	with	with	ADP
azojete-1	107	9	plastic	plastic	ADJ
azojete-1	107	10	deformations	deformation	NOUN
azojete-1	107	11	within	within	ADP
azojete-1	107	12	the	the	DET
azojete-1	107	13	frame	frame	NOUN
azojete-1	107	14	work	work	NOUN
azojete-1	107	15	of	of	ADP
azojete-1	107	16	non	non	ADJ
azojete-1	107	17	-	-	ADJ
azojete-1	107	18	linear	linear	ADJ
azojete-1	107	19	elasticity	elasticity	NOUN
azojete-1	107	20	,	,	PUNCT
azojete-1	107	21	where	where	SCONJ
azojete-1	107	22	the	the	DET
azojete-1	107	23	effective	effective	ADJ
azojete-1	107	24	secant	secant	ADJ
azojete-1	107	25	stiffness	stiffness	NOUN
azojete-1	107	26	tensor	tensor	NOUN
azojete-1	107	27	is	be	AUX
azojete-1	107	28	used	use	VERB
azojete-1	107	29	to	to	PART
azojete-1	107	30	assess	assess	VERB
azojete-1	107	31	the	the	DET
azojete-1	107	32	relationship	relationship	NOUN
azojete-1	107	33	between	between	ADP
azojete-1	107	34	the	the	DET
azojete-1	107	35	stress	stress	NOUN
azojete-1	107	36	and	and	CCONJ
azojete-1	107	37	strains	strain	NOUN
azojete-1	107	38	at	at	ADP
azojete-1	107	39	the	the	DET
azojete-1	107	40	elasto	elasto	NOUN
azojete-1	107	41	-	-	PUNCT
azojete-1	107	42	plastic	plastic	NOUN
azojete-1	107	43	stages	stage	NOUN
azojete-1	107	44	.	.	PUNCT
azojete-1	108	1	this	this	DET
azojete-1	108	2	approach	approach	NOUN
azojete-1	108	3	is	be	AUX
azojete-1	108	4	best	well	ADV
azojete-1	108	5	adopted	adopt	VERB
azojete-1	108	6	when	when	SCONJ
azojete-1	108	7	the	the	DET
azojete-1	108	8	composite	composite	ADJ
azojete-1	108	9	material	material	NOUN
azojete-1	108	10	is	be	AUX
azojete-1	108	11	subjected	subject	VERB
azojete-1	108	12	to	to	ADP
azojete-1	108	13	monotonic	monotonic	ADJ
azojete-1	108	14	and	and	CCONJ
azojete-1	108	15	proportional	proportional	ADJ
azojete-1	108	16	loading	loading	NOUN
azojete-1	108	17	(	(	PUNCT
azojete-1	108	18	llorca	llorca	NOUN
azojete-1	108	19	et	et	PROPN
azojete-1	108	20	al	al	PROPN
azojete-1	108	21	.	.	PROPN
azojete-1	108	22	,	,	PUNCT
azojete-1	108	23	2007	2007	NUM
azojete-1	108	24	)	)	PUNCT
azojete-1	108	25	.	.	PUNCT
azojete-1	109	1	the	the	DET
azojete-1	109	2	elasto	elasto	NOUN
azojete-1	109	3	-	-	PUNCT
azojete-1	109	4	plastic	plastic	NOUN
azojete-1	109	5	tangent	tangent	NOUN
azojete-1	109	6	modulus	modulus	NOUN
azojete-1	109	7	approach	approach	NOUN
azojete-1	109	8	for	for	ADP
azojete-1	109	9	evaluating	evaluate	VERB
azojete-1	109	10	the	the	DET
azojete-1	109	11	mechanical	mechanical	ADJ
azojete-1	109	12	response	response	NOUN
azojete-1	109	13	of	of	ADP
azojete-1	109	14	composites	composite	NOUN
azojete-1	109	15	was	be	AUX
azojete-1	109	16	presented	present	VERB
azojete-1	109	17	by	by	ADP
azojete-1	109	18	hill	hill	NOUN
azojete-1	109	19	(	(	PUNCT
azojete-1	109	20	1965	1965	NUM
azojete-1	109	21	)	)	PUNCT
azojete-1	109	22	where	where	SCONJ
azojete-1	109	23	he	he	PRON
azojete-1	109	24	linearized	linearize	VERB
azojete-1	109	25	the	the	DET
azojete-1	109	26	local	local	ADJ
azojete-1	109	27	constitutive	constitutive	ADJ
azojete-1	109	28	equation	equation	NOUN
azojete-1	109	29	by	by	ADP
azojete-1	109	30	bringing	bring	VERB
azojete-1	109	31	it	it	PRON
azojete-1	109	32	back	back	ADV
azojete-1	109	33	in	in	ADP
azojete-1	109	34	an	an	DET
azojete-1	109	35	incremental	incremental	ADJ
azojete-1	109	36	form	form	NOUN
azojete-1	109	37	:	:	PUNCT
azojete-1	109	38	�	�	PROPN
azojete-1	109	39	(	(	PUNCT
azojete-1	109	40	�	�	PROPN
azojete-1	109	41	)	)	PUNCT
azojete-1	109	42	=	=	SYM
azojete-1	109	43	�	�	PROPN
azojete-1	109	44	(	(	PUNCT
azojete-1	109	45	�	�	PROPN
azojete-1	109	46	):	):	SYM
azojete-1	109	47	�	�	PROPN
azojete-1	109	48	(	(	PUNCT
azojete-1	109	49	�	�	PROPN
azojete-1	109	50	)	)	PUNCT
azojete-1	109	51	(	(	PUNCT
azojete-1	109	52	24	24	NUM
azojete-1	109	53	)	)	PUNCT
azojete-1	109	54	where	where	SCONJ
azojete-1	109	55	:	:	PUNCT
azojete-1	109	56	l	l	NOUN
azojete-1	109	57	is	be	AUX
azojete-1	109	58	the	the	DET
azojete-1	109	59	tangent	tangent	ADJ
azojete-1	109	60	modulus	modulus	NOUN
azojete-1	109	61	(	(	PUNCT
azojete-1	109	62	konoute	konoute	NOUN
azojete-1	109	63	et	et	PROPN
azojete-1	109	64	al	al	PROPN
azojete-1	109	65	.	.	PROPN
azojete-1	109	66	,	,	PUNCT
azojete-1	109	67	2009	2009	NUM
azojete-1	109	68	)	)	PUNCT
azojete-1	109	69	.	.	PUNCT
azojete-1	110	1	the	the	DET
azojete-1	110	2	initial	initial	ADJ
azojete-1	110	3	models	model	NOUN
azojete-1	110	4	based	base	VERB
azojete-1	110	5	on	on	ADP
azojete-1	110	6	this	this	DET
azojete-1	110	7	approach	approach	NOUN
azojete-1	110	8	gave	give	VERB
azojete-1	110	9	very	very	ADV
azojete-1	110	10	stiff	stiff	ADJ
azojete-1	110	11	predictions	prediction	NOUN
azojete-1	110	12	of	of	ADP
azojete-1	110	13	the	the	DET
azojete-1	110	14	flow	flow	NOUN
azojete-1	110	15	stress	stress	NOUN
azojete-1	110	16	.	.	PUNCT
azojete-1	111	1	the	the	DET
azojete-1	111	2	source	source	NOUN
azojete-1	111	3	of	of	ADP
azojete-1	111	4	the	the	DET
azojete-1	111	5	inaccuracy	inaccuracy	NOUN
azojete-1	111	6	was	be	AUX
azojete-1	111	7	attributed	attribute	VERB
azojete-1	111	8	to	to	ADP
azojete-1	111	9	the	the	DET
azojete-1	111	10	anisotropic	anisotropic	NOUN
azojete-1	111	11	characteristic	characteristic	NOUN
azojete-1	111	12	of	of	ADP
azojete-1	111	13	the	the	DET
azojete-1	111	14	tangent	tangent	ADJ
azojete-1	111	15	stiffness	stiffness	NOUN
azojete-1	111	16	tensor	tensor	NOUN
azojete-1	111	17	.	.	PUNCT
azojete-1	112	1	more	more	ADV
azojete-1	112	2	accurate	accurate	ADJ
azojete-1	112	3	predictions	prediction	NOUN
azojete-1	112	4	of	of	ADP
azojete-1	112	5	the	the	DET
azojete-1	112	6	flow	flow	NOUN
azojete-1	112	7	stress	stress	NOUN
azojete-1	112	8	were	be	AUX
azojete-1	112	9	obtained	obtain	VERB
azojete-1	112	10	by	by	ADP
azojete-1	112	11	adopting	adopt	VERB
azojete-1	112	12	an	an	DET
azojete-1	112	13	isotropic	isotropic	ADJ
azojete-1	112	14	estimation	estimation	NOUN
azojete-1	112	15	of	of	ADP
azojete-1	112	16	the	the	DET
azojete-1	112	17	tangent	tangent	NOUN
azojete-1	112	18	operator	operator	NOUN
azojete-1	112	19	(	(	PUNCT
azojete-1	112	20	chaboche	chaboche	PROPN
azojete-1	112	21	et	et	PROPN
azojete-1	112	22	al	al	PROPN
azojete-1	112	23	.	.	PROPN
azojete-1	112	24	,	,	PUNCT
azojete-1	112	25	2005	2005	NUM
azojete-1	112	26	)	)	PUNCT
azojete-1	112	27	.	.	PUNCT
azojete-1	113	1	another	another	DET
azojete-1	113	2	homogenizational	homogenizational	ADJ
azojete-1	113	3	approach	approach	NOUN
azojete-1	113	4	is	be	AUX
azojete-1	113	5	the	the	DET
azojete-1	113	6	mathematical	mathematical	ADJ
azojete-1	113	7	asymptotic	asymptotic	ADJ
azojete-1	113	8	homogenization	homogenization	NOUN
azojete-1	113	9	theory	theory	NOUN
azojete-1	113	10	which	which	PRON
azojete-1	113	11	employs	employ	VERB
azojete-1	113	12	an	an	DET
azojete-1	113	13	asymptotic	asymptotic	ADJ
azojete-1	113	14	expansion	expansion	NOUN
azojete-1	113	15	of	of	ADP
azojete-1	113	16	the	the	DET
azojete-1	113	17	displacement	displacement	NOUN
azojete-1	113	18	and	and	CCONJ
azojete-1	113	19	stress	stress	NOUN
azojete-1	113	20	fields	field	NOUN
azojete-1	113	21	based	base	VERB
azojete-1	113	22	on	on	ADP
azojete-1	113	23	a	a	DET
azojete-1	113	24	ratio	ratio	NOUN
azojete-1	113	25	of	of	ADP
azojete-1	113	26	the	the	DET
azojete-1	113	27	length	length	NOUN
azojete-1	113	28	scales	scale	NOUN
azojete-1	113	29	(	(	PUNCT
azojete-1	113	30	�	�	PROPN
azojete-1	113	31	)	)	PUNCT
azojete-1	113	32	.	.	PUNCT
azojete-1	114	1	this	this	DET
azojete-1	114	2	technique	technique	NOUN
azojete-1	114	3	gives	give	VERB
azojete-1	114	4	both	both	CCONJ
azojete-1	114	5	the	the	DET
azojete-1	114	6	effective	effective	ADJ
azojete-1	114	7	overall	overall	ADJ
azojete-1	114	8	properties	property	NOUN
azojete-1	114	9	such	such	ADJ
azojete-1	114	10	as	as	ADP
azojete-1	114	11	the	the	DET
azojete-1	114	12	effective	effective	ADJ
azojete-1	114	13	stiffness	stiffness	NOUN
azojete-1	114	14	as	as	ADV
azojete-1	114	15	well	well	ADV
azojete-1	114	16	as	as	ADP
azojete-1	114	17	the	the	DET
azojete-1	114	18	local	local	ADJ
azojete-1	114	19	stress	stress	NOUN
azojete-1	114	20	and	and	CCONJ
azojete-1	114	21	strain	strain	ADJ
azojete-1	114	22	values	value	NOUN
azojete-1	114	23	(	(	PUNCT
azojete-1	114	24	kouznetsova	kouznetsova	NOUN
azojete-1	114	25	et	et	PROPN
azojete-1	114	26	al	al	PROPN
azojete-1	114	27	.	.	PROPN
azojete-1	114	28	,	,	PUNCT
azojete-1	114	29	2012	2012	NUM
azojete-1	114	30	)	)	PUNCT
azojete-1	114	31	.	.	PUNCT
azojete-1	115	1	2.2	2.2	NUM
azojete-1	115	2	numerical	numerical	ADJ
azojete-1	115	3	homogenization	homogenization	NOUN
azojete-1	115	4	schemes	scheme	NOUN
azojete-1	115	5	in	in	ADP
azojete-1	115	6	computational	computational	ADJ
azojete-1	115	7	micromechanics	micromechanic	NOUN
azojete-1	115	8	,	,	PUNCT
azojete-1	115	9	the	the	DET
azojete-1	115	10	macroscopic	macroscopic	ADJ
azojete-1	115	11	or	or	CCONJ
azojete-1	115	12	effective	effective	ADJ
azojete-1	115	13	behaviour	behaviour	NOUN
azojete-1	115	14	of	of	ADP
azojete-1	115	15	composites	composite	NOUN
azojete-1	115	16	is	be	AUX
azojete-1	115	17	obtained	obtain	VERB
azojete-1	115	18	through	through	ADP
azojete-1	115	19	the	the	DET
azojete-1	115	20	solution	solution	NOUN
azojete-1	115	21	of	of	ADP
azojete-1	115	22	the	the	DET
azojete-1	115	23	boundary	boundary	ADJ
azojete-1	115	24	value	value	NOUN
azojete-1	115	25	problem	problem	NOUN
azojete-1	115	26	(	(	PUNCT
azojete-1	115	27	bvp	bvp	PROPN
azojete-1	115	28	)	)	PUNCT
azojete-1	115	29	for	for	ADP
azojete-1	115	30	a	a	DET
azojete-1	115	31	representative	representative	ADJ
azojete-1	115	32	volume	volume	NOUN
azojete-1	115	33	element	element	NOUN
azojete-1	115	34	(	(	PUNCT
azojete-1	115	35	rve	rve	PROPN
azojete-1	115	36	)	)	PUNCT
azojete-1	115	37	of	of	ADP
azojete-1	115	38	the	the	DET
azojete-1	115	39	microstructure	microstructure	NOUN
azojete-1	115	40	by	by	ADP
azojete-1	115	41	using	use	VERB
azojete-1	115	42	numerical	numerical	ADJ
azojete-1	115	43	techniques	technique	NOUN
azojete-1	115	44	.	.	PUNCT
azojete-1	116	1	within	within	ADP
azojete-1	116	2	this	this	DET
azojete-1	116	3	frame	frame	NOUN
azojete-1	116	4	work	work	NOUN
azojete-1	116	5	,	,	PUNCT
azojete-1	116	6	it	it	PRON
azojete-1	116	7	is	be	AUX
azojete-1	116	8	possible	possible	ADJ
azojete-1	116	9	to	to	PART
azojete-1	116	10	obtain	obtain	VERB
azojete-1	116	11	the	the	DET
azojete-1	116	12	local	local	ADJ
azojete-1	116	13	values	value	NOUN
azojete-1	116	14	of	of	ADP
azojete-1	116	15	the	the	DET
azojete-1	116	16	field	field	NOUN
azojete-1	116	17	variable	variable	NOUN
azojete-1	116	18	which	which	PRON
azojete-1	116	19	facilitates	facilitate	VERB
azojete-1	116	20	the	the	DET
azojete-1	116	21	accurate	accurate	ADJ
azojete-1	116	22	simulation	simulation	NOUN
azojete-1	116	23	of	of	ADP
azojete-1	116	24	crack	crack	NOUN
azojete-1	116	25	nucleation	nucleation	NOUN
azojete-1	116	26	and	and	CCONJ
azojete-1	116	27	growth	growth	NOUN
azojete-1	116	28	of	of	ADP
azojete-1	116	29	damage	damage	NOUN
azojete-1	116	30	as	as	ADV
azojete-1	116	31	well	well	ADV
azojete-1	116	32	as	as	ADP
azojete-1	116	33	the	the	DET
azojete-1	116	34	localization	localization	NOUN
azojete-1	116	35	of	of	ADP
azojete-1	116	36	strains	strain	NOUN
azojete-1	116	37	leading	lead	VERB
azojete-1	116	38	to	to	ADP
azojete-1	116	39	damage	damage	NOUN
azojete-1	116	40	which	which	PRON
azojete-1	116	41	is	be	AUX
azojete-1	116	42	a	a	DET
azojete-1	116	43	major	major	ADJ
azojete-1	116	44	advantage	advantage	NOUN
azojete-1	116	45	of	of	ADP
azojete-1	116	46	the	the	DET
azojete-1	116	47	technique	technique	NOUN
azojete-1	116	48	over	over	ADP
azojete-1	116	49	analytical	analytical	ADJ
azojete-1	116	50	homogenizational	homogenizational	ADJ
azojete-1	116	51	schemes	scheme	NOUN
azojete-1	116	52	(	(	PUNCT
azojete-1	116	53	llorca	llorca	NOUN
azojete-1	116	54	et	et	PROPN
azojete-1	116	55	al	al	PROPN
azojete-1	116	56	.	.	PROPN
azojete-1	116	57	,	,	PUNCT
azojete-1	116	58	2007	2007	NUM
azojete-1	116	59	;	;	PUNCT
azojete-1	116	60	zohdi	zohdi	NOUN
azojete-1	116	61	and	and	CCONJ
azojete-1	116	62	wriggers	wrigger	NOUN
azojete-1	116	63	2005	2005	NUM
azojete-1	116	64	)	)	PUNCT
azojete-1	116	65	.	.	PUNCT
azojete-1	117	1	2.2.1	2.2.1	NUM
azojete-1	117	2	numerical	numerical	ADJ
azojete-1	117	3	simulation	simulation	NOUN
azojete-1	117	4	schemes	scheme	NOUN
azojete-1	117	5	the	the	DET
azojete-1	117	6	current	current	ADJ
azojete-1	117	7	advancements	advancement	NOUN
azojete-1	117	8	in	in	ADP
azojete-1	117	9	computing	compute	VERB
azojete-1	117	10	power	power	NOUN
azojete-1	117	11	and	and	CCONJ
azojete-1	117	12	simulation	simulation	NOUN
azojete-1	117	13	tools	tool	NOUN
azojete-1	117	14	,	,	PUNCT
azojete-1	117	15	facilitating	facilitate	VERB
azojete-1	117	16	the	the	DET
azojete-1	117	17	solution	solution	NOUN
azojete-1	117	18	of	of	ADP
azojete-1	117	19	boundary	boundary	ADJ
azojete-1	117	20	value	value	NOUN
azojete-1	117	21	problems	problem	NOUN
azojete-1	117	22	(	(	PUNCT
azojete-1	117	23	bvp	bvp	PROPN
azojete-1	117	24	)	)	PUNCT
azojete-1	117	25	of	of	ADP
azojete-1	117	26	representative	representative	ADJ
azojete-1	117	27	volume	volume	NOUN
azojete-1	117	28	element	element	NOUN
azojete-1	117	29	(	(	PUNCT
azojete-1	117	30	rve	rve	PROPN
azojete-1	117	31	)	)	PUNCT
azojete-1	117	32	of	of	ADP
azojete-1	117	33	composites	composite	NOUN
azojete-1	117	34	or	or	CCONJ
azojete-1	117	35	file:///c:/users	file:///c:/user	NOUN
azojete-1	117	36	/	/	SYM
azojete-1	117	37	user	user	NOUN
azojete-1	117	38	/	/	SYM
azojete-1	117	39	downloads	download	NOUN
azojete-1	117	40	/	/	SYM
azojete-1	117	41	azojete143	azojete143	PROPN
azojete-1	117	42	/	/	SYM
azojete-1	117	43	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	117	44	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	117	45	ohunene	ohunene	ADJ
azojete-1	117	46	hafsa	hafsa	PROPN
azojete-1	117	47	aliyu	aliyu	PROPN
azojete-1	117	48	:	:	PUNCT
azojete-1	117	49	analytical	analytical	ADJ
azojete-1	117	50	,	,	PUNCT
azojete-1	117	51	numerical	numerical	ADJ
azojete-1	117	52	and	and	CCONJ
azojete-1	117	53	computational	computational	ADJ
azojete-1	117	54	multiscale	multiscale	NOUN
azojete-1	117	55	modelling	model	VERB
azojete-1	117	56	techniques	technique	NOUN
azojete-1	117	57	for	for	ADP
azojete-1	117	58	heterogenous	heterogenous	ADJ
azojete-1	117	59	materials	material	NOUN
azojete-1	117	60	:	:	PUNCT
azojete-1	117	61	a	a	DET
azojete-1	117	62	review	review	NOUN
azojete-1	117	63	.	.	PUNCT
azojete-1	118	1	azojete	azojete	NOUN
azojete-1	118	2	,	,	PUNCT
azojete-1	118	3	15(3):488	15(3):488	PROPN
azojete-1	118	4	-	-	PUNCT
azojete-1	118	5	509	509	NUM
azojete-1	118	6	.	.	PUNCT
azojete-1	119	1	issn	issn	PROPN
azojete-1	119	2	1596	1596	NUM
azojete-1	119	3	-	-	SYM
azojete-1	119	4	2490	2490	NUM
azojete-1	119	5	;	;	PUNCT
azojete-1	119	6	e	e	X
azojete-1	119	7	-	-	NOUN
azojete-1	119	8	issn	issn	VERB
azojete-1	119	9	2545	2545	NUM
azojete-1	119	10	-	-	SYM
azojete-1	119	11	5818	5818	NUM
azojete-1	119	12	,	,	PUNCT
azojete-1	119	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	119	14	corresponding	correspond	VERB
azojete-1	119	15	author	author	NOUN
azojete-1	119	16	’s	’s	PART
azojete-1	119	17	e	e	NOUN
azojete-1	119	18	-	-	NOUN
azojete-1	119	19	mail	mail	NOUN
azojete-1	119	20	address	address	NOUN
azojete-1	119	21	:	:	PUNCT
azojete-1	119	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	119	23	496	496	NUM
azojete-1	119	24	heterogeneous	heterogeneous	ADJ
azojete-1	119	25	materials	material	NOUN
azojete-1	119	26	,	,	PUNCT
azojete-1	119	27	of	of	ADP
azojete-1	119	28	a	a	DET
azojete-1	119	29	size	size	NOUN
azojete-1	119	30	statistically	statistically	ADV
azojete-1	119	31	sufficient	sufficient	ADJ
azojete-1	119	32	enough	enough	ADV
azojete-1	119	33	to	to	PART
azojete-1	119	34	represent	represent	VERB
azojete-1	119	35	the	the	DET
azojete-1	119	36	microstructure	microstructure	NOUN
azojete-1	119	37	without	without	ADP
azojete-1	119	38	introducing	introduce	VERB
azojete-1	119	39	undesired	undesired	ADJ
azojete-1	119	40	or	or	CCONJ
azojete-1	119	41	non	non	ADJ
azojete-1	119	42	-	-	ADJ
azojete-1	119	43	existent	existent	ADJ
azojete-1	119	44	properties	property	NOUN
azojete-1	119	45	is	be	AUX
azojete-1	119	46	a	a	DET
azojete-1	119	47	welcome	welcome	ADJ
azojete-1	119	48	development	development	NOUN
azojete-1	119	49	in	in	ADP
azojete-1	119	50	the	the	DET
azojete-1	119	51	computational	computational	ADJ
azojete-1	119	52	micromechanics	micromechanic	NOUN
azojete-1	119	53	community	community	NOUN
azojete-1	119	54	.	.	PUNCT
azojete-1	120	1	these	these	DET
azojete-1	120	2	numerical	numerical	ADJ
azojete-1	120	3	strategies	strategy	NOUN
azojete-1	120	4	(	(	PUNCT
azojete-1	120	5	fast	fast	ADJ
azojete-1	120	6	fourier	fourier	NOUN
azojete-1	120	7	transform	transform	NOUN
azojete-1	120	8	algorithms	algorithm	NOUN
azojete-1	120	9	,	,	PUNCT
azojete-1	120	10	boundary	boundary	ADJ
azojete-1	120	11	element	element	NOUN
azojete-1	120	12	method	method	NOUN
azojete-1	120	13	as	as	ADV
azojete-1	120	14	well	well	ADV
azojete-1	120	15	as	as	ADP
azojete-1	120	16	the	the	DET
azojete-1	120	17	finite	finite	PROPN
azojete-1	120	18	element	element	PROPN
azojete-1	120	19	method	method	PROPN
azojete-1	120	20	fem	fem	PROPN
azojete-1	120	21	)	)	PUNCT
azojete-1	120	22	adopted	adopt	VERB
azojete-1	120	23	in	in	ADP
azojete-1	120	24	the	the	DET
azojete-1	120	25	solution	solution	NOUN
azojete-1	120	26	of	of	ADP
azojete-1	120	27	bvp	bvp	NOUN
azojete-1	120	28	are	be	AUX
azojete-1	120	29	not	not	PART
azojete-1	120	30	only	only	ADV
azojete-1	120	31	computationally	computationally	ADV
azojete-1	120	32	efficient	efficient	ADJ
azojete-1	120	33	but	but	CCONJ
azojete-1	120	34	also	also	ADV
azojete-1	120	35	facilitates	facilitate	VERB
azojete-1	120	36	the	the	DET
azojete-1	120	37	solution	solution	NOUN
azojete-1	120	38	of	of	ADP
azojete-1	120	39	problems	problem	NOUN
azojete-1	120	40	involving	involve	VERB
azojete-1	120	41	complex	complex	ADJ
azojete-1	120	42	geometries	geometry	NOUN
azojete-1	120	43	.	.	PUNCT
azojete-1	121	1	although	although	SCONJ
azojete-1	121	2	the	the	DET
azojete-1	121	3	fem	fem	NOUN
azojete-1	121	4	is	be	AUX
azojete-1	121	5	the	the	DET
azojete-1	121	6	most	most	ADV
azojete-1	121	7	preferred	preferred	ADJ
azojete-1	121	8	in	in	ADP
azojete-1	121	9	the	the	DET
azojete-1	121	10	micromechanics	micromechanic	NOUN
azojete-1	121	11	community	community	NOUN
azojete-1	121	12	because	because	SCONJ
azojete-1	121	13	of	of	ADP
azojete-1	121	14	its	its	PRON
azojete-1	121	15	mesh	mesh	NOUN
azojete-1	121	16	generation	generation	NOUN
azojete-1	121	17	capabilities	capability	NOUN
azojete-1	121	18	as	as	ADV
azojete-1	121	19	well	well	ADV
azojete-1	121	20	as	as	ADP
azojete-1	121	21	its	its	PRON
azojete-1	121	22	ability	ability	NOUN
azojete-1	121	23	to	to	PART
azojete-1	121	24	implement	implement	VERB
azojete-1	121	25	complex	complex	ADJ
azojete-1	121	26	constitutive	constitutive	ADJ
azojete-1	121	27	equations	equation	NOUN
azojete-1	121	28	;	;	PUNCT
azojete-1	121	29	it	it	PRON
azojete-1	121	30	tends	tend	VERB
azojete-1	121	31	to	to	PART
azojete-1	121	32	produce	produce	VERB
azojete-1	121	33	large	large	ADJ
azojete-1	121	34	models	model	NOUN
azojete-1	121	35	when	when	SCONJ
azojete-1	121	36	simulating	simulate	VERB
azojete-1	121	37	micro	micro	ADJ
azojete-1	121	38	fields	field	NOUN
azojete-1	121	39	in	in	ADP
azojete-1	121	40	regions	region	NOUN
azojete-1	121	41	with	with	ADP
azojete-1	121	42	large	large	ADJ
azojete-1	121	43	strain	strain	NOUN
azojete-1	121	44	gradient	gradient	NOUN
azojete-1	121	45	(	(	PUNCT
azojete-1	121	46	llorca	llorca	NOUN
azojete-1	121	47	et	et	PROPN
azojete-1	121	48	al	al	PROPN
azojete-1	121	49	.	.	PROPN
azojete-1	121	50	,	,	PUNCT
azojete-1	121	51	2007	2007	NUM
azojete-1	121	52	)	)	PUNCT
azojete-1	121	53	.	.	PUNCT
azojete-1	122	1	the	the	DET
azojete-1	122	2	voronoi	voronoi	PROPN
azojete-1	122	3	cell	cell	NOUN
azojete-1	122	4	finite	finite	PROPN
azojete-1	122	5	element	element	NOUN
azojete-1	122	6	method	method	NOUN
azojete-1	122	7	(	(	PUNCT
azojete-1	122	8	vcfem	vcfem	NOUN
azojete-1	122	9	)	)	PUNCT
azojete-1	122	10	was	be	AUX
azojete-1	122	11	introduced	introduce	VERB
azojete-1	122	12	as	as	ADP
azojete-1	122	13	an	an	DET
azojete-1	122	14	innovation	innovation	NOUN
azojete-1	122	15	to	to	ADP
azojete-1	122	16	the	the	DET
azojete-1	122	17	fem	fem	NOUN
azojete-1	122	18	in	in	ADP
azojete-1	122	19	solving	solve	VERB
azojete-1	122	20	non	non	ADJ
azojete-1	122	21	-	-	ADJ
azojete-1	122	22	linear	linear	ADJ
azojete-1	122	23	problems	problem	NOUN
azojete-1	122	24	in	in	ADP
azojete-1	122	25	composite	composite	ADJ
azojete-1	122	26	materials	material	NOUN
azojete-1	122	27	.	.	PUNCT
azojete-1	123	1	this	this	DET
azojete-1	123	2	technique	technique	NOUN
azojete-1	123	3	is	be	AUX
azojete-1	123	4	designed	design	VERB
azojete-1	123	5	to	to	PART
azojete-1	123	6	simulate	simulate	VERB
azojete-1	123	7	the	the	DET
azojete-1	123	8	behaviour	behaviour	NOUN
azojete-1	123	9	of	of	ADP
azojete-1	123	10	the	the	DET
azojete-1	123	11	composite	composite	ADJ
azojete-1	123	12	material	material	NOUN
azojete-1	123	13	microstructure	microstructure	NOUN
azojete-1	123	14	having	have	VERB
azojete-1	123	15	different	different	ADJ
azojete-1	123	16	morphologies	morphology	NOUN
azojete-1	123	17	.	.	PUNCT
azojete-1	124	1	in	in	ADP
azojete-1	124	2	order	order	NOUN
azojete-1	124	3	to	to	PART
azojete-1	124	4	capture	capture	VERB
azojete-1	124	5	the	the	DET
azojete-1	124	6	variation	variation	NOUN
azojete-1	124	7	in	in	ADP
azojete-1	124	8	morphology	morphology	NOUN
azojete-1	124	9	,	,	PUNCT
azojete-1	124	10	the	the	DET
azojete-1	124	11	finite	finite	ADJ
azojete-1	124	12	element	element	NOUN
azojete-1	124	13	discretization	discretization	NOUN
azojete-1	124	14	was	be	AUX
azojete-1	124	15	obtained	obtain	VERB
azojete-1	124	16	by	by	ADP
azojete-1	124	17	using	use	VERB
azojete-1	124	18	voronoi	voronoi	ADJ
azojete-1	124	19	tessellations	tessellation	NOUN
azojete-1	124	20	where	where	SCONJ
azojete-1	124	21	every	every	DET
azojete-1	124	22	voronoi	voronoi	ADJ
azojete-1	124	23	cell	cell	NOUN
azojete-1	124	24	contains	contain	VERB
azojete-1	124	25	an	an	DET
azojete-1	124	26	inclusion	inclusion	NOUN
azojete-1	124	27	embedded	embed	VERB
azojete-1	124	28	in	in	ADP
azojete-1	124	29	the	the	DET
azojete-1	124	30	matrix	matrix	NOUN
azojete-1	124	31	representing	represent	VERB
azojete-1	124	32	the	the	DET
azojete-1	124	33	basic	basic	ADJ
azojete-1	124	34	hybrid	hybrid	ADJ
azojete-1	124	35	finite	finite	NOUN
azojete-1	124	36	element	element	NOUN
azojete-1	124	37	(	(	PUNCT
azojete-1	124	38	moorthy	moorthy	PROPN
azojete-1	124	39	and	and	CCONJ
azojete-1	124	40	ghosh	ghosh	PROPN
azojete-1	124	41	1994	1994	NUM
azojete-1	124	42	;	;	PUNCT
azojete-1	124	43	llorca	llorca	PROPN
azojete-1	124	44	et	et	PROPN
azojete-1	124	45	al	al	PROPN
azojete-1	124	46	.	.	PROPN
azojete-1	124	47	,	,	PUNCT
azojete-1	124	48	2007	2007	NUM
azojete-1	124	49	)	)	PUNCT
azojete-1	124	50	.	.	PUNCT
azojete-1	125	1	this	this	DET
azojete-1	125	2	formulation	formulation	NOUN
azojete-1	125	3	lowers	lower	VERB
azojete-1	125	4	the	the	DET
azojete-1	125	5	cost	cost	NOUN
azojete-1	125	6	of	of	ADP
azojete-1	125	7	computation	computation	NOUN
azojete-1	125	8	in	in	ADP
azojete-1	125	9	determining	determine	VERB
azojete-1	125	10	the	the	DET
azojete-1	125	11	micro	micro	ADJ
azojete-1	125	12	fields	field	NOUN
azojete-1	125	13	in	in	ADP
azojete-1	125	14	heterogeneous	heterogeneous	ADJ
azojete-1	125	15	materials	material	NOUN
azojete-1	125	16	as	as	SCONJ
azojete-1	125	17	the	the	DET
azojete-1	125	18	hybrid	hybrid	ADJ
azojete-1	125	19	finite	finite	NOUN
azojete-1	125	20	element	element	NOUN
azojete-1	125	21	reduces	reduce	VERB
azojete-1	125	22	the	the	DET
azojete-1	125	23	number	number	NOUN
azojete-1	125	24	of	of	ADP
azojete-1	125	25	degrees	degree	NOUN
azojete-1	125	26	of	of	ADP
azojete-1	125	27	freedom	freedom	NOUN
azojete-1	125	28	(	(	PUNCT
azojete-1	125	29	d.o.f	d.o.f	NOUN
azojete-1	125	30	)	)	PUNCT
azojete-1	125	31	in	in	ADP
azojete-1	125	32	the	the	DET
azojete-1	125	33	analysis	analysis	NOUN
azojete-1	125	34	(	(	PUNCT
azojete-1	125	35	moorthy	moorthy	PROPN
azojete-1	125	36	and	and	CCONJ
azojete-1	125	37	ghosh	ghosh	PROPN
azojete-1	125	38	1996	1996	NUM
azojete-1	125	39	,	,	PUNCT
azojete-1	125	40	2000	2000	NUM
azojete-1	125	41	)	)	PUNCT
azojete-1	125	42	.	.	PUNCT
azojete-1	126	1	a	a	DET
azojete-1	126	2	three	three	NUM
azojete-1	126	3	-	-	PUNCT
azojete-1	126	4	dimensional	dimensional	ADJ
azojete-1	126	5	vcfem	vcfem	NOUN
azojete-1	126	6	(	(	PUNCT
azojete-1	126	7	figure	figure	NOUN
azojete-1	126	8	5	5	NUM
azojete-1	126	9	)	)	PUNCT
azojete-1	126	10	for	for	ADP
azojete-1	126	11	analysing	analyse	VERB
azojete-1	126	12	composite	composite	ADJ
azojete-1	126	13	material	material	NOUN
azojete-1	126	14	with	with	ADP
azojete-1	126	15	randomly	randomly	ADV
azojete-1	126	16	distributed	distribute	VERB
azojete-1	126	17	composites	composite	NOUN
azojete-1	126	18	was	be	AUX
azojete-1	126	19	developed	develop	VERB
azojete-1	126	20	by	by	ADP
azojete-1	126	21	ghosh	ghosh	PROPN
azojete-1	126	22	and	and	CCONJ
azojete-1	126	23	moorth	moorth	ADJ
azojete-1	126	24	(	(	PUNCT
azojete-1	126	25	2004	2004	NUM
azojete-1	126	26	)	)	PUNCT
azojete-1	126	27	.	.	PUNCT
azojete-1	127	1	figure	figure	VERB
azojete-1	127	2	5	5	NUM
azojete-1	127	3	:	:	PUNCT
azojete-1	127	4	a	a	DET
azojete-1	127	5	two	two	NUM
azojete-1	127	6	-	-	PUNCT
azojete-1	127	7	dimensional	dimensional	ADJ
azojete-1	127	8	voronoi	voronoi	NOUN
azojete-1	127	9	cell	cell	NOUN
azojete-1	127	10	finite	finite	ADJ
azojete-1	127	11	-	-	ADJ
azojete-1	127	12	element	element	ADJ
azojete-1	127	13	mesh	mesh	NOUN
azojete-1	127	14	and	and	CCONJ
azojete-1	127	15	detail	detail	NOUN
azojete-1	127	16	of	of	ADP
azojete-1	127	17	one	one	NUM
azojete-1	127	18	voronoi	voronoi	ADJ
azojete-1	127	19	finite	finite	PROPN
azojete-1	127	20	element	element	NOUN
azojete-1	127	21	adapted	adapt	VERB
azojete-1	127	22	from	from	ADP
azojete-1	127	23	llorca	llorca	PROPN
azojete-1	127	24	et	et	PROPN
azojete-1	127	25	al	al	PROPN
azojete-1	127	26	.	.	PROPN
azojete-1	128	1	(	(	PUNCT
azojete-1	128	2	2007	2007	NUM
azojete-1	128	3	)	)	PUNCT
azojete-1	128	4	this	this	DET
azojete-1	128	5	technique	technique	NOUN
azojete-1	128	6	was	be	AUX
azojete-1	128	7	further	far	ADV
azojete-1	128	8	extended	extend	VERB
azojete-1	128	9	by	by	ADP
azojete-1	128	10	li	li	PROPN
azojete-1	128	11	and	and	CCONJ
azojete-1	128	12	ghosh	ghosh	PROPN
azojete-1	128	13	(	(	PUNCT
azojete-1	128	14	2006	2006	NUM
azojete-1	128	15	)	)	PUNCT
azojete-1	128	16	.	.	PUNCT
azojete-1	129	1	they	they	PRON
azojete-1	129	2	came	come	VERB
azojete-1	129	3	up	up	ADP
azojete-1	129	4	with	with	ADP
azojete-1	129	5	the	the	DET
azojete-1	129	6	extended	extended	ADJ
azojete-1	129	7	voronoi	voronoi	NOUN
azojete-1	129	8	cell	cell	NOUN
azojete-1	129	9	finite	finite	PROPN
azojete-1	129	10	element	element	NOUN
azojete-1	129	11	method	method	NOUN
azojete-1	129	12	(	(	PUNCT
azojete-1	129	13	x	x	NOUN
azojete-1	129	14	-	-	ADJ
azojete-1	129	15	vcfem	vcfem	NOUN
azojete-1	129	16	)	)	PUNCT
azojete-1	129	17	used	use	VERB
azojete-1	129	18	to	to	PART
azojete-1	129	19	model	model	VERB
azojete-1	129	20	interfacial	interfacial	ADJ
azojete-1	129	21	debonding	debonding	NOUN
azojete-1	129	22	in	in	ADP
azojete-1	129	23	heterogeneous	heterogeneous	ADJ
azojete-1	129	24	materials	material	NOUN
azojete-1	129	25	.	.	PUNCT
azojete-1	130	1	in	in	ADP
azojete-1	130	2	computational	computational	ADJ
azojete-1	130	3	micromechanics	micromechanic	NOUN
azojete-1	130	4	,	,	PUNCT
azojete-1	130	5	the	the	DET
azojete-1	130	6	use	use	NOUN
azojete-1	130	7	of	of	ADP
azojete-1	130	8	efficient	efficient	ADJ
azojete-1	130	9	simulation	simulation	NOUN
azojete-1	130	10	tools	tool	NOUN
azojete-1	130	11	(	(	PUNCT
azojete-1	130	12	that	that	PRON
azojete-1	130	13	is	be	AUX
azojete-1	130	14	the	the	DET
azojete-1	130	15	domain	domain	NOUN
azojete-1	130	16	decomposition	decomposition	NOUN
azojete-1	130	17	method	method	NOUN
azojete-1	130	18	,	,	PUNCT
azojete-1	130	19	iterative	iterative	NOUN
azojete-1	130	20	solvers	solver	NOUN
azojete-1	130	21	such	such	ADJ
azojete-1	130	22	as	as	ADP
azojete-1	130	23	:	:	PUNCT
azojete-1	130	24	the	the	DET
azojete-1	130	25	conjugate	conjugate	ADJ
azojete-1	130	26	gradient	gradient	NOUN
azojete-1	130	27	method	method	NOUN
azojete-1	130	28	)	)	PUNCT
azojete-1	130	29	capable	capable	ADJ
azojete-1	130	30	of	of	ADP
azojete-1	130	31	solving	solve	VERB
azojete-1	130	32	bvp	bvp	NOUN
azojete-1	130	33	for	for	ADP
azojete-1	130	34	rve	rve	PROPN
azojete-1	130	35	is	be	AUX
azojete-1	130	36	key	key	ADJ
azojete-1	130	37	as	as	SCONJ
azojete-1	130	38	most	most	ADJ
azojete-1	130	39	micromechanics	micromechanic	NOUN
azojete-1	130	40	simulations	simulation	NOUN
azojete-1	130	41	require	require	VERB
azojete-1	130	42	very	very	ADV
azojete-1	130	43	large	large	ADJ
azojete-1	130	44	models	model	NOUN
azojete-1	130	45	with	with	ADP
azojete-1	130	46	complex	complex	ADJ
azojete-1	130	47	non	non	ADJ
azojete-1	130	48	-	-	ADJ
azojete-1	130	49	linear	linear	ADJ
azojete-1	130	50	behaviour	behaviour	NOUN
azojete-1	130	51	(	(	PUNCT
azojete-1	130	52	zohdi	zohdi	NOUN
azojete-1	130	53	and	and	CCONJ
azojete-1	130	54	wriggers	wrigger	NOUN
azojete-1	130	55	,	,	PUNCT
azojete-1	130	56	2005	2005	NUM
azojete-1	130	57	)	)	PUNCT
azojete-1	130	58	.	.	PUNCT
azojete-1	131	1	the	the	DET
azojete-1	131	2	numerical	numerical	PROPN
azojete-1	131	3	homogenization	homogenization	NOUN
azojete-1	131	4	discussed	discuss	VERB
azojete-1	131	5	,	,	PUNCT
azojete-1	131	6	gives	give	VERB
azojete-1	131	7	emphasis	emphasis	NOUN
azojete-1	131	8	on	on	ADP
azojete-1	131	9	multiscale	multiscale	ADJ
azojete-1	131	10	techniques	technique	NOUN
azojete-1	131	11	based	base	VERB
azojete-1	131	12	on	on	ADP
azojete-1	131	13	coupled	couple	VERB
azojete-1	131	14	homogenization	homogenization	NOUN
azojete-1	131	15	techniques	technique	NOUN
azojete-1	131	16	and	and	CCONJ
azojete-1	131	17	numerical	numerical	ADJ
azojete-1	131	18	analysis	analysis	NOUN
azojete-1	131	19	of	of	ADP
azojete-1	131	20	the	the	DET
azojete-1	131	21	rve	rve	NOUN
azojete-1	131	22	for	for	ADP
azojete-1	131	23	both	both	CCONJ
azojete-1	131	24	periodic	periodic	ADJ
azojete-1	131	25	and	and	CCONJ
azojete-1	131	26	non	non	ADJ
azojete-1	131	27	periodic	periodic	ADJ
azojete-1	131	28	(	(	PUNCT
azojete-1	131	29	random	random	ADJ
azojete-1	131	30	)	)	PUNCT
azojete-1	131	31	microstructure	microstructure	ADJ
azojete-1	131	32	morphological	morphological	ADJ
azojete-1	131	33	compositions	composition	NOUN
azojete-1	131	34	as	as	SCONJ
azojete-1	131	35	shown	show	VERB
azojete-1	131	36	in	in	ADP
azojete-1	131	37	figure	figure	NOUN
azojete-1	131	38	4	4	NUM
azojete-1	131	39	.	.	PUNCT
azojete-1	131	40	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	131	41	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	131	42	arid	arid	NOUN
azojete-1	131	43	zone	zone	NOUN
azojete-1	131	44	journal	journal	NOUN
azojete-1	131	45	of	of	ADP
azojete-1	131	46	engineering	engineering	NOUN
azojete-1	131	47	,	,	PUNCT
azojete-1	131	48	technology	technology	NOUN
azojete-1	131	49	and	and	CCONJ
azojete-1	131	50	environment	environment	NOUN
azojete-1	131	51	,	,	PUNCT
azojete-1	131	52	september	september	PROPN
azojete-1	131	53	,	,	PUNCT
azojete-1	131	54	2019	2019	NUM
azojete-1	131	55	;	;	PUNCT
azojete-1	132	1	vol	vol	NOUN
azojete-1	132	2	.	.	PUNCT
azojete-1	133	1	15(3):488	15(3):488	NUM
azojete-1	133	2	-	-	PUNCT
azojete-1	133	3	509	509	NUM
azojete-1	133	4	.	.	PUNCT
azojete-1	134	1	issn	issn	PROPN
azojete-1	134	2	1596	1596	NUM
azojete-1	134	3	-	-	SYM
azojete-1	134	4	2490	2490	NUM
azojete-1	134	5	;	;	PUNCT
azojete-1	134	6	e	e	X
azojete-1	134	7	-	-	NOUN
azojete-1	134	8	issn	issn	VERB
azojete-1	134	9	2545	2545	NUM
azojete-1	134	10	-	-	SYM
azojete-1	134	11	5818	5818	NUM
azojete-1	134	12	;	;	PUNCT
azojete-1	134	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	134	14	corresponding	correspond	VERB
azojete-1	134	15	author	author	NOUN
azojete-1	134	16	’s	’s	PART
azojete-1	134	17	e	e	NOUN
azojete-1	134	18	-	-	NOUN
azojete-1	134	19	mail	mail	NOUN
azojete-1	134	20	address	address	NOUN
azojete-1	134	21	:	:	PUNCT
azojete-1	134	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	134	23	497	497	NUM
azojete-1	134	24	figure	figure	NOUN
azojete-1	134	25	6	6	NUM
azojete-1	134	26	:	:	PUNCT
azojete-1	134	27	schematic	schematic	ADJ
azojete-1	134	28	representation	representation	NOUN
azojete-1	134	29	of	of	ADP
azojete-1	134	30	periodic	periodic	ADJ
azojete-1	134	31	and	and	CCONJ
azojete-1	134	32	non	non	ADJ
azojete-1	134	33	periodic	periodic	ADJ
azojete-1	134	34	rve	rve	NOUN
azojete-1	134	35	from	from	ADP
azojete-1	134	36	nguyen	nguyen	PROPN
azojete-1	134	37	et	et	PROPN
azojete-1	134	38	al	al	PROPN
azojete-1	134	39	.	.	PROPN
azojete-1	134	40	(	(	PUNCT
azojete-1	134	41	2012	2012	NUM
azojete-1	134	42	)	)	PUNCT
azojete-1	134	43	.	.	PUNCT
azojete-1	135	1	2.2.2	2.2.2	NUM
azojete-1	135	2	asymptotic	asymptotic	ADJ
azojete-1	135	3	homogenization	homogenization	NOUN
azojete-1	135	4	one	one	NUM
azojete-1	135	5	such	such	ADJ
azojete-1	135	6	multiscale	multiscale	ADJ
azojete-1	135	7	modelling	modelling	NOUN
azojete-1	135	8	technique	technique	NOUN
azojete-1	135	9	is	be	AUX
azojete-1	135	10	the	the	DET
azojete-1	135	11	coupling	coupling	NOUN
azojete-1	135	12	of	of	ADP
azojete-1	135	13	asymptotic	asymptotic	ADJ
azojete-1	135	14	homogenization	homogenization	NOUN
azojete-1	135	15	and	and	CCONJ
azojete-1	135	16	finite	finite	ADJ
azojete-1	135	17	elements	element	NOUN
azojete-1	135	18	.	.	PUNCT
azojete-1	136	1	in	in	ADP
azojete-1	136	2	this	this	DET
azojete-1	136	3	method	method	NOUN
azojete-1	136	4	the	the	DET
azojete-1	136	5	mathematical	mathematical	ADJ
azojete-1	136	6	asymptotic	asymptotic	ADJ
azojete-1	136	7	concept	concept	NOUN
azojete-1	136	8	is	be	AUX
azojete-1	136	9	adopted	adopt	VERB
azojete-1	136	10	in	in	ADP
azojete-1	136	11	solving	solve	VERB
azojete-1	136	12	multiple	multiple	ADJ
azojete-1	136	13	scale	scale	NOUN
azojete-1	136	14	problems	problem	NOUN
azojete-1	136	15	by	by	ADP
azojete-1	136	16	coupling	couple	VERB
azojete-1	136	17	finite	finite	PROPN
azojete-1	136	18	element	element	NOUN
azojete-1	136	19	problems	problem	NOUN
azojete-1	136	20	across	across	ADP
azojete-1	136	21	length	length	NOUN
azojete-1	136	22	scales	scale	NOUN
azojete-1	136	23	.	.	PUNCT
azojete-1	137	1	this	this	DET
azojete-1	137	2	homogenization	homogenization	NOUN
azojete-1	137	3	technique	technique	NOUN
azojete-1	137	4	adopts	adopt	VERB
azojete-1	137	5	an	an	DET
azojete-1	137	6	asymptotic	asymptotic	ADJ
azojete-1	137	7	expansion	expansion	NOUN
azojete-1	137	8	of	of	ADP
azojete-1	137	9	the	the	DET
azojete-1	137	10	displacement	displacement	NOUN
azojete-1	137	11	and	and	CCONJ
azojete-1	137	12	stress	stress	NOUN
azojete-1	137	13	field	field	NOUN
azojete-1	137	14	on	on	ADP
azojete-1	137	15	natural	natural	ADJ
azojete-1	137	16	scale	scale	NOUN
azojete-1	137	17	parameters	parameter	NOUN
azojete-1	137	18	see	see	VERB
azojete-1	137	19	eqn	eqn	NOUN
azojete-1	137	20	.	.	PUNCT
azojete-1	138	1	(	(	PUNCT
azojete-1	138	2	25	25	NUM
azojete-1	138	3	)	)	PUNCT
azojete-1	138	4	(	(	PUNCT
azojete-1	138	5	kanoute	kanoute	VERB
azojete-1	138	6	et	et	PROPN
azojete-1	138	7	al	al	PROPN
azojete-1	138	8	.	.	PROPN
azojete-1	138	9	,	,	PUNCT
azojete-1	138	10	2009	2009	NUM
azojete-1	138	11	;	;	PUNCT
azojete-1	138	12	nguyen	nguyen	PROPN
azojete-1	138	13	et	et	PROPN
azojete-1	138	14	al	al	PROPN
azojete-1	138	15	.	.	PROPN
azojete-1	138	16	,	,	PUNCT
azojete-1	138	17	2012	2012	NUM
azojete-1	138	18	)	)	PUNCT
azojete-1	138	19	.	.	PUNCT
azojete-1	139	1	as	as	ADP
azojete-1	139	2	such	such	ADJ
azojete-1	139	3	,	,	PUNCT
azojete-1	139	4	it	it	PRON
azojete-1	139	5	is	be	AUX
azojete-1	139	6	important	important	ADJ
azojete-1	139	7	to	to	PART
azojete-1	139	8	distinguish	distinguish	VERB
azojete-1	139	9	both	both	DET
azojete-1	139	10	length	length	NOUN
azojete-1	139	11	scales	scale	NOUN
azojete-1	139	12	,	,	PUNCT
azojete-1	139	13	as	as	SCONJ
azojete-1	139	14	the	the	DET
azojete-1	139	15	ratio	ratio	NOUN
azojete-1	139	16	of	of	ADP
azojete-1	139	17	the	the	DET
azojete-1	139	18	length	length	NOUN
azojete-1	139	19	scales	scale	NOUN
azojete-1	139	20	�	�	PROPN
azojete-1	139	21	�	�	PROPN
azojete-1	139	22	describes	describe	VERB
azojete-1	139	23	the	the	DET
azojete-1	139	24	small	small	ADJ
azojete-1	139	25	parameter	parameter	NOUN
azojete-1	139	26	(	(	PUNCT
azojete-1	139	27	�	�	PROPN
azojete-1	139	28	㇀	㇀	PROPN
azojete-1	139	29	ඟ	ඟ	PROPN
azojete-1	139	30	�	�	PROPN
azojete-1	139	31	�	�	PROPN
azojete-1	139	32	◠	◠	PROPN
azojete-1	139	33	�	�	PROPN
azojete-1	139	34	�	�	PROPN
azojete-1	139	35	=	=	SYM
azojete-1	139	36	�	�	PROPN
azojete-1	139	37	(	(	PUNCT
azojete-1	139	38	25	25	NUM
azojete-1	139	39	)	)	PUNCT
azojete-1	140	1	where	where	SCONJ
azojete-1	140	2	:	:	PUNCT
azojete-1	140	3	r	r	NOUN
azojete-1	140	4	and	and	CCONJ
azojete-1	140	5	r	r	NOUN
azojete-1	140	6	are	be	AUX
azojete-1	140	7	the	the	DET
azojete-1	140	8	position	position	NOUN
azojete-1	140	9	vectors	vector	NOUN
azojete-1	140	10	on	on	ADP
azojete-1	140	11	the	the	DET
azojete-1	140	12	macro	macro	NOUN
azojete-1	140	13	and	and	CCONJ
azojete-1	140	14	microscale	microscale	NOUN
azojete-1	140	15	respectively	respectively	ADV
azojete-1	140	16	(	(	PUNCT
azojete-1	140	17	figure	figure	NOUN
azojete-1	140	18	6	6	NUM
azojete-1	140	19	)	)	PUNCT
azojete-1	140	20	.	.	PUNCT
azojete-1	141	1	u	u	PRON
azojete-1	141	2	r	r	NOUN
azojete-1	141	3	,	,	PUNCT
azojete-1	141	4	r	r	NOUN
azojete-1	141	5	=	=	SYM
azojete-1	141	6	r	r	NOUN
azojete-1	141	7	�	�	PROPN
azojete-1	141	8	=	=	SYM
azojete-1	141	9	u	u	NOUN
azojete-1	141	10	�	�	PROPN
azojete-1	141	11	r	r	NOUN
azojete-1	141	12	+	+	NUM
azojete-1	141	13	�	�	PROPN
azojete-1	141	14	u1	u1	NOUN
azojete-1	141	15	r	r	NOUN
azojete-1	141	16	,	,	PUNCT
azojete-1	141	17	r	r	NOUN
azojete-1	141	18	+	+	CCONJ
azojete-1	141	19	o2	o2	PROPN
azojete-1	141	20	(	(	PUNCT
azojete-1	141	21	26	26	NUM
azojete-1	141	22	)	)	PUNCT
azojete-1	141	23	eqn	eqn	NOUN
azojete-1	141	24	.	.	PUNCT
azojete-1	142	1	(	(	PUNCT
azojete-1	142	2	26	26	NUM
azojete-1	142	3	)	)	PUNCT
azojete-1	142	4	gives	give	VERB
azojete-1	142	5	the	the	DET
azojete-1	142	6	asymptotic	asymptotic	ADJ
azojete-1	142	7	expansion	expansion	NOUN
azojete-1	142	8	of	of	ADP
azojete-1	142	9	the	the	DET
azojete-1	142	10	displacement	displacement	ADJ
azojete-1	142	11	field	field	NOUN
azojete-1	142	12	where	where	SCONJ
azojete-1	142	13	:	:	PUNCT
azojete-1	142	14	�	�	PROPN
azojete-1	142	15	�	�	PROPN
azojete-1	142	16	�	�	PROPN
azojete-1	142	17	–	–	PUNCT
azojete-1	142	18	macroscopic	macroscopic	ADJ
azojete-1	142	19	displacement	displacement	ADJ
azojete-1	142	20	field	field	NOUN
azojete-1	142	21	�	�	PROPN
azojete-1	142	22	1	1	NUM
azojete-1	142	23	�	�	PROPN
azojete-1	142	24	,	,	PUNCT
azojete-1	142	25	㌠	㌠	NUM
azojete-1	142	26	–	–	PUNCT
azojete-1	142	27	periodic	periodic	ADJ
azojete-1	142	28	first	first	ADJ
azojete-1	142	29	order	order	NOUN
azojete-1	142	30	fluctuations	fluctuation	NOUN
azojete-1	142	31	or	or	CCONJ
azojete-1	142	32	perturbations	perturbation	NOUN
azojete-1	142	33	due	due	ADP
azojete-1	142	34	to	to	ADP
azojete-1	142	35	the	the	DET
azojete-1	142	36	microstructure	microstructure	NOUN
azojete-1	142	37	referred	refer	VERB
azojete-1	142	38	to	to	ADP
azojete-1	142	39	as	as	ADV
azojete-1	142	40	fast	fast	ADJ
azojete-1	142	41	and	and	CCONJ
azojete-1	142	42	slow	slow	ADJ
azojete-1	142	43	variables	variable	NOUN
azojete-1	142	44	respectively	respectively	ADV
azojete-1	142	45	.	.	PUNCT
azojete-1	143	1	�	�	PROPN
azojete-1	143	2	a	a	DET
azojete-1	143	3	small	small	ADJ
azojete-1	143	4	positive	positive	ADJ
azojete-1	143	5	number	number	NOUN
azojete-1	143	6	linking	link	VERB
azojete-1	143	7	the	the	DET
azojete-1	143	8	length	length	NOUN
azojete-1	143	9	scales	scale	NOUN
azojete-1	143	10	at	at	ADP
azojete-1	143	11	the	the	DET
azojete-1	143	12	macro	macro	NOUN
azojete-1	143	13	and	and	CCONJ
azojete-1	143	14	micro	micro	ADJ
azojete-1	143	15	level	level	NOUN
azojete-1	143	16	udisplacement	udisplacement	NOUN
azojete-1	143	17	field	field	NOUN
azojete-1	143	18	figure	figure	NOUN
azojete-1	143	19	7	7	NUM
azojete-1	143	20	:	:	PUNCT
azojete-1	143	21	schematic	schematic	ADJ
azojete-1	143	22	strategy	strategy	NOUN
azojete-1	143	23	for	for	ADP
azojete-1	143	24	the	the	DET
azojete-1	143	25	multi	multi	ADJ
azojete-1	143	26	-	-	ADJ
azojete-1	143	27	scale	scale	ADJ
azojete-1	143	28	simulation	simulation	NOUN
azojete-1	143	29	based	base	VERB
azojete-1	143	30	on	on	ADP
azojete-1	143	31	the	the	DET
azojete-1	143	32	finite	finite	ADJ
azojete-1	143	33	element	element	NOUN
azojete-1	143	34	method	method	NOUN
azojete-1	143	35	and	and	CCONJ
azojete-1	143	36	asymptotic	asymptotic	ADJ
azojete-1	143	37	homogenization	homogenization	NOUN
azojete-1	143	38	adapted	adapt	VERB
azojete-1	143	39	from	from	ADP
azojete-1	143	40	llorca	llorca	PROPN
azojete-1	143	41	et	et	PROPN
azojete-1	143	42	al	al	PROPN
azojete-1	143	43	.	.	PROPN
azojete-1	144	1	(	(	PUNCT
azojete-1	144	2	2007	2007	NUM
azojete-1	144	3	)	)	PUNCT
azojete-1	144	4	this	this	DET
azojete-1	144	5	asymptotic	asymptotic	ADJ
azojete-1	144	6	expansion	expansion	NOUN
azojete-1	144	7	is	be	AUX
azojete-1	144	8	regarded	regard	VERB
azojete-1	144	9	as	as	ADP
azojete-1	144	10	an	an	DET
azojete-1	144	11	approximate	approximate	ADJ
azojete-1	144	12	solution	solution	NOUN
azojete-1	144	13	of	of	ADP
azojete-1	144	14	the	the	DET
azojete-1	144	15	boundary	boundary	ADJ
azojete-1	144	16	value	value	NOUN
azojete-1	144	17	problem	problem	NOUN
azojete-1	144	18	(	(	PUNCT
azojete-1	144	19	bvp	bvp	NOUN
azojete-1	144	20	)	)	PUNCT
azojete-1	144	21	especially	especially	ADV
azojete-1	144	22	when	when	SCONJ
azojete-1	144	23	�	�	PROPN
azojete-1	144	24	is	be	AUX
azojete-1	144	25	reasonably	reasonably	ADV
azojete-1	144	26	small	small	ADJ
azojete-1	144	27	.	.	PUNCT
azojete-1	145	1	the	the	DET
azojete-1	145	2	stress	stress	NOUN
azojete-1	145	3	field	field	NOUN
azojete-1	145	4	is	be	AUX
azojete-1	145	5	given	give	VERB
azojete-1	145	6	as	as	ADP
azojete-1	145	7	:	:	PUNCT
azojete-1	145	8	ϵ	ϵ	X
azojete-1	145	9	r	r	NOUN
azojete-1	145	10	,	,	PUNCT
azojete-1	145	11	r	r	NOUN
azojete-1	145	12	=	=	SYM
azojete-1	145	13	grad	grad	PROPN
azojete-1	145	14	�	�	PROPN
azojete-1	145	15	�	�	PROPN
azojete-1	145	16	�	�	PROPN
azojete-1	145	17	�	�	PROPN
azojete-1	145	18	�	�	PROPN
azojete-1	145	19	s	s	PART
azojete-1	145	20	u	u	NOUN
azojete-1	145	21	=	=	X
azojete-1	145	22	gradsu	gradsu	PROPN
azojete-1	145	23	+	+	CCONJ
azojete-1	145	24	1	1	NUM
azojete-1	145	25	�	�	PROPN
azojete-1	145	26	gradsu	gradsu	NOUN
azojete-1	145	27	=	=	SYM
azojete-1	145	28	gradsu	gradsu	PROPN
azojete-1	145	29	�	�	PROPN
azojete-1	145	30	+	+	CCONJ
azojete-1	145	31	gradsu1	gradsu1	PROPN
azojete-1	146	1	+	+	CCONJ
azojete-1	146	2	�	�	PROPN
azojete-1	146	3	gradsu	gradsu	PROPN
azojete-1	146	4	�	�	PROPN
azojete-1	146	5	1	1	NUM
azojete-1	146	6	(	(	PUNCT
azojete-1	146	7	27	27	NUM
azojete-1	146	8	)	)	PUNCT
azojete-1	146	9	file:///c:/users	file:///c:/user	NOUN
azojete-1	146	10	/	/	SYM
azojete-1	146	11	user	user	NOUN
azojete-1	146	12	/	/	SYM
azojete-1	146	13	downloads	download	NOUN
azojete-1	146	14	/	/	SYM
azojete-1	146	15	azojete143	azojete143	PROPN
azojete-1	146	16	/	/	SYM
azojete-1	146	17	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	146	18	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	146	19	ohunene	ohunene	ADJ
azojete-1	146	20	hafsa	hafsa	PROPN
azojete-1	146	21	aliyu	aliyu	PROPN
azojete-1	146	22	:	:	PUNCT
azojete-1	146	23	analytical	analytical	ADJ
azojete-1	146	24	,	,	PUNCT
azojete-1	146	25	numerical	numerical	ADJ
azojete-1	146	26	and	and	CCONJ
azojete-1	146	27	computational	computational	ADJ
azojete-1	146	28	multiscale	multiscale	NOUN
azojete-1	146	29	modelling	model	VERB
azojete-1	146	30	techniques	technique	NOUN
azojete-1	146	31	for	for	ADP
azojete-1	146	32	heterogenous	heterogenous	ADJ
azojete-1	146	33	materials	material	NOUN
azojete-1	146	34	:	:	PUNCT
azojete-1	146	35	a	a	DET
azojete-1	146	36	review	review	NOUN
azojete-1	146	37	.	.	PUNCT
azojete-1	147	1	azojete	azojete	NOUN
azojete-1	147	2	,	,	PUNCT
azojete-1	147	3	15(3):488	15(3):488	PROPN
azojete-1	147	4	-	-	PUNCT
azojete-1	147	5	509	509	NUM
azojete-1	147	6	.	.	PUNCT
azojete-1	148	1	issn	issn	PROPN
azojete-1	148	2	1596	1596	NUM
azojete-1	148	3	-	-	SYM
azojete-1	148	4	2490	2490	NUM
azojete-1	148	5	;	;	PUNCT
azojete-1	148	6	e	e	X
azojete-1	148	7	-	-	NOUN
azojete-1	148	8	issn	issn	VERB
azojete-1	148	9	2545	2545	NUM
azojete-1	148	10	-	-	SYM
azojete-1	148	11	5818	5818	NUM
azojete-1	148	12	,	,	PUNCT
azojete-1	148	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	148	14	corresponding	correspond	VERB
azojete-1	148	15	author	author	NOUN
azojete-1	148	16	’s	’s	PART
azojete-1	148	17	e	e	NOUN
azojete-1	148	18	-	-	NOUN
azojete-1	148	19	mail	mail	NOUN
azojete-1	148	20	address	address	NOUN
azojete-1	148	21	:	:	PUNCT
azojete-1	148	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	148	23	498	498	NUM
azojete-1	148	24	while	while	SCONJ
azojete-1	148	25	the	the	DET
azojete-1	148	26	asymptotic	asymptotic	ADJ
azojete-1	148	27	expansion	expansion	NOUN
azojete-1	148	28	of	of	ADP
azojete-1	148	29	the	the	DET
azojete-1	148	30	stress	stress	NOUN
azojete-1	148	31	field	field	NOUN
azojete-1	148	32	assuming	assume	VERB
azojete-1	148	33	a	a	DET
azojete-1	148	34	linear	linear	ADJ
azojete-1	148	35	elastic	elastic	ADJ
azojete-1	148	36	behaviour	behaviour	NOUN
azojete-1	148	37	is	be	AUX
azojete-1	148	38	given	give	VERB
azojete-1	148	39	in	in	ADP
azojete-1	148	40	eqn	eqn	NOUN
azojete-1	148	41	.	.	PUNCT
azojete-1	149	1	(	(	PUNCT
azojete-1	149	2	28	28	NUM
azojete-1	149	3	)	)	PUNCT
azojete-1	149	4	as	as	ADP
azojete-1	149	5	:	:	PUNCT
azojete-1	149	6	σ	σ	PROPN
azojete-1	149	7	r	r	NOUN
azojete-1	149	8	,	,	PUNCT
azojete-1	149	9	r	r	NOUN
azojete-1	149	10	=	=	SYM
azojete-1	149	11	l	l	NOUN
azojete-1	149	12	:	:	PUNCT
azojete-1	149	13	ϵ	ϵ	X
azojete-1	149	14	r	r	NOUN
azojete-1	149	15	,	,	PUNCT
azojete-1	149	16	r	r	NOUN
azojete-1	149	17	=	=	SYM
azojete-1	149	18	l	l	NOUN
azojete-1	149	19	:	:	PUNCT
azojete-1	149	20	grad	grad	PROPN
azojete-1	149	21	�	�	PROPN
azojete-1	149	22	�	�	PROPN
azojete-1	149	23	�	�	PROPN
azojete-1	149	24	�	�	PROPN
azojete-1	149	25	�	�	PROPN
azojete-1	149	26	s	s	PART
azojete-1	149	27	u	u	NOUN
azojete-1	149	28	=	=	PROPN
azojete-1	149	29	σ1	σ1	PROPN
azojete-1	149	30	r	r	NOUN
azojete-1	149	31	,	,	PUNCT
azojete-1	149	32	r	r	NOUN
azojete-1	149	33	+	+	NUM
azojete-1	149	34	�	�	PROPN
azojete-1	149	35	σ2	σ2	NOUN
azojete-1	149	36	r	r	NOUN
azojete-1	149	37	,	,	PUNCT
azojete-1	149	38	r	r	NOUN
azojete-1	149	39	+	+	NUM
azojete-1	149	40	…	…	PUNCT
azojete-1	149	41	(	(	PUNCT
azojete-1	149	42	28	28	NUM
azojete-1	149	43	)	)	PUNCT
azojete-1	149	44	the	the	DET
azojete-1	149	45	homogenized	homogenized	ADJ
azojete-1	149	46	stiffness	stiffness	ADJ
azojete-1	149	47	tensor	tensor	NOUN
azojete-1	149	48	l	l	NOUN
azojete-1	149	49	�	�	PROPN
azojete-1	149	50	according	accord	VERB
azojete-1	149	51	to	to	ADP
azojete-1	149	52	llorca	llorca	PROPN
azojete-1	149	53	et	et	PROPN
azojete-1	149	54	al	al	PROPN
azojete-1	149	55	.	.	PROPN
azojete-1	150	1	(	(	PUNCT
azojete-1	150	2	2007	2007	NUM
azojete-1	150	3	)	)	PUNCT
azojete-1	150	4	is	be	AUX
azojete-1	150	5	computed	compute	VERB
azojete-1	150	6	from	from	ADP
azojete-1	150	7	mean	mean	ADJ
azojete-1	150	8	strain	strain	NOUN
azojete-1	150	9	value	value	NOUN
azojete-1	150	10	�	�	PROPN
azojete-1	150	11	�	�	NOUN
azojete-1	150	12	−1	−1	NOUN
azojete-1	150	13	as	as	ADP
azojete-1	150	14	:	:	PUNCT
azojete-1	150	15	σ	σ	PROPN
azojete-1	150	16	�	�	PROPN
azojete-1	150	17	=	=	SYM
azojete-1	150	18	1	1	NUM
azojete-1	150	19	ω	ω	NUM
azojete-1	150	20	ωσ	ωσ	PROPN
azojete-1	150	21	1	1	NUM
azojete-1	150	22	�	�	PROPN
azojete-1	150	23	dω	dω	ADP
azojete-1	150	24	=	=	SYM
azojete-1	150	25	1	1	NUM
azojete-1	150	26	ω	ω	NUM
azojete-1	150	27	ω	ω	NUM
azojete-1	150	28	l	l	NOUN
azojete-1	150	29	:	:	PUNCT
azojete-1	151	1	i	i	PRON
azojete-1	151	2	+	+	NUM
azojete-1	151	3	∂χ	∂χ	PROPN
azojete-1	151	4	r	r	NOUN
azojete-1	152	1	∂r	∂r	NOUN
azojete-1	153	1	dω	dω	PRON
azojete-1	153	2	�	�	PROPN
azojete-1	153	3	:	:	PUNCT
azojete-1	153	4	gradsu	gradsu	PROPN
azojete-1	153	5	�	�	PROPN
azojete-1	153	6	=	=	SYM
azojete-1	153	7	l	l	PROPN
azojete-1	153	8	�	�	PROPN
azojete-1	153	9	:	:	PUNCT
azojete-1	153	10	gradsu	gradsu	PROPN
azojete-1	153	11	�	�	PROPN
azojete-1	153	12	(	(	PUNCT
azojete-1	153	13	29	29	NUM
azojete-1	153	14	)	)	PUNCT
azojete-1	153	15	although	although	SCONJ
azojete-1	153	16	,	,	PUNCT
azojete-1	153	17	this	this	DET
azojete-1	153	18	technique	technique	NOUN
azojete-1	153	19	can	can	AUX
azojete-1	153	20	be	be	AUX
azojete-1	153	21	used	use	VERB
azojete-1	153	22	for	for	ADP
azojete-1	153	23	composites	composite	NOUN
azojete-1	153	24	with	with	ADP
azojete-1	153	25	either	either	CCONJ
azojete-1	153	26	a	a	DET
azojete-1	153	27	local	local	ADJ
azojete-1	153	28	periodic	periodic	ADJ
azojete-1	153	29	microstructure	microstructure	NOUN
azojete-1	153	30	(	(	PUNCT
azojete-1	153	31	that	that	PRON
azojete-1	153	32	is	be	AUX
azojete-1	153	33	microstructure	microstructure	ADJ
azojete-1	153	34	having	have	VERB
azojete-1	153	35	different	different	ADJ
azojete-1	153	36	morphologies	morphology	NOUN
azojete-1	153	37	)	)	PUNCT
azojete-1	153	38	or	or	CCONJ
azojete-1	153	39	global	global	ADJ
azojete-1	153	40	periodicity	periodicity	NOUN
azojete-1	153	41	(	(	PUNCT
azojete-1	153	42	that	that	PRON
azojete-1	153	43	is	be	AUX
azojete-1	153	44	having	have	VERB
azojete-1	153	45	repetitive	repetitive	ADJ
azojete-1	153	46	cell	cell	NOUN
azojete-1	153	47	units	unit	NOUN
azojete-1	153	48	)	)	PUNCT
azojete-1	153	49	as	as	SCONJ
azojete-1	153	50	shown	show	VERB
azojete-1	153	51	in	in	ADP
azojete-1	153	52	figure	figure	NOUN
azojete-1	153	53	7	7	NUM
azojete-1	153	54	,	,	PUNCT
azojete-1	153	55	it	it	PRON
azojete-1	153	56	is	be	AUX
azojete-1	153	57	however	however	ADV
azojete-1	153	58	,	,	PUNCT
azojete-1	153	59	mostly	mostly	ADV
azojete-1	153	60	restricted	restrict	VERB
azojete-1	153	61	to	to	ADP
azojete-1	153	62	simple	simple	ADJ
azojete-1	153	63	microscopic	microscopic	ADJ
azojete-1	153	64	geometries	geometry	NOUN
azojete-1	153	65	at	at	ADP
azojete-1	153	66	very	very	ADV
azojete-1	153	67	small	small	ADJ
azojete-1	153	68	strains	strain	NOUN
azojete-1	153	69	(	(	PUNCT
azojete-1	153	70	)	)	PUNCT
azojete-1	153	71	as	as	ADV
azojete-1	153	72	well	well	ADV
azojete-1	153	73	as	as	ADP
azojete-1	153	74	simple	simple	ADJ
azojete-1	153	75	material	material	NOUN
azojete-1	153	76	models	model	NOUN
azojete-1	153	77	(	(	PUNCT
azojete-1	153	78	mostly	mostly	ADV
azojete-1	153	79	at	at	ADP
azojete-1	153	80	small	small	ADJ
azojete-1	153	81	strains	strain	NOUN
azojete-1	153	82	)	)	PUNCT
azojete-1	153	83	where	where	SCONJ
azojete-1	153	84	the	the	DET
azojete-1	153	85	macroscopic	macroscopic	ADJ
azojete-1	153	86	fields	field	NOUN
azojete-1	153	87	are	be	AUX
azojete-1	153	88	virtually	virtually	ADV
azojete-1	153	89	stable	stable	ADJ
azojete-1	153	90	at	at	ADP
azojete-1	153	91	the	the	DET
azojete-1	153	92	microscopic	microscopic	ADJ
azojete-1	153	93	length	length	NOUN
azojete-1	153	94	scale	scale	NOUN
azojete-1	153	95	.	.	PUNCT
azojete-1	154	1	figure	figure	NOUN
azojete-1	154	2	8	8	NUM
azojete-1	154	3	:	:	PUNCT
azojete-1	154	4	a	a	DET
azojete-1	154	5	representation	representation	NOUN
azojete-1	154	6	of	of	ADP
azojete-1	154	7	a	a	DET
azojete-1	154	8	microstructure	microstructure	NOUN
azojete-1	154	9	(	(	PUNCT
azojete-1	154	10	a	a	NOUN
azojete-1	154	11	)	)	PUNCT
azojete-1	154	12	with	with	ADP
azojete-1	154	13	local	local	ADJ
azojete-1	154	14	periodicity	periodicity	NOUN
azojete-1	154	15	and	and	CCONJ
azojete-1	154	16	(	(	PUNCT
azojete-1	154	17	b	b	NOUN
azojete-1	154	18	)	)	PUNCT
azojete-1	154	19	with	with	ADP
azojete-1	154	20	global	global	ADJ
azojete-1	154	21	periodicity	periodicity	NOUN
azojete-1	154	22	from	from	ADP
azojete-1	154	23	kouznetsova	kouznetsova	PROPN
azojete-1	154	24	et	et	PROPN
azojete-1	154	25	al	al	PROPN
azojete-1	154	26	.	.	PROPN
azojete-1	154	27	cited	cite	VERB
azojete-1	154	28	in	in	ADP
azojete-1	154	29	galvanetto	galvanetto	NOUN
azojete-1	154	30	and	and	CCONJ
azojete-1	154	31	aliabadi	aliabadi	NOUN
azojete-1	154	32	(	(	PUNCT
azojete-1	154	33	2010	2010	NUM
azojete-1	154	34	)	)	PUNCT
azojete-1	154	35	this	this	DET
azojete-1	154	36	homogenizational	homogenizational	ADJ
azojete-1	154	37	approach	approach	NOUN
azojete-1	154	38	offers	offer	VERB
azojete-1	154	39	not	not	PART
azojete-1	154	40	only	only	ADV
azojete-1	154	41	the	the	DET
azojete-1	154	42	effective	effective	ADJ
azojete-1	154	43	material	material	NOUN
azojete-1	154	44	properties	property	NOUN
azojete-1	154	45	,	,	PUNCT
azojete-1	154	46	but	but	CCONJ
azojete-1	154	47	also	also	ADV
azojete-1	154	48	gives	give	VERB
azojete-1	154	49	information	information	NOUN
azojete-1	154	50	on	on	ADP
azojete-1	154	51	the	the	DET
azojete-1	154	52	local	local	PROPN
azojete-1	154	53	micro	micro	PROPN
azojete-1	154	54	fields	field	NOUN
azojete-1	154	55	(	(	PUNCT
azojete-1	154	56	llorca	llorca	PROPN
azojete-1	154	57	et	et	PROPN
azojete-1	154	58	al	al	PROPN
azojete-1	154	59	.	.	PROPN
azojete-1	154	60	,	,	PUNCT
azojete-1	154	61	2007	2007	NUM
azojete-1	154	62	;	;	PUNCT
azojete-1	154	63	kanoute	kanoute	VERB
azojete-1	154	64	et	et	PROPN
azojete-1	154	65	al	al	PROPN
azojete-1	154	66	.	.	PROPN
azojete-1	154	67	,	,	PUNCT
azojete-1	154	68	2009	2009	NUM
azojete-1	154	69	;	;	PUNCT
azojete-1	154	70	kouznetsova	kouznetsova	PROPN
azojete-1	154	71	et	et	PROPN
azojete-1	154	72	al	al	PROPN
azojete-1	154	73	.	.	PROPN
azojete-1	154	74	,	,	PUNCT
azojete-1	154	75	2001	2001	NUM
azojete-1	154	76	)	)	PUNCT
azojete-1	154	77	.	.	PUNCT
azojete-1	155	1	2.2.3	2.2.3	NUM
azojete-1	155	2	mesh	mesh	NOUN
azojete-1	155	3	superposition	superposition	NOUN
azojete-1	155	4	method	method	NOUN
azojete-1	155	5	this	this	DET
azojete-1	155	6	multiscale	multiscale	ADJ
azojete-1	155	7	technique	technique	NOUN
azojete-1	155	8	was	be	AUX
azojete-1	155	9	introduced	introduce	VERB
azojete-1	155	10	by	by	ADP
azojete-1	155	11	fish	fish	NOUN
azojete-1	155	12	(	(	PUNCT
azojete-1	155	13	1992	1992	NUM
azojete-1	155	14	)	)	PUNCT
azojete-1	155	15	,	,	PUNCT
azojete-1	155	16	where	where	SCONJ
azojete-1	155	17	he	he	PRON
azojete-1	155	18	superimposed	superimpose	VERB
azojete-1	155	19	an	an	DET
azojete-1	155	20	additional	additional	ADJ
azojete-1	155	21	mesh	mesh	NOUN
azojete-1	155	22	on	on	ADP
azojete-1	155	23	the	the	DET
azojete-1	155	24	macroscopic	macroscopic	ADJ
azojete-1	155	25	(	(	PUNCT
azojete-1	155	26	or	or	CCONJ
azojete-1	155	27	global	global	ADJ
azojete-1	155	28	)	)	PUNCT
azojete-1	155	29	mesh	mesh	NOUN
azojete-1	155	30	especially	especially	ADV
azojete-1	155	31	in	in	ADP
azojete-1	155	32	the	the	DET
azojete-1	155	33	regions	region	NOUN
azojete-1	155	34	of	of	ADP
azojete-1	155	35	high	high	ADJ
azojete-1	155	36	stress	stress	NOUN
azojete-1	155	37	and	and	CCONJ
azojete-1	155	38	strain	strain	ADJ
azojete-1	155	39	gradients	gradient	NOUN
azojete-1	155	40	with	with	ADP
azojete-1	155	41	the	the	DET
azojete-1	155	42	aim	aim	NOUN
azojete-1	155	43	of	of	ADP
azojete-1	155	44	obtaining	obtain	VERB
azojete-1	155	45	detailed	detailed	ADJ
azojete-1	155	46	information	information	NOUN
azojete-1	155	47	on	on	ADP
azojete-1	155	48	the	the	DET
azojete-1	155	49	heterogeneous	heterogeneous	ADJ
azojete-1	155	50	material	material	NOUN
azojete-1	155	51	microstructure	microstructure	NOUN
azojete-1	155	52	at	at	ADP
azojete-1	155	53	critical	critical	ADJ
azojete-1	155	54	regions	region	NOUN
azojete-1	155	55	(	(	PUNCT
azojete-1	155	56	crack	crack	VERB
azojete-1	155	57	tips	tip	NOUN
azojete-1	155	58	,	,	PUNCT
azojete-1	155	59	interfaces	interface	NOUN
azojete-1	155	60	et	et	NOUN
azojete-1	155	61	cetera).the	cetera).the	DET
azojete-1	155	62	less	less	ADV
azojete-1	155	63	critical	critical	ADJ
azojete-1	155	64	benign	benign	ADJ
azojete-1	155	65	regions	region	NOUN
azojete-1	155	66	of	of	ADP
azojete-1	155	67	the	the	DET
azojete-1	155	68	heterogeneous	heterogeneous	ADJ
azojete-1	155	69	materials	material	NOUN
azojete-1	155	70	,	,	PUNCT
azojete-1	155	71	were	be	AUX
azojete-1	155	72	modelled	model	VERB
azojete-1	155	73	using	use	VERB
azojete-1	155	74	coupled	couple	VERB
azojete-1	155	75	finite	finite	ADJ
azojete-1	155	76	element	element	NOUN
azojete-1	155	77	method	method	NOUN
azojete-1	155	78	with	with	ADP
azojete-1	155	79	asymptotic	asymptotic	ADJ
azojete-1	155	80	homogenization	homogenization	NOUN
azojete-1	155	81	technique	technique	NOUN
azojete-1	155	82	.	.	PUNCT
azojete-1	156	1	in	in	ADP
azojete-1	156	2	summary	summary	NOUN
azojete-1	156	3	,	,	PUNCT
azojete-1	156	4	numerical	numerical	ADJ
azojete-1	156	5	homogenization	homogenization	NOUN
azojete-1	156	6	is	be	AUX
azojete-1	156	7	used	use	VERB
azojete-1	156	8	in	in	ADP
azojete-1	156	9	the	the	DET
azojete-1	156	10	field	field	NOUN
azojete-1	156	11	having	have	VERB
azojete-1	156	12	benign	benign	ADJ
azojete-1	156	13	deformations	deformation	NOUN
azojete-1	156	14	while	while	SCONJ
azojete-1	156	15	concurrent	concurrent	ADJ
azojete-1	156	16	method	method	NOUN
azojete-1	156	17	is	be	AUX
azojete-1	156	18	used	use	VERB
azojete-1	156	19	in	in	ADP
azojete-1	156	20	the	the	DET
azojete-1	156	21	critical	critical	ADJ
azojete-1	156	22	regions	region	NOUN
azojete-1	156	23	of	of	ADP
azojete-1	156	24	high	high	ADJ
azojete-1	156	25	stress	stress	NOUN
azojete-1	156	26	and	and	CCONJ
azojete-1	156	27	strain	strain	NOUN
azojete-1	156	28	gradients	gradient	NOUN
azojete-1	156	29	where	where	SCONJ
azojete-1	156	30	there	there	PRON
azojete-1	156	31	is	be	VERB
azojete-1	156	32	a	a	DET
azojete-1	156	33	substantial	substantial	ADJ
azojete-1	156	34	variation	variation	NOUN
azojete-1	156	35	in	in	ADP
azojete-1	156	36	the	the	DET
azojete-1	156	37	macroscopic	macroscopic	ADJ
azojete-1	156	38	field	field	NOUN
azojete-1	156	39	as	as	SCONJ
azojete-1	156	40	shown	show	VERB
azojete-1	156	41	in	in	ADP
azojete-1	156	42	figure	figure	NOUN
azojete-1	156	43	9	9	NUM
azojete-1	156	44	(	(	PUNCT
azojete-1	156	45	nguyen	nguyen	NOUN
azojete-1	156	46	et	et	PROPN
azojete-1	156	47	al	al	PROPN
azojete-1	156	48	.	.	PROPN
azojete-1	156	49	,	,	PUNCT
azojete-1	156	50	2012	2012	NUM
azojete-1	156	51	)	)	PUNCT
azojete-1	156	52	.	.	PUNCT
azojete-1	157	1	the	the	DET
azojete-1	157	2	grading	grade	VERB
azojete-1	157	3	arrangement	arrangement	NOUN
azojete-1	157	4	of	of	ADP
azojete-1	157	5	the	the	DET
azojete-1	157	6	displacement	displacement	ADJ
azojete-1	157	7	field	field	NOUN
azojete-1	157	8	(	(	PUNCT
azojete-1	157	9	u	u	NOUN
azojete-1	157	10	)	)	PUNCT
azojete-1	157	11	in	in	ADP
azojete-1	157	12	figure	figure	NOUN
azojete-1	157	13	9	9	NUM
azojete-1	157	14	is	be	AUX
azojete-1	157	15	of	of	ADP
azojete-1	157	16	a	a	DET
azojete-1	157	17	hierarchical	hierarchical	ADJ
azojete-1	157	18	nature	nature	NOUN
azojete-1	157	19	as	as	SCONJ
azojete-1	157	20	the	the	DET
azojete-1	157	21	displacement	displacement	ADJ
azojete-1	157	22	field	field	NOUN
azojete-1	157	23	has	have	AUX
azojete-1	157	24	been	be	AUX
azojete-1	157	25	separated	separate	VERB
azojete-1	157	26	into	into	ADP
azojete-1	157	27	global	global	ADJ
azojete-1	157	28	and	and	CCONJ
azojete-1	157	29	local	local	ADJ
azojete-1	157	30	regions	region	NOUN
azojete-1	157	31	respectively	respectively	ADV
azojete-1	157	32	that	that	ADV
azojete-1	157	33	is	be	AUX
azojete-1	157	34	(	(	PUNCT
azojete-1	157	35	30	30	NUM
azojete-1	157	36	)	)	PUNCT
azojete-1	157	37	(	(	PUNCT
azojete-1	157	38	31	31	NUM
azojete-1	157	39	)	)	PUNCT
azojete-1	157	40	ul	ul	PROPN
azojete-1	157	41	�	�	PROPN
azojete-1	157	42	displacement	displacement	ADJ
azojete-1	157	43	field	field	NOUN
azojete-1	157	44	in	in	ADP
azojete-1	157	45	the	the	DET
azojete-1	157	46	local	local	ADJ
azojete-1	157	47	mesh	mesh	NOUN
azojete-1	157	48	with	with	ADP
azojete-1	157	49	respect	respect	NOUN
azojete-1	157	50	to	to	ADP
azojete-1	157	51	the	the	DET
azojete-1	157	52	global	global	ADJ
azojete-1	157	53	mesh	mesh	PROPN
azojete-1	157	54	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	157	55	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	157	56	arid	arid	NOUN
azojete-1	157	57	zone	zone	NOUN
azojete-1	157	58	journal	journal	NOUN
azojete-1	157	59	of	of	ADP
azojete-1	157	60	engineering	engineering	NOUN
azojete-1	157	61	,	,	PUNCT
azojete-1	157	62	technology	technology	NOUN
azojete-1	157	63	and	and	CCONJ
azojete-1	157	64	environment	environment	NOUN
azojete-1	157	65	,	,	PUNCT
azojete-1	157	66	september	september	PROPN
azojete-1	157	67	,	,	PUNCT
azojete-1	157	68	2019	2019	NUM
azojete-1	157	69	;	;	PUNCT
azojete-1	158	1	vol	vol	NOUN
azojete-1	158	2	.	.	PUNCT
azojete-1	159	1	15(3):488	15(3):488	NUM
azojete-1	159	2	-	-	PUNCT
azojete-1	159	3	509	509	NUM
azojete-1	159	4	.	.	PUNCT
azojete-1	160	1	issn	issn	PROPN
azojete-1	160	2	1596	1596	NUM
azojete-1	160	3	-	-	SYM
azojete-1	160	4	2490	2490	NUM
azojete-1	160	5	;	;	PUNCT
azojete-1	160	6	e	e	X
azojete-1	160	7	-	-	NOUN
azojete-1	160	8	issn	issn	VERB
azojete-1	160	9	2545	2545	NUM
azojete-1	160	10	-	-	SYM
azojete-1	160	11	5818	5818	NUM
azojete-1	160	12	;	;	PUNCT
azojete-1	160	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	160	14	corresponding	correspond	VERB
azojete-1	160	15	author	author	NOUN
azojete-1	160	16	’s	’s	PART
azojete-1	160	17	e	e	NOUN
azojete-1	160	18	-	-	NOUN
azojete-1	160	19	mail	mail	NOUN
azojete-1	160	20	address	address	NOUN
azojete-1	160	21	:	:	PUNCT
azojete-1	160	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	160	23	499	499	NUM
azojete-1	160	24	.	.	PUNCT
azojete-1	161	1	figure	figure	VERB
azojete-1	161	2	9	9	NUM
azojete-1	161	3	:	:	PUNCT
azojete-1	161	4	schematic	schematic	ADJ
azojete-1	161	5	representation	representation	NOUN
azojete-1	161	6	of	of	ADP
azojete-1	161	7	the	the	DET
azojete-1	161	8	mesh	mesh	NOUN
azojete-1	161	9	superposition	superposition	NOUN
azojete-1	161	10	method	method	NOUN
azojete-1	161	11	from	from	ADP
azojete-1	161	12	llorca	llorca	PROPN
azojete-1	161	13	et	et	PROPN
azojete-1	161	14	al	al	PROPN
azojete-1	161	15	.	.	PUNCT
azojete-1	162	1	(	(	PUNCT
azojete-1	162	2	2007	2007	NUM
azojete-1	162	3	)	)	PUNCT
azojete-1	162	4	.	.	PUNCT
azojete-1	163	1	this	this	DET
azojete-1	163	2	hierarchical	hierarchical	ADJ
azojete-1	163	3	nature	nature	NOUN
azojete-1	163	4	of	of	ADP
azojete-1	163	5	the	the	DET
azojete-1	163	6	displacement	displacement	ADJ
azojete-1	163	7	field	field	NOUN
azojete-1	163	8	facilitates	facilitate	VERB
azojete-1	163	9	the	the	DET
azojete-1	163	10	modelling	modelling	NOUN
azojete-1	163	11	of	of	ADP
azojete-1	163	12	the	the	DET
azojete-1	163	13	exact	exact	ADJ
azojete-1	163	14	behaviour	behaviour	NOUN
azojete-1	163	15	of	of	ADP
azojete-1	163	16	the	the	DET
azojete-1	163	17	heterogeneous	heterogeneous	ADJ
azojete-1	163	18	material	material	NOUN
azojete-1	163	19	microstructure	microstructure	NOUN
azojete-1	163	20	in	in	ADP
azojete-1	163	21	areas	area	NOUN
azojete-1	163	22	of	of	ADP
azojete-1	163	23	high	high	ADJ
azojete-1	163	24	strain	strain	NOUN
azojete-1	163	25	gradient	gradient	NOUN
azojete-1	163	26	.	.	PUNCT
azojete-1	164	1	to	to	PART
azojete-1	164	2	ensure	ensure	VERB
azojete-1	164	3	homogenous	homogenous	ADJ
azojete-1	164	4	displacement	displacement	ADJ
azojete-1	164	5	compatibility	compatibility	NOUN
azojete-1	164	6	at	at	ADP
azojete-1	164	7	the	the	DET
azojete-1	164	8	boundary	boundary	ADJ
azojete-1	164	9	points	point	NOUN
azojete-1	164	10	between	between	ADP
azojete-1	164	11	the	the	DET
azojete-1	164	12	local	local	ADJ
azojete-1	164	13	and	and	CCONJ
azojete-1	164	14	global	global	ADJ
azojete-1	164	15	meshes	mesh	NOUN
azojete-1	164	16	,	,	PUNCT
azojete-1	164	17	the	the	DET
azojete-1	164	18	local	local	ADJ
azojete-1	164	19	displacement	displacement	ADJ
azojete-1	164	20	field	field	NOUN
azojete-1	164	21	must	must	AUX
azojete-1	164	22	equal	equal	VERB
azojete-1	164	23	zero	zero	NUM
azojete-1	164	24	(	(	PUNCT
azojete-1	164	25	that	that	PRON
azojete-1	164	26	is	be	AUX
azojete-1	164	27	ul	ul	INTJ
azojete-1	164	28	=	=	SYM
azojete-1	164	29	�	�	PROPN
azojete-1	164	30	at	at	ADP
azojete-1	164	31	∂ω	∂ω	PROPN
azojete-1	164	32	)	)	PUNCT
azojete-1	164	33	while	while	SCONJ
azojete-1	164	34	stiffness	stiffness	ADJ
azojete-1	164	35	matrix	matrix	NOUN
azojete-1	164	36	(	(	PUNCT
azojete-1	164	37	�	�	NOUN
azojete-1	164	38	gl	gl	PROPN
azojete-1	164	39	)	)	PUNCT
azojete-1	164	40	that	that	PRON
azojete-1	164	41	links	link	VERB
azojete-1	164	42	the	the	DET
azojete-1	164	43	displacement	displacement	ADJ
azojete-1	164	44	degrees	degree	NOUN
azojete-1	164	45	of	of	ADP
azojete-1	164	46	freedom	freedom	NOUN
azojete-1	164	47	of	of	ADP
azojete-1	164	48	the	the	DET
azojete-1	164	49	global	global	ADJ
azojete-1	164	50	and	and	CCONJ
azojete-1	164	51	local	local	ADJ
azojete-1	164	52	meshes	mesh	NOUN
azojete-1	164	53	are	be	AUX
azojete-1	164	54	obtained	obtain	VERB
azojete-1	164	55	from	from	ADP
azojete-1	164	56	a	a	DET
azojete-1	164	57	system	system	NOUN
azojete-1	164	58	of	of	ADP
azojete-1	164	59	equilibrium	equilibrium	NOUN
azojete-1	164	60	equations	equation	NOUN
azojete-1	164	61	as	as	SCONJ
azojete-1	164	62	given	give	VERB
azojete-1	164	63	in	in	ADP
azojete-1	164	64	eqn	eqn	NOUN
azojete-1	164	65	.	.	PUNCT
azojete-1	165	1	(	(	PUNCT
azojete-1	165	2	32	32	NUM
azojete-1	165	3	)	)	PUNCT
azojete-1	165	4	kg	kg	PROPN
azojete-1	165	5	kgl	kgl	PROPN
azojete-1	165	6	kgl	kgl	PROPN
azojete-1	165	7	kl	kl	VERB
azojete-1	165	8	ug	ug	ADV
azojete-1	165	9	ul	ul	PROPN
azojete-1	165	10	=	=	SYM
azojete-1	165	11	f	f	PROPN
azojete-1	165	12	�	�	PROPN
azojete-1	165	13	(	(	PUNCT
azojete-1	165	14	32	32	NUM
azojete-1	165	15	)	)	PUNCT
azojete-1	165	16	which	which	PRON
azojete-1	165	17	can	can	AUX
azojete-1	165	18	be	be	AUX
azojete-1	165	19	arrived	arrive	VERB
azojete-1	165	20	at	at	ADP
azojete-1	165	21	by	by	ADP
azojete-1	165	22	deriving	derive	VERB
azojete-1	165	23	the	the	DET
azojete-1	165	24	navier	navi	ADJ
azojete-1	165	25	equations	equation	NOUN
azojete-1	165	26	from	from	ADP
azojete-1	165	27	the	the	DET
azojete-1	165	28	overall	overall	ADJ
azojete-1	165	29	displacement	displacement	ADJ
azojete-1	165	30	field	field	NOUN
azojete-1	165	31	given	give	VERB
azojete-1	165	32	in	in	ADP
azojete-1	165	33	eqn	eqn	NOUN
azojete-1	165	34	.	.	PUNCT
azojete-1	166	1	(	(	PUNCT
azojete-1	166	2	30	30	NUM
azojete-1	166	3	)	)	PUNCT
azojete-1	167	1	where	where	SCONJ
azojete-1	167	2	:	:	PUNCT
azojete-1	167	3	kg	kg	NOUN
azojete-1	167	4	and	and	CCONJ
azojete-1	167	5	kl	kl	INTJ
azojete-1	167	6	–	–	PUNCT
azojete-1	167	7	stiffness	stiffness	NOUN
azojete-1	167	8	matrix	matrix	NOUN
azojete-1	167	9	obtained	obtain	VERB
azojete-1	167	10	from	from	ADP
azojete-1	167	11	local	local	ADJ
azojete-1	167	12	and	and	CCONJ
azojete-1	167	13	global	global	ADJ
azojete-1	167	14	meshes	mesh	NOUN
azojete-1	167	15	kgl	kgl	PROPN
azojete-1	167	16	stiffness	stiffness	ADJ
azojete-1	167	17	matrix	matrix	NOUN
azojete-1	167	18	that	that	PRON
azojete-1	167	19	combines	combine	VERB
azojete-1	167	20	the	the	DET
azojete-1	167	21	displacement	displacement	ADJ
azojete-1	167	22	d.o.f	d.o.f	NOUN
azojete-1	167	23	of	of	ADP
azojete-1	167	24	the	the	DET
azojete-1	167	25	global	global	ADJ
azojete-1	167	26	and	and	CCONJ
azojete-1	167	27	local	local	ADJ
azojete-1	167	28	meshes	mesh	NOUN
azojete-1	167	29	f	f	PROPN
azojete-1	167	30	nodal	nodal	NOUN
azojete-1	167	31	force	force	NOUN
azojete-1	167	32	vector	vector	NOUN
azojete-1	167	33	2.2.4	2.2.4	NUM
azojete-1	167	34	embedded	embed	VERB
azojete-1	167	35	cell	cell	NOUN
azojete-1	167	36	method	method	NOUN
azojete-1	167	37	for	for	ADP
azojete-1	167	38	this	this	DET
azojete-1	167	39	technique	technique	NOUN
azojete-1	167	40	the	the	DET
azojete-1	167	41	model	model	NOUN
azojete-1	167	42	adopted	adopt	VERB
azojete-1	167	43	describes	describe	VERB
azojete-1	167	44	the	the	DET
azojete-1	167	45	characteristics	characteristic	NOUN
azojete-1	167	46	of	of	ADP
azojete-1	167	47	the	the	DET
azojete-1	167	48	microstructure	microstructure	NOUN
azojete-1	167	49	in	in	ADP
azojete-1	167	50	detail	detail	NOUN
azojete-1	167	51	at	at	ADP
azojete-1	167	52	critical	critical	ADJ
azojete-1	167	53	core	core	NOUN
azojete-1	167	54	regions	region	NOUN
azojete-1	167	55	which	which	PRON
azojete-1	167	56	are	be	AUX
azojete-1	167	57	then	then	ADV
azojete-1	167	58	embedded	embed	VERB
azojete-1	167	59	within	within	ADP
azojete-1	167	60	a	a	DET
azojete-1	167	61	homogenous	homogenous	ADJ
azojete-1	167	62	medium	medium	NOUN
azojete-1	167	63	.	.	PUNCT
azojete-1	168	1	the	the	DET
azojete-1	168	2	finite	finite	PROPN
azojete-1	168	3	element	element	NOUN
azojete-1	168	4	mesh	mesh	NOUN
azojete-1	168	5	of	of	ADP
azojete-1	168	6	the	the	DET
azojete-1	168	7	core	core	NOUN
azojete-1	168	8	region	region	NOUN
azojete-1	168	9	is	be	AUX
azojete-1	168	10	much	much	ADV
azojete-1	168	11	finer	fine	ADJ
azojete-1	168	12	than	than	ADP
azojete-1	168	13	the	the	DET
azojete-1	168	14	embedding	embed	VERB
azojete-1	168	15	medium	medium	NOUN
azojete-1	168	16	hence	hence	ADV
azojete-1	168	17	;	;	PUNCT
azojete-1	168	18	it	it	PRON
azojete-1	168	19	is	be	AUX
azojete-1	168	20	capable	capable	ADJ
azojete-1	168	21	of	of	ADP
azojete-1	168	22	capturing	capture	VERB
azojete-1	168	23	fast	fast	ADJ
azojete-1	168	24	variations	variation	NOUN
azojete-1	168	25	in	in	ADP
azojete-1	168	26	field	field	NOUN
azojete-1	168	27	which	which	PRON
azojete-1	168	28	ensues	ensue	VERB
azojete-1	168	29	as	as	ADP
azojete-1	168	30	a	a	DET
azojete-1	168	31	result	result	NOUN
azojete-1	168	32	of	of	ADP
azojete-1	168	33	damage	damage	NOUN
azojete-1	168	34	.	.	PUNCT
azojete-1	169	1	the	the	DET
azojete-1	169	2	mesh	mesh	NOUN
azojete-1	169	3	of	of	ADP
azojete-1	169	4	the	the	DET
azojete-1	169	5	embedding	embed	VERB
azojete-1	169	6	medium	medium	NOUN
azojete-1	169	7	is	be	AUX
azojete-1	169	8	coarse	coarse	ADJ
azojete-1	169	9	,	,	PUNCT
azojete-1	169	10	it	it	PRON
azojete-1	169	11	is	be	AUX
azojete-1	169	12	able	able	ADJ
azojete-1	169	13	to	to	PART
azojete-1	169	14	relay	relay	VERB
azojete-1	169	15	the	the	DET
azojete-1	169	16	macroscopic	macroscopic	ADJ
azojete-1	169	17	far	far	ADJ
azojete-1	169	18	field	field	NOUN
azojete-1	169	19	to	to	ADP
azojete-1	169	20	the	the	DET
azojete-1	169	21	core	core	NOUN
azojete-1	169	22	region	region	NOUN
azojete-1	169	23	by	by	ADP
azojete-1	169	24	implementing	implement	VERB
azojete-1	169	25	displacement	displacement	ADJ
azojete-1	169	26	continuity	continuity	NOUN
azojete-1	169	27	which	which	PRON
azojete-1	169	28	links	link	VERB
azojete-1	169	29	the	the	DET
azojete-1	169	30	core	core	NOUN
azojete-1	169	31	and	and	CCONJ
azojete-1	169	32	the	the	DET
azojete-1	169	33	embedding	embed	VERB
azojete-1	169	34	region	region	NOUN
azojete-1	169	35	(	(	PUNCT
azojete-1	169	36	llorca	llorca	PROPN
azojete-1	169	37	et	et	PROPN
azojete-1	169	38	al	al	PROPN
azojete-1	169	39	.	.	PROPN
azojete-1	169	40	,	,	PUNCT
azojete-1	169	41	2007	2007	NUM
azojete-1	169	42	;	;	PUNCT
azojete-1	169	43	nguyen	nguyen	PROPN
azojete-1	169	44	et	et	PROPN
azojete-1	169	45	al	al	PROPN
azojete-1	169	46	.	.	PROPN
azojete-1	169	47	,	,	PUNCT
azojete-1	169	48	2012	2012	NUM
azojete-1	169	49	)	)	PUNCT
azojete-1	169	50	.	.	PUNCT
azojete-1	170	1	this	this	DET
azojete-1	170	2	technique	technique	NOUN
azojete-1	170	3	has	have	AUX
azojete-1	170	4	proven	prove	VERB
azojete-1	170	5	to	to	PART
azojete-1	170	6	be	be	AUX
azojete-1	170	7	quite	quite	ADV
azojete-1	170	8	invaluable	invaluable	ADJ
azojete-1	170	9	in	in	ADP
azojete-1	170	10	accurately	accurately	ADV
azojete-1	170	11	simulating	simulate	VERB
azojete-1	170	12	the	the	DET
azojete-1	170	13	fracture	fracture	NOUN
azojete-1	170	14	process	process	NOUN
azojete-1	170	15	in	in	ADP
azojete-1	170	16	localized	localized	ADJ
azojete-1	170	17	regions	region	NOUN
azojete-1	170	18	.	.	PUNCT
azojete-1	171	1	the	the	DET
azojete-1	171	2	technique	technique	NOUN
azojete-1	171	3	as	as	SCONJ
azojete-1	171	4	shown	show	VERB
azojete-1	171	5	in	in	ADP
azojete-1	171	6	figure	figure	NOUN
azojete-1	171	7	10	10	NUM
azojete-1	171	8	was	be	AUX
azojete-1	171	9	adopted	adopt	VERB
azojete-1	171	10	gonzalez	gonzalez	PROPN
azojete-1	171	11	and	and	CCONJ
azojete-1	171	12	llorca	llorca	PROPN
azojete-1	171	13	(	(	PUNCT
azojete-1	171	14	2006	2006	NUM
azojete-1	171	15	)	)	PUNCT
azojete-1	171	16	,	,	PUNCT
azojete-1	171	17	in	in	ADP
azojete-1	171	18	simulating	simulate	VERB
azojete-1	171	19	fracture	fracture	NOUN
azojete-1	171	20	behaviour	behaviour	NOUN
azojete-1	171	21	in	in	ADP
azojete-1	171	22	fibre	fibre	NOUN
azojete-1	171	23	reinforced	reinforce	VERB
azojete-1	171	24	composites	composite	NOUN
azojete-1	171	25	.	.	PUNCT
azojete-1	172	1	they	they	PRON
azojete-1	172	2	were	be	AUX
azojete-1	172	3	able	able	ADJ
azojete-1	172	4	to	to	PART
azojete-1	172	5	accurately	accurately	ADV
azojete-1	172	6	show	show	VERB
azojete-1	172	7	from	from	ADP
azojete-1	172	8	the	the	DET
azojete-1	172	9	multiscale	multiscale	ADJ
azojete-1	172	10	computational	computational	ADJ
azojete-1	172	11	model	model	NOUN
azojete-1	172	12	the	the	DET
azojete-1	172	13	main	main	ADJ
azojete-1	172	14	deformation	deformation	NOUN
azojete-1	172	15	and	and	CCONJ
azojete-1	172	16	failure	failure	NOUN
azojete-1	172	17	micromechanism	micromechanism	NOUN
azojete-1	172	18	.	.	PUNCT
azojete-1	173	1	file:///c:/users	file:///c:/user	NOUN
azojete-1	173	2	/	/	SYM
azojete-1	173	3	user	user	NOUN
azojete-1	173	4	/	/	SYM
azojete-1	173	5	downloads	download	NOUN
azojete-1	173	6	/	/	SYM
azojete-1	173	7	azojete143	azojete143	PROPN
azojete-1	173	8	/	/	SYM
azojete-1	173	9	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	173	10	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	173	11	ohunene	ohunene	ADJ
azojete-1	173	12	hafsa	hafsa	PROPN
azojete-1	173	13	aliyu	aliyu	PROPN
azojete-1	173	14	:	:	PUNCT
azojete-1	173	15	analytical	analytical	ADJ
azojete-1	173	16	,	,	PUNCT
azojete-1	173	17	numerical	numerical	ADJ
azojete-1	173	18	and	and	CCONJ
azojete-1	173	19	computational	computational	ADJ
azojete-1	173	20	multiscale	multiscale	NOUN
azojete-1	173	21	modelling	model	VERB
azojete-1	173	22	techniques	technique	NOUN
azojete-1	173	23	for	for	ADP
azojete-1	173	24	heterogenous	heterogenous	ADJ
azojete-1	173	25	materials	material	NOUN
azojete-1	173	26	:	:	PUNCT
azojete-1	173	27	a	a	DET
azojete-1	173	28	review	review	NOUN
azojete-1	173	29	.	.	PUNCT
azojete-1	174	1	azojete	azojete	NOUN
azojete-1	174	2	,	,	PUNCT
azojete-1	174	3	15(3):488	15(3):488	PROPN
azojete-1	174	4	-	-	PUNCT
azojete-1	174	5	509	509	NUM
azojete-1	174	6	.	.	PUNCT
azojete-1	175	1	issn	issn	PROPN
azojete-1	175	2	1596	1596	NUM
azojete-1	175	3	-	-	SYM
azojete-1	175	4	2490	2490	NUM
azojete-1	175	5	;	;	PUNCT
azojete-1	175	6	e	e	X
azojete-1	175	7	-	-	NOUN
azojete-1	175	8	issn	issn	VERB
azojete-1	175	9	2545	2545	NUM
azojete-1	175	10	-	-	SYM
azojete-1	175	11	5818	5818	NUM
azojete-1	175	12	,	,	PUNCT
azojete-1	175	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	175	14	corresponding	correspond	VERB
azojete-1	175	15	author	author	NOUN
azojete-1	175	16	’s	’s	PART
azojete-1	175	17	e	e	NOUN
azojete-1	175	18	-	-	NOUN
azojete-1	175	19	mail	mail	NOUN
azojete-1	175	20	address	address	NOUN
azojete-1	175	21	:	:	PUNCT
azojete-1	175	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	175	23	500	500	NUM
azojete-1	175	24	figure	figure	NOUN
azojete-1	175	25	10	10	NUM
azojete-1	175	26	:	:	PUNCT
azojete-1	175	27	schematic	schematic	ADJ
azojete-1	175	28	representation	representation	NOUN
azojete-1	175	29	of	of	ADP
azojete-1	175	30	the	the	DET
azojete-1	175	31	embedded	embed	VERB
azojete-1	175	32	cell	cell	NOUN
azojete-1	175	33	method	method	NOUN
azojete-1	175	34	from	from	ADP
azojete-1	175	35	llorca	llorca	PROPN
azojete-1	175	36	et	et	PROPN
azojete-1	175	37	al	al	PROPN
azojete-1	175	38	.	.	PUNCT
azojete-1	176	1	(	(	PUNCT
azojete-1	176	2	2007	2007	NUM
azojete-1	176	3	)	)	PUNCT
azojete-1	176	4	.	.	PUNCT
azojete-1	177	1	2.3	2.3	NUM
azojete-1	177	2	modern	modern	ADJ
azojete-1	177	3	multiscale	multiscale	NOUN
azojete-1	177	4	modelling	modelling	NOUN
azojete-1	177	5	as	as	SCONJ
azojete-1	177	6	stated	state	VERB
azojete-1	177	7	earlier	early	ADV
azojete-1	177	8	the	the	DET
azojete-1	177	9	essence	essence	NOUN
azojete-1	177	10	of	of	ADP
azojete-1	177	11	multi	multi	ADJ
azojete-1	177	12	-	-	NOUN
azojete-1	177	13	scale	scale	ADJ
azojete-1	177	14	modelling	modelling	NOUN
azojete-1	177	15	is	be	AUX
azojete-1	177	16	to	to	PART
azojete-1	177	17	take	take	VERB
azojete-1	177	18	advantage	advantage	NOUN
azojete-1	177	19	of	of	ADP
azojete-1	177	20	simplicity	simplicity	NOUN
azojete-1	177	21	and	and	CCONJ
azojete-1	177	22	efficiency	efficiency	NOUN
azojete-1	177	23	that	that	PRON
azojete-1	177	24	exists	exist	VERB
azojete-1	177	25	by	by	ADP
azojete-1	177	26	coupling	couple	VERB
azojete-1	177	27	both	both	CCONJ
azojete-1	177	28	microscopic	microscopic	ADJ
azojete-1	177	29	and	and	CCONJ
azojete-1	177	30	macroscopic	macroscopic	ADJ
azojete-1	177	31	models	model	NOUN
azojete-1	177	32	.	.	PUNCT
azojete-1	178	1	it	it	PRON
azojete-1	178	2	can	can	AUX
azojete-1	178	3	therefore	therefore	ADV
azojete-1	178	4	be	be	AUX
azojete-1	178	5	stated	state	VERB
azojete-1	178	6	that	that	SCONJ
azojete-1	178	7	the	the	DET
azojete-1	178	8	task	task	NOUN
azojete-1	178	9	of	of	ADP
azojete-1	178	10	multiscale	multiscale	ADJ
azojete-1	178	11	modelling	modelling	NOUN
azojete-1	178	12	is	be	AUX
azojete-1	178	13	to	to	PART
azojete-1	178	14	devise	devise	VERB
azojete-1	178	15	a	a	DET
azojete-1	178	16	coupled	couple	VERB
azojete-1	178	17	macroscopic	macroscopic	ADJ
azojete-1	178	18	-	-	PUNCT
azojete-1	178	19	microscopic	microscopic	ADJ
azojete-1	178	20	computational	computational	ADJ
azojete-1	178	21	method	method	NOUN
azojete-1	178	22	which	which	PRON
azojete-1	178	23	is	be	AUX
azojete-1	178	24	not	not	PART
azojete-1	178	25	only	only	ADV
azojete-1	178	26	efficient	efficient	ADJ
azojete-1	178	27	but	but	CCONJ
azojete-1	178	28	also	also	ADV
azojete-1	178	29	capable	capable	ADJ
azojete-1	178	30	of	of	ADP
azojete-1	178	31	giving	give	VERB
azojete-1	178	32	the	the	DET
azojete-1	178	33	required	require	VERB
azojete-1	178	34	information	information	NOUN
azojete-1	178	35	with	with	ADP
azojete-1	178	36	the	the	DET
azojete-1	178	37	desired	desire	VERB
azojete-1	178	38	accuracy	accuracy	NOUN
azojete-1	178	39	as	as	SCONJ
azojete-1	178	40	opposed	oppose	VERB
azojete-1	178	41	to	to	ADP
azojete-1	178	42	solving	solve	VERB
azojete-1	178	43	the	the	DET
azojete-1	178	44	full	full	ADJ
azojete-1	178	45	microscopic	microscopic	ADJ
azojete-1	178	46	model	model	NOUN
azojete-1	178	47	(	(	PUNCT
azojete-1	178	48	weinan	weinan	NOUN
azojete-1	178	49	and	and	CCONJ
azojete-1	178	50	jianfeng	jianfeng	NOUN
azojete-1	178	51	,	,	PUNCT
azojete-1	178	52	2011	2011	NUM
azojete-1	178	53	)	)	PUNCT
azojete-1	178	54	.	.	PUNCT
azojete-1	179	1	while	while	SCONJ
azojete-1	179	2	the	the	DET
azojete-1	179	3	traditional	traditional	ADJ
azojete-1	179	4	multiscale	multiscale	ADJ
azojete-1	179	5	solvers	solver	NOUN
azojete-1	179	6	as	as	SCONJ
azojete-1	179	7	given	give	VERB
azojete-1	179	8	in	in	ADP
azojete-1	179	9	table	table	NOUN
azojete-1	179	10	1	1	NUM
azojete-1	179	11	are	be	AUX
azojete-1	179	12	general	general	ADJ
azojete-1	179	13	purpose	purpose	NOUN
azojete-1	179	14	microslovers	microslover	NOUN
azojete-1	179	15	which	which	PRON
azojete-1	179	16	give	give	VERB
azojete-1	179	17	solution	solution	NOUN
azojete-1	179	18	of	of	ADP
azojete-1	179	19	the	the	DET
azojete-1	179	20	microscale	microscale	ADJ
azojete-1	179	21	model	model	NOUN
azojete-1	179	22	(	(	PUNCT
azojete-1	179	23	that	that	PRON
azojete-1	179	24	is	is	ADV
azojete-1	179	25	it	it	PRON
azojete-1	179	26	focuses	focus	VERB
azojete-1	179	27	on	on	ADP
azojete-1	179	28	just	just	ADV
azojete-1	179	29	on	on	ADP
azojete-1	179	30	scale	scale	NOUN
azojete-1	179	31	)	)	PUNCT
azojete-1	179	32	,	,	PUNCT
azojete-1	179	33	the	the	DET
azojete-1	179	34	modern	modern	ADJ
azojete-1	179	35	multiscale	multiscale	NOUN
azojete-1	179	36	method	method	NOUN
azojete-1	179	37	also	also	ADV
azojete-1	179	38	listed	list	VERB
azojete-1	179	39	in	in	ADP
azojete-1	179	40	table	table	NOUN
azojete-1	179	41	1	1	NUM
azojete-1	179	42	gives	give	VERB
azojete-1	179	43	macroscopic	macroscopic	ADJ
azojete-1	179	44	behaviour	behaviour	NOUN
azojete-1	179	45	from	from	ADP
azojete-1	179	46	data	datum	NOUN
azojete-1	179	47	obtained	obtain	VERB
azojete-1	179	48	from	from	ADP
azojete-1	179	49	the	the	DET
azojete-1	179	50	microstructure	microstructure	NOUN
azojete-1	179	51	either	either	CCONJ
azojete-1	179	52	sequentially	sequentially	ADV
azojete-1	179	53	or	or	CCONJ
azojete-1	179	54	concurrently	concurrently	ADV
azojete-1	179	55	at	at	ADP
azojete-1	179	56	a	a	DET
azojete-1	179	57	cost	cost	NOUN
azojete-1	179	58	much	much	ADV
azojete-1	179	59	less	less	ADJ
azojete-1	179	60	than	than	ADP
azojete-1	179	61	the	the	DET
azojete-1	179	62	general	general	ADJ
azojete-1	179	63	microsolvers	microsolver	NOUN
azojete-1	179	64	such	such	ADJ
azojete-1	179	65	that	that	SCONJ
azojete-1	179	66	:	:	PUNCT
azojete-1	179	67	cost	cost	NOUN
azojete-1	179	68	of	of	ADP
azojete-1	179	69	multiscale	multiscale	ADJ
azojete-1	179	70	method	method	NOUN
azojete-1	179	71	cost	cost	NOUN
azojete-1	179	72	of	of	ADP
azojete-1	179	73	microscale	microscale	NOUN
azojete-1	179	74	slover	slover	ADV
azojete-1	179	75	on	on	ADP
azojete-1	179	76	the	the	DET
azojete-1	179	77	full	full	ADJ
azojete-1	179	78	domain	domain	NOUN
azojete-1	179	79	≪	≪	PUNCT
azojete-1	179	80	1	1	NUM
azojete-1	179	81	(	(	PUNCT
azojete-1	179	82	33	33	NUM
azojete-1	179	83	)	)	PUNCT
azojete-1	179	84	table	table	NOUN
azojete-1	179	85	1	1	NUM
azojete-1	179	86	:	:	PUNCT
azojete-1	179	87	classical	classical	ADJ
azojete-1	179	88	and	and	CCONJ
azojete-1	179	89	modern	modern	ADJ
azojete-1	179	90	multiscale	multiscale	ADJ
azojete-1	179	91	technique	technique	NOUN
azojete-1	179	92	traditional	traditional	ADJ
azojete-1	179	93	multiscale	multiscale	ADJ
azojete-1	179	94	methods	method	NOUN
azojete-1	179	95	new	new	ADJ
azojete-1	179	96	multiscale	multiscale	NOUN
azojete-1	179	97	techniques	technique	NOUN
azojete-1	179	98	multigrid	multigrid	NOUN
azojete-1	179	99	method	method	NOUN
azojete-1	179	100	carparrinello	carparrinello	PROPN
azojete-1	179	101	method	method	NOUN
azojete-1	179	102	domain	domain	NOUN
azojete-1	179	103	decomposition	decomposition	NOUN
azojete-1	179	104	method	method	NOUN
azojete-1	179	105	quasi	quasi	ADJ
azojete-1	179	106	-	-	ADJ
azojete-1	179	107	continuum	continuum	ADJ
azojete-1	179	108	method	method	NOUN
azojete-1	179	109	wavelet	wavelet	NOUN
azojete-1	179	110	-	-	PUNCT
azojete-1	179	111	based	base	VERB
azojete-1	179	112	methods	method	NOUN
azojete-1	179	113	optimal	optimal	ADJ
azojete-1	179	114	prediction	prediction	NOUN
azojete-1	179	115	adaptive	adaptive	ADJ
azojete-1	179	116	mesh	mesh	NOUN
azojete-1	179	117	refinement	refinement	NOUN
azojete-1	179	118	heterogeneous	heterogeneous	ADJ
azojete-1	179	119	multiscale	multiscale	NOUN
azojete-1	179	120	method	method	NOUN
azojete-1	179	121	fast	fast	ADJ
azojete-1	179	122	multipole	multipole	NOUN
azojete-1	179	123	method	method	NOUN
azojete-1	179	124	gap	gap	NOUN
azojete-1	179	125	-	-	PUNCT
azojete-1	179	126	tooth	tooth	NOUN
azojete-1	179	127	scheme	scheme	NOUN
azojete-1	179	128	conjugate	conjugate	ADJ
azojete-1	179	129	gradient	gradient	NOUN
azojete-1	179	130	method	method	NOUN
azojete-1	179	131	adaptive	adaptive	ADJ
azojete-1	179	132	mode	mode	NOUN
azojete-1	179	133	refinement	refinement	NOUN
azojete-1	179	134	adapted	adapt	VERB
azojete-1	179	135	from	from	ADP
azojete-1	179	136	weinan	weinan	PROPN
azojete-1	179	137	et	et	PROPN
azojete-1	179	138	al	al	PROPN
azojete-1	179	139	.	.	PUNCT
azojete-1	180	1	(	(	PUNCT
azojete-1	180	2	2007	2007	NUM
azojete-1	180	3	)	)	PUNCT
azojete-1	180	4	.	.	PUNCT
azojete-1	181	1	the	the	DET
azojete-1	181	2	objective	objective	NOUN
azojete-1	181	3	of	of	ADP
azojete-1	181	4	multiscale	multiscale	ADJ
azojete-1	181	5	modelling	modelling	NOUN
azojete-1	181	6	,	,	PUNCT
azojete-1	181	7	is	be	AUX
azojete-1	181	8	striking	strike	VERB
azojete-1	181	9	a	a	DET
azojete-1	181	10	balance	balance	NOUN
azojete-1	181	11	between	between	ADP
azojete-1	181	12	accuracy	accuracy	NOUN
azojete-1	181	13	and	and	CCONJ
azojete-1	181	14	feasibility	feasibility	NOUN
azojete-1	181	15	hence	hence	ADV
azojete-1	181	16	,	,	PUNCT
azojete-1	181	17	the	the	DET
azojete-1	181	18	focus	focus	NOUN
azojete-1	181	19	here	here	ADV
azojete-1	181	20	will	will	AUX
azojete-1	181	21	be	be	AUX
azojete-1	181	22	on	on	ADP
azojete-1	181	23	the	the	DET
azojete-1	181	24	heterogeneous	heterogeneous	ADJ
azojete-1	181	25	multiscale	multiscale	NOUN
azojete-1	181	26	method	method	NOUN
azojete-1	181	27	(	(	PUNCT
azojete-1	181	28	hmm	hmm	INTJ
azojete-1	181	29	)	)	PUNCT
azojete-1	181	30	with	with	ADP
azojete-1	181	31	a	a	DET
azojete-1	181	32	close	close	ADJ
azojete-1	181	33	methodology	methodology	NOUN
azojete-1	181	34	to	to	ADP
azojete-1	181	35	the	the	DET
azojete-1	181	36	computational	computational	ADJ
azojete-1	181	37	homogenization	homogenization	NOUN
azojete-1	181	38	method	method	NOUN
azojete-1	181	39	used	use	VERB
azojete-1	181	40	in	in	ADP
azojete-1	181	41	computational	computational	ADJ
azojete-1	181	42	mechanics	mechanic	NOUN
azojete-1	181	43	(	(	PUNCT
azojete-1	181	44	matous	matous	PROPN
azojete-1	181	45	et	et	PROPN
azojete-1	181	46	al	al	PROPN
azojete-1	181	47	.	.	PROPN
azojete-1	181	48	,	,	PUNCT
azojete-1	181	49	2017	2017	NUM
azojete-1	181	50	)	)	PUNCT
azojete-1	181	51	.	.	PUNCT
azojete-1	182	1	the	the	DET
azojete-1	182	2	idea	idea	NOUN
azojete-1	182	3	behind	behind	ADP
azojete-1	182	4	this	this	DET
azojete-1	182	5	technique	technique	NOUN
azojete-1	182	6	is	be	AUX
azojete-1	182	7	to	to	PART
azojete-1	182	8	work	work	VERB
azojete-1	182	9	out	out	ADP
azojete-1	182	10	the	the	DET
azojete-1	182	11	incomplete	incomplete	ADJ
azojete-1	182	12	macroscopic	macroscopic	ADJ
azojete-1	182	13	model	model	NOUN
azojete-1	182	14	by	by	ADP
azojete-1	182	15	obtaining	obtain	VERB
azojete-1	182	16	the	the	DET
azojete-1	182	17	required	require	VERB
azojete-1	182	18	data	datum	NOUN
azojete-1	182	19	from	from	ADP
azojete-1	182	20	the	the	DET
azojete-1	182	21	microstructural	microstructural	ADJ
azojete-1	182	22	model	model	NOUN
azojete-1	182	23	.	.	PUNCT
azojete-1	183	1	there	there	PRON
azojete-1	183	2	are	be	VERB
azojete-1	183	3	two	two	NUM
azojete-1	183	4	major	major	ADJ
azojete-1	183	5	components	component	NOUN
azojete-1	183	6	to	to	ADP
azojete-1	183	7	the	the	DET
azojete-1	183	8	heterogenous	heterogenous	ADJ
azojete-1	183	9	multiscale	multiscale	ADJ
azojete-1	183	10	methodology	methodology	NOUN
azojete-1	183	11	namely	namely	ADV
azojete-1	183	12	:	:	PUNCT
azojete-1	183	13	the	the	DET
azojete-1	183	14	overall	overall	ADJ
azojete-1	183	15	macroscopic	macroscopic	ADJ
azojete-1	183	16	scheme	scheme	NOUN
azojete-1	183	17	for	for	ADP
azojete-1	183	18	approximating	approximate	VERB
azojete-1	183	19	the	the	DET
azojete-1	183	20	macroscopic	macroscopic	ADJ
azojete-1	183	21	variable	variable	ADJ
azojete-1	183	22	u	u	PROPN
azojete-1	183	23	u	u	NOUN
azojete-1	183	24	=	=	PROPN
azojete-1	183	25	qu	qu	X
azojete-1	183	26	(	(	PUNCT
azojete-1	183	27	34	34	NUM
azojete-1	183	28	)	)	PUNCT
azojete-1	183	29	also	also	ADV
azojete-1	183	30	known	know	VERB
azojete-1	183	31	as	as	ADP
azojete-1	183	32	the	the	DET
azojete-1	183	33	compression	compression	NOUN
azojete-1	183	34	operator	operator	NOUN
azojete-1	183	35	,	,	PUNCT
azojete-1	183	36	where	where	SCONJ
azojete-1	183	37	:	:	PUNCT
azojete-1	183	38	http://www.azojete.com.ng	http://www.azojete.com.ng	ADJ
azojete-1	183	39	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	183	40	arid	arid	NOUN
azojete-1	183	41	zone	zone	NOUN
azojete-1	183	42	journal	journal	NOUN
azojete-1	183	43	of	of	ADP
azojete-1	183	44	engineering	engineering	NOUN
azojete-1	183	45	,	,	PUNCT
azojete-1	183	46	technology	technology	NOUN
azojete-1	183	47	and	and	CCONJ
azojete-1	183	48	environment	environment	NOUN
azojete-1	183	49	,	,	PUNCT
azojete-1	183	50	september	september	PROPN
azojete-1	183	51	,	,	PUNCT
azojete-1	183	52	2019	2019	NUM
azojete-1	183	53	;	;	PUNCT
azojete-1	183	54	vol	vol	NOUN
azojete-1	183	55	.	.	PUNCT
azojete-1	184	1	15(3):488	15(3):488	NUM
azojete-1	184	2	-	-	PUNCT
azojete-1	184	3	509	509	NUM
azojete-1	184	4	.	.	PUNCT
azojete-1	185	1	issn	issn	PROPN
azojete-1	185	2	1596	1596	NUM
azojete-1	185	3	-	-	SYM
azojete-1	185	4	2490	2490	NUM
azojete-1	185	5	;	;	PUNCT
azojete-1	185	6	e	e	X
azojete-1	185	7	-	-	NOUN
azojete-1	185	8	issn	issn	VERB
azojete-1	185	9	2545	2545	NUM
azojete-1	185	10	-	-	SYM
azojete-1	185	11	5818	5818	NUM
azojete-1	185	12	;	;	PUNCT
azojete-1	185	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	185	14	corresponding	correspond	VERB
azojete-1	185	15	author	author	NOUN
azojete-1	185	16	’s	’s	PART
azojete-1	185	17	e	e	NOUN
azojete-1	185	18	-	-	NOUN
azojete-1	185	19	mail	mail	NOUN
azojete-1	185	20	address	address	NOUN
azojete-1	185	21	:	:	PUNCT
azojete-1	185	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	185	23	501	501	NUM
azojete-1	185	24	uis	ui	NOUN
azojete-1	185	25	the	the	DET
azojete-1	185	26	local	local	ADJ
azojete-1	185	27	averages	average	NOUN
azojete-1	185	28	of	of	ADP
azojete-1	185	29	the	the	DET
azojete-1	185	30	microscopic	microscopic	ADJ
azojete-1	185	31	variables	variable	NOUN
azojete-1	185	32	(	(	PUNCT
azojete-1	185	33	�	�	PROPN
azojete-1	185	34	)	)	PUNCT
azojete-1	185	35	over	over	ADP
azojete-1	185	36	the	the	DET
azojete-1	185	37	macro	macro	ADJ
azojete-1	185	38	cells	cell	NOUN
azojete-1	185	39	the	the	DET
azojete-1	185	40	scheme	scheme	NOUN
azojete-1	185	41	for	for	ADP
azojete-1	185	42	evaluating	evaluate	VERB
azojete-1	185	43	the	the	DET
azojete-1	185	44	missing	miss	VERB
azojete-1	185	45	macroscopic	macroscopic	ADJ
azojete-1	185	46	data	datum	NOUN
azojete-1	185	47	from	from	ADP
azojete-1	185	48	the	the	DET
azojete-1	185	49	microscopic	microscopic	ADJ
azojete-1	185	50	model	model	NOUN
azojete-1	185	51	u	u	NOUN
azojete-1	185	52	the	the	DET
azojete-1	185	53	overall	overall	ADJ
azojete-1	185	54	macroscopic	macroscopic	ADJ
azojete-1	185	55	scheme	scheme	NOUN
azojete-1	185	56	for	for	ADP
azojete-1	185	57	approximating	approximate	VERB
azojete-1	185	58	the	the	DET
azojete-1	185	59	missing	miss	VERB
azojete-1	185	60	macroscopic	macroscopic	ADJ
azojete-1	185	61	data	datum	NOUN
azojete-1	185	62	(	(	PUNCT
azojete-1	185	63	for	for	ADP
azojete-1	185	64	example	example	NOUN
azojete-1	185	65	the	the	DET
azojete-1	185	66	stiffness	stiffness	ADJ
azojete-1	185	67	matrix	matrix	NOUN
azojete-1	185	68	,	,	PUNCT
azojete-1	185	69	transition	transition	NOUN
azojete-1	185	70	rates	rate	NOUN
azojete-1	185	71	and	and	CCONJ
azojete-1	185	72	so	so	ADV
azojete-1	185	73	on	on	ADV
azojete-1	185	74	)	)	PUNCT
azojete-1	185	75	from	from	ADP
azojete-1	185	76	the	the	DET
azojete-1	185	77	microscopic	microscopic	ADJ
azojete-1	185	78	model	model	NOUN
azojete-1	185	79	is	be	AUX
azojete-1	185	80	achieved	achieve	VERB
azojete-1	185	81	by	by	ADP
azojete-1	185	82	solving	solve	VERB
azojete-1	185	83	the	the	DET
azojete-1	185	84	micro	micro	ADJ
azojete-1	185	85	models	model	NOUN
azojete-1	185	86	locally	locally	ADV
azojete-1	185	87	subject	subject	ADJ
azojete-1	185	88	to	to	ADP
azojete-1	185	89	the	the	DET
azojete-1	185	90	following	follow	VERB
azojete-1	185	91	constraint	constraint	NOUN
azojete-1	185	92	:	:	PUNCT
azojete-1	185	93	q	q	X
azojete-1	185	94	�	�	SYM
azojete-1	185	95	u	u	NOUN
azojete-1	185	96	=	=	PROPN
azojete-1	185	97	u	u	PROPN
azojete-1	185	98	(	(	PUNCT
azojete-1	185	99	35	35	NUM
azojete-1	185	100	)	)	PUNCT
azojete-1	185	101	where	where	SCONJ
azojete-1	185	102	:	:	PUNCT
azojete-1	185	103	-is	-is	ADP
azojete-1	185	104	an	an	DET
azojete-1	185	105	estimate	estimate	NOUN
azojete-1	185	106	of	of	ADP
azojete-1	185	107	and	and	CCONJ
azojete-1	185	108	in	in	ADP
azojete-1	185	109	the	the	DET
azojete-1	185	110	present	present	ADJ
azojete-1	185	111	state	state	NOUN
azojete-1	185	112	of	of	ADP
azojete-1	185	113	the	the	DET
azojete-1	185	114	macrostructure	macrostructure	NOUN
azojete-1	185	115	the	the	DET
azojete-1	185	116	above	above	ADJ
azojete-1	185	117	two	two	NUM
azojete-1	185	118	processes	process	NOUN
azojete-1	185	119	(	(	PUNCT
azojete-1	185	120	1	1	NUM
azojete-1	185	121	and	and	CCONJ
azojete-1	185	122	2	2	NUM
azojete-1	185	123	)	)	PUNCT
azojete-1	185	124	as	as	ADV
azojete-1	185	125	well	well	ADV
azojete-1	185	126	as	as	ADP
azojete-1	185	127	the	the	DET
azojete-1	185	128	macro	macro	ADJ
azojete-1	185	129	state	state	NOUN
azojete-1	185	130	variable	variable	ADJ
azojete-1	185	131	u	u	NOUN
azojete-1	185	132	are	be	AUX
azojete-1	185	133	linked	link	VERB
azojete-1	185	134	to	to	ADP
azojete-1	185	135	each	each	DET
azojete-1	185	136	other	other	ADJ
azojete-1	185	137	by	by	ADP
azojete-1	185	138	the	the	DET
azojete-1	185	139	compression	compression	NOUN
azojete-1	185	140	(	(	PUNCT
azojete-1	185	141	u	u	NOUN
azojete-1	185	142	)	)	PUNCT
azojete-1	185	143	as	as	ADV
azojete-1	185	144	well	well	ADV
azojete-1	185	145	as	as	ADP
azojete-1	185	146	the	the	DET
azojete-1	185	147	reconstruction	reconstruction	NOUN
azojete-1	185	148	(	(	PUNCT
azojete-1	185	149	r	r	NOUN
azojete-1	185	150	)	)	PUNCT
azojete-1	185	151	operators	operator	NOUN
azojete-1	185	152	given	give	VERB
azojete-1	185	153	in	in	ADP
azojete-1	185	154	eqns	eqns	PROPN
azojete-1	185	155	.	.	PUNCT
azojete-1	186	1	(	(	PUNCT
azojete-1	186	2	36	36	NUM
azojete-1	186	3	)	)	PUNCT
azojete-1	186	4	and	and	CCONJ
azojete-1	186	5	(	(	PUNCT
azojete-1	186	6	37	37	NUM
azojete-1	186	7	)	)	PUNCT
azojete-1	186	8	in	in	ADP
azojete-1	186	9	that	that	DET
azojete-1	186	10	order	order	NOUN
azojete-1	186	11	;	;	PUNCT
azojete-1	186	12	having	have	VERB
azojete-1	186	13	the	the	DET
azojete-1	186	14	property	property	NOUN
azojete-1	186	15	known	know	VERB
azojete-1	186	16	as	as	ADP
azojete-1	186	17	the	the	DET
azojete-1	186	18	gradient	gradient	NOUN
azojete-1	186	19	operator	operator	NOUN
azojete-1	186	20	given	give	VERB
azojete-1	186	21	in	in	ADP
azojete-1	186	22	equation	equation	NOUN
azojete-1	186	23	(	(	PUNCT
azojete-1	186	24	38	38	NUM
azojete-1	186	25	)	)	PUNCT
azojete-1	186	26	.	.	PUNCT
azojete-1	187	1	u	u	NOUN
azojete-1	187	2	=	=	PROPN
azojete-1	187	3	qu	qu	PROPN
azojete-1	187	4	(	(	PUNCT
azojete-1	187	5	36	36	NUM
azojete-1	187	6	)	)	PUNCT
azojete-1	187	7	ru	ru	NOUN
azojete-1	187	8	=	=	SYM
azojete-1	187	9	u	u	PROPN
azojete-1	187	10	(	(	PUNCT
azojete-1	187	11	37	37	NUM
azojete-1	187	12	)	)	PUNCT
azojete-1	187	13	in	in	ADP
azojete-1	187	14	summary	summary	NOUN
azojete-1	187	15	,	,	PUNCT
azojete-1	187	16	the	the	DET
azojete-1	187	17	heterogeneous	heterogeneous	ADJ
azojete-1	187	18	multiscale	multiscale	ADJ
azojete-1	187	19	methodology	methodology	NOUN
azojete-1	187	20	,	,	PUNCT
azojete-1	187	21	essentially	essentially	ADV
azojete-1	187	22	entails	entail	VERB
azojete-1	187	23	reconstructing	reconstruct	VERB
azojete-1	187	24	the	the	DET
azojete-1	187	25	micro	micro	ADJ
azojete-1	187	26	state	state	NOUN
azojete-1	187	27	from	from	ADP
azojete-1	187	28	u	u	NOUN
azojete-1	187	29	then	then	ADV
azojete-1	187	30	evolving	evolve	VERB
azojete-1	187	31	the	the	DET
azojete-1	187	32	micro	micro	ADJ
azojete-1	187	33	state	state	NOUN
azojete-1	187	34	using	use	VERB
azojete-1	187	35	the	the	DET
azojete-1	187	36	microscopic	microscopic	ADJ
azojete-1	187	37	model	model	NOUN
azojete-1	187	38	subject	subject	ADJ
azojete-1	187	39	to	to	ADP
azojete-1	187	40	certain	certain	ADJ
azojete-1	187	41	constraint	constraint	NOUN
azojete-1	187	42	(	(	PUNCT
azojete-1	187	43	)	)	PUNCT
azojete-1	187	44	to	to	PART
azojete-1	187	45	evaluate	evaluate	VERB
azojete-1	187	46	the	the	DET
azojete-1	187	47	missing	miss	VERB
azojete-1	187	48	data	datum	NOUN
azojete-1	187	49	from	from	ADP
azojete-1	187	50	u.	u.	NOUN
azojete-1	187	51	this	this	DET
azojete-1	187	52	way	way	NOUN
azojete-1	187	53	the	the	DET
azojete-1	187	54	coupling	coupling	NOUN
azojete-1	187	55	between	between	ADP
azojete-1	187	56	both	both	CCONJ
azojete-1	187	57	the	the	DET
azojete-1	187	58	macro	macro	ADJ
azojete-1	187	59	and	and	CCONJ
azojete-1	187	60	micro	micro	NOUN
azojete-1	187	61	models	model	NOUN
azojete-1	187	62	is	be	AUX
azojete-1	187	63	done	do	VERB
azojete-1	187	64	in	in	ADP
azojete-1	187	65	such	such	DET
azojete-1	187	66	a	a	DET
azojete-1	187	67	way	way	NOUN
azojete-1	187	68	that	that	PRON
azojete-1	187	69	the	the	DET
azojete-1	187	70	constraints	constraint	NOUN
azojete-1	187	71	for	for	ADP
azojete-1	187	72	setting	set	VERB
azojete-1	187	73	up	up	ADP
azojete-1	187	74	the	the	DET
azojete-1	187	75	micro	micro	ADJ
azojete-1	187	76	models	model	NOUN
azojete-1	187	77	are	be	AUX
azojete-1	187	78	obtained	obtain	VERB
azojete-1	187	79	from	from	ADP
azojete-1	187	80	the	the	DET
azojete-1	187	81	macro	macro	ADJ
azojete-1	187	82	models	model	NOUN
azojete-1	187	83	while	while	SCONJ
azojete-1	187	84	the	the	DET
azojete-1	187	85	micro	micro	ADJ
azojete-1	187	86	model	model	NOUN
azojete-1	187	87	in	in	ADP
azojete-1	187	88	turn	turn	NOUN
azojete-1	187	89	,	,	PUNCT
azojete-1	187	90	provides	provide	VERB
azojete-1	187	91	the	the	DET
azojete-1	187	92	much	much	ADV
azojete-1	187	93	needed	need	VERB
azojete-1	187	94	constitutive	constitutive	ADJ
azojete-1	187	95	data	datum	NOUN
azojete-1	187	96	for	for	ADP
azojete-1	187	97	the	the	DET
azojete-1	187	98	macro	macro	ADJ
azojete-1	187	99	model	model	NOUN
azojete-1	187	100	(	(	PUNCT
azojete-1	187	101	weinan	weinan	NOUN
azojete-1	187	102	and	and	CCONJ
azojete-1	187	103	jianfeng	jianfeng	NOUN
azojete-1	187	104	,	,	PUNCT
azojete-1	187	105	2011;weinan	2011;weinan	NOUN
azojete-1	187	106	et	et	NOUN
azojete-1	187	107	al	al	PROPN
azojete-1	187	108	.	.	PROPN
azojete-1	187	109	,	,	PUNCT
azojete-1	187	110	2007	2007	NUM
azojete-1	187	111	;	;	PUNCT
azojete-1	187	112	weinan	weinan	PROPN
azojete-1	187	113	et	et	PROPN
azojete-1	187	114	al	al	PROPN
azojete-1	187	115	.	.	PROPN
azojete-1	187	116	,	,	PUNCT
azojete-1	187	117	2003	2003	NUM
azojete-1	187	118	)	)	PUNCT
azojete-1	187	119	.	.	PUNCT
azojete-1	188	1	2.3.1	2.3.1	NUM
azojete-1	188	2	computational	computational	ADJ
azojete-1	188	3	homogenization	homogenization	NOUN
azojete-1	188	4	the	the	DET
azojete-1	188	5	last	last	ADJ
azojete-1	188	6	few	few	ADJ
azojete-1	188	7	decades	decade	NOUN
azojete-1	188	8	have	have	AUX
azojete-1	188	9	seen	see	VERB
azojete-1	188	10	the	the	DET
azojete-1	188	11	development	development	NOUN
azojete-1	188	12	of	of	ADP
azojete-1	188	13	an	an	DET
azojete-1	188	14	alternative	alternative	ADJ
azojete-1	188	15	multiscale	multiscale	ADJ
azojete-1	188	16	method	method	NOUN
azojete-1	188	17	for	for	ADP
azojete-1	188	18	micromacro	micromacro	PROPN
azojete-1	188	19	coupling	coupling	NOUN
azojete-1	188	20	adopted	adopt	VERB
azojete-1	188	21	in	in	ADP
azojete-1	188	22	the	the	DET
azojete-1	188	23	homogenization	homogenization	NOUN
azojete-1	188	24	of	of	ADP
azojete-1	188	25	complex	complex	ADJ
azojete-1	188	26	heterogeneous	heterogeneous	ADJ
azojete-1	188	27	materials	material	NOUN
azojete-1	188	28	know	know	VERB
azojete-1	188	29	as	as	SCONJ
azojete-1	188	30	the	the	DET
azojete-1	188	31	computational	computational	ADJ
azojete-1	188	32	homogenizational	homogenizational	ADJ
azojete-1	188	33	technique	technique	NOUN
azojete-1	188	34	also	also	ADV
azojete-1	188	35	called	call	VERB
azojete-1	188	36	global	global	ADJ
azojete-1	188	37	-	-	PUNCT
azojete-1	188	38	local	local	ADJ
azojete-1	188	39	analysis	analysis	NOUN
azojete-1	188	40	or	or	CCONJ
azojete-1	188	41	finite	finite	ADJ
azojete-1	188	42	element	element	NOUN
azojete-1	188	43	analysis	analysis	NOUN
azojete-1	188	44	in	in	ADP
azojete-1	188	45	a	a	DET
azojete-1	188	46	more	more	ADV
azojete-1	188	47	particular	particular	ADJ
azojete-1	188	48	form	form	NOUN
azojete-1	188	49	(	(	PUNCT
azojete-1	188	50	kouznetsova	kouznetsova	NOUN
azojete-1	188	51	et	et	PROPN
azojete-1	188	52	al	al	PROPN
azojete-1	188	53	.	.	PROPN
azojete-1	188	54	,	,	PUNCT
azojete-1	188	55	2012	2012	NUM
azojete-1	188	56	)	)	PUNCT
azojete-1	188	57	.	.	PUNCT
azojete-1	189	1	with	with	ADP
azojete-1	189	2	computational	computational	ADJ
azojete-1	189	3	homogenization	homogenization	NOUN
azojete-1	189	4	the	the	DET
azojete-1	189	5	details	detail	NOUN
azojete-1	189	6	of	of	ADP
azojete-1	189	7	the	the	DET
azojete-1	189	8	macroscale	macroscale	NOUN
azojete-1	189	9	models	model	NOUN
azojete-1	189	10	are	be	AUX
azojete-1	189	11	computed	compute	VERB
azojete-1	189	12	on	on	ADP
azojete-1	189	13	-	-	PUNCT
azojete-1	189	14	the	the	DET
azojete-1	189	15	-	-	PUNCT
azojete-1	189	16	fly	fly	NOUN
azojete-1	189	17	from	from	ADP
azojete-1	189	18	the	the	DET
azojete-1	189	19	microscale	microscale	ADJ
azojete-1	189	20	models	model	NOUN
azojete-1	189	21	as	as	SCONJ
azojete-1	189	22	simulations	simulation	NOUN
azojete-1	189	23	are	be	AUX
azojete-1	189	24	ongoing	ongoing	ADJ
azojete-1	189	25	(	(	PUNCT
azojete-1	189	26	weinan	weinan	NOUN
azojete-1	189	27	and	and	CCONJ
azojete-1	189	28	jianfeng	jianfeng	NOUN
azojete-1	189	29	,	,	PUNCT
azojete-1	189	30	2011	2011	NUM
azojete-1	189	31	)	)	PUNCT
azojete-1	189	32	.	.	PUNCT
azojete-1	190	1	this	this	DET
azojete-1	190	2	characteristic	characteristic	ADJ
azojete-1	190	3	nature	nature	NOUN
azojete-1	190	4	of	of	ADP
azojete-1	190	5	the	the	DET
azojete-1	190	6	computational	computational	ADJ
azojete-1	190	7	homogenizational	homogenizational	ADJ
azojete-1	190	8	method	method	NOUN
azojete-1	190	9	makes	make	VERB
azojete-1	190	10	it	it	PRON
azojete-1	190	11	suitable	suitable	ADJ
azojete-1	190	12	in	in	ADP
azojete-1	190	13	obtaining	obtain	VERB
azojete-1	190	14	the	the	DET
azojete-1	190	15	effective	effective	ADJ
azojete-1	190	16	mechanical	mechanical	ADJ
azojete-1	190	17	behaviour	behaviour	NOUN
azojete-1	190	18	of	of	ADP
azojete-1	190	19	materials	material	NOUN
azojete-1	190	20	with	with	ADP
azojete-1	190	21	evolving	evolve	VERB
azojete-1	190	22	microstructural	microstructural	ADJ
azojete-1	190	23	geometries	geometry	NOUN
azojete-1	190	24	,	,	PUNCT
azojete-1	190	25	phase	phase	NOUN
azojete-1	190	26	transformation	transformation	NOUN
azojete-1	190	27	as	as	ADV
azojete-1	190	28	well	well	ADV
azojete-1	190	29	as	as	ADP
azojete-1	190	30	nonlinear	nonlinear	ADJ
azojete-1	190	31	mechanical	mechanical	ADJ
azojete-1	190	32	problems	problem	NOUN
azojete-1	190	33	(	(	PUNCT
azojete-1	190	34	large	large	ADJ
azojete-1	190	35	deformations	deformation	NOUN
azojete-1	190	36	,	,	PUNCT
azojete-1	190	37	initiation	initiation	NOUN
azojete-1	190	38	and	and	CCONJ
azojete-1	190	39	propagation	propagation	NOUN
azojete-1	190	40	of	of	ADP
azojete-1	190	41	cracks	crack	NOUN
azojete-1	190	42	,	,	PUNCT
azojete-1	190	43	dislocation	dislocation	NOUN
azojete-1	190	44	mechanics	mechanic	NOUN
azojete-1	190	45	and	and	CCONJ
azojete-1	190	46	defects	defect	NOUN
azojete-1	190	47	,	,	PUNCT
azojete-1	190	48	creep	creep	NOUN
azojete-1	190	49	and	and	CCONJ
azojete-1	190	50	stress	stress	NOUN
azojete-1	190	51	relaxation	relaxation	NOUN
azojete-1	190	52	)	)	PUNCT
azojete-1	190	53	(	(	PUNCT
azojete-1	190	54	matous	matous	PROPN
azojete-1	190	55	et	et	PROPN
azojete-1	190	56	al	al	PROPN
azojete-1	190	57	.	.	PROPN
azojete-1	190	58	,	,	PUNCT
azojete-1	190	59	2017	2017	NUM
azojete-1	190	60	)	)	PUNCT
azojete-1	190	61	.	.	PUNCT
azojete-1	191	1	in	in	ADP
azojete-1	191	2	this	this	DET
azojete-1	191	3	method	method	NOUN
azojete-1	191	4	,	,	PUNCT
azojete-1	191	5	materials	material	NOUN
azojete-1	191	6	are	be	AUX
azojete-1	191	7	generally	generally	ADV
azojete-1	191	8	examined	examine	VERB
azojete-1	191	9	using	use	VERB
azojete-1	191	10	characteristic	characteristic	ADJ
azojete-1	191	11	volume	volume	NOUN
azojete-1	191	12	(	(	PUNCT
azojete-1	191	13	that	that	PRON
azojete-1	191	14	is	be	AUX
azojete-1	191	15	rv	rv	PROPN
azojete-1	191	16	�	�	NOUN
azojete-1	191	17	◠	◠	VERB
azojete-1	191	18	)	)	PUNCT
azojete-1	191	19	as	as	SCONJ
azojete-1	191	20	shown	show	VERB
azojete-1	191	21	in	in	ADP
azojete-1	191	22	figure	figure	NOUN
azojete-1	191	23	11	11	NUM
azojete-1	191	24	.	.	PUNCT
azojete-1	192	1	figure	figure	VERB
azojete-1	192	2	11	11	NUM
azojete-1	192	3	:	:	PUNCT
azojete-1	192	4	a	a	DET
azojete-1	192	5	two	two	NUM
azojete-1	192	6	dimensional	dimensional	ADJ
azojete-1	192	7	representative	representative	ADJ
azojete-1	192	8	volume	volume	NOUN
azojete-1	192	9	element	element	NOUN
azojete-1	192	10	from	from	ADP
azojete-1	192	11	kouznetsova	kouznetsova	PROPN
azojete-1	192	12	et	et	PROPN
azojete-1	192	13	al	al	PROPN
azojete-1	192	14	.	.	PROPN
azojete-1	192	15	(	(	PUNCT
azojete-1	192	16	2001	2001	NUM
azojete-1	192	17	)	)	PUNCT
azojete-1	192	18	.	.	PUNCT
azojete-1	193	1	file:///c:/users	file:///c:/user	NOUN
azojete-1	193	2	/	/	SYM
azojete-1	193	3	user	user	NOUN
azojete-1	193	4	/	/	SYM
azojete-1	193	5	downloads	download	NOUN
azojete-1	193	6	/	/	SYM
azojete-1	193	7	azojete143	azojete143	PROPN
azojete-1	193	8	/	/	SYM
azojete-1	193	9	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	193	10	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	193	11	ohunene	ohunene	ADJ
azojete-1	193	12	hafsa	hafsa	PROPN
azojete-1	193	13	aliyu	aliyu	PROPN
azojete-1	193	14	:	:	PUNCT
azojete-1	193	15	analytical	analytical	ADJ
azojete-1	193	16	,	,	PUNCT
azojete-1	193	17	numerical	numerical	ADJ
azojete-1	193	18	and	and	CCONJ
azojete-1	193	19	computational	computational	ADJ
azojete-1	193	20	multiscale	multiscale	NOUN
azojete-1	193	21	modelling	model	VERB
azojete-1	193	22	techniques	technique	NOUN
azojete-1	193	23	for	for	ADP
azojete-1	193	24	heterogenous	heterogenous	ADJ
azojete-1	193	25	materials	material	NOUN
azojete-1	193	26	:	:	PUNCT
azojete-1	193	27	a	a	DET
azojete-1	193	28	review	review	NOUN
azojete-1	193	29	.	.	PUNCT
azojete-1	194	1	azojete	azojete	NOUN
azojete-1	194	2	,	,	PUNCT
azojete-1	194	3	15(3):488	15(3):488	PROPN
azojete-1	194	4	-	-	PUNCT
azojete-1	194	5	509	509	NUM
azojete-1	194	6	.	.	PUNCT
azojete-1	195	1	issn	issn	PROPN
azojete-1	195	2	1596	1596	NUM
azojete-1	195	3	-	-	SYM
azojete-1	195	4	2490	2490	NUM
azojete-1	195	5	;	;	PUNCT
azojete-1	195	6	e	e	X
azojete-1	195	7	-	-	NOUN
azojete-1	195	8	issn	issn	VERB
azojete-1	195	9	2545	2545	NUM
azojete-1	195	10	-	-	SYM
azojete-1	195	11	5818	5818	NUM
azojete-1	195	12	,	,	PUNCT
azojete-1	195	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	195	14	corresponding	correspond	VERB
azojete-1	195	15	author	author	NOUN
azojete-1	195	16	’s	’s	PART
azojete-1	195	17	e	e	NOUN
azojete-1	195	18	-	-	NOUN
azojete-1	195	19	mail	mail	NOUN
azojete-1	195	20	address	address	NOUN
azojete-1	195	21	:	:	PUNCT
azojete-1	195	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	195	23	502	502	NUM
azojete-1	195	24	while	while	SCONJ
azojete-1	195	25	the	the	DET
azojete-1	195	26	homogenization	homogenization	NOUN
azojete-1	195	27	process	process	NOUN
azojete-1	195	28	relies	rely	VERB
azojete-1	195	29	on	on	ADP
azojete-1	195	30	the	the	DET
azojete-1	195	31	principles	principle	NOUN
azojete-1	195	32	of	of	ADP
azojete-1	195	33	separation	separation	NOUN
azojete-1	195	34	of	of	ADP
azojete-1	195	35	scales	scale	NOUN
azojete-1	195	36	where	where	SCONJ
azojete-1	195	37	the	the	DET
azojete-1	195	38	molecular	molecular	ADJ
azojete-1	195	39	length	length	NOUN
azojete-1	195	40	scale	scale	NOUN
azojete-1	195	41	is	be	AUX
azojete-1	195	42	smaller	small	ADJ
azojete-1	195	43	than	than	ADP
azojete-1	195	44	microscopic	microscopic	ADJ
azojete-1	195	45	length	length	NOUN
azojete-1	195	46	scale	scale	NOUN
azojete-1	195	47	of	of	ADP
azojete-1	195	48	the	the	DET
azojete-1	195	49	rve	rve	NOUN
azojete-1	195	50	which	which	PRON
azojete-1	195	51	in	in	ADP
azojete-1	195	52	turn	turn	NOUN
azojete-1	195	53	is	be	AUX
azojete-1	195	54	much	much	ADV
azojete-1	195	55	smaller	small	ADJ
azojete-1	195	56	than	than	ADP
azojete-1	195	57	the	the	DET
azojete-1	195	58	typical	typical	ADJ
azojete-1	195	59	size	size	NOUN
azojete-1	195	60	of	of	ADP
azojete-1	195	61	the	the	DET
azojete-1	195	62	macroscopic	macroscopic	ADJ
azojete-1	195	63	sample	sample	NOUN
azojete-1	195	64	that	that	PRON
azojete-1	195	65	is	be	AUX
azojete-1	195	66	as	as	SCONJ
azojete-1	195	67	shown	show	VERB
azojete-1	195	68	in	in	ADP
azojete-1	195	69	figure	figure	NOUN
azojete-1	195	70	12	12	NUM
azojete-1	195	71	.	.	PUNCT
azojete-1	196	1	the	the	DET
azojete-1	196	2	information	information	NOUN
azojete-1	196	3	obtained	obtain	VERB
azojete-1	196	4	from	from	ADP
azojete-1	196	5	this	this	DET
azojete-1	196	6	length	length	NOUN
azojete-1	196	7	scales	scale	NOUN
azojete-1	196	8	are	be	AUX
azojete-1	196	9	volumetrically	volumetrically	ADV
azojete-1	196	10	averaged	average	VERB
azojete-1	196	11	in	in	ADP
azojete-1	196	12	a	a	DET
azojete-1	196	13	hierarchical	hierarchical	ADJ
azojete-1	196	14	order	order	NOUN
azojete-1	196	15	(	(	PUNCT
azojete-1	196	16	that	that	PRON
azojete-1	196	17	is	is	ADV
azojete-1	196	18	)	)	PUNCT
azojete-1	196	19	to	to	PART
azojete-1	196	20	obtain	obtain	VERB
azojete-1	196	21	the	the	DET
azojete-1	196	22	homogenous	homogenous	ADJ
azojete-1	196	23	macroscopic	macroscopic	ADJ
azojete-1	196	24	properties	property	NOUN
azojete-1	196	25	such	such	ADJ
azojete-1	196	26	as	as	ADP
azojete-1	196	27	stiffness	stiffness	ADJ
azojete-1	196	28	tensor	tensor	NOUN
azojete-1	196	29	,	,	PUNCT
azojete-1	196	30	the	the	DET
azojete-1	196	31	gradient	gradient	NOUN
azojete-1	196	32	tensor	tensor	NOUN
azojete-1	196	33	(	(	PUNCT
azojete-1	196	34	fm	fm	PROPN
azojete-1	196	35	)	)	PUNCT
azojete-1	196	36	,	,	PUNCT
azojete-1	196	37	the	the	DET
azojete-1	196	38	stress	stress	NOUN
azojete-1	196	39	tensor	tensor	NOUN
azojete-1	196	40	(	(	PUNCT
azojete-1	196	41	pm	pm	NOUN
azojete-1	196	42	)	)	PUNCT
azojete-1	196	43	and	and	CCONJ
azojete-1	196	44	so	so	ADV
azojete-1	196	45	on	on	ADV
azojete-1	196	46	(	(	PUNCT
azojete-1	196	47	kouznetsova	kouznetsova	NOUN
azojete-1	196	48	et	et	PROPN
azojete-1	196	49	al	al	PROPN
azojete-1	196	50	.	.	PROPN
azojete-1	196	51	,	,	PUNCT
azojete-1	196	52	2012	2012	NUM
azojete-1	196	53	)	)	PUNCT
azojete-1	196	54	;	;	PUNCT
azojete-1	196	55	geers	geer	NOUN
azojete-1	196	56	et	et	PROPN
azojete-1	196	57	al	al	PROPN
azojete-1	196	58	.	.	PROPN
azojete-1	196	59	,	,	PUNCT
azojete-1	196	60	2010	2010	NUM
azojete-1	196	61	;	;	PUNCT
azojete-1	196	62	matous	matous	PROPN
azojete-1	196	63	et	et	PROPN
azojete-1	196	64	al	al	PROPN
azojete-1	196	65	.	.	PROPN
azojete-1	196	66	,	,	PUNCT
azojete-1	196	67	2017	2017	NUM
azojete-1	196	68	)	)	PUNCT
azojete-1	196	69	.	.	PUNCT
azojete-1	197	1	figure	figure	VERB
azojete-1	197	2	12	12	NUM
azojete-1	197	3	:	:	PUNCT
azojete-1	197	4	length	length	NOUN
azojete-1	197	5	scales	scale	VERB
azojete-1	197	6	relevant	relevant	ADJ
azojete-1	197	7	for	for	ADP
azojete-1	197	8	the	the	DET
azojete-1	197	9	separation	separation	NOUN
azojete-1	197	10	of	of	ADP
azojete-1	197	11	scales	scale	NOUN
azojete-1	197	12	principles	principle	NOUN
azojete-1	197	13	adapted	adapt	VERB
azojete-1	197	14	from	from	ADP
azojete-1	197	15	matous	matous	PROPN
azojete-1	197	16	et	et	PROPN
azojete-1	197	17	al	al	PROPN
azojete-1	197	18	.	.	PROPN
azojete-1	198	1	(	(	PUNCT
azojete-1	198	2	2017	2017	NUM
azojete-1	198	3	)	)	PUNCT
azojete-1	198	4	.	.	PUNCT
azojete-1	199	1	2.3.2	2.3.2	NUM
azojete-1	199	2	basic	basic	ADJ
azojete-1	199	3	theory	theory	NOUN
azojete-1	199	4	of	of	ADP
azojete-1	199	5	micro	micro	NOUN
azojete-1	199	6	-	-	NOUN
azojete-1	199	7	macro	macro	ADJ
azojete-1	199	8	modelling	modelling	NOUN
azojete-1	199	9	in	in	ADP
azojete-1	199	10	computational	computational	ADJ
azojete-1	199	11	homogenization	homogenization	NOUN
azojete-1	199	12	,	,	PUNCT
azojete-1	199	13	the	the	DET
azojete-1	199	14	macroscopic	macroscopic	ADJ
azojete-1	199	15	or	or	CCONJ
azojete-1	199	16	effective	effective	ADJ
azojete-1	199	17	behaviour	behaviour	NOUN
azojete-1	199	18	of	of	ADP
azojete-1	199	19	composites	composite	NOUN
azojete-1	199	20	is	be	AUX
azojete-1	199	21	obtained	obtain	VERB
azojete-1	199	22	by	by	ADP
azojete-1	199	23	the	the	DET
azojete-1	199	24	following	following	ADJ
azojete-1	199	25	basic	basic	ADJ
azojete-1	199	26	procedures	procedure	NOUN
azojete-1	199	27	listed	list	VERB
azojete-1	199	28	below	below	ADV
azojete-1	199	29	and	and	CCONJ
azojete-1	199	30	schematically	schematically	NOUN
azojete-1	199	31	shown	show	VERB
azojete-1	199	32	in	in	ADP
azojete-1	199	33	figure	figure	NOUN
azojete-1	199	34	13	13	NUM
azojete-1	199	35	.	.	PUNCT
azojete-1	200	1	firstly	firstly	ADV
azojete-1	200	2	,	,	PUNCT
azojete-1	200	3	define	define	VERB
azojete-1	200	4	the	the	DET
azojete-1	200	5	rve	rve	NOUN
azojete-1	200	6	and	and	CCONJ
azojete-1	200	7	the	the	DET
azojete-1	200	8	local	local	ADJ
azojete-1	200	9	constitutive	constitutive	ADJ
azojete-1	200	10	equations	equation	NOUN
azojete-1	200	11	to	to	PART
azojete-1	200	12	obtain	obtain	VERB
azojete-1	200	13	input	input	NOUN
azojete-1	200	14	variables	variable	NOUN
azojete-1	200	15	.	.	PUNCT
azojete-1	201	1	next	next	ADV
azojete-1	201	2	carry	carry	VERB
azojete-1	201	3	out	out	ADP
azojete-1	201	4	a	a	DET
azojete-1	201	5	construction	construction	NOUN
azojete-1	201	6	of	of	ADP
azojete-1	201	7	boundary	boundary	ADJ
azojete-1	201	8	conditions	condition	NOUN
azojete-1	201	9	for	for	ADP
azojete-1	201	10	the	the	DET
azojete-1	201	11	rv	rv	PROPN
azojete-1	201	12	from	from	ADP
azojete-1	201	13	the	the	DET
azojete-1	201	14	above	above	ADJ
azojete-1	201	15	input	input	NOUN
azojete-1	201	16	variables	variable	NOUN
azojete-1	201	17	as	as	ADV
azojete-1	201	18	well	well	ADV
azojete-1	201	19	as	as	ADP
azojete-1	201	20	the	the	DET
azojete-1	201	21	solution	solution	NOUN
azojete-1	201	22	of	of	ADP
azojete-1	201	23	the	the	DET
azojete-1	201	24	boundary	boundary	ADJ
azojete-1	201	25	value	value	NOUN
azojete-1	201	26	problem	problem	NOUN
azojete-1	201	27	(	(	PUNCT
azojete-1	201	28	bvp	bvp	PROPN
azojete-1	201	29	)	)	PUNCT
azojete-1	201	30	for	for	ADP
azojete-1	201	31	the	the	DET
azojete-1	201	32	(	(	PUNCT
azojete-1	201	33	rv	rv	NOUN
azojete-1	201	34	)	)	PUNCT
azojete-1	201	35	of	of	ADP
azojete-1	201	36	the	the	DET
azojete-1	201	37	composite	composite	NOUN
azojete-1	201	38	using	use	VERB
azojete-1	201	39	numerical	numerical	ADJ
azojete-1	201	40	techniques	technique	NOUN
azojete-1	201	41	.	.	PUNCT
azojete-1	202	1	this	this	PRON
azojete-1	202	2	is	be	AUX
azojete-1	202	3	also	also	ADV
azojete-1	202	4	known	know	VERB
azojete-1	202	5	as	as	ADP
azojete-1	202	6	down	down	ADP
azojete-1	202	7	scaling	scaling	NOUN
azojete-1	202	8	or	or	CCONJ
azojete-1	202	9	macro	macro	NOUN
azojete-1	202	10	-	-	PUNCT
azojete-1	202	11	to	to	ADP
azojete-1	202	12	-	-	PUNCT
azojete-1	202	13	micro	micro	NOUN
azojete-1	202	14	transition	transition	NOUN
azojete-1	202	15	.	.	PUNCT
azojete-1	203	1	the	the	DET
azojete-1	203	2	internal	internal	ADJ
azojete-1	203	3	fields	field	NOUN
azojete-1	203	4	(	(	PUNCT
azojete-1	203	5	output	output	NOUN
azojete-1	203	6	variables	variable	NOUN
azojete-1	203	7	)	)	PUNCT
azojete-1	203	8	obtained	obtain	VERB
azojete-1	203	9	from	from	ADP
azojete-1	203	10	the	the	DET
azojete-1	203	11	solution	solution	NOUN
azojete-1	203	12	of	of	ADP
azojete-1	203	13	the	the	DET
azojete-1	203	14	bvp	bvp	NOUN
azojete-1	203	15	of	of	ADP
azojete-1	203	16	the	the	DET
azojete-1	203	17	rv	rv	PROPN
azojete-1	203	18	are	be	AUX
azojete-1	203	19	then	then	ADV
azojete-1	203	20	volumetrically	volumetrically	ADV
azojete-1	203	21	averaged	average	VERB
azojete-1	203	22	(	(	PUNCT
azojete-1	203	23	or	or	CCONJ
azojete-1	203	24	homogenized	homogenize	VERB
azojete-1	203	25	)	)	PUNCT
azojete-1	203	26	using	use	VERB
azojete-1	203	27	averaging	average	VERB
azojete-1	203	28	theorems	theorem	NOUN
azojete-1	203	29	(	(	PUNCT
azojete-1	203	30	i.e.	i.e.	X
azojete-1	203	31	coupling	coupling	NOUN
azojete-1	203	32	between	between	ADP
azojete-1	203	33	micro	micro	ADJ
azojete-1	203	34	and	and	CCONJ
azojete-1	203	35	macro	macro	ADJ
azojete-1	203	36	levels	level	NOUN
azojete-1	203	37	)	)	PUNCT
azojete-1	203	38	to	to	PART
azojete-1	203	39	obtain	obtain	VERB
azojete-1	203	40	the	the	DET
azojete-1	203	41	regularized	regularized	ADJ
azojete-1	203	42	or	or	CCONJ
azojete-1	203	43	effective	effective	ADJ
azojete-1	203	44	material	material	NOUN
azojete-1	203	45	properties	property	NOUN
azojete-1	203	46	used	use	VERB
azojete-1	203	47	in	in	ADP
azojete-1	203	48	the	the	DET
azojete-1	203	49	macroscopic	macroscopic	ADJ
azojete-1	203	50	analysis	analysis	NOUN
azojete-1	203	51	at	at	ADP
azojete-1	203	52	component	component	NOUN
azojete-1	203	53	level	level	NOUN
azojete-1	203	54	.	.	PUNCT
azojete-1	204	1	this	this	PRON
azojete-1	204	2	is	be	AUX
azojete-1	204	3	also	also	ADV
azojete-1	204	4	known	know	VERB
azojete-1	204	5	as	as	ADP
azojete-1	204	6	up	up	ADP
azojete-1	204	7	scaling	scaling	NOUN
azojete-1	204	8	or	or	CCONJ
azojete-1	204	9	micro	micro	NOUN
azojete-1	204	10	-	-	PUNCT
azojete-1	204	11	to	to	ADP
azojete-1	204	12	-	-	PUNCT
azojete-1	204	13	macro	macro	NOUN
azojete-1	204	14	transition	transition	NOUN
azojete-1	204	15	(	(	PUNCT
azojete-1	204	16	kouznetsova	kouznetsova	NOUN
azojete-1	204	17	et	et	PROPN
azojete-1	204	18	al	al	PROPN
azojete-1	204	19	.	.	PROPN
azojete-1	204	20	,	,	PUNCT
azojete-1	204	21	2001	2001	NUM
azojete-1	204	22	;	;	PUNCT
azojete-1	204	23	grytz	grytz	NOUN
azojete-1	204	24	and	and	CCONJ
azojete-1	204	25	mechke	mechke	ADJ
azojete-1	204	26	2007	2007	NUM
azojete-1	204	27	;	;	PUNCT
azojete-1	204	28	nguyen	nguyen	PROPN
azojete-1	204	29	et	et	PROPN
azojete-1	204	30	al	al	PROPN
azojete-1	204	31	.	.	PROPN
azojete-1	204	32	,	,	PUNCT
azojete-1	204	33	2012	2012	NUM
azojete-1	204	34	;	;	PUNCT
azojete-1	204	35	petracca	petracca	NOUN
azojete-1	204	36	et	et	PROPN
azojete-1	204	37	al	al	PROPN
azojete-1	204	38	.	.	PROPN
azojete-1	204	39	,	,	PUNCT
azojete-1	204	40	2016	2016	NUM
azojete-1	204	41	)	)	PUNCT
azojete-1	204	42	.	.	PUNCT
azojete-1	205	1	this	this	DET
azojete-1	205	2	regularization	regularization	NOUN
azojete-1	205	3	process	process	NOUN
azojete-1	205	4	is	be	AUX
azojete-1	205	5	therefore	therefore	ADV
azojete-1	205	6	referred	refer	VERB
azojete-1	205	7	to	to	ADP
azojete-1	205	8	as	as	ADP
azojete-1	205	9	“	"	PUNCT
azojete-1	205	10	homogenization	homogenization	NOUN
azojete-1	205	11	”	"	PUNCT
azojete-1	205	12	(	(	PUNCT
azojete-1	205	13	zohdi	zohdi	NOUN
azojete-1	205	14	and	and	CCONJ
azojete-1	205	15	wriggers	wrigger	NOUN
azojete-1	205	16	2008	2008	NUM
azojete-1	205	17	)	)	PUNCT
azojete-1	205	18	.	.	PUNCT
azojete-1	206	1	an	an	DET
azojete-1	206	2	advantage	advantage	NOUN
azojete-1	206	3	of	of	ADP
azojete-1	206	4	this	this	DET
azojete-1	206	5	computational	computational	ADJ
azojete-1	206	6	homogenization	homogenization	NOUN
azojete-1	206	7	over	over	ADP
azojete-1	206	8	other	other	ADJ
azojete-1	206	9	homogenizational	homogenizational	ADJ
azojete-1	206	10	schemes	scheme	NOUN
azojete-1	206	11	is	be	AUX
azojete-1	206	12	that	that	SCONJ
azojete-1	206	13	the	the	DET
azojete-1	206	14	microscopic	microscopic	ADJ
azojete-1	206	15	constitutive	constitutive	ADJ
azojete-1	206	16	behaviour	behaviour	NOUN
azojete-1	206	17	is	be	AUX
azojete-1	206	18	defined	define	VERB
azojete-1	206	19	as	as	SCONJ
azojete-1	206	20	the	the	DET
azojete-1	206	21	simulations	simulation	NOUN
azojete-1	206	22	are	be	AUX
azojete-1	206	23	ongoing	ongoing	ADJ
azojete-1	206	24	thus	thus	ADV
azojete-1	206	25	,	,	PUNCT
azojete-1	206	26	making	make	VERB
azojete-1	206	27	it	it	PRON
azojete-1	206	28	suitable	suitable	ADJ
azojete-1	206	29	for	for	ADP
azojete-1	206	30	predicting	predict	VERB
azojete-1	206	31	the	the	DET
azojete-1	206	32	mechanical	mechanical	ADJ
azojete-1	206	33	behaviour	behaviour	NOUN
azojete-1	206	34	of	of	ADP
azojete-1	206	35	composites	composite	NOUN
azojete-1	206	36	with	with	ADP
azojete-1	206	37	complex	complex	ADJ
azojete-1	206	38	microstructure	microstructure	NOUN
azojete-1	206	39	as	as	ADV
azojete-1	206	40	well	well	ADV
azojete-1	206	41	as	as	ADP
azojete-1	206	42	adequately	adequately	ADV
azojete-1	206	43	accounting	account	VERB
azojete-1	206	44	for	for	ADP
azojete-1	206	45	microstructure	microstructure	ADJ
azojete-1	206	46	evolution	evolution	NOUN
azojete-1	206	47	under	under	ADP
azojete-1	206	48	complex	complex	ADJ
azojete-1	206	49	loading	loading	NOUN
azojete-1	206	50	(	(	PUNCT
azojete-1	206	51	feyel	feyel	NOUN
azojete-1	206	52	and	and	CCONJ
azojete-1	206	53	chaboche	chaboche	PROPN
azojete-1	206	54	2000	2000	NUM
azojete-1	206	55	;	;	PUNCT
azojete-1	206	56	kouznetsova	kouznetsova	PROPN
azojete-1	206	57	et	et	PROPN
azojete-1	206	58	al	al	PROPN
azojete-1	206	59	.	.	PROPN
azojete-1	206	60	,	,	PUNCT
azojete-1	206	61	2001	2001	NUM
azojete-1	206	62	;	;	PUNCT
azojete-1	206	63	ozedmir	ozedmir	PROPN
azojete-1	206	64	et	et	PROPN
azojete-1	206	65	al	al	PROPN
azojete-1	206	66	.	.	PROPN
azojete-1	206	67	,	,	PUNCT
azojete-1	206	68	2008	2008	NUM
azojete-1	206	69	;	;	PUNCT
azojete-1	206	70	weinan	weinan	PROPN
azojete-1	206	71	and	and	CCONJ
azojete-1	206	72	jianfeng	jianfeng	PROPN
azojete-1	206	73	,	,	PUNCT
azojete-1	206	74	2011	2011	NUM
azojete-1	206	75	;	;	PUNCT
azojete-1	206	76	weinan	weinan	PROPN
azojete-1	206	77	et	et	PROPN
azojete-1	206	78	al	al	PROPN
azojete-1	206	79	.	.	PROPN
azojete-1	206	80	,	,	PUNCT
azojete-1	206	81	2007	2007	NUM
azojete-1	206	82	;	;	PUNCT
azojete-1	206	83	nguyen	nguyen	PROPN
azojete-1	206	84	et	et	PROPN
azojete-1	206	85	al	al	PROPN
azojete-1	206	86	.	.	PROPN
azojete-1	206	87	,	,	PUNCT
azojete-1	206	88	2012	2012	NUM
azojete-1	206	89	)	)	PUNCT
azojete-1	206	90	.	.	PUNCT
azojete-1	207	1	figure	figure	VERB
azojete-1	207	2	13	13	NUM
azojete-1	207	3	:	:	PUNCT
azojete-1	207	4	a	a	DET
azojete-1	207	5	schematic	schematic	ADJ
azojete-1	207	6	representation	representation	NOUN
azojete-1	207	7	of	of	ADP
azojete-1	207	8	the	the	DET
azojete-1	207	9	computational	computational	ADJ
azojete-1	207	10	homogenizational	homogenizational	ADJ
azojete-1	207	11	scheme	scheme	NOUN
azojete-1	207	12	adapted	adapt	VERB
azojete-1	207	13	from	from	ADP
azojete-1	207	14	kouznetsova	kouznetsova	PROPN
azojete-1	207	15	et	et	PROPN
azojete-1	207	16	al	al	PROPN
azojete-1	207	17	.	.	PROPN
azojete-1	207	18	,	,	PUNCT
azojete-1	207	19	cited	cite	VERB
azojete-1	207	20	in	in	ADP
azojete-1	207	21	galvanetto	galvanetto	NOUN
azojete-1	207	22	and	and	CCONJ
azojete-1	207	23	aliabadi	aliabadi	NOUN
azojete-1	207	24	(	(	PUNCT
azojete-1	207	25	2010	2010	NUM
azojete-1	207	26	)	)	PUNCT
azojete-1	207	27	.	.	PUNCT
azojete-1	208	1	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	208	2	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	208	3	arid	arid	NOUN
azojete-1	208	4	zone	zone	NOUN
azojete-1	208	5	journal	journal	NOUN
azojete-1	208	6	of	of	ADP
azojete-1	208	7	engineering	engineering	NOUN
azojete-1	208	8	,	,	PUNCT
azojete-1	208	9	technology	technology	NOUN
azojete-1	208	10	and	and	CCONJ
azojete-1	208	11	environment	environment	NOUN
azojete-1	208	12	,	,	PUNCT
azojete-1	208	13	september	september	PROPN
azojete-1	208	14	,	,	PUNCT
azojete-1	208	15	2019	2019	NUM
azojete-1	208	16	;	;	PUNCT
azojete-1	208	17	vol	vol	NOUN
azojete-1	208	18	.	.	PUNCT
azojete-1	209	1	15(3):488	15(3):488	NUM
azojete-1	209	2	-	-	PUNCT
azojete-1	209	3	509	509	NUM
azojete-1	209	4	.	.	PUNCT
azojete-1	210	1	issn	issn	PROPN
azojete-1	210	2	1596	1596	NUM
azojete-1	210	3	-	-	SYM
azojete-1	210	4	2490	2490	NUM
azojete-1	210	5	;	;	PUNCT
azojete-1	210	6	e	e	X
azojete-1	210	7	-	-	NOUN
azojete-1	210	8	issn	issn	VERB
azojete-1	210	9	2545	2545	NUM
azojete-1	210	10	-	-	SYM
azojete-1	210	11	5818	5818	NUM
azojete-1	210	12	;	;	PUNCT
azojete-1	210	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	210	14	corresponding	correspond	VERB
azojete-1	210	15	author	author	NOUN
azojete-1	210	16	’s	’s	PART
azojete-1	210	17	e	e	NOUN
azojete-1	210	18	-	-	NOUN
azojete-1	210	19	mail	mail	NOUN
azojete-1	210	20	address	address	NOUN
azojete-1	210	21	:	:	PUNCT
azojete-1	210	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	210	23	503	503	NUM
azojete-1	210	24	in	in	ADP
azojete-1	210	25	the	the	DET
azojete-1	210	26	computational	computational	ADJ
azojete-1	210	27	homogenizational	homogenizational	ADJ
azojete-1	210	28	scheme	scheme	NOUN
azojete-1	210	29	shown	show	VERB
azojete-1	210	30	,	,	PUNCT
azojete-1	210	31	is	be	AUX
azojete-1	210	32	the	the	DET
azojete-1	210	33	gradient	gradient	ADJ
azojete-1	210	34	tensor	tensor	NOUN
azojete-1	210	35	for	for	ADP
azojete-1	210	36	any	any	DET
azojete-1	210	37	point	point	NOUN
azojete-1	210	38	on	on	ADP
azojete-1	210	39	the	the	DET
azojete-1	210	40	macro	macro	NOUN
azojete-1	210	41	solid	solid	ADJ
azojete-1	210	42	which	which	PRON
azojete-1	210	43	is	be	AUX
azojete-1	210	44	used	use	VERB
azojete-1	210	45	to	to	PART
azojete-1	210	46	set	set	VERB
azojete-1	210	47	up	up	ADP
azojete-1	210	48	the	the	DET
azojete-1	210	49	boundary	boundary	ADJ
azojete-1	210	50	condition	condition	NOUN
azojete-1	210	51	imposed	impose	VERB
azojete-1	210	52	on	on	ADP
azojete-1	210	53	the	the	DET
azojete-1	210	54	rve	rve	PROPN
azojete-1	210	55	boundary	boundary	PROPN
azojete-1	210	56	(	(	PUNCT
azojete-1	210	57	figures	figure	NOUN
azojete-1	210	58	11	11	NUM
azojete-1	210	59	and	and	CCONJ
azojete-1	210	60	12	12	NUM
azojete-1	210	61	)	)	PUNCT
azojete-1	210	62	with	with	ADP
azojete-1	210	63	a	a	DET
azojete-1	210	64	microscopic	microscopic	ADJ
azojete-1	210	65	domain	domain	NOUN
azojete-1	210	66	of	of	ADP
azojete-1	210	67	size	size	NOUN
azojete-1	210	68	.	.	PUNCT
azojete-1	211	1	a	a	DET
azojete-1	211	2	solution	solution	NOUN
azojete-1	211	3	of	of	ADP
azojete-1	211	4	the	the	DET
azojete-1	211	5	bvp	bvp	NOUN
azojete-1	211	6	for	for	ADP
azojete-1	211	7	the	the	DET
azojete-1	211	8	rve	rve	PROPN
azojete-1	211	9	should	should	AUX
azojete-1	211	10	give	give	VERB
azojete-1	211	11	the	the	DET
azojete-1	211	12	macroscopic	macroscopic	ADJ
azojete-1	211	13	stress	stress	NOUN
azojete-1	211	14	tensor	tensor	NOUN
azojete-1	211	15	which	which	PRON
azojete-1	211	16	is	be	AUX
azojete-1	211	17	achieved	achieve	VERB
azojete-1	211	18	by	by	ADP
azojete-1	211	19	the	the	DET
azojete-1	211	20	volume	volume	NOUN
azojete-1	211	21	averaging	averaging	NOUN
azojete-1	211	22	of	of	ADP
azojete-1	211	23	the	the	DET
azojete-1	211	24	microstructural	microstructural	ADJ
azojete-1	211	25	stresses	stress	NOUN
azojete-1	211	26	over	over	ADP
azojete-1	211	27	the	the	DET
azojete-1	211	28	rve	rve	PROPN
azojete-1	211	29	(	(	PUNCT
azojete-1	211	30	kouznetsova	kouznetsova	PROPN
azojete-1	211	31	et	et	PROPN
azojete-1	211	32	al	al	PROPN
azojete-1	211	33	.	.	PROPN
azojete-1	211	34	,	,	PUNCT
azojete-1	211	35	cited	cite	VERB
azojete-1	211	36	in	in	ADP
azojete-1	211	37	galvanetto	galvanetto	NOUN
azojete-1	211	38	and	and	CCONJ
azojete-1	211	39	aliabadi	aliabadi	NOUN
azojete-1	211	40	2010	2010	NUM
azojete-1	211	41	)	)	PUNCT
azojete-1	211	42	.	.	PUNCT
azojete-1	212	1	implementing	implement	VERB
azojete-1	212	2	the	the	DET
azojete-1	212	3	above	above	ADJ
azojete-1	212	4	process	process	NOUN
azojete-1	212	5	in	in	ADP
azojete-1	212	6	a	a	DET
azojete-1	212	7	finite	finite	ADJ
azojete-1	212	8	element	element	NOUN
azojete-1	212	9	frame	frame	NOUN
azojete-1	212	10	work	work	NOUN
azojete-1	212	11	gives	give	VERB
azojete-1	212	12	the	the	DET
azojete-1	212	13	finite	finite	ADJ
azojete-1	212	14	element	element	NOUN
azojete-1	212	15	method	method	NOUN
azojete-1	212	16	for	for	ADP
azojete-1	212	17	computational	computational	ADJ
azojete-1	212	18	homogenization	homogenization	NOUN
azojete-1	212	19	which	which	PRON
azojete-1	212	20	has	have	AUX
azojete-1	212	21	been	be	AUX
azojete-1	212	22	used	use	VERB
azojete-1	212	23	in	in	ADP
azojete-1	212	24	twodimensional	twodimensional	ADJ
azojete-1	212	25	problems	problem	NOUN
azojete-1	212	26	.	.	PUNCT
azojete-1	213	1	the	the	DET
azojete-1	213	2	results	result	NOUN
azojete-1	213	3	from	from	ADP
azojete-1	213	4	two	two	NUM
azojete-1	213	5	-	-	PUNCT
azojete-1	213	6	dimensional	dimensional	ADJ
azojete-1	213	7	scheme	scheme	NOUN
azojete-1	213	8	showed	show	VERB
azojete-1	213	9	the	the	DET
azojete-1	213	10	importance	importance	NOUN
azojete-1	213	11	of	of	ADP
azojete-1	213	12	fibre	fibre	NOUN
azojete-1	213	13	/	/	SYM
azojete-1	213	14	matrix	matrix	NOUN
azojete-1	213	15	interface	interface	NOUN
azojete-1	213	16	strength	strength	NOUN
azojete-1	213	17	on	on	ADP
azojete-1	213	18	the	the	DET
azojete-1	213	19	macroscopic	macroscopic	ADJ
azojete-1	213	20	behaviour	behaviour	NOUN
azojete-1	213	21	(	(	PUNCT
azojete-1	213	22	damage	damage	NOUN
azojete-1	213	23	and	and	CCONJ
azojete-1	213	24	failure	failure	NOUN
azojete-1	213	25	phases	phase	NOUN
azojete-1	213	26	)	)	PUNCT
azojete-1	213	27	of	of	ADP
azojete-1	213	28	the	the	DET
azojete-1	213	29	composite	composite	ADJ
azojete-1	213	30	materials	material	NOUN
azojete-1	213	31	(	(	PUNCT
azojete-1	213	32	feyel	feyel	NOUN
azojete-1	213	33	1999	1999	NUM
azojete-1	213	34	;	;	PUNCT
azojete-1	213	35	kouznetsova	kouznetsova	PROPN
azojete-1	213	36	et	et	PROPN
azojete-1	213	37	al	al	PROPN
azojete-1	213	38	.	.	PROPN
azojete-1	213	39	,	,	PUNCT
azojete-1	213	40	2001	2001	NUM
azojete-1	213	41	)	)	PUNCT
azojete-1	213	42	.	.	PUNCT
azojete-1	214	1	this	this	DET
azojete-1	214	2	scheme	scheme	NOUN
azojete-1	214	3	has	have	AUX
azojete-1	214	4	been	be	AUX
azojete-1	214	5	further	far	ADV
azojete-1	214	6	extended	extend	VERB
azojete-1	214	7	to	to	PART
azojete-1	214	8	treat	treat	VERB
azojete-1	214	9	three	three	NUM
azojete-1	214	10	dimensional	dimensional	ADJ
azojete-1	214	11	problems	problem	NOUN
azojete-1	214	12	by	by	ADP
azojete-1	214	13	facilitating	facilitate	VERB
azojete-1	214	14	large	large	ADJ
azojete-1	214	15	deformations	deformation	NOUN
azojete-1	214	16	and	and	CCONJ
azojete-1	214	17	rotations	rotation	NOUN
azojete-1	214	18	making	make	VERB
azojete-1	214	19	it	it	PRON
azojete-1	214	20	appropriate	appropriate	ADJ
azojete-1	214	21	for	for	ADP
azojete-1	214	22	dynamic	dynamic	ADJ
azojete-1	214	23	problems	problem	NOUN
azojete-1	214	24	on	on	ADP
azojete-1	214	25	a	a	DET
azojete-1	214	26	finer	fine	ADJ
azojete-1	214	27	scale	scale	NOUN
azojete-1	214	28	.	.	PUNCT
azojete-1	215	1	it	it	PRON
azojete-1	215	2	can	can	AUX
azojete-1	215	3	also	also	ADV
azojete-1	215	4	be	be	AUX
azojete-1	215	5	used	use	VERB
azojete-1	215	6	on	on	ADP
azojete-1	215	7	homogenous	homogenous	ADJ
azojete-1	215	8	materials	material	NOUN
azojete-1	215	9	(	(	PUNCT
azojete-1	215	10	on	on	ADP
azojete-1	215	11	a	a	DET
azojete-1	215	12	finer	fine	ADJ
azojete-1	215	13	-	-	PUNCT
azojete-1	215	14	scale	scale	NOUN
azojete-1	215	15	)	)	PUNCT
azojete-1	215	16	with	with	ADP
azojete-1	215	17	various	various	ADJ
azojete-1	215	18	shapes	shape	NOUN
azojete-1	215	19	of	of	ADP
azojete-1	215	20	rve	rve	PROPN
azojete-1	215	21	(	(	PUNCT
azojete-1	215	22	wiechert	wiechert	PROPN
azojete-1	215	23	and	and	CCONJ
azojete-1	215	24	wall	wall	NOUN
azojete-1	215	25	2010	2010	NUM
azojete-1	215	26	)	)	PUNCT
azojete-1	215	27	.	.	PUNCT
azojete-1	216	1	2.3.3	2.3.3	NUM
azojete-1	216	2	averaging	average	VERB
azojete-1	216	3	theorems	theorem	NOUN
azojete-1	216	4	based	base	VERB
azojete-1	216	5	on	on	ADP
azojete-1	216	6	the	the	DET
azojete-1	216	7	principles	principle	NOUN
azojete-1	216	8	of	of	ADP
azojete-1	216	9	separation	separation	NOUN
azojete-1	216	10	of	of	ADP
azojete-1	216	11	scales	scale	NOUN
azojete-1	216	12	,	,	PUNCT
azojete-1	216	13	the	the	DET
azojete-1	216	14	rve	rve	PROPN
azojete-1	216	15	is	be	AUX
azojete-1	216	16	much	much	ADV
azojete-1	216	17	smaller	small	ADJ
azojete-1	216	18	than	than	ADP
azojete-1	216	19	the	the	DET
azojete-1	216	20	characteristic	characteristic	ADJ
azojete-1	216	21	macroscopic	macroscopic	ADJ
azojete-1	216	22	sample	sample	NOUN
azojete-1	216	23	that	that	PRON
azojete-1	216	24	is	be	AUX
azojete-1	216	25	therefore	therefore	ADV
azojete-1	216	26	;	;	PUNCT
azojete-1	216	27	the	the	DET
azojete-1	216	28	internal	internal	ADJ
azojete-1	216	29	body	body	NOUN
azojete-1	216	30	forces	force	NOUN
azojete-1	216	31	at	at	ADP
azojete-1	216	32	the	the	DET
azojete-1	216	33	macroscale	macroscale	NOUN
azojete-1	216	34	are	be	AUX
azojete-1	216	35	generally	generally	ADV
azojete-1	216	36	overlooked	overlook	VERB
azojete-1	216	37	so	so	SCONJ
azojete-1	216	38	that	that	SCONJ
azojete-1	216	39	the	the	DET
azojete-1	216	40	static	static	ADJ
azojete-1	216	41	equilibrium	equilibrium	NOUN
azojete-1	216	42	state	state	NOUN
azojete-1	216	43	of	of	ADP
azojete-1	216	44	the	the	DET
azojete-1	216	45	rve	rve	PROPN
azojete-1	216	46	is	be	AUX
azojete-1	216	47	mathematically	mathematically	ADV
azojete-1	216	48	expressed	express	VERB
azojete-1	216	49	as	as	ADP
azojete-1	216	50	:	:	PUNCT
azojete-1	216	51	∇m	∇m	NOUN
azojete-1	216	52	.	.	PUNCT
azojete-1	216	53	σm	σm	PUNCT
azojete-1	217	1	=	=	PUNCT
azojete-1	217	2	�	�	PROPN
azojete-1	217	3	in	in	ADP
azojete-1	217	4	ωm	ωm	PROPN
azojete-1	217	5	(	(	PUNCT
azojete-1	217	6	39	39	NUM
azojete-1	217	7	)	)	PUNCT
azojete-1	217	8	(	(	PUNCT
azojete-1	217	9	kouznetsova	kouznetsova	NOUN
azojete-1	217	10	et	et	PROPN
azojete-1	217	11	al	al	PROPN
azojete-1	217	12	.	.	PROPN
azojete-1	217	13	,	,	PUNCT
azojete-1	217	14	cited	cite	VERB
azojete-1	217	15	in	in	ADP
azojete-1	217	16	galvanetto	galvanetto	NOUN
azojete-1	217	17	and	and	CCONJ
azojete-1	217	18	aliabadi	aliabadi	NOUN
azojete-1	217	19	2010	2010	NUM
azojete-1	217	20	)	)	PUNCT
azojete-1	217	21	where	where	SCONJ
azojete-1	217	22	:	:	PUNCT
azojete-1	217	23	–	–	PUNCT
azojete-1	217	24	gradient	gradient	NOUN
azojete-1	217	25	operator	operator	NOUN
azojete-1	217	26	–	–	PUNCT
azojete-1	217	27	microscopic	microscopic	NOUN
azojete-1	217	28	stresses	stress	VERB
azojete-1	217	29	2.3.3.1	2.3.3.1	NUM
azojete-1	217	30	deformation	deformation	NOUN
azojete-1	217	31	averaging	averaging	NOUN
azojete-1	217	32	theorem	theorem	NOUN
azojete-1	217	33	as	as	ADP
azojete-1	217	34	the	the	DET
azojete-1	217	35	actual	actual	ADJ
azojete-1	217	36	coupling	coupling	NOUN
azojete-1	217	37	of	of	ADP
azojete-1	217	38	the	the	DET
azojete-1	217	39	micro	micro	ADJ
azojete-1	217	40	-	-	ADJ
azojete-1	217	41	macro	macro	ADJ
azojete-1	217	42	kinematic	kinematic	ADJ
azojete-1	217	43	quantities	quantity	NOUN
azojete-1	217	44	are	be	AUX
azojete-1	217	45	based	base	VERB
azojete-1	217	46	on	on	ADP
azojete-1	217	47	averaging	average	VERB
azojete-1	217	48	theorems	theorem	NOUN
azojete-1	217	49	(	(	PUNCT
azojete-1	217	50	kouznetsova	kouznetsova	NOUN
azojete-1	217	51	et	et	PROPN
azojete-1	217	52	al	al	PROPN
azojete-1	217	53	.	.	PROPN
azojete-1	217	54	,	,	PUNCT
azojete-1	217	55	cited	cite	VERB
azojete-1	217	56	in	in	ADP
azojete-1	217	57	galvanetto	galvanetto	NOUN
azojete-1	217	58	and	and	CCONJ
azojete-1	217	59	aliabadi	aliabadi	NOUN
azojete-1	217	60	2010	2010	NUM
azojete-1	217	61	)	)	PUNCT
azojete-1	217	62	,	,	PUNCT
azojete-1	217	63	the	the	DET
azojete-1	217	64	deformation	deformation	NOUN
azojete-1	217	65	gradient	gradient	NOUN
azojete-1	217	66	tensor	tensor	NOUN
azojete-1	217	67	at	at	ADP
azojete-1	217	68	any	any	DET
azojete-1	217	69	point	point	NOUN
azojete-1	217	70	on	on	ADP
azojete-1	217	71	the	the	DET
azojete-1	217	72	macroscopic	macroscopic	ADJ
azojete-1	217	73	solid	solid	ADJ
azojete-1	217	74	(	(	PUNCT
azojete-1	217	75	figure	figure	NOUN
azojete-1	217	76	13	13	NUM
azojete-1	217	77	)	)	PUNCT
azojete-1	217	78	is	be	AUX
azojete-1	217	79	given	give	VERB
azojete-1	217	80	by	by	ADP
azojete-1	217	81	volume	volume	NOUN
azojete-1	217	82	averages	average	NOUN
azojete-1	217	83	of	of	ADP
azojete-1	217	84	the	the	DET
azojete-1	217	85	microstructural	microstructural	ADJ
azojete-1	217	86	deformation	deformation	NOUN
azojete-1	217	87	gradient	gradient	NOUN
azojete-1	217	88	tensor	tensor	NOUN
azojete-1	217	89	.	.	PUNCT
azojete-1	218	1	fm	fm	PROPN
azojete-1	219	1	=	=	NOUN
azojete-1	219	2	1	1	NUM
azojete-1	219	3	vo	vo	X
azojete-1	219	4	vo	vo	PROPN
azojete-1	219	5	fm	fm	PROPN
azojete-1	219	6	�	�	PROPN
azojete-1	219	7	dvo	dvo	PROPN
azojete-1	219	8	=	=	PUNCT
azojete-1	219	9	1	1	NUM
azojete-1	219	10	vo	vo	NOUN
azojete-1	219	11	γo	γo	PROPN
azojete-1	219	12	x	x	SYM
azojete-1	219	13	n	n	CCONJ
azojete-1	219	14	�	�	PROPN
azojete-1	219	15	dγo	dγo	PROPN
azojete-1	219	16	(	(	PUNCT
azojete-1	219	17	4	4	NUM
azojete-1	219	18	�	�	NOUN
azojete-1	219	19	)	)	PUNCT
azojete-1	219	20	the	the	DET
azojete-1	219	21	above	above	ADJ
azojete-1	219	22	expression	expression	NOUN
azojete-1	219	23	for	for	ADP
azojete-1	219	24	was	be	AUX
azojete-1	219	25	obtained	obtain	VERB
azojete-1	219	26	after	after	ADP
azojete-1	219	27	transforming	transform	VERB
azojete-1	219	28	the	the	DET
azojete-1	219	29	integral	integral	NOUN
azojete-1	219	30	of	of	ADP
azojete-1	219	31	the	the	DET
azojete-1	219	32	un	un	ADJ
azojete-1	219	33	-	-	ADJ
azojete-1	219	34	deformed	deform	VERB
azojete-1	219	35	volume	volume	NOUN
azojete-1	219	36	of	of	ADP
azojete-1	219	37	the	the	DET
azojete-1	219	38	rve	rve	PROPN
azojete-1	219	39	to	to	ADP
azojete-1	219	40	a	a	DET
azojete-1	219	41	surface	surface	NOUN
azojete-1	219	42	integral	integral	ADJ
azojete-1	219	43	using	use	VERB
azojete-1	219	44	the	the	DET
azojete-1	219	45	divergent	divergent	ADJ
azojete-1	219	46	theorem	theorem	NOUN
azojete-1	219	47	(	(	PUNCT
azojete-1	219	48	kouznetsova	kouznetsova	NOUN
azojete-1	219	49	et	et	PROPN
azojete-1	219	50	al	al	PROPN
azojete-1	219	51	.	.	PROPN
azojete-1	219	52	,	,	PUNCT
azojete-1	219	53	cited	cite	VERB
azojete-1	219	54	in	in	ADP
azojete-1	219	55	galvanetto	galvanetto	NOUN
azojete-1	219	56	and	and	CCONJ
azojete-1	219	57	aliabadi	aliabadi	NOUN
azojete-1	219	58	2010	2010	NUM
azojete-1	219	59	)	)	PUNCT
azojete-1	219	60	.	.	PUNCT
azojete-1	220	1	where	where	SCONJ
azojete-1	220	2	:	:	PUNCT
azojete-1	220	3	�	�	PROPN
azojete-1	220	4	�	�	PROPN
azojete-1	220	5	macroscopic	macroscopic	ADJ
azojete-1	220	6	deformation	deformation	NOUN
azojete-1	220	7	gradient	gradient	NOUN
azojete-1	220	8	tensor	tensor	NOUN
azojete-1	220	9	�	�	PROPN
azojete-1	220	10	�	�	PROPN
azojete-1	220	11	microscopic	microscopic	ADJ
azojete-1	220	12	deformation	deformation	NOUN
azojete-1	220	13	gradient	gradient	NOUN
azojete-1	220	14	tensor	tensor	NOUN
azojete-1	220	15	�	�	PROPN
azojete-1	220	16	�	�	PROPN
azojete-1	220	17	–	–	PUNCT
azojete-1	220	18	reference	reference	NOUN
azojete-1	220	19	domain	domain	NOUN
azojete-1	220	20	�	�	PROPN
azojete-1	220	21	for	for	ADP
azojete-1	220	22	every	every	DET
azojete-1	220	23	�	�	NOUN
azojete-1	220	24	x	x	PROPN
azojete-1	220	25	in	in	ADP
azojete-1	220	26	the	the	DET
azojete-1	220	27	domain	domain	NOUN
azojete-1	220	28	�	�	PROPN
azojete-1	220	29	–	–	PUNCT
azojete-1	220	30	un	un	ADJ
azojete-1	220	31	-	-	ADJ
azojete-1	220	32	deformed	deform	VERB
azojete-1	220	33	position	position	NOUN
azojete-1	220	34	x	x	PUNCT
azojete-1	220	35	deformed	deform	VERB
azojete-1	220	36	position	position	NOUN
azojete-1	220	37	(	(	PUNCT
azojete-1	220	38	kouznetsova	kouznetsova	NOUN
azojete-1	220	39	et	et	PROPN
azojete-1	220	40	al	al	PROPN
azojete-1	220	41	.	.	PROPN
azojete-1	220	42	,	,	PUNCT
azojete-1	220	43	cited	cite	VERB
azojete-1	220	44	in	in	ADP
azojete-1	220	45	galvanetto	galvanetto	NOUN
azojete-1	220	46	and	and	CCONJ
azojete-1	220	47	aliabadi	aliabadi	NOUN
azojete-1	220	48	2010	2010	NUM
azojete-1	220	49	)	)	PUNCT
azojete-1	220	50	.	.	PUNCT
azojete-1	221	1	file:///c:/users	file:///c:/user	NOUN
azojete-1	221	2	/	/	SYM
azojete-1	221	3	user	user	NOUN
azojete-1	221	4	/	/	SYM
azojete-1	221	5	downloads	download	NOUN
azojete-1	221	6	/	/	SYM
azojete-1	221	7	azojete143	azojete143	PROPN
azojete-1	221	8	/	/	SYM
azojete-1	221	9	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	221	10	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	221	11	ohunene	ohunene	ADJ
azojete-1	221	12	hafsa	hafsa	PROPN
azojete-1	221	13	aliyu	aliyu	PROPN
azojete-1	221	14	:	:	PUNCT
azojete-1	221	15	analytical	analytical	ADJ
azojete-1	221	16	,	,	PUNCT
azojete-1	221	17	numerical	numerical	ADJ
azojete-1	221	18	and	and	CCONJ
azojete-1	221	19	computational	computational	ADJ
azojete-1	221	20	multiscale	multiscale	NOUN
azojete-1	221	21	modelling	model	VERB
azojete-1	221	22	techniques	technique	NOUN
azojete-1	221	23	for	for	ADP
azojete-1	221	24	heterogenous	heterogenous	ADJ
azojete-1	221	25	materials	material	NOUN
azojete-1	221	26	:	:	PUNCT
azojete-1	221	27	a	a	DET
azojete-1	221	28	review	review	NOUN
azojete-1	221	29	.	.	PUNCT
azojete-1	222	1	azojete	azojete	NOUN
azojete-1	222	2	,	,	PUNCT
azojete-1	222	3	15(3):488	15(3):488	PROPN
azojete-1	222	4	-	-	PUNCT
azojete-1	222	5	509	509	NUM
azojete-1	222	6	.	.	PUNCT
azojete-1	223	1	issn	issn	PROPN
azojete-1	223	2	1596	1596	NUM
azojete-1	223	3	-	-	SYM
azojete-1	223	4	2490	2490	NUM
azojete-1	223	5	;	;	PUNCT
azojete-1	223	6	e	e	X
azojete-1	223	7	-	-	NOUN
azojete-1	223	8	issn	issn	VERB
azojete-1	223	9	2545	2545	NUM
azojete-1	223	10	-	-	SYM
azojete-1	223	11	5818	5818	NUM
azojete-1	223	12	,	,	PUNCT
azojete-1	223	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	223	14	corresponding	correspond	VERB
azojete-1	223	15	author	author	NOUN
azojete-1	223	16	’s	’s	PART
azojete-1	223	17	e	e	NOUN
azojete-1	223	18	-	-	NOUN
azojete-1	223	19	mail	mail	NOUN
azojete-1	223	20	address	address	NOUN
azojete-1	223	21	:	:	PUNCT
azojete-1	223	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	223	23	504	504	NUM
azojete-1	223	24	2.3.3.2	2.3.3.2	NUM
azojete-1	223	25	energy	energy	NOUN
azojete-1	223	26	averaging	averaging	NOUN
azojete-1	223	27	theorem	theorem	NOUN
azojete-1	223	28	generally	generally	ADV
azojete-1	223	29	referred	refer	VERB
azojete-1	223	30	to	to	ADP
azojete-1	223	31	as	as	ADP
azojete-1	223	32	the	the	DET
azojete-1	223	33	hill	hill	PROPN
azojete-1	223	34	-	-	PUNCT
azojete-1	223	35	mandel	mandel	PROPN
azojete-1	223	36	macro	macro	NOUN
azojete-1	223	37	-	-	NOUN
azojete-1	223	38	homogeneity	homogeneity	NOUN
azojete-1	223	39	principle	principle	NOUN
azojete-1	223	40	,	,	PUNCT
azojete-1	223	41	ascertains	ascertain	VERB
azojete-1	223	42	that	that	SCONJ
azojete-1	223	43	the	the	DET
azojete-1	223	44	macroscopic	macroscopic	ADJ
azojete-1	223	45	volume	volume	NOUN
azojete-1	223	46	averages	average	NOUN
azojete-1	223	47	on	on	ADP
azojete-1	223	48	the	the	DET
azojete-1	223	49	rve	rve	PROPN
azojete-1	223	50	(	(	PUNCT
azojete-1	223	51	given	give	VERB
azojete-1	223	52	by	by	ADP
azojete-1	223	53	the	the	DET
azojete-1	223	54	expression	expression	NOUN
azojete-1	223	55	in	in	ADP
azojete-1	223	56	eqn	eqn	NOUN
azojete-1	223	57	.	.	PUNCT
azojete-1	224	1	(	(	PUNCT
azojete-1	224	2	41	41	NUM
azojete-1	224	3	)	)	PUNCT
azojete-1	224	4	which	which	PRON
azojete-1	224	5	is	be	AUX
azojete-1	224	6	expressed	express	VERB
azojete-1	224	7	in	in	ADP
azojete-1	224	8	terms	term	NOUN
azojete-1	224	9	of	of	ADP
azojete-1	224	10	work	work	NOUN
azojete-1	224	11	conjugate	conjugate	NOUN
azojete-1	224	12	set	set	VERB
azojete-1	224	13	as	as	SCONJ
azojete-1	224	14	given	give	VERB
azojete-1	224	15	in	in	ADP
azojete-1	224	16	eqn	eqn	NOUN
azojete-1	224	17	.	.	PUNCT
azojete-1	225	1	(	(	PUNCT
azojete-1	225	2	41	41	NUM
azojete-1	225	3	)	)	PUNCT
azojete-1	225	4	can	can	AUX
azojete-1	225	5	also	also	ADV
azojete-1	225	6	be	be	AUX
azojete-1	225	7	stated	state	VERB
azojete-1	225	8	in	in	ADP
azojete-1	225	9	terms	term	NOUN
azojete-1	225	10	of	of	ADP
azojete-1	225	11	rve	rve	PROPN
azojete-1	225	12	surface	surface	NOUN
azojete-1	225	13	quantities	quantity	NOUN
azojete-1	225	14	given	give	VERB
azojete-1	225	15	in	in	ADP
azojete-1	225	16	eqn	eqn	NOUN
azojete-1	225	17	.	.	PUNCT
azojete-1	226	1	(	(	PUNCT
azojete-1	226	2	42	42	NUM
azojete-1	226	3	)	)	PUNCT
azojete-1	226	4	.	.	PUNCT
azojete-1	227	1	1	1	NUM
azojete-1	227	2	�	�	PROPN
azojete-1	227	3	�	�	PROPN
azojete-1	227	4	�	�	PROPN
azojete-1	227	5	�	�	PROPN
azojete-1	227	6	�	�	PROPN
azojete-1	227	7	�	�	PROPN
azojete-1	227	8	:	:	PUNCT
azojete-1	227	9	�	�	PROPN
azojete-1	227	10	�	�	PROPN
azojete-1	227	11	�	�	PROPN
azojete-1	227	12	�	�	PROPN
azojete-1	227	13	�	�	PROPN
azojete-1	227	14	�	�	PROPN
azojete-1	227	15	�	�	PROPN
azojete-1	227	16	�	�	PROPN
azojete-1	227	17	=	=	SYM
azojete-1	227	18	�	�	PROPN
azojete-1	227	19	�	�	PROPN
azojete-1	227	20	:	:	PUNCT
azojete-1	227	21	�	�	PROPN
azojete-1	227	22	�	�	PROPN
azojete-1	227	23	�	�	PROPN
azojete-1	227	24	�	�	PROPN
azojete-1	227	25	(	(	PUNCT
azojete-1	227	26	41	41	NUM
azojete-1	227	27	)	)	PUNCT
azojete-1	227	28	δwom	δwom	NOUN
azojete-1	227	29	=	=	SYM
azojete-1	227	30	1	1	NUM
azojete-1	227	31	vo	vo	X
azojete-1	227	32	vo	vo	X
azojete-1	227	33	pm	pm	PROPN
azojete-1	227	34	:	:	PUNCT
azojete-1	227	35	δfmc	δfmc	PROPN
azojete-1	227	36	�	�	PROPN
azojete-1	227	37	dvo	dvo	PROPN
azojete-1	227	38	=	=	SYM
azojete-1	227	39	1	1	NUM
azojete-1	227	40	vo	vo	NOUN
azojete-1	227	41	γo	γo	ADP
azojete-1	227	42	p.	p.	PROPN
azojete-1	227	43	�	�	PROPN
azojete-1	227	44	δxdγo	δxdγo	PROPN
azojete-1	227	45	(	(	PUNCT
azojete-1	227	46	42	42	NUM
azojete-1	227	47	)	)	PUNCT
azojete-1	227	48	where	where	SCONJ
azojete-1	227	49	:	:	PUNCT
azojete-1	227	50	�	�	PROPN
azojete-1	227	51	�	�	PROPN
azojete-1	227	52	is	be	AUX
azojete-1	227	53	the	the	DET
azojete-1	227	54	first	first	ADJ
azojete-1	227	55	piola	piola	PROPN
azojete-1	227	56	–	–	PUNCT
azojete-1	227	57	kirchhoff	kirchhoff	PROPN
azojete-1	227	58	stress	stress	PROPN
azojete-1	227	59	tensor	tensor	NOUN
azojete-1	227	60	(	(	PUNCT
azojete-1	227	61	grytz	grytz	NOUN
azojete-1	227	62	and	and	CCONJ
azojete-1	227	63	mechke	mechke	ADJ
azojete-1	227	64	2007	2007	NUM
azojete-1	227	65	;	;	PUNCT
azojete-1	227	66	kouznetsova	kouznetsova	PROPN
azojete-1	227	67	et	et	PROPN
azojete-1	227	68	al	al	PROPN
azojete-1	227	69	.	.	PROPN
azojete-1	227	70	,	,	PUNCT
azojete-1	227	71	cited	cite	VERB
azojete-1	227	72	in	in	ADP
azojete-1	227	73	galvanetto	galvanetto	NOUN
azojete-1	227	74	and	and	CCONJ
azojete-1	227	75	aliabadi	aliabadi	NOUN
azojete-1	227	76	2010	2010	NUM
azojete-1	227	77	)	)	PUNCT
azojete-1	227	78	.	.	PUNCT
azojete-1	228	1	2.3.4	2.3.4	NUM
azojete-1	228	2	representative	representative	ADJ
azojete-1	228	3	volume	volume	NOUN
azojete-1	228	4	elements	element	NOUN
azojete-1	228	5	(	(	PUNCT
azojete-1	228	6	rv	rv	PROPN
azojete-1	228	7	�	�	PROPN
azojete-1	228	8	�	�	PROPN
azojete-1	228	9	)	)	PUNCT
azojete-1	228	10	the	the	DET
azojete-1	228	11	rve	rve	PROPN
azojete-1	228	12	is	be	AUX
azojete-1	228	13	the	the	DET
azojete-1	228	14	smallest	small	ADJ
azojete-1	228	15	material	material	NOUN
azojete-1	228	16	volume	volume	NOUN
azojete-1	228	17	statistically	statistically	ADV
azojete-1	228	18	representative	representative	NOUN
azojete-1	228	19	of	of	ADP
azojete-1	228	20	the	the	DET
azojete-1	228	21	microstructure	microstructure	NOUN
azojete-1	228	22	of	of	ADP
azojete-1	228	23	the	the	DET
azojete-1	228	24	heterogeneous	heterogeneous	ADJ
azojete-1	228	25	material	material	NOUN
azojete-1	228	26	or	or	CCONJ
azojete-1	228	27	the	the	DET
azojete-1	228	28	smallest	small	ADJ
azojete-1	228	29	volume	volume	NOUN
azojete-1	228	30	of	of	ADP
azojete-1	228	31	the	the	DET
azojete-1	228	32	heterogeneous	heterogeneous	ADJ
azojete-1	228	33	material	material	NOUN
azojete-1	228	34	that	that	PRON
azojete-1	228	35	exactly	exactly	ADV
azojete-1	228	36	replicates	replicate	VERB
azojete-1	228	37	the	the	DET
azojete-1	228	38	macroscopic	macroscopic	ADJ
azojete-1	228	39	behaviour	behaviour	NOUN
azojete-1	228	40	(	(	PUNCT
azojete-1	228	41	drugan	drugan	VERB
azojete-1	228	42	and	and	CCONJ
azojete-1	228	43	willis	willis	PROPN
azojete-1	228	44	1996	1996	NUM
azojete-1	228	45	;	;	PUNCT
azojete-1	228	46	llorca	llorca	NOUN
azojete-1	228	47	et	et	PROPN
azojete-1	228	48	al	al	PROPN
azojete-1	228	49	.	.	PROPN
azojete-1	228	50	,	,	PUNCT
azojete-1	228	51	2007	2007	NUM
azojete-1	228	52	;	;	PUNCT
azojete-1	228	53	kouznetsova	kouznetsova	PROPN
azojete-1	228	54	et	et	PROPN
azojete-1	228	55	al	al	PROPN
azojete-1	228	56	.	.	PROPN
azojete-1	228	57	,	,	PUNCT
azojete-1	228	58	cited	cite	VERB
azojete-1	228	59	in	in	ADP
azojete-1	228	60	galvanetto	galvanetto	NOUN
azojete-1	228	61	and	and	CCONJ
azojete-1	228	62	aliabadi	aliabadi	NOUN
azojete-1	228	63	2010	2010	NUM
azojete-1	228	64	)	)	PUNCT
azojete-1	228	65	.	.	PUNCT
azojete-1	229	1	accurate	accurate	ADJ
azojete-1	229	2	simulations	simulation	NOUN
azojete-1	229	3	in	in	ADP
azojete-1	229	4	continuum	continuum	ADJ
azojete-1	229	5	micromechanics	micromechanic	NOUN
azojete-1	229	6	rely	rely	VERB
azojete-1	229	7	on	on	ADP
azojete-1	229	8	simulating	simulate	VERB
azojete-1	229	9	the	the	DET
azojete-1	229	10	behaviour	behaviour	NOUN
azojete-1	229	11	of	of	ADP
azojete-1	229	12	the	the	DET
azojete-1	229	13	rve	rve	PROPN
azojete-1	229	14	of	of	ADP
azojete-1	229	15	the	the	DET
azojete-1	229	16	heterogeneous	heterogeneous	ADJ
azojete-1	229	17	material	material	NOUN
azojete-1	229	18	.	.	PUNCT
azojete-1	230	1	with	with	ADP
azojete-1	230	2	traditional	traditional	ADJ
azojete-1	230	3	computational	computational	ADJ
azojete-1	230	4	homogenizational	homogenizational	ADJ
azojete-1	230	5	models	model	NOUN
azojete-1	230	6	,	,	PUNCT
azojete-1	230	7	different	different	ADJ
azojete-1	230	8	rv	rv	PROPN
azojete-1	230	9	�	�	NOUN
azojete-1	230	10	◠	◠	NOUN
azojete-1	230	11	have	have	AUX
azojete-1	230	12	been	be	AUX
azojete-1	230	13	used	use	VERB
azojete-1	230	14	at	at	ADP
azojete-1	230	15	various	various	ADJ
azojete-1	230	16	points	point	NOUN
azojete-1	230	17	on	on	ADP
azojete-1	230	18	the	the	DET
azojete-1	230	19	microstructure	microstructure	NOUN
azojete-1	230	20	to	to	PART
azojete-1	230	21	ensure	ensure	VERB
azojete-1	230	22	accuracy	accuracy	NOUN
azojete-1	230	23	(	(	PUNCT
azojete-1	230	24	llorca	llorca	NOUN
azojete-1	230	25	et	et	PROPN
azojete-1	230	26	al	al	PROPN
azojete-1	230	27	.	.	PROPN
azojete-1	230	28	,	,	PUNCT
azojete-1	230	29	2007	2007	NUM
azojete-1	230	30	)	)	PUNCT
azojete-1	230	31	.	.	PUNCT
azojete-1	231	1	based	base	VERB
azojete-1	231	2	on	on	ADP
azojete-1	231	3	the	the	DET
azojete-1	231	4	model	model	NOUN
azojete-1	231	5	introduced	introduce	VERB
azojete-1	231	6	by	by	ADP
azojete-1	231	7	grytz	grytz	NOUN
azojete-1	231	8	and	and	CCONJ
azojete-1	231	9	meschike	meschike	ADJ
azojete-1	231	10	(	(	PUNCT
azojete-1	231	11	2007	2007	NUM
azojete-1	231	12	)	)	PUNCT
azojete-1	231	13	shown	show	VERB
azojete-1	231	14	in	in	ADP
azojete-1	231	15	figure	figure	NOUN
azojete-1	231	16	14	14	NUM
azojete-1	231	17	it	it	PRON
azojete-1	231	18	is	be	AUX
azojete-1	231	19	possible	possible	ADJ
azojete-1	231	20	to	to	PART
azojete-1	231	21	use	use	VERB
azojete-1	231	22	the	the	DET
azojete-1	231	23	same	same	ADJ
azojete-1	231	24	rve	rve	NOUN
azojete-1	231	25	at	at	ADP
azojete-1	231	26	all	all	DET
azojete-1	231	27	points	point	NOUN
azojete-1	231	28	on	on	ADP
azojete-1	231	29	the	the	DET
azojete-1	231	30	microstructure	microstructure	NOUN
azojete-1	231	31	.	.	PUNCT
azojete-1	232	1	figure	figure	NOUN
azojete-1	232	2	14	14	NUM
azojete-1	232	3	schematic	schematic	ADJ
azojete-1	232	4	representation	representation	NOUN
azojete-1	232	5	of	of	ADP
azojete-1	232	6	the	the	DET
azojete-1	232	7	micro	micro	ADJ
azojete-1	232	8	-	-	ADJ
azojete-1	232	9	macro	macro	ADJ
azojete-1	232	10	computational	computational	ADJ
azojete-1	232	11	homogenization	homogenization	NOUN
azojete-1	232	12	of	of	ADP
azojete-1	232	13	finite	finite	ADJ
azojete-1	232	14	deformation	deformation	NOUN
azojete-1	232	15	in	in	ADP
azojete-1	232	16	curvilinear	curvilinear	PROPN
azojete-1	232	17	coordinates	coordinate	NOUN
azojete-1	232	18	adapted	adapt	VERB
azojete-1	232	19	from	from	ADP
azojete-1	232	20	grytz	grytz	NOUN
azojete-1	232	21	and	and	CCONJ
azojete-1	232	22	mechke	mechke	ADJ
azojete-1	232	23	(	(	PUNCT
azojete-1	232	24	2007	2007	NUM
azojete-1	232	25	)	)	PUNCT
azojete-1	232	26	.	.	PUNCT
azojete-1	233	1	similarly	similarly	ADV
azojete-1	233	2	,	,	PUNCT
azojete-1	233	3	the	the	DET
azojete-1	233	4	computational	computational	ADJ
azojete-1	233	5	schemes	scheme	NOUN
azojete-1	233	6	addressed	address	VERB
azojete-1	233	7	so	so	ADV
azojete-1	233	8	far	far	ADV
azojete-1	233	9	are	be	AUX
azojete-1	233	10	applicable	applicable	ADJ
azojete-1	233	11	in	in	ADP
azojete-1	233	12	the	the	DET
azojete-1	233	13	standard	standard	ADJ
azojete-1	233	14	cartesian	cartesian	ADJ
azojete-1	233	15	coordinates	coordinate	NOUN
azojete-1	233	16	(	(	PUNCT
azojete-1	233	17	that	that	PRON
azojete-1	233	18	is	be	AUX
azojete-1	233	19	one	one	NUM
azojete-1	233	20	physical	physical	ADJ
azojete-1	233	21	space	space	NOUN
azojete-1	233	22	)	)	PUNCT
azojete-1	233	23	,	,	PUNCT
azojete-1	233	24	but	but	CCONJ
azojete-1	233	25	with	with	ADP
azojete-1	233	26	this	this	DET
azojete-1	233	27	development	development	NOUN
azojete-1	233	28	,	,	PUNCT
azojete-1	233	29	the	the	DET
azojete-1	233	30	scheme	scheme	NOUN
azojete-1	233	31	can	can	AUX
azojete-1	233	32	be	be	AUX
azojete-1	233	33	applied	apply	VERB
azojete-1	233	34	to	to	PART
azojete-1	233	35	address	address	VERB
azojete-1	233	36	problems	problem	NOUN
azojete-1	233	37	formulated	formulate	VERB
azojete-1	233	38	in	in	ADP
azojete-1	233	39	curvilinear	curvilinear	PROPN
azojete-1	233	40	coordinates	coordinate	NOUN
azojete-1	233	41	in	in	ADP
azojete-1	233	42	the	the	DET
azojete-1	233	43	three	three	NUM
azojete-1	233	44	-	-	PUNCT
azojete-1	233	45	dimensional	dimensional	ADJ
azojete-1	233	46	euclidean	euclidean	ADJ
azojete-1	233	47	space	space	NOUN
azojete-1	233	48	both	both	CCONJ
azojete-1	233	49	at	at	ADP
azojete-1	233	50	the	the	DET
azojete-1	233	51	macro	macro	ADJ
azojete-1	233	52	and	and	CCONJ
azojete-1	233	53	micro	micro	ADJ
azojete-1	233	54	levels	level	NOUN
azojete-1	233	55	.	.	PUNCT
azojete-1	234	1	grytz	grytz	NOUN
azojete-1	234	2	and	and	CCONJ
azojete-1	234	3	mechke	mechke	ADJ
azojete-1	234	4	2007	2007	NUM
azojete-1	234	5	,	,	PUNCT
azojete-1	234	6	employed	employ	VERB
azojete-1	234	7	this	this	DET
azojete-1	234	8	technique	technique	NOUN
azojete-1	234	9	in	in	ADP
azojete-1	234	10	the	the	DET
azojete-1	234	11	multiscale	multiscale	ADJ
azojete-1	234	12	analysis	analysis	NOUN
azojete-1	234	13	of	of	ADP
azojete-1	234	14	a	a	DET
azojete-1	234	15	spherical	spherical	ADJ
azojete-1	234	16	shell	shell	NOUN
azojete-1	234	17	subjected	subject	VERB
azojete-1	234	18	to	to	ADP
azojete-1	234	19	internal	internal	ADJ
azojete-1	234	20	pressure	pressure	NOUN
azojete-1	234	21	shown	show	VERB
azojete-1	234	22	in	in	ADP
azojete-1	234	23	figure	figure	NOUN
azojete-1	234	24	15	15	NUM
azojete-1	234	25	where	where	SCONJ
azojete-1	234	26	the	the	DET
azojete-1	234	27	homogenization	homogenization	NOUN
azojete-1	234	28	of	of	ADP
azojete-1	234	29	the	the	DET
azojete-1	234	30	3d	3d	NUM
azojete-1	234	31	microstructure	microstructure	NOUN
azojete-1	234	32	was	be	AUX
azojete-1	234	33	carried	carry	VERB
azojete-1	234	34	out	out	ADP
azojete-1	234	35	numerically	numerically	ADV
azojete-1	234	36	at	at	ADP
azojete-1	234	37	the	the	DET
azojete-1	234	38	macro	macro	ADJ
azojete-1	234	39	level	level	NOUN
azojete-1	234	40	.	.	PUNCT
azojete-1	235	1	similarly	similarly	ADV
azojete-1	235	2	,	,	PUNCT
azojete-1	235	3	only	only	ADV
azojete-1	235	4	two	two	NUM
azojete-1	235	5	rves	rf	NOUN
azojete-1	235	6	were	be	AUX
azojete-1	235	7	considered	consider	VERB
azojete-1	235	8	all	all	ADV
azojete-1	235	9	through	through	ADP
azojete-1	235	10	the	the	DET
azojete-1	235	11	shell	shell	ADJ
azojete-1	235	12	thickness	thickness	NOUN
azojete-1	235	13	.	.	PUNCT
azojete-1	236	1	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	236	2	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	236	3	arid	arid	NOUN
azojete-1	236	4	zone	zone	NOUN
azojete-1	236	5	journal	journal	NOUN
azojete-1	236	6	of	of	ADP
azojete-1	236	7	engineering	engineering	NOUN
azojete-1	236	8	,	,	PUNCT
azojete-1	236	9	technology	technology	NOUN
azojete-1	236	10	and	and	CCONJ
azojete-1	236	11	environment	environment	NOUN
azojete-1	236	12	,	,	PUNCT
azojete-1	236	13	september	september	PROPN
azojete-1	236	14	,	,	PUNCT
azojete-1	236	15	2019	2019	NUM
azojete-1	236	16	;	;	PUNCT
azojete-1	236	17	vol	vol	NOUN
azojete-1	236	18	.	.	PUNCT
azojete-1	237	1	15(3):488	15(3):488	NUM
azojete-1	237	2	-	-	PUNCT
azojete-1	237	3	509	509	NUM
azojete-1	237	4	.	.	PUNCT
azojete-1	238	1	issn	issn	PROPN
azojete-1	238	2	1596	1596	NUM
azojete-1	238	3	-	-	SYM
azojete-1	238	4	2490	2490	NUM
azojete-1	238	5	;	;	PUNCT
azojete-1	238	6	e	e	X
azojete-1	238	7	-	-	NOUN
azojete-1	238	8	issn	issn	VERB
azojete-1	238	9	2545	2545	NUM
azojete-1	238	10	-	-	SYM
azojete-1	238	11	5818	5818	NUM
azojete-1	238	12	;	;	PUNCT
azojete-1	238	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	238	14	corresponding	correspond	VERB
azojete-1	238	15	author	author	NOUN
azojete-1	238	16	’s	’s	PART
azojete-1	238	17	e	e	NOUN
azojete-1	238	18	-	-	NOUN
azojete-1	238	19	mail	mail	NOUN
azojete-1	238	20	address	address	NOUN
azojete-1	238	21	:	:	PUNCT
azojete-1	238	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	238	23	505	505	NUM
azojete-1	238	24	figure	figure	NOUN
azojete-1	238	25	15	15	NUM
azojete-1	238	26	:	:	PUNCT
azojete-1	238	27	spherical	spherical	ADJ
azojete-1	238	28	shell	shell	NOUN
azojete-1	238	29	subjected	subject	VERB
azojete-1	238	30	to	to	ADP
azojete-1	238	31	internal	internal	ADJ
azojete-1	238	32	pressure	pressure	NOUN
azojete-1	238	33	-	-	PUNCT
azojete-1	238	34	undeformed	undeformed	ADJ
azojete-1	238	35	and	and	CCONJ
azojete-1	238	36	deformed	deformed	ADJ
azojete-1	238	37	configurations	configuration	NOUN
azojete-1	238	38	of	of	ADP
azojete-1	238	39	the	the	DET
azojete-1	238	40	macro	macro	NOUN
azojete-1	238	41	-	-	NOUN
azojete-1	238	42	structure	structure	NOUN
azojete-1	238	43	and	and	CCONJ
azojete-1	238	44	the	the	DET
azojete-1	238	45	underlying	underlying	ADJ
azojete-1	238	46	micro	micro	NOUN
azojete-1	238	47	-	-	NOUN
azojete-1	238	48	structure	structure	NOUN
azojete-1	238	49	with	with	ADP
azojete-1	238	50	the	the	DET
azojete-1	238	51	distribution	distribution	NOUN
azojete-1	238	52	of	of	ADP
azojete-1	238	53	the	the	DET
azojete-1	238	54	cauchy	cauchy	NOUN
azojete-1	238	55	stresses	stress	NOUN
azojete-1	238	56	�	�	PROPN
azojete-1	238	57	�	�	PROPN
azojete-1	238	58	11	11	NUM
azojete-1	238	59	adapted	adapt	VERB
azojete-1	238	60	from	from	ADP
azojete-1	238	61	grytz	grytz	NOUN
azojete-1	238	62	and	and	CCONJ
azojete-1	238	63	mechke	mechke	ADJ
azojete-1	238	64	(	(	PUNCT
azojete-1	238	65	2007	2007	NUM
azojete-1	238	66	)	)	PUNCT
azojete-1	238	67	.	.	PUNCT
azojete-1	239	1	from	from	ADP
azojete-1	239	2	their	their	PRON
azojete-1	239	3	study	study	NOUN
azojete-1	239	4	,	,	PUNCT
azojete-1	239	5	they	they	PRON
azojete-1	239	6	came	come	VERB
azojete-1	239	7	to	to	ADP
azojete-1	239	8	the	the	DET
azojete-1	239	9	conclusion	conclusion	NOUN
azojete-1	239	10	that	that	SCONJ
azojete-1	239	11	simplification	simplification	NOUN
azojete-1	239	12	of	of	ADP
azojete-1	239	13	recommended	recommend	VERB
azojete-1	239	14	computational	computational	ADJ
azojete-1	239	15	scheme	scheme	NOUN
azojete-1	239	16	for	for	ADP
azojete-1	239	17	problems	problem	NOUN
azojete-1	239	18	formulated	formulate	VERB
azojete-1	239	19	in	in	ADP
azojete-1	239	20	curvilinear	curvilinear	PROPN
azojete-1	239	21	coordinates	coordinate	NOUN
azojete-1	239	22	(	(	PUNCT
azojete-1	239	23	such	such	ADJ
azojete-1	239	24	as	as	ADP
azojete-1	239	25	the	the	DET
azojete-1	239	26	use	use	NOUN
azojete-1	239	27	of	of	ADP
azojete-1	239	28	the	the	DET
azojete-1	239	29	same	same	ADJ
azojete-1	239	30	rve	rve	NOUN
azojete-1	239	31	and	and	CCONJ
azojete-1	239	32	so	so	ADV
azojete-1	239	33	on	on	ADV
azojete-1	239	34	)	)	PUNCT
azojete-1	239	35	,	,	PUNCT
azojete-1	239	36	greatly	greatly	ADV
azojete-1	239	37	simplified	simplify	VERB
azojete-1	239	38	the	the	DET
azojete-1	239	39	solution	solution	NOUN
azojete-1	239	40	of	of	ADP
azojete-1	239	41	the	the	DET
azojete-1	239	42	multiscale	multiscale	ADJ
azojete-1	239	43	problem	problem	NOUN
azojete-1	239	44	when	when	SCONJ
azojete-1	239	45	assessed	assess	VERB
azojete-1	239	46	against	against	ADP
azojete-1	239	47	the	the	DET
azojete-1	239	48	traditional	traditional	ADJ
azojete-1	239	49	approaches	approach	NOUN
azojete-1	239	50	using	use	VERB
azojete-1	239	51	only	only	ADV
azojete-1	239	52	a	a	DET
azojete-1	239	53	single	single	ADJ
azojete-1	239	54	physical	physical	ADJ
azojete-1	239	55	space	space	NOUN
azojete-1	239	56	for	for	ADP
azojete-1	239	57	both	both	DET
azojete-1	239	58	micro	micro	ADJ
azojete-1	239	59	and	and	CCONJ
azojete-1	239	60	macro	macro	ADJ
azojete-1	239	61	scales	scale	NOUN
azojete-1	239	62	thus	thus	ADV
azojete-1	239	63	demonstrating	demonstrate	VERB
azojete-1	239	64	the	the	DET
azojete-1	239	65	efficiency	efficiency	NOUN
azojete-1	239	66	of	of	ADP
azojete-1	239	67	the	the	DET
azojete-1	239	68	proposed	propose	VERB
azojete-1	239	69	scheme	scheme	NOUN
azojete-1	239	70	over	over	ADP
azojete-1	239	71	the	the	DET
azojete-1	239	72	traditional	traditional	ADJ
azojete-1	239	73	schemes	scheme	NOUN
azojete-1	239	74	particularly	particularly	ADV
azojete-1	239	75	for	for	ADP
azojete-1	239	76	problems	problem	NOUN
azojete-1	239	77	in	in	ADP
azojete-1	239	78	3d	3d	PROPN
azojete-1	239	79	euclidean	euclidean	ADJ
azojete-1	239	80	space	space	NOUN
azojete-1	239	81	.	.	PUNCT
azojete-1	240	1	from	from	ADP
azojete-1	240	2	this	this	DET
azojete-1	240	3	study	study	NOUN
azojete-1	240	4	,	,	PUNCT
azojete-1	240	5	the	the	DET
azojete-1	240	6	efficient	efficient	ADJ
azojete-1	240	7	application	application	NOUN
azojete-1	240	8	of	of	ADP
azojete-1	240	9	computational	computational	ADJ
azojete-1	240	10	homogenization	homogenization	NOUN
azojete-1	240	11	in	in	ADP
azojete-1	240	12	different	different	ADJ
azojete-1	240	13	physical	physical	ADJ
azojete-1	240	14	space	space	NOUN
azojete-1	240	15	at	at	ADP
azojete-1	240	16	different	different	ADJ
azojete-1	240	17	scales	scale	NOUN
azojete-1	240	18	was	be	AUX
azojete-1	240	19	demonstrated	demonstrate	VERB
azojete-1	240	20	(	(	PUNCT
azojete-1	240	21	grytz	grytz	NOUN
azojete-1	240	22	and	and	CCONJ
azojete-1	240	23	mechke	mechke	ADJ
azojete-1	240	24	2007	2007	NUM
azojete-1	240	25	)	)	PUNCT
azojete-1	240	26	.	.	PUNCT
azojete-1	241	1	3	3	X
azojete-1	241	2	.	.	X
azojete-1	241	3	conclusion	conclusion	NOUN
azojete-1	241	4	from	from	ADP
azojete-1	241	5	the	the	DET
azojete-1	241	6	review	review	NOUN
azojete-1	241	7	of	of	ADP
azojete-1	241	8	the	the	DET
azojete-1	241	9	existing	exist	VERB
azojete-1	241	10	mathematical	mathematical	ADJ
azojete-1	241	11	,	,	PUNCT
azojete-1	241	12	numerical	numerical	ADJ
azojete-1	241	13	and	and	CCONJ
azojete-1	241	14	computational	computational	ADJ
azojete-1	241	15	homogenizational	homogenizational	ADJ
azojete-1	241	16	scheme	scheme	NOUN
azojete-1	241	17	for	for	ADP
azojete-1	241	18	composite	composite	ADJ
azojete-1	241	19	materials	material	NOUN
azojete-1	241	20	,	,	PUNCT
azojete-1	241	21	it	it	PRON
azojete-1	241	22	has	have	AUX
azojete-1	241	23	been	be	AUX
azojete-1	241	24	shown	show	VERB
azojete-1	241	25	that	that	SCONJ
azojete-1	241	26	:	:	PUNCT
azojete-1	241	27	prior	prior	ADV
azojete-1	241	28	to	to	ADP
azojete-1	241	29	the	the	DET
azojete-1	241	30	development	development	NOUN
azojete-1	241	31	of	of	ADP
azojete-1	241	32	digital	digital	ADJ
azojete-1	241	33	computers	computer	NOUN
azojete-1	241	34	as	as	ADV
azojete-1	241	35	well	well	ADV
azojete-1	241	36	as	as	ADP
azojete-1	241	37	the	the	DET
azojete-1	241	38	corresponding	corresponding	ADJ
azojete-1	241	39	development	development	NOUN
azojete-1	241	40	in	in	ADP
azojete-1	241	41	simulation	simulation	NOUN
azojete-1	241	42	tools	tool	NOUN
azojete-1	241	43	(	(	PUNCT
azojete-1	241	44	that	that	PRON
azojete-1	241	45	is	be	AUX
azojete-1	241	46	the	the	DET
azojete-1	241	47	fast	fast	ADJ
azojete-1	241	48	fourier	fourier	NOUN
azojete-1	241	49	transform	transform	NOUN
azojete-1	241	50	,	,	PUNCT
azojete-1	241	51	the	the	DET
azojete-1	241	52	boundary	boundary	ADJ
azojete-1	241	53	element	element	NOUN
azojete-1	241	54	method	method	NOUN
azojete-1	241	55	and	and	CCONJ
azojete-1	241	56	more	more	ADV
azojete-1	241	57	recently	recently	ADV
azojete-1	241	58	the	the	DET
azojete-1	241	59	finite	finite	ADJ
azojete-1	241	60	element	element	NOUN
azojete-1	241	61	method	method	NOUN
azojete-1	241	62	)	)	PUNCT
azojete-1	241	63	as	as	ADP
azojete-1	241	64	a	a	DET
azojete-1	241	65	means	means	NOUN
azojete-1	241	66	of	of	ADP
azojete-1	241	67	analysing	analyse	VERB
azojete-1	241	68	multi	multi	ADJ
azojete-1	241	69	-	-	ADJ
azojete-1	241	70	scale	scale	ADJ
azojete-1	241	71	models	model	NOUN
azojete-1	241	72	,	,	PUNCT
azojete-1	241	73	the	the	DET
azojete-1	241	74	analytical	analytical	ADJ
azojete-1	241	75	/	/	SYM
azojete-1	241	76	mathematical	mathematical	ADJ
azojete-1	241	77	homogenization	homogenization	NOUN
azojete-1	241	78	technique	technique	NOUN
azojete-1	241	79	was	be	AUX
azojete-1	241	80	considered	consider	VERB
azojete-1	241	81	the	the	DET
azojete-1	241	82	main	main	ADJ
azojete-1	241	83	workhorse	workhorse	NOUN
azojete-1	241	84	to	to	PART
azojete-1	241	85	simulate	simulate	VERB
azojete-1	241	86	the	the	DET
azojete-1	241	87	macroscopic	macroscopic	ADJ
azojete-1	241	88	mechanical	mechanical	ADJ
azojete-1	241	89	behaviour	behaviour	NOUN
azojete-1	241	90	of	of	ADP
azojete-1	241	91	multi	multi	ADJ
azojete-1	241	92	-	-	ADJ
azojete-1	241	93	phase	phase	ADJ
azojete-1	241	94	heterogeneous	heterogeneous	ADJ
azojete-1	241	95	material	material	NOUN
azojete-1	241	96	from	from	ADP
azojete-1	241	97	the	the	DET
azojete-1	241	98	behaviour	behaviour	NOUN
azojete-1	241	99	of	of	ADP
azojete-1	241	100	the	the	DET
azojete-1	241	101	representative	representative	ADJ
azojete-1	241	102	volume	volume	NOUN
azojete-1	241	103	element	element	NOUN
azojete-1	241	104	(	(	PUNCT
azojete-1	241	105	rve	rve	PROPN
azojete-1	241	106	)	)	PUNCT
azojete-1	241	107	of	of	ADP
azojete-1	241	108	the	the	DET
azojete-1	241	109	microstructure	microstructure	NOUN
azojete-1	241	110	of	of	ADP
azojete-1	241	111	the	the	DET
azojete-1	241	112	material	material	NOUN
azojete-1	241	113	.	.	PUNCT
azojete-1	242	1	the	the	DET
azojete-1	242	2	straight	straight	ADJ
azojete-1	242	3	forwardness	forwardness	NOUN
azojete-1	242	4	of	of	ADP
azojete-1	242	5	the	the	DET
azojete-1	242	6	fundamental	fundamental	ADJ
azojete-1	242	7	assumptions	assumption	NOUN
azojete-1	242	8	of	of	ADP
azojete-1	242	9	the	the	DET
azojete-1	242	10	technique	technique	NOUN
azojete-1	242	11	made	make	VERB
azojete-1	242	12	it	it	PRON
azojete-1	242	13	quite	quite	ADV
azojete-1	242	14	popular	popular	ADJ
azojete-1	242	15	.	.	PUNCT
azojete-1	243	1	despite	despite	SCONJ
azojete-1	243	2	its	its	PRON
azojete-1	243	3	popularity	popularity	NOUN
azojete-1	243	4	(	(	PUNCT
azojete-1	243	5	in	in	ADP
azojete-1	243	6	computing	compute	VERB
azojete-1	243	7	internal	internal	ADJ
azojete-1	243	8	stress	stress	NOUN
azojete-1	243	9	in	in	ADP
azojete-1	243	10	multiphase	multiphase	NOUN
azojete-1	243	11	materials	material	NOUN
azojete-1	243	12	during	during	ADP
azojete-1	243	13	deformation	deformation	NOUN
azojete-1	243	14	)	)	PUNCT
azojete-1	243	15	the	the	DET
azojete-1	243	16	inability	inability	NOUN
azojete-1	243	17	of	of	ADP
azojete-1	243	18	the	the	DET
azojete-1	243	19	method	method	NOUN
azojete-1	243	20	to	to	PART
azojete-1	243	21	capture	capture	VERB
azojete-1	243	22	rapid	rapid	ADJ
azojete-1	243	23	localization	localization	NOUN
azojete-1	243	24	of	of	ADP
azojete-1	243	25	damage	damage	NOUN
azojete-1	243	26	has	have	AUX
azojete-1	243	27	limited	limit	VERB
azojete-1	243	28	the	the	DET
azojete-1	243	29	application	application	NOUN
azojete-1	243	30	of	of	ADP
azojete-1	243	31	the	the	DET
azojete-1	243	32	method	method	NOUN
azojete-1	243	33	in	in	ADP
azojete-1	243	34	computing	compute	VERB
azojete-1	243	35	mechanical	mechanical	ADJ
azojete-1	243	36	behaviour	behaviour	NOUN
azojete-1	243	37	of	of	ADP
azojete-1	243	38	material	material	NOUN
azojete-1	243	39	where	where	SCONJ
azojete-1	243	40	progressive	progressive	ADJ
azojete-1	243	41	damage	damage	NOUN
azojete-1	243	42	is	be	AUX
azojete-1	243	43	involved	involve	VERB
azojete-1	243	44	.	.	PUNCT
azojete-1	244	1	although	although	SCONJ
azojete-1	244	2	,	,	PUNCT
azojete-1	244	3	the	the	DET
azojete-1	244	4	method	method	NOUN
azojete-1	244	5	describes	describe	VERB
azojete-1	244	6	quite	quite	ADV
azojete-1	244	7	accurately	accurately	ADV
azojete-1	244	8	the	the	DET
azojete-1	244	9	effective	effective	ADJ
azojete-1	244	10	macroscopic	macroscopic	ADJ
azojete-1	244	11	properties	property	NOUN
azojete-1	244	12	of	of	ADP
azojete-1	244	13	the	the	DET
azojete-1	244	14	heterogeneous	heterogeneous	ADJ
azojete-1	244	15	material	material	NOUN
azojete-1	244	16	in	in	ADP
azojete-1	244	17	the	the	DET
azojete-1	244	18	elastic	elastic	ADJ
azojete-1	244	19	system	system	NOUN
azojete-1	244	20	it	it	PRON
azojete-1	244	21	is	be	AUX
azojete-1	244	22	not	not	PART
azojete-1	244	23	as	as	ADV
azojete-1	244	24	effective	effective	ADJ
azojete-1	244	25	in	in	ADP
azojete-1	244	26	the	the	DET
azojete-1	244	27	nonlinear	nonlinear	ADJ
azojete-1	244	28	regime	regime	NOUN
azojete-1	244	29	which	which	PRON
azojete-1	244	30	has	have	AUX
azojete-1	244	31	been	be	AUX
azojete-1	244	32	the	the	DET
azojete-1	244	33	major	major	ADJ
azojete-1	244	34	drawback	drawback	NOUN
azojete-1	244	35	for	for	ADP
azojete-1	244	36	this	this	DET
azojete-1	244	37	technique	technique	NOUN
azojete-1	244	38	.	.	PUNCT
azojete-1	245	1	with	with	SCONJ
azojete-1	245	2	the	the	DET
azojete-1	245	3	current	current	ADJ
azojete-1	245	4	technological	technological	ADJ
azojete-1	245	5	developments	development	NOUN
azojete-1	245	6	in	in	ADP
azojete-1	245	7	simulating	simulate	VERB
azojete-1	245	8	technologies	technology	NOUN
azojete-1	245	9	the	the	DET
azojete-1	245	10	above	above	ADJ
azojete-1	245	11	limitation	limitation	NOUN
azojete-1	245	12	of	of	ADP
azojete-1	245	13	the	the	DET
azojete-1	245	14	mathematical	mathematical	ADJ
azojete-1	245	15	homogenization	homogenization	NOUN
azojete-1	245	16	schemes	scheme	NOUN
azojete-1	245	17	in	in	ADP
azojete-1	245	18	simulating	simulate	VERB
azojete-1	245	19	the	the	DET
azojete-1	245	20	effective	effective	ADJ
azojete-1	245	21	non	non	ADJ
azojete-1	245	22	linear	linear	ADJ
azojete-1	245	23	heterogeneous	heterogeneous	ADJ
azojete-1	245	24	material	material	NOUN
azojete-1	245	25	behaviour	behaviour	NOUN
azojete-1	245	26	were	be	AUX
azojete-1	245	27	addressed	address	VERB
azojete-1	245	28	by	by	ADP
azojete-1	245	29	adopting	adopt	VERB
azojete-1	245	30	computational	computational	ADJ
azojete-1	245	31	homogenizational	homogenizational	ADJ
azojete-1	245	32	schemes	scheme	NOUN
azojete-1	245	33	which	which	PRON
azojete-1	245	34	rely	rely	VERB
azojete-1	245	35	on	on	ADP
azojete-1	245	36	established	establish	VERB
azojete-1	245	37	constitutive	constitutive	ADJ
azojete-1	245	38	relations	relation	NOUN
azojete-1	245	39	for	for	ADP
azojete-1	245	40	the	the	DET
azojete-1	245	41	macroscopic	macroscopic	ADJ
azojete-1	245	42	problems	problem	NOUN
azojete-1	245	43	in	in	ADP
azojete-1	245	44	a	a	DET
azojete-1	245	45	numerical	numerical	ADJ
azojete-1	245	46	form	form	NOUN
azojete-1	245	47	through	through	ADP
azojete-1	245	48	which	which	PRON
azojete-1	245	49	the	the	DET
azojete-1	245	50	macroscopic	macroscopic	ADJ
azojete-1	245	51	problems	problem	NOUN
azojete-1	245	52	are	be	AUX
azojete-1	245	53	constructed	construct	VERB
azojete-1	245	54	and	and	CCONJ
azojete-1	245	55	solved	solve	VERB
azojete-1	245	56	in	in	ADP
azojete-1	245	57	a	a	DET
azojete-1	245	58	nested	nested	ADJ
azojete-1	245	59	manner	manner	NOUN
azojete-1	245	60	.	.	PUNCT
azojete-1	246	1	it	it	PRON
azojete-1	246	2	can	can	AUX
azojete-1	246	3	therefore	therefore	ADV
azojete-1	246	4	be	be	AUX
azojete-1	246	5	seen	see	VERB
azojete-1	246	6	that	that	SCONJ
azojete-1	246	7	:	:	PUNCT
azojete-1	246	8	file:///c:/users	file:///c:/user	NOUN
azojete-1	246	9	/	/	SYM
azojete-1	246	10	user	user	NOUN
azojete-1	246	11	/	/	SYM
azojete-1	246	12	downloads	download	NOUN
azojete-1	246	13	/	/	SYM
azojete-1	246	14	azojete143	azojete143	PROPN
azojete-1	246	15	/	/	SYM
azojete-1	246	16	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	246	17	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	246	18	ohunene	ohunene	ADJ
azojete-1	246	19	hafsa	hafsa	PROPN
azojete-1	246	20	aliyu	aliyu	PROPN
azojete-1	246	21	:	:	PUNCT
azojete-1	246	22	analytical	analytical	ADJ
azojete-1	246	23	,	,	PUNCT
azojete-1	246	24	numerical	numerical	ADJ
azojete-1	246	25	and	and	CCONJ
azojete-1	246	26	computational	computational	ADJ
azojete-1	246	27	multiscale	multiscale	NOUN
azojete-1	246	28	modelling	model	VERB
azojete-1	246	29	techniques	technique	NOUN
azojete-1	246	30	for	for	ADP
azojete-1	246	31	heterogenous	heterogenous	ADJ
azojete-1	246	32	materials	material	NOUN
azojete-1	246	33	:	:	PUNCT
azojete-1	246	34	a	a	DET
azojete-1	246	35	review	review	NOUN
azojete-1	246	36	.	.	PUNCT
azojete-1	247	1	azojete	azojete	NOUN
azojete-1	247	2	,	,	PUNCT
azojete-1	247	3	15(3):488	15(3):488	PROPN
azojete-1	247	4	-	-	PUNCT
azojete-1	247	5	509	509	NUM
azojete-1	247	6	.	.	PUNCT
azojete-1	248	1	issn	issn	PROPN
azojete-1	248	2	1596	1596	NUM
azojete-1	248	3	-	-	SYM
azojete-1	248	4	2490	2490	NUM
azojete-1	248	5	;	;	PUNCT
azojete-1	248	6	e	e	X
azojete-1	248	7	-	-	NOUN
azojete-1	248	8	issn	issn	VERB
azojete-1	248	9	2545	2545	NUM
azojete-1	248	10	-	-	SYM
azojete-1	248	11	5818	5818	NUM
azojete-1	248	12	,	,	PUNCT
azojete-1	248	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	248	14	corresponding	correspond	VERB
azojete-1	248	15	author	author	NOUN
azojete-1	248	16	’s	’s	PART
azojete-1	248	17	e	e	NOUN
azojete-1	248	18	-	-	NOUN
azojete-1	248	19	mail	mail	NOUN
azojete-1	248	20	address	address	NOUN
azojete-1	248	21	:	:	PUNCT
azojete-1	248	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	248	23	506	506	NUM
azojete-1	248	24	the	the	DET
azojete-1	248	25	homogenization	homogenization	NOUN
azojete-1	248	26	schemes	scheme	NOUN
azojete-1	248	27	in	in	ADP
azojete-1	248	28	general	general	ADJ
azojete-1	248	29	,	,	PUNCT
azojete-1	248	30	have	have	AUX
azojete-1	248	31	proven	prove	VERB
azojete-1	248	32	to	to	PART
azojete-1	248	33	be	be	AUX
azojete-1	248	34	an	an	DET
azojete-1	248	35	invaluable	invaluable	ADJ
azojete-1	248	36	tool	tool	NOUN
azojete-1	248	37	for	for	ADP
azojete-1	248	38	obtaining	obtain	VERB
azojete-1	248	39	heterogeneous	heterogeneous	ADJ
azojete-1	248	40	macroscopic	macroscopic	ADJ
azojete-1	248	41	material	material	NOUN
azojete-1	248	42	properties	property	NOUN
azojete-1	248	43	from	from	ADP
azojete-1	248	44	the	the	DET
azojete-1	248	45	mechanical	mechanical	ADJ
azojete-1	248	46	properties	property	NOUN
azojete-1	248	47	of	of	ADP
azojete-1	248	48	the	the	DET
azojete-1	248	49	material	material	NOUN
azojete-1	248	50	microstructure	microstructure	NOUN
azojete-1	248	51	.	.	PUNCT
azojete-1	249	1	the	the	DET
azojete-1	249	2	accuracy	accuracy	NOUN
azojete-1	249	3	of	of	ADP
azojete-1	249	4	the	the	DET
azojete-1	249	5	analytical	analytical	ADJ
azojete-1	249	6	schemes	scheme	NOUN
azojete-1	249	7	is	be	AUX
azojete-1	249	8	limited	limit	VERB
azojete-1	249	9	to	to	ADP
azojete-1	249	10	elastic	elastic	ADJ
azojete-1	249	11	systems	system	NOUN
azojete-1	249	12	which	which	PRON
azojete-1	249	13	are	be	AUX
azojete-1	249	14	mostly	mostly	ADV
azojete-1	249	15	applicable	applicable	ADJ
azojete-1	249	16	for	for	ADP
azojete-1	249	17	accurately	accurately	ADV
azojete-1	249	18	modelling	model	VERB
azojete-1	249	19	microstructures	microstructure	NOUN
azojete-1	249	20	with	with	ADP
azojete-1	249	21	simple	simple	ADJ
azojete-1	249	22	geometrical	geometrical	ADJ
azojete-1	249	23	features	feature	NOUN
azojete-1	249	24	.	.	PUNCT
azojete-1	250	1	a	a	DET
azojete-1	250	2	limitation	limitation	NOUN
azojete-1	250	3	which	which	PRON
azojete-1	250	4	has	have	AUX
azojete-1	250	5	largely	largely	ADV
azojete-1	250	6	been	be	AUX
azojete-1	250	7	attributed	attribute	VERB
azojete-1	250	8	to	to	ADP
azojete-1	250	9	the	the	DET
azojete-1	250	10	simplifications	simplification	NOUN
azojete-1	250	11	adopted	adopt	VERB
azojete-1	250	12	in	in	ADP
azojete-1	250	13	the	the	DET
azojete-1	250	14	analytical	analytical	ADJ
azojete-1	250	15	homogenisation	homogenisation	NOUN
azojete-1	250	16	models	model	NOUN
azojete-1	250	17	preventing	prevent	VERB
azojete-1	250	18	it	it	PRON
azojete-1	250	19	from	from	ADP
azojete-1	250	20	capturing	capture	VERB
azojete-1	250	21	rapid	rapid	ADJ
azojete-1	250	22	localization	localization	NOUN
azojete-1	250	23	of	of	ADP
azojete-1	250	24	strains	strain	NOUN
azojete-1	250	25	,	,	PUNCT
azojete-1	250	26	nucleation	nucleation	NOUN
azojete-1	250	27	,	,	PUNCT
azojete-1	250	28	growth	growth	NOUN
azojete-1	250	29	of	of	ADP
azojete-1	250	30	damage	damage	NOUN
azojete-1	250	31	as	as	ADV
azojete-1	250	32	well	well	ADV
azojete-1	250	33	as	as	ADP
azojete-1	250	34	complex	complex	ADJ
azojete-1	250	35	loading	loading	NOUN
azojete-1	250	36	paths	path	NOUN
azojete-1	250	37	which	which	PRON
azojete-1	250	38	causes	cause	VERB
azojete-1	250	39	phase	phase	NOUN
azojete-1	250	40	transformation	transformation	NOUN
azojete-1	250	41	.	.	PUNCT
azojete-1	251	1	computational	computational	ADJ
azojete-1	251	2	homogenization	homogenization	NOUN
azojete-1	251	3	on	on	ADP
azojete-1	251	4	the	the	DET
azojete-1	251	5	other	other	ADJ
azojete-1	251	6	hand	hand	NOUN
azojete-1	251	7	,	,	PUNCT
azojete-1	251	8	has	have	AUX
azojete-1	251	9	been	be	AUX
azojete-1	251	10	able	able	ADJ
azojete-1	251	11	to	to	PART
azojete-1	251	12	give	give	VERB
azojete-1	251	13	accurate	accurate	ADJ
azojete-1	251	14	predictions	prediction	NOUN
azojete-1	251	15	of	of	ADP
azojete-1	251	16	the	the	DET
azojete-1	251	17	macroscopic	macroscopic	ADJ
azojete-1	251	18	material	material	NOUN
azojete-1	251	19	behaviour	behaviour	NOUN
azojete-1	251	20	in	in	ADP
azojete-1	251	21	non	non	ADJ
azojete-1	251	22	-	-	ADJ
azojete-1	251	23	linear	linear	ADJ
azojete-1	251	24	systems	system	NOUN
azojete-1	251	25	.	.	PUNCT
azojete-1	252	1	it	it	PRON
azojete-1	252	2	allows	allow	VERB
azojete-1	252	3	the	the	DET
azojete-1	252	4	pragmatic	pragmatic	ADJ
azojete-1	252	5	assumption	assumption	NOUN
azojete-1	252	6	of	of	ADP
azojete-1	252	7	local	local	ADJ
azojete-1	252	8	periodicity	periodicity	NOUN
azojete-1	252	9	in	in	ADP
azojete-1	252	10	the	the	DET
azojete-1	252	11	material	material	NOUN
azojete-1	252	12	microstructure	microstructure	NOUN
azojete-1	252	13	which	which	PRON
azojete-1	252	14	further	far	ADV
azojete-1	252	15	improves	improve	VERB
azojete-1	252	16	on	on	ADP
azojete-1	252	17	the	the	DET
azojete-1	252	18	accuracy	accuracy	NOUN
azojete-1	252	19	of	of	ADP
azojete-1	252	20	the	the	DET
azojete-1	252	21	results	result	NOUN
azojete-1	252	22	obtained	obtain	VERB
azojete-1	252	23	.	.	PUNCT
azojete-1	253	1	the	the	DET
azojete-1	253	2	major	major	ADJ
azojete-1	253	3	drawback	drawback	NOUN
azojete-1	253	4	of	of	ADP
azojete-1	253	5	this	this	DET
azojete-1	253	6	technique	technique	NOUN
azojete-1	253	7	is	be	AUX
azojete-1	253	8	that	that	SCONJ
azojete-1	253	9	the	the	DET
azojete-1	253	10	completely	completely	ADV
azojete-1	253	11	coupled	couple	VERB
azojete-1	253	12	micro	micro	ADJ
azojete-1	253	13	-	-	ADJ
azojete-1	253	14	macro	macro	ADJ
azojete-1	253	15	technique	technique	NOUN
azojete-1	253	16	is	be	AUX
azojete-1	253	17	quite	quite	ADV
azojete-1	253	18	expensive	expensive	ADJ
azojete-1	253	19	to	to	PART
azojete-1	253	20	simulate	simulate	VERB
azojete-1	253	21	computationally	computationally	ADV
azojete-1	253	22	.	.	PUNCT
azojete-1	254	1	this	this	PRON
azojete-1	254	2	has	have	AUX
azojete-1	254	3	however	however	ADV
azojete-1	254	4	been	be	AUX
azojete-1	254	5	compensated	compensate	VERB
azojete-1	254	6	for	for	ADP
azojete-1	254	7	by	by	ADP
azojete-1	254	8	adopting	adopt	VERB
azojete-1	254	9	numerical	numerical	ADJ
azojete-1	254	10	strategies	strategy	NOUN
azojete-1	254	11	where	where	SCONJ
azojete-1	254	12	the	the	DET
azojete-1	254	13	benign	benign	ADJ
azojete-1	254	14	fields	field	NOUN
azojete-1	254	15	are	be	AUX
azojete-1	254	16	modelled	model	VERB
azojete-1	254	17	using	use	VERB
azojete-1	254	18	coupled	couple	VERB
azojete-1	254	19	homogenization	homogenization	NOUN
azojete-1	254	20	and	and	CCONJ
azojete-1	254	21	finite	finite	ADJ
azojete-1	254	22	elements	element	NOUN
azojete-1	254	23	and	and	CCONJ
azojete-1	254	24	then	then	ADV
azojete-1	254	25	carrying	carry	VERB
azojete-1	254	26	out	out	ADP
azojete-1	254	27	detailed	detailed	ADJ
azojete-1	254	28	micro	micro	ADJ
azojete-1	254	29	-	-	NOUN
azojete-1	254	30	macro	macro	ADJ
azojete-1	254	31	analysis	analysis	NOUN
azojete-1	254	32	in	in	ADP
azojete-1	254	33	the	the	DET
azojete-1	254	34	core	core	ADJ
azojete-1	254	35	regions	region	NOUN
azojete-1	254	36	(	(	PUNCT
azojete-1	254	37	crack	crack	VERB
azojete-1	254	38	tips	tip	NOUN
azojete-1	254	39	,	,	PUNCT
azojete-1	254	40	interfaces	interface	NOUN
azojete-1	254	41	)	)	PUNCT
azojete-1	254	42	where	where	SCONJ
azojete-1	254	43	it	it	PRON
azojete-1	254	44	is	be	AUX
azojete-1	254	45	essential	essential	ADJ
azojete-1	254	46	to	to	PART
azojete-1	254	47	obtain	obtain	VERB
azojete-1	254	48	a	a	DET
azojete-1	254	49	detailed	detailed	ADJ
azojete-1	254	50	information	information	NOUN
azojete-1	254	51	of	of	ADP
azojete-1	254	52	the	the	DET
azojete-1	254	53	stress	stress	NOUN
azojete-1	254	54	and	and	CCONJ
azojete-1	254	55	strain	strain	VERB
azojete-1	254	56	fields	field	NOUN
azojete-1	254	57	at	at	ADP
azojete-1	254	58	the	the	DET
azojete-1	254	59	core	core	ADJ
azojete-1	254	60	regions	region	NOUN
azojete-1	254	61	since	since	SCONJ
azojete-1	254	62	it	it	PRON
azojete-1	254	63	is	be	AUX
azojete-1	254	64	the	the	DET
azojete-1	254	65	information	information	NOUN
azojete-1	254	66	from	from	ADP
azojete-1	254	67	these	these	DET
azojete-1	254	68	regions	region	NOUN
azojete-1	254	69	that	that	PRON
azojete-1	254	70	govern	govern	VERB
azojete-1	254	71	failure	failure	NOUN
azojete-1	254	72	mechanisms	mechanism	NOUN
azojete-1	254	73	.	.	PUNCT
azojete-1	255	1	4	4	X
azojete-1	255	2	.	.	X
azojete-1	255	3	future	future	ADJ
azojete-1	255	4	trends	trend	NOUN
azojete-1	255	5	a	a	DET
azojete-1	255	6	major	major	ADJ
azojete-1	255	7	hindrance	hindrance	NOUN
azojete-1	255	8	of	of	ADP
azojete-1	255	9	the	the	DET
azojete-1	255	10	computational	computational	ADJ
azojete-1	255	11	homogenizational	homogenizational	ADJ
azojete-1	255	12	scheme	scheme	NOUN
azojete-1	255	13	is	be	AUX
azojete-1	255	14	in	in	ADP
azojete-1	255	15	the	the	DET
azojete-1	255	16	development	development	NOUN
azojete-1	255	17	of	of	ADP
azojete-1	255	18	a	a	DET
azojete-1	255	19	fully	fully	ADV
azojete-1	255	20	coupled	couple	VERB
azojete-1	255	21	micro	micro	ADJ
azojete-1	255	22	-	-	ADJ
azojete-1	255	23	macro	macro	ADJ
azojete-1	255	24	technique	technique	NOUN
azojete-1	255	25	.	.	PUNCT
azojete-1	256	1	a	a	DET
azojete-1	256	2	development	development	NOUN
azojete-1	256	3	of	of	ADP
azojete-1	256	4	a	a	DET
azojete-1	256	5	fully	fully	ADV
azojete-1	256	6	coupled	couple	VERB
azojete-1	256	7	scheme	scheme	NOUN
azojete-1	256	8	is	be	AUX
azojete-1	256	9	highly	highly	ADV
azojete-1	256	10	needed	need	VERB
azojete-1	256	11	in	in	ADP
azojete-1	256	12	order	order	NOUN
azojete-1	256	13	to	to	PART
azojete-1	256	14	be	be	AUX
azojete-1	256	15	able	able	ADJ
azojete-1	256	16	to	to	PART
azojete-1	256	17	validate	validate	VERB
azojete-1	256	18	computational	computational	ADJ
azojete-1	256	19	homogenizational	homogenizational	ADJ
azojete-1	256	20	multiscale	multiscale	NOUN
azojete-1	256	21	models	model	NOUN
azojete-1	256	22	against	against	ADP
azojete-1	256	23	experimental	experimental	ADJ
azojete-1	256	24	results	result	NOUN
azojete-1	256	25	without	without	ADP
azojete-1	256	26	have	have	AUX
azojete-1	256	27	any	any	DET
azojete-1	256	28	discrepancies	discrepancy	NOUN
azojete-1	256	29	at	at	ADP
azojete-1	256	30	relatively	relatively	ADV
azojete-1	256	31	low	low	ADJ
azojete-1	256	32	cost	cost	NOUN
azojete-1	256	33	.	.	PUNCT
azojete-1	257	1	furthermore	furthermore	ADV
azojete-1	257	2	,	,	PUNCT
azojete-1	257	3	the	the	DET
azojete-1	257	4	application	application	NOUN
azojete-1	257	5	of	of	ADP
azojete-1	257	6	this	this	DET
azojete-1	257	7	computational	computational	ADJ
azojete-1	257	8	homogenizational	homogenizational	ADJ
azojete-1	257	9	scheme	scheme	NOUN
azojete-1	257	10	in	in	ADP
azojete-1	257	11	designing	design	VERB
azojete-1	257	12	as	as	ADV
azojete-1	257	13	well	well	ADV
azojete-1	257	14	as	as	ADP
azojete-1	257	15	enhancing	enhance	VERB
azojete-1	257	16	existing	exist	VERB
azojete-1	257	17	engineering	engineering	NOUN
azojete-1	257	18	materials	material	NOUN
azojete-1	257	19	by	by	ADP
azojete-1	257	20	manipulating	manipulate	VERB
azojete-1	257	21	the	the	DET
azojete-1	257	22	microstructure	microstructure	NOUN
azojete-1	257	23	is	be	AUX
azojete-1	257	24	still	still	ADV
azojete-1	257	25	lacking	lack	VERB
azojete-1	257	26	and	and	CCONJ
azojete-1	257	27	needs	need	VERB
azojete-1	257	28	more	more	ADJ
azojete-1	257	29	study	study	NOUN
azojete-1	257	30	.	.	PUNCT
azojete-1	258	1	a	a	DET
azojete-1	258	2	significant	significant	ADJ
azojete-1	258	3	improvement	improvement	NOUN
azojete-1	258	4	in	in	ADP
azojete-1	258	5	this	this	DET
azojete-1	258	6	area	area	NOUN
azojete-1	258	7	will	will	AUX
azojete-1	258	8	be	be	AUX
azojete-1	258	9	highly	highly	ADV
azojete-1	258	10	invaluable	invaluable	ADJ
azojete-1	258	11	in	in	ADP
azojete-1	258	12	applications	application	NOUN
azojete-1	258	13	of	of	ADP
azojete-1	258	14	engineering	engineering	NOUN
azojete-1	258	15	material	material	NOUN
azojete-1	258	16	for	for	ADP
azojete-1	258	17	particular	particular	ADJ
azojete-1	258	18	industrial	industrial	ADJ
azojete-1	258	19	applications	application	NOUN
azojete-1	258	20	.	.	PUNCT
azojete-1	259	1	for	for	ADP
azojete-1	259	2	example	example	NOUN
azojete-1	259	3	,	,	PUNCT
azojete-1	259	4	the	the	DET
azojete-1	259	5	designing	designing	NOUN
azojete-1	259	6	of	of	ADP
azojete-1	259	7	novel	novel	ADJ
azojete-1	259	8	lightweight	lightweight	ADJ
azojete-1	259	9	materials	material	NOUN
azojete-1	259	10	such	such	ADJ
azojete-1	259	11	as	as	ADP
azojete-1	259	12	:	:	PUNCT
azojete-1	259	13	magnesium	magnesium	NOUN
azojete-1	259	14	alloys	alloy	NOUN
azojete-1	259	15	,	,	PUNCT
azojete-1	259	16	aluminium	aluminium	NOUN
azojete-1	259	17	alloys	alloy	NOUN
azojete-1	259	18	,	,	PUNCT
azojete-1	259	19	amorphous	amorphous	ADJ
azojete-1	259	20	polymers	polymer	NOUN
azojete-1	259	21	etcetera	etcetera	NOUN
azojete-1	259	22	which	which	PRON
azojete-1	259	23	are	be	AUX
azojete-1	259	24	energy	energy	NOUN
azojete-1	259	25	efficient	efficient	ADJ
azojete-1	259	26	and	and	CCONJ
azojete-1	259	27	aid	aid	NOUN
azojete-1	259	28	in	in	ADP
azojete-1	259	29	facilitating	facilitate	VERB
azojete-1	259	30	the	the	DET
azojete-1	259	31	reduction	reduction	NOUN
azojete-1	259	32	of	of	ADP
azojete-1	259	33	greenhouse	greenhouse	NOUN
azojete-1	259	34	gas	gas	NOUN
azojete-1	259	35	emissions	emission	NOUN
azojete-1	259	36	from	from	ADP
azojete-1	259	37	buildings	building	NOUN
azojete-1	259	38	,	,	PUNCT
azojete-1	259	39	transportation	transportation	NOUN
azojete-1	259	40	and	and	CCONJ
azojete-1	259	41	industrial	industrial	ADJ
azojete-1	259	42	sector	sector	NOUN
azojete-1	259	43	.	.	PUNCT
azojete-1	260	1	references	reference	NOUN
azojete-1	260	2	aliyu	aliyu	VERB
azojete-1	260	3	,	,	PUNCT
azojete-1	260	4	o.	o.	PROPN
azojete-1	260	5	2019	2019	NUM
azojete-1	260	6	.	.	PUNCT
azojete-1	261	1	design	design	NOUN
azojete-1	261	2	recommendations	recommendation	NOUN
azojete-1	261	3	for	for	ADP
azojete-1	261	4	steel	steel	NOUN
azojete-1	261	5	beams	beam	NOUN
azojete-1	261	6	to	to	PART
azojete-1	261	7	prevent	prevent	VERB
azojete-1	261	8	brittle	brittle	ADJ
azojete-1	261	9	fracture	fracture	NOUN
azojete-1	261	10	.	.	PUNCT
azojete-1	262	1	nigerian	nigerian	ADJ
azojete-1	262	2	journal	journal	NOUN
azojete-1	262	3	of	of	ADP
azojete-1	262	4	technologycal	technologycal	ADJ
azojete-1	262	5	development	development	NOUN
azojete-1	262	6	,	,	PUNCT
azojete-1	262	7	16(2	16(2	NUM
azojete-1	262	8	):	):	PUNCT
azojete-1	262	9	78	78	NUM
azojete-1	262	10	-	-	SYM
azojete-1	262	11	84	84	NUM
azojete-1	262	12	.	.	PUNCT
azojete-1	263	1	chaboche	chaboche	NOUN
azojete-1	263	2	,	,	PUNCT
azojete-1	263	3	jl	jl	PROPN
azojete-1	263	4	.	.	PROPN
azojete-1	263	5	,	,	PUNCT
azojete-1	263	6	kanoute	kanoute	VERB
azojete-1	263	7	,	,	PUNCT
azojete-1	263	8	p.	p.	NOUN
azojete-1	263	9	and	and	CCONJ
azojete-1	263	10	roos	roo	NOUN
azojete-1	263	11	,	,	PUNCT
azojete-1	263	12	a.	a.	NOUN
azojete-1	263	13	2005	2005	NUM
azojete-1	263	14	.	.	PUNCT
azojete-1	264	1	on	on	ADP
azojete-1	264	2	the	the	DET
azojete-1	264	3	capabilities	capability	NOUN
azojete-1	264	4	of	of	ADP
azojete-1	264	5	mean	mean	ADJ
azojete-1	264	6	-	-	PUNCT
azojete-1	264	7	field	field	NOUN
azojete-1	264	8	approaches	approach	NOUN
azojete-1	264	9	for	for	ADP
azojete-1	264	10	the	the	DET
azojete-1	264	11	description	description	NOUN
azojete-1	264	12	of	of	ADP
azojete-1	264	13	plasticity	plasticity	NOUN
azojete-1	264	14	in	in	ADP
azojete-1	264	15	metal	metal	NOUN
azojete-1	264	16	matrix	matrix	NOUN
azojete-1	264	17	composites	composite	NOUN
azojete-1	264	18	.	.	PUNCT
azojete-1	265	1	international	international	ADJ
azojete-1	265	2	journal	journal	PROPN
azojete-1	265	3	of	of	ADP
azojete-1	265	4	plasticity	plasticity	NOUN
azojete-1	265	5	,	,	PUNCT
azojete-1	265	6	22	22	NUM
azojete-1	265	7	:	:	SYM
azojete-1	265	8	1879	1879	NUM
azojete-1	265	9	-	-	SYM
azojete-1	265	10	1898	1898	NUM
azojete-1	265	11	.	.	PUNCT
azojete-1	266	1	drugan	drugan	PROPN
azojete-1	266	2	,	,	PUNCT
azojete-1	266	3	wj	wj	PROPN
azojete-1	266	4	.	.	PUNCT
azojete-1	266	5	,	,	PUNCT
azojete-1	266	6	and	and	CCONJ
azojete-1	266	7	willis	willis	PROPN
azojete-1	266	8	,	,	PUNCT
azojete-1	266	9	jr	jr	PROPN
azojete-1	266	10	.	.	PROPN
azojete-1	266	11	1996	1996	NUM
azojete-1	266	12	.	.	PUNCT
azojete-1	267	1	a	a	DET
azojete-1	267	2	micromechanics	micromechanic	NOUN
azojete-1	267	3	-	-	PUNCT
azojete-1	267	4	based	base	VERB
azojete-1	267	5	non	non	ADJ
azojete-1	267	6	local	local	ADJ
azojete-1	267	7	constitutive	constitutive	ADJ
azojete-1	267	8	equation	equation	NOUN
azojete-1	267	9	and	and	CCONJ
azojete-1	267	10	estimates	estimate	NOUN
azojete-1	267	11	of	of	ADP
azojete-1	267	12	representative	representative	ADJ
azojete-1	267	13	volume	volume	NOUN
azojete-1	267	14	element	element	NOUN
azojete-1	267	15	size	size	NOUN
azojete-1	267	16	for	for	ADP
azojete-1	267	17	elastic	elastic	ADJ
azojete-1	267	18	composites	composite	NOUN
azojete-1	267	19	.	.	PUNCT
azojete-1	268	1	journal	journal	PROPN
azojete-1	268	2	of	of	ADP
azojete-1	268	3	mechanics	mechanic	NOUN
azojete-1	268	4	and	and	CCONJ
azojete-1	268	5	physics	physic	NOUN
azojete-1	268	6	of	of	ADP
azojete-1	268	7	solids	solid	NOUN
azojete-1	268	8	,	,	PUNCT
azojete-1	268	9	44(44	44(44	NOUN
azojete-1	268	10	):	):	PUNCT
azojete-1	268	11	457	457	NUM
azojete-1	268	12	-	-	SYM
azojete-1	268	13	524	524	NUM
azojete-1	268	14	.	.	PUNCT
azojete-1	269	1	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	269	2	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	269	3	arid	arid	NOUN
azojete-1	269	4	zone	zone	NOUN
azojete-1	269	5	journal	journal	NOUN
azojete-1	269	6	of	of	ADP
azojete-1	269	7	engineering	engineering	NOUN
azojete-1	269	8	,	,	PUNCT
azojete-1	269	9	technology	technology	NOUN
azojete-1	269	10	and	and	CCONJ
azojete-1	269	11	environment	environment	NOUN
azojete-1	269	12	,	,	PUNCT
azojete-1	269	13	september	september	PROPN
azojete-1	269	14	,	,	PUNCT
azojete-1	269	15	2019	2019	NUM
azojete-1	269	16	;	;	PUNCT
azojete-1	269	17	vol	vol	NOUN
azojete-1	269	18	.	.	PUNCT
azojete-1	270	1	15(3):488	15(3):488	NUM
azojete-1	270	2	-	-	PUNCT
azojete-1	270	3	509	509	NUM
azojete-1	270	4	.	.	PUNCT
azojete-1	271	1	issn	issn	PROPN
azojete-1	271	2	1596	1596	NUM
azojete-1	271	3	-	-	SYM
azojete-1	271	4	2490	2490	NUM
azojete-1	271	5	;	;	PUNCT
azojete-1	271	6	e	e	X
azojete-1	271	7	-	-	NOUN
azojete-1	271	8	issn	issn	VERB
azojete-1	271	9	2545	2545	NUM
azojete-1	271	10	-	-	SYM
azojete-1	271	11	5818	5818	NUM
azojete-1	271	12	;	;	PUNCT
azojete-1	271	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	271	14	corresponding	correspond	VERB
azojete-1	271	15	author	author	NOUN
azojete-1	271	16	’s	’s	PART
azojete-1	271	17	e	e	NOUN
azojete-1	271	18	-	-	NOUN
azojete-1	271	19	mail	mail	NOUN
azojete-1	271	20	address	address	NOUN
azojete-1	271	21	:	:	PUNCT
azojete-1	271	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	271	23	507	507	NUM
azojete-1	271	24	engquist	engquist	NOUN
azojete-1	271	25	,	,	PUNCT
azojete-1	271	26	ew	ew	PROPN
azojete-1	271	27	.	.	PROPN
azojete-1	271	28	,	,	PUNCT
azojete-1	271	29	lix	lix	PROPN
azojete-1	271	30	,	,	PUNCT
azojete-1	271	31	ren	ren	PROPN
azojete-1	271	32	,	,	PUNCT
azojete-1	271	33	w.	w.	PROPN
azojete-1	271	34	,	,	PUNCT
azojete-1	271	35	vanden	vanden	PROPN
azojete-1	271	36	-	-	PUNCT
azojete-1	271	37	eijnden	eijnden	NOUN
azojete-1	271	38	,	,	PUNCT
azojete-1	271	39	e.	e.	PROPN
azojete-1	271	40	2007	2007	NUM
azojete-1	271	41	.	.	PUNCT
azojete-1	272	1	heterogenous	heterogenous	ADJ
azojete-1	272	2	multiscale	multiscale	ADJ
azojete-1	272	3	methods	method	NOUN
azojete-1	272	4	:	:	PUNCT
azojete-1	272	5	a	a	DET
azojete-1	272	6	review	review	NOUN
azojete-1	272	7	.	.	PUNCT
azojete-1	273	1	community	community	NOUN
azojete-1	273	2	of	of	ADP
azojete-1	273	3	computational	computational	ADJ
azojete-1	273	4	.	.	PUNCT
azojete-1	274	1	physics	physics	NOUN
azojete-1	274	2	,	,	PUNCT
azojete-1	274	3	21	21	NUM
azojete-1	274	4	:	:	PUNCT
azojete-1	274	5	367	367	NUM
azojete-1	274	6	-	-	SYM
azojete-1	274	7	450	450	NUM
azojete-1	274	8	.	.	PUNCT
azojete-1	275	1	eshelby	eshelby	PROPN
azojete-1	275	2	,	,	PUNCT
azojete-1	275	3	j.	j.	PROPN
azojete-1	275	4	1957	1957	NUM
azojete-1	275	5	.	.	PUNCT
azojete-1	276	1	the	the	DET
azojete-1	276	2	determination	determination	NOUN
azojete-1	276	3	of	of	ADP
azojete-1	276	4	the	the	DET
azojete-1	276	5	elastic	elastic	ADJ
azojete-1	276	6	field	field	NOUN
azojete-1	276	7	of	of	ADP
azojete-1	276	8	an	an	DET
azojete-1	276	9	ellipsoidal	ellipsoidal	ADJ
azojete-1	276	10	inclusion	inclusion	NOUN
azojete-1	276	11	and	and	CCONJ
azojete-1	276	12	related	related	ADJ
azojete-1	276	13	problems	problem	NOUN
azojete-1	276	14	.	.	PUNCT
azojete-1	277	1	proceecings	proceecing	NOUN
azojete-1	277	2	of	of	ADP
azojete-1	277	3	the	the	DET
azojete-1	277	4	royal	royal	ADJ
azojete-1	277	5	society	society	NOUN
azojete-1	277	6	of	of	ADP
azojete-1	277	7	london	london	PROPN
azojete-1	277	8	series	series	PROPN
azojete-1	277	9	a	a	PRON
azojete-1	277	10	:	:	PUNCT
azojete-1	277	11	a241	a241	PROPN
azojete-1	277	12	-3967doi	-3967doi	NUM
azojete-1	277	13	:	:	PUNCT
azojete-1	277	14	10	10	NUM
azojete-1	277	15	.	.	X
azojete-1	277	16	1098	1098	NUM
azojete-1	277	17	/	/	SYM
azojete-1	277	18	rspa.1957.0133	rspa.1957.0133	PROPN
azojete-1	277	19	feyel	feyel	NOUN
azojete-1	277	20	,	,	PUNCT
azojete-1	277	21	f.	f.	PROPN
azojete-1	277	22	1999	1999	NUM
azojete-1	277	23	.	.	PUNCT
azojete-1	278	1	multiscale	multiscale	ADJ
azojete-1	278	2	elastoviscoplastic	elastoviscoplastic	ADJ
azojete-1	278	3	analysis	analysis	NOUN
azojete-1	278	4	of	of	ADP
azojete-1	278	5	composite	composite	ADJ
azojete-1	278	6	structures	structure	NOUN
azojete-1	278	7	.	.	PUNCT
azojete-1	279	1	compuational	compuational	ADJ
azojete-1	279	2	materials	material	NOUN
azojete-1	279	3	science	science	NOUN
azojete-1	279	4	,	,	PUNCT
azojete-1	279	5	16(1	16(1	PROPN
azojete-1	279	6	-	-	SYM
azojete-1	279	7	4	4	NUM
azojete-1	279	8	):	):	PUNCT
azojete-1	279	9	344	344	NUM
azojete-1	279	10	-	-	SYM
azojete-1	279	11	354	354	NUM
azojete-1	279	12	.	.	PUNCT
azojete-1	279	13	feyel	feyel	PROPN
azojete-1	279	14	,	,	PUNCT
azojete-1	279	15	f.	f.	PROPN
azojete-1	279	16	and	and	CCONJ
azojete-1	279	17	chaboche	chaboche	PROPN
azojete-1	279	18	,	,	PUNCT
azojete-1	279	19	jl	jl	PROPN
azojete-1	279	20	.	.	PROPN
azojete-1	279	21	2000	2000	NUM
azojete-1	279	22	.	.	PUNCT
azojete-1	280	1	multiscale	multiscale	ADJ
azojete-1	280	2	approch	approch	NOUN
azojete-1	280	3	for	for	ADP
azojete-1	280	4	modelling	model	VERB
azojete-1	280	5	the	the	DET
azojete-1	280	6	elastoviscoplastic	elastoviscoplastic	ADJ
azojete-1	280	7	behaviour	behaviour	NOUN
azojete-1	280	8	of	of	ADP
azojete-1	280	9	long	long	ADJ
azojete-1	280	10	fiber	fiber	NOUN
azojete-1	280	11	sic	sic	ADJ
azojete-1	280	12	/	/	SYM
azojete-1	280	13	ti	ti	NOUN
azojete-1	280	14	composite	composite	ADJ
azojete-1	280	15	materials	material	NOUN
azojete-1	280	16	.	.	PUNCT
azojete-1	281	1	computer	computer	NOUN
azojete-1	281	2	methods	method	NOUN
azojete-1	281	3	in	in	ADP
azojete-1	281	4	applied	applied	ADJ
azojete-1	281	5	mechanics	mechanic	NOUN
azojete-1	281	6	and	and	CCONJ
azojete-1	281	7	engineering	engineering	NOUN
azojete-1	281	8	,	,	PUNCT
azojete-1	281	9	183(3	183(3	NUM
azojete-1	281	10	-	-	SYM
azojete-1	281	11	4	4	NUM
azojete-1	281	12	):	):	PUNCT
azojete-1	281	13	309	309	NUM
azojete-1	281	14	-	-	SYM
azojete-1	281	15	330	330	NUM
azojete-1	281	16	.	.	PUNCT
azojete-1	282	1	fish	fish	NOUN
azojete-1	282	2	,	,	PUNCT
azojete-1	282	3	j.	j.	PROPN
azojete-1	282	4	1992	1992	NUM
azojete-1	282	5	.	.	PUNCT
azojete-1	283	1	the	the	DET
azojete-1	283	2	s	s	NOUN
azojete-1	283	3	-	-	PUNCT
azojete-1	283	4	version	version	NOUN
azojete-1	283	5	of	of	ADP
azojete-1	283	6	the	the	DET
azojete-1	283	7	finite	finite	ADJ
azojete-1	283	8	element	element	NOUN
azojete-1	283	9	method	method	NOUN
azojete-1	283	10	.	.	PUNCT
azojete-1	284	1	computers	computer	NOUN
azojete-1	284	2	and	and	CCONJ
azojete-1	284	3	structures	structure	NOUN
azojete-1	284	4	,	,	PUNCT
azojete-1	284	5	43(3	43(3	NUM
azojete-1	284	6	):	):	PUNCT
azojete-1	284	7	539547	539547	NUM
azojete-1	284	8	.	.	PUNCT
azojete-1	285	1	galvanetto	galvanetto	NOUN
azojete-1	285	2	,	,	PUNCT
azojete-1	285	3	u.	u.	PROPN
azojete-1	285	4	and	and	CCONJ
azojete-1	285	5	aliabadi	aliabadi	PROPN
azojete-1	285	6	,	,	PUNCT
azojete-1	285	7	mh	mh	PROPN
azojete-1	285	8	.	.	PROPN
azojete-1	285	9	2010	2010	NUM
azojete-1	285	10	.	.	PUNCT
azojete-1	286	1	multiscale	multiscale	NOUN
azojete-1	286	2	modelling	modelling	NOUN
azojete-1	286	3	in	in	ADP
azojete-1	286	4	solid	solid	ADJ
azojete-1	286	5	mechanics	mechanic	NOUN
azojete-1	286	6	.	.	PUNCT
azojete-1	287	1	3	3	NUM
azojete-1	287	2	:	:	SYM
azojete-1	287	3	1	1	NUM
azojete-1	287	4	-	-	SYM
azojete-1	287	5	42	42	NUM
azojete-1	287	6	imperial	imperial	ADJ
azojete-1	287	7	college	college	NOUN
azojete-1	287	8	press	press	NOUN
azojete-1	287	9	57	57	NUM
azojete-1	287	10	covent	covent	NOUN
azojete-1	287	11	garden	garden	PROPN
azojete-1	287	12	london	london	PROPN
azojete-1	287	13	.	.	PUNCT
azojete-1	288	1	geers	geer	NOUN
azojete-1	288	2	,	,	PUNCT
azojete-1	288	3	mgd	mgd	PROPN
azojete-1	288	4	.	.	PROPN
azojete-1	288	5	,	,	PUNCT
azojete-1	288	6	kouznetsova	kouznetsova	PROPN
azojete-1	288	7	,	,	PUNCT
azojete-1	288	8	vg	vg	PROPN
azojete-1	288	9	.	.	PROPN
azojete-1	288	10	,	,	PUNCT
azojete-1	288	11	and	and	CCONJ
azojete-1	288	12	brekelmans	brekelman	NOUN
azojete-1	288	13	,	,	PUNCT
azojete-1	288	14	wam	wam	PROPN
azojete-1	288	15	.	.	PROPN
azojete-1	288	16	,	,	PUNCT
azojete-1	288	17	2010	2010	NUM
azojete-1	288	18	.	.	PUNCT
azojete-1	289	1	muliti	muliti	ADJ
azojete-1	289	2	-	-	PUNCT
azojete-1	289	3	scale	scale	NOUN
azojete-1	289	4	compuational	compuational	ADJ
azojete-1	289	5	homogenization	homogenization	NOUN
azojete-1	289	6	:	:	PUNCT
azojete-1	289	7	trends	trend	NOUN
azojete-1	289	8	and	and	CCONJ
azojete-1	289	9	challenges	challenge	NOUN
azojete-1	289	10	.	.	PUNCT
azojete-1	290	1	journal	journal	NOUN
azojete-1	290	2	of	of	ADP
azojete-1	290	3	compuational	compuational	ADJ
azojete-1	290	4	and	and	CCONJ
azojete-1	290	5	applied	applied	ADJ
azojete-1	290	6	mathematics	mathematic	NOUN
azojete-1	290	7	,	,	PUNCT
azojete-1	290	8	234(7	234(7	NUM
azojete-1	290	9	):	):	PUNCT
azojete-1	290	10	2175	2175	NUM
azojete-1	290	11	-	-	SYM
azojete-1	290	12	2182	2182	NUM
azojete-1	290	13	.	.	PUNCT
azojete-1	291	1	gonzalez	gonzalez	PROPN
azojete-1	291	2	,	,	PUNCT
azojete-1	291	3	c.	c.	PROPN
azojete-1	291	4	and	and	CCONJ
azojete-1	291	5	llorca	llorca	PROPN
azojete-1	291	6	,	,	PUNCT
azojete-1	291	7	j.	j.	PROPN
azojete-1	291	8	2006	2006	NUM
azojete-1	291	9	.	.	PUNCT
azojete-1	292	1	multiscale	multiscale	NOUN
azojete-1	292	2	modelling	modelling	NOUN
azojete-1	292	3	of	of	ADP
azojete-1	292	4	fracture	fracture	NOUN
azojete-1	292	5	in	in	ADP
azojete-1	292	6	fiber	fiber	NOUN
azojete-1	292	7	reinforced	reinforce	VERB
azojete-1	292	8	compostites	compostite	NOUN
azojete-1	292	9	.	.	PUNCT
azojete-1	293	1	acta	acta	PROPN
azojete-1	293	2	mater	mater	PROPN
azojete-1	293	3	,	,	PUNCT
azojete-1	293	4	54	54	NUM
azojete-1	293	5	:	:	SYM
azojete-1	293	6	4171	4171	NUM
azojete-1	293	7	-	-	SYM
azojete-1	293	8	4181	4181	NUM
azojete-1	293	9	.	.	PUNCT
azojete-1	294	1	ghosh	ghosh	PROPN
azojete-1	294	2	,	,	PUNCT
azojete-1	294	3	s.	s.	PROPN
azojete-1	294	4	and	and	CCONJ
azojete-1	294	5	moorthy	moorthy	PROPN
azojete-1	294	6	,	,	PUNCT
azojete-1	294	7	s.	s.	PROPN
azojete-1	294	8	1994	1994	NUM
azojete-1	294	9	.	.	PUNCT
azojete-1	295	1	elastic	elastic	ADJ
azojete-1	295	2	-	-	PUNCT
azojete-1	295	3	plastic	plastic	NOUN
azojete-1	295	4	analysis	analysis	NOUN
azojete-1	295	5	of	of	ADP
azojete-1	295	6	arbitrary	arbitrary	ADJ
azojete-1	295	7	heterogenous	heterogenous	ADJ
azojete-1	295	8	materials	material	NOUN
azojete-1	295	9	with	with	ADP
azojete-1	295	10	the	the	DET
azojete-1	295	11	voronoi	voronoi	ADJ
azojete-1	295	12	cell	cell	NOUN
azojete-1	295	13	finite	finite	PROPN
azojete-1	295	14	element	element	NOUN
azojete-1	295	15	method	method	NOUN
azojete-1	295	16	.	.	PUNCT
azojete-1	296	1	computer	computer	NOUN
azojete-1	296	2	methods	method	NOUN
azojete-1	296	3	in	in	ADP
azojete-1	296	4	applied	applied	ADJ
azojete-1	296	5	mechanics	mechanic	NOUN
azojete-1	296	6	and	and	CCONJ
azojete-1	296	7	engineering	engineering	NOUN
azojete-1	296	8	121	121	NUM
azojete-1	296	9	:	:	PUNCT
azojete-1	296	10	373	373	NUM
azojete-1	296	11	-	-	SYM
azojete-1	296	12	401	401	NUM
azojete-1	296	13	ghosh	ghosh	PROPN
azojete-1	296	14	,	,	PUNCT
azojete-1	296	15	s.	s.	PROPN
azojete-1	296	16	and	and	CCONJ
azojete-1	296	17	moorthy	moorthy	PROPN
azojete-1	296	18	,	,	PUNCT
azojete-1	296	19	s.	s.	PROPN
azojete-1	296	20	2004	2004	NUM
azojete-1	296	21	.	.	PUNCT
azojete-1	297	1	three	three	NUM
azojete-1	297	2	dimensional	dimensional	ADJ
azojete-1	297	3	voronoi	voronoi	NOUN
azojete-1	297	4	cell	cell	NOUN
azojete-1	297	5	finite	finite	PROPN
azojete-1	297	6	element	element	NOUN
azojete-1	297	7	model	model	NOUN
azojete-1	297	8	for	for	ADP
azojete-1	297	9	microstructures	microstructure	NOUN
azojete-1	297	10	with	with	ADP
azojete-1	297	11	ellopsoidal	ellopsoidal	ADJ
azojete-1	297	12	heterogeneities	heterogeneity	NOUN
azojete-1	297	13	.	.	PUNCT
azojete-1	298	1	computatonal	computatonal	ADJ
azojete-1	298	2	.	.	PUNCT
azojete-1	298	3	mechanics	mechanic	NOUN
azojete-1	298	4	,	,	PUNCT
azojete-1	298	5	34	34	NUM
azojete-1	298	6	:	:	SYM
azojete-1	298	7	510	510	NUM
azojete-1	298	8	-	-	SYM
azojete-1	298	9	531	531	NUM
azojete-1	298	10	.	.	PUNCT
azojete-1	299	1	grytz	grytz	PROPN
azojete-1	299	2	,	,	PUNCT
azojete-1	299	3	r.	r.	NOUN
azojete-1	299	4	and	and	CCONJ
azojete-1	299	5	meschke	meschke	NOUN
azojete-1	299	6	,	,	PUNCT
azojete-1	299	7	g.	g.	PROPN
azojete-1	299	8	2007	2007	NUM
azojete-1	299	9	.	.	PUNCT
azojete-1	300	1	consistent	consistent	ADJ
azojete-1	300	2	micro	micro	ADJ
azojete-1	300	3	-	-	ADJ
azojete-1	300	4	macro	macro	ADJ
azojete-1	300	5	transition	transition	NOUN
azojete-1	300	6	at	at	ADP
azojete-1	300	7	larte	larte	NOUN
azojete-1	300	8	objective	objective	ADJ
azojete-1	300	9	strains	strain	NOUN
azojete-1	300	10	in	in	ADP
azojete-1	300	11	curvilinear	curvilinear	ADJ
azojete-1	300	12	connective	connective	ADJ
azojete-1	300	13	coordinates	coordinate	NOUN
azojete-1	300	14	.	.	PUNCT
azojete-1	301	1	international	international	ADJ
azojete-1	301	2	journal	journal	PROPN
azojete-1	301	3	for	for	ADP
azojete-1	301	4	numerical	numerical	ADJ
azojete-1	301	5	methods	method	NOUN
azojete-1	301	6	in	in	ADP
azojete-1	301	7	engingineering	engingineere	VERB
azojete-1	301	8	,	,	PUNCT
azojete-1	301	9	doi	doi	NOUN
azojete-1	301	10	:	:	PUNCT
azojete-1	301	11	10.1002	10.1002	NUM
azojete-1	301	12	/	/	SYM
azojete-1	301	13	nme.2105	nme.2105	PROPN
azojete-1	301	14	hashin	hashin	NOUN
azojete-1	301	15	,	,	PUNCT
azojete-1	301	16	z.	z.	PROPN
azojete-1	301	17	and	and	CCONJ
azojete-1	301	18	shtrikman	shtrikman	PROPN
azojete-1	301	19	,	,	PUNCT
azojete-1	301	20	s.	s.	PROPN
azojete-1	301	21	1962	1962	NUM
azojete-1	301	22	.	.	PUNCT
azojete-1	302	1	a	a	DET
azojete-1	302	2	variational	variational	ADJ
azojete-1	302	3	approach	approach	NOUN
azojete-1	302	4	ot	ot	ADP
azojete-1	302	5	the	the	DET
azojete-1	302	6	theory	theory	NOUN
azojete-1	302	7	of	of	ADP
azojete-1	302	8	elastic	elastic	ADJ
azojete-1	302	9	behaviour	behaviour	NOUN
azojete-1	302	10	of	of	ADP
azojete-1	302	11	ploycrystalls	ploycrystall	NOUN
azojete-1	302	12	.	.	PUNCT
azojete-1	303	1	journal	journal	PROPN
azojete-1	303	2	of	of	ADP
azojete-1	303	3	mechanics	mechanic	NOUN
azojete-1	303	4	and	and	CCONJ
azojete-1	303	5	physics	physics	NOUN
azojete-1	303	6	solids	solid	NOUN
azojete-1	303	7	,	,	PUNCT
azojete-1	303	8	10	10	NUM
azojete-1	303	9	:	:	SYM
azojete-1	303	10	335	335	NUM
azojete-1	303	11	-	-	SYM
azojete-1	303	12	345	345	NUM
azojete-1	303	13	.	.	PUNCT
azojete-1	304	1	hashin	hashin	PROPN
azojete-1	304	2	,	,	PUNCT
azojete-1	304	3	z.	z.	PROPN
azojete-1	304	4	and	and	CCONJ
azojete-1	304	5	shtrikman	shtrikman	PROPN
azojete-1	304	6	,	,	PUNCT
azojete-1	304	7	s.	s.	PROPN
azojete-1	304	8	1962	1962	NUM
azojete-1	304	9	.	.	PUNCT
azojete-1	305	1	on	on	ADP
azojete-1	305	2	some	some	DET
azojete-1	305	3	variational	variational	ADJ
azojete-1	305	4	principles	principle	NOUN
azojete-1	305	5	in	in	ADP
azojete-1	305	6	anisotropic	anisotropic	NOUN
azojete-1	305	7	and	and	CCONJ
azojete-1	305	8	homogeneous	homogeneous	ADJ
azojete-1	305	9	elasticity	elasticity	NOUN
azojete-1	305	10	.	.	PUNCT
azojete-1	306	1	journal	journal	NOUN
azojete-1	306	2	of	of	ADP
azojete-1	306	3	mechanics	mechanic	NOUN
azojete-1	306	4	and	and	CCONJ
azojete-1	306	5	physics	physics	NOUN
azojete-1	306	6	solids	solid	NOUN
azojete-1	306	7	,	,	PUNCT
azojete-1	306	8	10	10	NUM
azojete-1	306	9	:	:	SYM
azojete-1	306	10	335	335	NUM
azojete-1	306	11	-	-	SYM
azojete-1	306	12	342	342	NUM
azojete-1	306	13	.	.	PUNCT
azojete-1	307	1	hashin	hashin	PROPN
azojete-1	307	2	,	,	PUNCT
azojete-1	307	3	z.	z.	PROPN
azojete-1	307	4	and	and	CCONJ
azojete-1	307	5	shtrikman	shtrikman	PROPN
azojete-1	307	6	,	,	PUNCT
azojete-1	307	7	s.	s.	PROPN
azojete-1	307	8	1963	1963	NUM
azojete-1	307	9	.	.	PUNCT
azojete-1	308	1	a	a	DET
azojete-1	308	2	variational	variational	ADJ
azojete-1	308	3	approach	approach	NOUN
azojete-1	308	4	ot	ot	ADP
azojete-1	308	5	the	the	DET
azojete-1	308	6	theory	theory	NOUN
azojete-1	308	7	of	of	ADP
azojete-1	308	8	elastic	elastic	ADJ
azojete-1	308	9	behaviour	behaviour	NOUN
azojete-1	308	10	of	of	ADP
azojete-1	308	11	mulitphase	mulitphase	VERB
azojete-1	308	12	materials	material	NOUN
azojete-1	308	13	.	.	PUNCT
azojete-1	309	1	journal	journal	PROPN
azojete-1	309	2	of	of	ADP
azojete-1	309	3	mechanics	mechanic	NOUN
azojete-1	309	4	and	and	CCONJ
azojete-1	309	5	physics	physics	NOUN
azojete-1	309	6	solids	solid	NOUN
azojete-1	309	7	,	,	PUNCT
azojete-1	309	8	11	11	NUM
azojete-1	309	9	:	:	PUNCT
azojete-1	309	10	127	127	NUM
azojete-1	309	11	-	-	SYM
azojete-1	309	12	140	140	NUM
azojete-1	309	13	.	.	PUNCT
azojete-1	310	1	hill	hill	PROPN
azojete-1	310	2	,	,	PUNCT
azojete-1	310	3	r.	r.	PROPN
azojete-1	310	4	1965	1965	NUM
azojete-1	310	5	.	.	PUNCT
azojete-1	311	1	a	a	DET
azojete-1	311	2	self	self	NOUN
azojete-1	311	3	-	-	PUNCT
azojete-1	311	4	consitent	consitent	NOUN
azojete-1	311	5	mechanics	mechanic	NOUN
azojete-1	311	6	of	of	ADP
azojete-1	311	7	compoiste	compoiste	NOUN
azojete-1	311	8	materials	material	NOUN
azojete-1	311	9	.	.	PUNCT
azojete-1	312	1	journal	journal	PROPN
azojete-1	312	2	of	of	ADP
azojete-1	312	3	mechanics	mechanic	NOUN
azojete-1	312	4	and	and	CCONJ
azojete-1	312	5	physics	physics	NOUN
azojete-1	312	6	solids	solid	NOUN
azojete-1	312	7	,	,	PUNCT
azojete-1	312	8	13	13	NUM
azojete-1	312	9	:	:	SYM
azojete-1	312	10	213	213	NUM
azojete-1	312	11	-	-	SYM
azojete-1	312	12	222	222	NUM
azojete-1	312	13	.	.	PUNCT
azojete-1	313	1	hill	hill	PROPN
azojete-1	313	2	,	,	PUNCT
azojete-1	313	3	r.	r.	PROPN
azojete-1	313	4	1963	1963	NUM
azojete-1	313	5	.	.	PUNCT
azojete-1	314	1	elastic	elastic	ADJ
azojete-1	314	2	properties	property	NOUN
azojete-1	314	3	of	of	ADP
azojete-1	314	4	reinforced	reinforced	ADJ
azojete-1	314	5	sloids	sloid	NOUN
azojete-1	314	6	:	:	PUNCT
azojete-1	314	7	some	some	DET
azojete-1	314	8	theoretical	theoretical	ADJ
azojete-1	314	9	principles	principle	NOUN
azojete-1	314	10	.	.	PUNCT
azojete-1	315	1	journal	journal	NOUN
azojete-1	315	2	of	of	ADP
azojete-1	315	3	mechanics	mechanic	NOUN
azojete-1	315	4	and	and	CCONJ
azojete-1	315	5	physics	physics	NOUN
azojete-1	315	6	solids	solid	NOUN
azojete-1	315	7	,	,	PUNCT
azojete-1	315	8	13	13	NUM
azojete-1	315	9	:	:	SYM
azojete-1	315	10	213	213	NUM
azojete-1	315	11	-	-	SYM
azojete-1	315	12	222	222	NUM
azojete-1	315	13	.	.	PUNCT
azojete-1	316	1	hill	hill	PROPN
azojete-1	316	2	,	,	PUNCT
azojete-1	316	3	r.	r.	PROPN
azojete-1	316	4	1963	1963	NUM
azojete-1	316	5	.	.	PUNCT
azojete-1	317	1	the	the	DET
azojete-1	317	2	elastic	elastic	ADJ
azojete-1	317	3	behahiour	behahiour	NOUN
azojete-1	317	4	of	of	ADP
azojete-1	317	5	crystalline	crystalline	NOUN
azojete-1	317	6	aggregate	aggregate	NOUN
azojete-1	317	7	.	.	PUNCT
azojete-1	318	1	proceecings	proceecing	NOUN
azojete-1	318	2	of	of	ADP
azojete-1	318	3	the	the	DET
azojete-1	318	4	royal	royal	ADJ
azojete-1	318	5	society	society	NOUN
azojete-1	318	6	of	of	ADP
azojete-1	318	7	london	london	PROPN
azojete-1	318	8	series	series	PROPN
azojete-1	318	9	a	a	PROPN
azojete-1	318	10	,	,	PUNCT
azojete-1	318	11	65	65	NUM
azojete-1	318	12	:	:	SYM
azojete-1	318	13	349	349	NUM
azojete-1	318	14	-	-	SYM
azojete-1	318	15	354	354	NUM
azojete-1	318	16	.	.	PUNCT
azojete-1	319	1	hutchinson	hutchinson	PROPN
azojete-1	319	2	,	,	PUNCT
azojete-1	319	3	j.	j.	PROPN
azojete-1	319	4	1963	1963	NUM
azojete-1	319	5	.	.	PUNCT
azojete-1	320	1	bonds	bond	NOUN
azojete-1	320	2	and	and	CCONJ
azojete-1	320	3	self	self	NOUN
azojete-1	320	4	-	-	PUNCT
azojete-1	320	5	consistent	consistent	ADJ
azojete-1	320	6	estimates	estimate	NOUN
azojete-1	320	7	for	for	ADP
azojete-1	320	8	creep	creep	NOUN
azojete-1	320	9	and	and	CCONJ
azojete-1	320	10	polycrystalline	polycrystalline	ADJ
azojete-1	320	11	materials	material	NOUN
azojete-1	320	12	.	.	PUNCT
azojete-1	321	1	proceecings	proceecing	NOUN
azojete-1	321	2	of	of	ADP
azojete-1	321	3	the	the	DET
azojete-1	321	4	royal	royal	ADJ
azojete-1	321	5	society	society	NOUN
azojete-1	321	6	of	of	ADP
azojete-1	321	7	london	london	PROPN
azojete-1	321	8	series	series	PROPN
azojete-1	321	9	a	a	DET
azojete-1	321	10	348	348	NUM
azojete-1	321	11	:	:	PUNCT
azojete-1	321	12	101	101	NUM
azojete-1	321	13	-	-	SYM
azojete-1	321	14	127	127	NUM
azojete-1	321	15	.	.	PUNCT
azojete-1	322	1	kanoute	kanoute	PROPN
azojete-1	322	2	,	,	PUNCT
azojete-1	322	3	p.	p.	NOUN
azojete-1	322	4	,	,	PUNCT
azojete-1	322	5	boso	boso	PROPN
azojete-1	322	6	,	,	PUNCT
azojete-1	322	7	pd	pd	PROPN
azojete-1	322	8	.	.	PROPN
azojete-1	322	9	,	,	PUNCT
azojete-1	322	10	chaboche	chaboche	PROPN
azojete-1	322	11	,	,	PUNCT
azojete-1	322	12	jl	jl	PROPN
azojete-1	322	13	.	.	PROPN
azojete-1	322	14	,	,	PUNCT
azojete-1	322	15	schreller	schreller	PROPN
azojete-1	322	16	,	,	PUNCT
azojete-1	322	17	ba	ba	PROPN
azojete-1	322	18	.	.	PROPN
azojete-1	322	19	2009	2009	NUM
azojete-1	322	20	.	.	PUNCT
azojete-1	323	1	multiscale	multiscale	ADJ
azojete-1	323	2	methods	method	NOUN
azojete-1	323	3	for	for	ADP
azojete-1	323	4	composites	composite	NOUN
azojete-1	323	5	:	:	PUNCT
azojete-1	323	6	a	a	DET
azojete-1	323	7	review	review	NOUN
azojete-1	323	8	.	.	PUNCT
azojete-1	324	1	arch	arch	ADJ
azojete-1	324	2	comput	comput	PROPN
azojete-1	324	3	methods	method	NOUN
azojete-1	324	4	eng	eng	PROPN
azojete-1	324	5	,	,	PUNCT
azojete-1	324	6	16	16	NUM
azojete-1	324	7	:	:	PUNCT
azojete-1	324	8	31	31	NUM
azojete-1	324	9	-	-	SYM
azojete-1	324	10	75	75	NUM
azojete-1	324	11	.	.	PUNCT
azojete-1	325	1	doi	doi	PROPN
azojete-1	325	2	20.1007	20.1007	NUM
azojete-1	325	3	/	/	SYM
azojete-1	325	4	s11831	s11831	NOUN
azojete-1	325	5	-	-	PUNCT
azojete-1	325	6	008	008	NUM
azojete-1	325	7	-	-	PUNCT
azojete-1	325	8	9028	9028	NUM
azojete-1	325	9	-	-	SYM
azojete-1	325	10	8	8	NUM
azojete-1	325	11	file:///c:/users	file:///c:/user	NOUN
azojete-1	325	12	/	/	SYM
azojete-1	325	13	user	user	NOUN
azojete-1	325	14	/	/	SYM
azojete-1	325	15	downloads	download	NOUN
azojete-1	325	16	/	/	SYM
azojete-1	325	17	azojete143	azojete143	PROPN
azojete-1	325	18	/	/	SYM
azojete-1	325	19	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	325	20	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NUM
azojete-1	325	21	ohunene	ohunene	ADJ
azojete-1	325	22	hafsa	hafsa	PROPN
azojete-1	325	23	aliyu	aliyu	PROPN
azojete-1	325	24	:	:	PUNCT
azojete-1	326	1	analytical	analytical	ADJ
azojete-1	326	2	,	,	PUNCT
azojete-1	326	3	numerical	numerical	ADJ
azojete-1	326	4	and	and	CCONJ
azojete-1	326	5	computational	computational	ADJ
azojete-1	326	6	multiscale	multiscale	NOUN
azojete-1	326	7	modelling	model	VERB
azojete-1	326	8	techniques	technique	NOUN
azojete-1	326	9	for	for	ADP
azojete-1	326	10	heterogenous	heterogenous	ADJ
azojete-1	326	11	materials	material	NOUN
azojete-1	326	12	:	:	PUNCT
azojete-1	326	13	a	a	DET
azojete-1	326	14	review	review	NOUN
azojete-1	326	15	.	.	PUNCT
azojete-1	327	1	azojete	azojete	NOUN
azojete-1	327	2	,	,	PUNCT
azojete-1	327	3	15(3):488	15(3):488	PROPN
azojete-1	327	4	-	-	PUNCT
azojete-1	327	5	509	509	NUM
azojete-1	327	6	.	.	PUNCT
azojete-1	328	1	issn	issn	PROPN
azojete-1	328	2	1596	1596	NUM
azojete-1	328	3	-	-	SYM
azojete-1	328	4	2490	2490	NUM
azojete-1	328	5	;	;	PUNCT
azojete-1	328	6	e	e	X
azojete-1	328	7	-	-	NOUN
azojete-1	328	8	issn	issn	VERB
azojete-1	328	9	2545	2545	NUM
azojete-1	328	10	-	-	SYM
azojete-1	328	11	5818	5818	NUM
azojete-1	328	12	,	,	PUNCT
azojete-1	328	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	328	14	corresponding	correspond	VERB
azojete-1	328	15	author	author	NOUN
azojete-1	328	16	’s	’s	PART
azojete-1	328	17	e	e	NOUN
azojete-1	328	18	-	-	NOUN
azojete-1	328	19	mail	mail	NOUN
azojete-1	328	20	address	address	NOUN
azojete-1	328	21	:	:	PUNCT
azojete-1	328	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	328	23	508	508	NUM
azojete-1	328	24	kouznetsova	kouznetsova	NOUN
azojete-1	328	25	,	,	PUNCT
azojete-1	328	26	v.	v.	ADV
azojete-1	328	27	,	,	PUNCT
azojete-1	328	28	brekelmans	brekelman	NOUN
azojete-1	328	29	.	.	PUNCT
azojete-1	329	1	wam	wam	PROPN
azojete-1	329	2	.	.	PROPN
azojete-1	329	3	,	,	PUNCT
azojete-1	329	4	and	and	CCONJ
azojete-1	329	5	baaijens	baaijen	NOUN
azojete-1	329	6	,	,	PUNCT
azojete-1	329	7	fpt	fpt	PROPN
azojete-1	329	8	.	.	PUNCT
azojete-1	329	9	2001	2001	NUM
azojete-1	329	10	.	.	PUNCT
azojete-1	330	1	an	an	DET
azojete-1	330	2	approach	approach	NOUN
azojete-1	330	3	to	to	ADP
azojete-1	330	4	micro	micro	NOUN
azojete-1	330	5	-	-	NOUN
azojete-1	330	6	macro	macro	ADJ
azojete-1	330	7	modelling	modelling	NOUN
azojete-1	330	8	of	of	ADP
azojete-1	330	9	heterogeneous	heterogeneous	ADJ
azojete-1	330	10	materials	material	NOUN
azojete-1	330	11	.	.	PUNCT
azojete-1	331	1	compuatational	compuatational	ADJ
azojete-1	331	2	mechanics	mechanic	NOUN
azojete-1	331	3	,	,	PUNCT
azojete-1	331	4	27(1	27(1	NUM
azojete-1	331	5	):	):	PUNCT
azojete-1	331	6	37	37	NUM
azojete-1	331	7	-	-	SYM
azojete-1	331	8	48	48	NUM
azojete-1	331	9	.	.	PUNCT
azojete-1	332	1	kröner	kröner	NOUN
azojete-1	332	2	,	,	PUNCT
azojete-1	332	3	e.	e.	PROPN
azojete-1	332	4	1958	1958	NUM
azojete-1	332	5	.	.	PUNCT
azojete-1	333	1	berechnung	berechnung	ADJ
azojete-1	333	2	der	der	NOUN
azojete-1	333	3	elastischen	elastischen	ADV
azojete-1	333	4	konstanten	konstanten	PROPN
azojete-1	333	5	desvielkristalls	desvielkristall	NOUN
azojete-1	333	6	aus	aus	PROPN
azojete-1	333	7	den	den	PROPN
azojete-1	333	8	konstanten	konstanten	PROPN
azojete-1	333	9	des	des	PROPN
azojete-1	333	10	einkristalls	einkristall	NOUN
azojete-1	333	11	.	.	PUNCT
azojete-1	334	1	z	z	NOUN
azojete-1	334	2	phys	phy	NOUN
azojete-1	334	3	,	,	PUNCT
azojete-1	334	4	504	504	NUM
azojete-1	334	5	-	-	SYM
azojete-1	334	6	5	5	NUM
azojete-1	334	7	li	li	NOUN
azojete-1	334	8	,	,	PUNCT
azojete-1	334	9	s.	s.	PROPN
azojete-1	334	10	and	and	CCONJ
azojete-1	334	11	ghosh	ghosh	PROPN
azojete-1	334	12	,	,	PUNCT
azojete-1	334	13	s.	s.	PROPN
azojete-1	334	14	2006	2006	NUM
azojete-1	334	15	.	.	PUNCT
azojete-1	335	1	extended	extend	VERB
azojete-1	335	2	voronoi	voronoi	ADJ
azojete-1	335	3	cell	cell	NOUN
azojete-1	335	4	finite	finite	PROPN
azojete-1	335	5	element	element	NOUN
azojete-1	335	6	model	model	NOUN
azojete-1	335	7	for	for	ADP
azojete-1	335	8	mulitple	mulitple	NOUN
azojete-1	335	9	cohesive	cohesive	ADJ
azojete-1	335	10	crack	crack	NOUN
azojete-1	335	11	propagation	propagation	NOUN
azojete-1	335	12	in	in	ADP
azojete-1	335	13	brittle	brittle	ADJ
azojete-1	335	14	materials	material	NOUN
azojete-1	335	15	.	.	PUNCT
azojete-1	336	1	international	international	ADJ
azojete-1	336	2	journal	journal	PROPN
azojete-1	336	3	for	for	ADP
azojete-1	336	4	numerical	numerical	ADJ
azojete-1	336	5	method	method	NOUN
azojete-1	336	6	in	in	ADP
azojete-1	336	7	engineering	engineering	NOUN
azojete-1	336	8	,	,	PUNCT
azojete-1	336	9	65(7	65(7	NUM
azojete-1	336	10	):	):	PUNCT
azojete-1	336	11	1028	1028	NUM
azojete-1	336	12	-	-	SYM
azojete-1	336	13	1067	1067	NUM
azojete-1	336	14	.	.	PUNCT
azojete-1	337	1	llorca	llorca	PROPN
azojete-1	337	2	,	,	PUNCT
azojete-1	337	3	j.	j.	PROPN
azojete-1	337	4	,	,	PUNCT
azojete-1	337	5	gonzalez	gonzalez	PROPN
azojete-1	337	6	,	,	PUNCT
azojete-1	337	7	c.	c.	PROPN
azojete-1	337	8	,	,	PUNCT
azojete-1	337	9	and	and	CCONJ
azojete-1	337	10	segurado	segurado	NOUN
azojete-1	337	11	,	,	PUNCT
azojete-1	337	12	j.	j.	PROPN
azojete-1	337	13	2007	2007	NUM
azojete-1	337	14	.	.	PUNCT
azojete-1	338	1	finite	finite	PROPN
azojete-1	338	2	element	element	NOUN
azojete-1	338	3	and	and	CCONJ
azojete-1	338	4	homogenization	homogenization	NOUN
azojete-1	338	5	modelling	modelling	NOUN
azojete-1	338	6	of	of	ADP
azojete-1	338	7	materials	material	NOUN
azojete-1	338	8	in	in	ADP
azojete-1	338	9	:	:	PUNCT
azojete-1	338	10	gou	gou	PROPN
azojete-1	338	11	xiao	xiao	PROPN
azojete-1	338	12	z.	z.	PROPN
azojete-1	338	13	(	(	PUNCT
azojete-1	338	14	ed	ed	NOUN
azojete-1	338	15	.	.	PUNCT
azojete-1	338	16	)	)	PUNCT
azojete-1	339	1	multiscale	multiscale	ADJ
azojete-1	339	2	materials	material	NOUN
azojete-1	339	3	modelling.cambridge	modelling.cambridge	VERB
azojete-1	339	4	england	england	PROPN
azojete-1	339	5	:	:	PUNCT
azojete-1	339	6	woodhead	woodhead	NOUN
azojete-1	339	7	publishing	publishing	NOUN
azojete-1	339	8	and	and	CCONJ
azojete-1	339	9	maney	maney	NOUN
azojete-1	339	10	publishing	publishing	NOUN
azojete-1	339	11	,	,	PUNCT
azojete-1	339	12	121	121	NUM
azojete-1	339	13	-	-	SYM
azojete-1	339	14	144	144	NUM
azojete-1	339	15	matous	matous	ADJ
azojete-1	339	16	,	,	PUNCT
azojete-1	339	17	k.	k.	PROPN
azojete-1	339	18	,	,	PUNCT
azojete-1	339	19	geere	geere	PROPN
azojete-1	339	20	,	,	PUNCT
azojete-1	339	21	mgo	mgo	PROPN
azojete-1	339	22	.	.	PROPN
azojete-1	339	23	,	,	PUNCT
azojete-1	339	24	kouznetsova	kouznetsova	PROPN
azojete-1	339	25	,	,	PUNCT
azojete-1	339	26	vg	vg	PROPN
azojete-1	339	27	.	.	PROPN
azojete-1	339	28	,	,	PUNCT
azojete-1	339	29	gillman	gillman	PROPN
azojete-1	339	30	,	,	PUNCT
azojete-1	339	31	a.	a.	NOUN
azojete-1	339	32	2017	2017	NUM
azojete-1	339	33	.	.	PUNCT
azojete-1	340	1	a	a	DET
azojete-1	340	2	review	review	NOUN
azojete-1	340	3	of	of	ADP
azojete-1	340	4	predictive	predictive	ADJ
azojete-1	340	5	nonlinear	nonlinear	ADJ
azojete-1	340	6	theories	theory	NOUN
azojete-1	340	7	of	of	ADP
azojete-1	340	8	multiscale	multiscale	ADJ
azojete-1	340	9	modelling	modelling	NOUN
azojete-1	340	10	of	of	ADP
azojete-1	340	11	heterogenous	heterogenous	ADJ
azojete-1	340	12	materials	material	NOUN
azojete-1	340	13	.	.	PUNCT
azojete-1	341	1	journal	journal	NOUN
azojete-1	341	2	of	of	ADP
azojete-1	341	3	computational	computational	ADJ
azojete-1	341	4	physics	physics	NOUN
azojete-1	341	5	,	,	PUNCT
azojete-1	341	6	330	330	NUM
azojete-1	341	7	:	:	SYM
azojete-1	341	8	192	192	NUM
azojete-1	341	9	-	-	SYM
azojete-1	341	10	220	220	NUM
azojete-1	341	11	.	.	PUNCT
azojete-1	342	1	moorthy	moorthy	PROPN
azojete-1	342	2	,	,	PUNCT
azojete-1	342	3	s.	s.	PROPN
azojete-1	342	4	and	and	CCONJ
azojete-1	342	5	ghosh	ghosh	PROPN
azojete-1	342	6	,	,	PUNCT
azojete-1	342	7	s.	s.	PROPN
azojete-1	342	8	1996	1996	NUM
azojete-1	342	9	.	.	PUNCT
azojete-1	343	1	a	a	DET
azojete-1	343	2	model	model	NOUN
azojete-1	343	3	for	for	ADP
azojete-1	343	4	analysis	analysis	NOUN
azojete-1	343	5	of	of	ADP
azojete-1	343	6	arbitrary	arbitrary	ADJ
azojete-1	343	7	composite	composite	NOUN
azojete-1	343	8	and	and	CCONJ
azojete-1	343	9	poros	poros	PROPN
azojete-1	343	10	microstructure	microstructure	VERB
azojete-1	343	11	with	with	ADP
azojete-1	343	12	voronoi	voronoi	ADJ
azojete-1	343	13	cell	cell	NOUN
azojete-1	343	14	finite	finite	PROPN
azojete-1	343	15	element	element	NOUN
azojete-1	343	16	.	.	PUNCT
azojete-1	344	1	international	international	ADJ
azojete-1	344	2	journal	journal	PROPN
azojete-1	344	3	for	for	ADP
azojete-1	344	4	numerical	numerical	ADJ
azojete-1	344	5	method	method	NOUN
azojete-1	344	6	in	in	ADP
azojete-1	344	7	engineering	engineering	NOUN
azojete-1	344	8	,	,	PUNCT
azojete-1	344	9	39	39	NUM
azojete-1	344	10	:	:	PUNCT
azojete-1	344	11	2363	2363	NUM
azojete-1	344	12	-	-	SYM
azojete-1	344	13	2398	2398	NUM
azojete-1	344	14	moorthy	moorthy	PROPN
azojete-1	344	15	,	,	PUNCT
azojete-1	344	16	s.	s.	PROPN
azojete-1	344	17	and	and	CCONJ
azojete-1	344	18	ghosh	ghosh	PROPN
azojete-1	344	19	,	,	PUNCT
azojete-1	344	20	s.	s.	PROPN
azojete-1	344	21	2000	2000	NUM
azojete-1	344	22	.	.	PUNCT
azojete-1	345	1	adaptivity	adaptivity	NOUN
azojete-1	345	2	and	and	CCONJ
azojete-1	345	3	converganc	converganc	NOUN
azojete-1	345	4	in	in	ADP
azojete-1	345	5	the	the	DET
azojete-1	345	6	voronoi	voronoi	ADJ
azojete-1	345	7	cell	cell	NOUN
azojete-1	345	8	finite	finite	PROPN
azojete-1	345	9	element	element	NOUN
azojete-1	345	10	model	model	NOUN
azojete-1	345	11	for	for	ADP
azojete-1	345	12	analyzing	analyze	VERB
azojete-1	345	13	heterogeneous	heterogeneous	ADJ
azojete-1	345	14	materials	material	NOUN
azojete-1	345	15	.	.	PUNCT
azojete-1	346	1	computer	computer	NOUN
azojete-1	346	2	method	method	NOUN
azojete-1	346	3	in	in	ADP
azojete-1	346	4	applied	apply	VERB
azojete-1	346	5	mechanics	mechanic	NOUN
azojete-1	346	6	and	and	CCONJ
azojete-1	346	7	engieering	engieering	NOUN
azojete-1	346	8	,	,	PUNCT
azojete-1	346	9	185(7	185(7	NUM
azojete-1	346	10	):	):	PUNCT
azojete-1	346	11	37	37	NUM
azojete-1	346	12	-	-	SYM
azojete-1	346	13	74	74	NUM
azojete-1	346	14	.	.	PUNCT
azojete-1	347	1	nemat	nemat	NOUN
azojete-1	347	2	-	-	PUNCT
azojete-1	347	3	nasser	nasser	PROPN
azojete-1	347	4	,	,	PUNCT
azojete-1	347	5	s.	s.	PROPN
azojete-1	347	6	and	and	CCONJ
azojete-1	347	7	hori	hori	PROPN
azojete-1	347	8	,	,	PUNCT
azojete-1	347	9	m.	m.	NOUN
azojete-1	347	10	1999	1999	NUM
azojete-1	347	11	.	.	PUNCT
azojete-1	348	1	micromechanics	micromechanic	NOUN
azojete-1	348	2	:	:	PUNCT
azojete-1	348	3	overall	overall	ADJ
azojete-1	348	4	properties	property	NOUN
azojete-1	348	5	of	of	ADP
azojete-1	348	6	heterogeneous	heterogeneous	ADJ
azojete-1	348	7	material	material	NOUN
azojete-1	348	8	.	.	PUNCT
azojete-1	349	1	2nd	2nd	PROPN
azojete-1	349	2	edition	edition	PROPN
azojete-1	349	3	elsevier	elsevier	PROPN
azojete-1	349	4	amsterdam	amsterdam	PROPN
azojete-1	349	5	–	–	PUNCT
azojete-1	349	6	lausanne	lausanne	PROPN
azojete-1	349	7	–	–	PUNCT
azojete-1	349	8	new	new	PROPN
azojete-1	349	9	york	york	PROPN
azojete-1	349	10	–	–	PUNCT
azojete-1	349	11	oxford	oxford	PROPN
azojete-1	349	12	–	–	PUNCT
azojete-1	349	13	shannon	shannon	PROPN
azojete-1	349	14	–	–	PUNCT
azojete-1	349	15	singapore	singapore	PROPN
azojete-1	349	16	tokyo	tokyo	PROPN
azojete-1	349	17	nguyen	nguyen	NOUN
azojete-1	349	18	,	,	PUNCT
azojete-1	349	19	vp	vp	PROPN
azojete-1	349	20	.	.	PROPN
azojete-1	349	21	,	,	PUNCT
azojete-1	349	22	stroven	stroven	ADJ
azojete-1	349	23	,	,	PUNCT
azojete-1	349	24	m.	m.	NOUN
azojete-1	349	25	sluys	sluys	PROPN
azojete-1	349	26	,	,	PUNCT
azojete-1	349	27	lj	lj	PROPN
azojete-1	349	28	.	.	PROPN
azojete-1	349	29	,	,	PUNCT
azojete-1	349	30	2012	2012	NUM
azojete-1	349	31	.	.	PUNCT
azojete-1	350	1	mulitiscale	mulitiscale	NOUN
azojete-1	350	2	continuous	continuous	ADJ
azojete-1	350	3	and	and	CCONJ
azojete-1	350	4	discontinuous	discontinuous	ADJ
azojete-1	350	5	modelling	modelling	NOUN
azojete-1	350	6	of	of	ADP
azojete-1	350	7	heterogeneous	heterogeneous	ADJ
azojete-1	350	8	mateials	mateial	NOUN
azojete-1	350	9	:	:	PUNCT
azojete-1	350	10	a	a	DET
azojete-1	350	11	review	review	NOUN
azojete-1	350	12	on	on	ADP
azojete-1	350	13	recent	recent	ADJ
azojete-1	350	14	developments	development	NOUN
azojete-1	350	15	.	.	PUNCT
azojete-1	351	1	journal	journal	NOUN
azojete-1	351	2	of	of	ADP
azojete-1	351	3	multiscale	multiscale	PROPN
azojete-1	351	4	modelling	modelling	NOUN
azojete-1	351	5	,	,	PUNCT
azojete-1	351	6	4	4	NUM
azojete-1	351	7	(	(	PUNCT
azojete-1	351	8	3	3	NUM
azojete-1	351	9	):	):	PUNCT
azojete-1	351	10	1	1	NUM
azojete-1	351	11	-	-	SYM
azojete-1	351	12	42	42	NUM
azojete-1	351	13	imperial	imperial	ADJ
azojete-1	351	14	college	college	NOUN
azojete-1	351	15	press	press	NOUN
azojete-1	351	16	doi	doi	NOUN
azojete-1	351	17	:	:	PUNCT
azojete-1	351	18	10.1142	10.1142	NUM
azojete-1	351	19	/	/	SYM
azojete-1	352	1	s1756973711000509	s1756973711000509	NOUN
azojete-1	352	2	.	.	PUNCT
azojete-1	352	3	olson	olson	NOUN
azojete-1	352	4	,	,	PUNCT
azojete-1	352	5	t.	t.	PROPN
azojete-1	352	6	1994	1994	NUM
azojete-1	352	7	.	.	PUNCT
azojete-1	353	1	improvements	improvement	NOUN
azojete-1	353	2	on	on	ADP
azojete-1	353	3	a	a	DET
azojete-1	353	4	taylors	taylor	NOUN
azojete-1	353	5	upper	upper	ADV
azojete-1	353	6	bound	bind	VERB
azojete-1	353	7	for	for	ADP
azojete-1	353	8	rigid	rigid	ADJ
azojete-1	353	9	-	-	PUNCT
azojete-1	353	10	plastic	plastic	NOUN
azojete-1	353	11	composites	composite	NOUN
azojete-1	353	12	.	.	PUNCT
azojete-1	354	1	material	material	NOUN
azojete-1	354	2	science	science	PROPN
azojete-1	354	3	engineering	engineering	NOUN
azojete-1	354	4	,	,	PUNCT
azojete-1	354	5	a175	a175	PROPN
azojete-1	354	6	:	:	PUNCT
azojete-1	354	7	15	15	NUM
azojete-1	354	8	-	-	SYM
azojete-1	354	9	19	19	NUM
azojete-1	354	10	.	.	PUNCT
azojete-1	354	11	ozdemir	ozdemir	PROPN
azojete-1	354	12	,	,	PUNCT
azojete-1	354	13	i.	i.	PROPN
azojete-1	354	14	,	,	PUNCT
azojete-1	354	15	brekelmans	brekelman	NOUN
azojete-1	354	16	,	,	PUNCT
azojete-1	354	17	wam	wam	PROPN
azojete-1	354	18	.	.	PROPN
azojete-1	354	19	,	,	PUNCT
azojete-1	354	20	and	and	CCONJ
azojete-1	354	21	geers	geer	NOUN
azojete-1	354	22	,	,	PUNCT
azojete-1	354	23	mgo	mgo	PROPN
azojete-1	354	24	.	.	PROPN
azojete-1	354	25	2008	2008	NUM
azojete-1	354	26	.	.	PUNCT
azojete-1	355	1	computational	computational	ADJ
azojete-1	355	2	homogenization	homogenization	NOUN
azojete-1	355	3	for	for	ADP
azojete-1	355	4	heat	heat	NOUN
azojete-1	355	5	conduction	conduction	NOUN
azojete-1	355	6	in	in	ADP
azojete-1	355	7	heterogeneous	heterogeneous	ADJ
azojete-1	355	8	solids	solid	NOUN
azojete-1	355	9	.	.	PUNCT
azojete-1	356	1	international	international	ADJ
azojete-1	356	2	journal	journal	PROPN
azojete-1	356	3	of	of	ADP
azojete-1	356	4	numerical	numerical	ADJ
azojete-1	356	5	methods	method	NOUN
azojete-1	356	6	in	in	ADP
azojete-1	356	7	engineering	engineering	NOUN
azojete-1	356	8	,	,	PUNCT
azojete-1	356	9	73	73	NUM
azojete-1	356	10	:	:	SYM
azojete-1	356	11	185	185	NUM
azojete-1	356	12	-	-	SYM
azojete-1	356	13	204	204	NUM
azojete-1	356	14	.	.	PUNCT
azojete-1	357	1	ponte	ponte	PROPN
azojete-1	357	2	casta	casta	PROPN
azojete-1	357	3	eda	eda	PROPN
azojete-1	357	4	,	,	PUNCT
azojete-1	357	5	p.	p.	NOUN
azojete-1	357	6	1996	1996	NUM
azojete-1	357	7	.	.	PUNCT
azojete-1	358	1	exact	exact	ADJ
azojete-1	358	2	second	second	ADJ
azojete-1	358	3	-	-	PUNCT
azojete-1	358	4	order	order	NOUN
azojete-1	358	5	estimates	estimate	NOUN
azojete-1	358	6	for	for	ADP
azojete-1	358	7	the	the	DET
azojete-1	358	8	effective	effective	ADJ
azojete-1	358	9	mechanical	mechanical	ADJ
azojete-1	358	10	properties	property	NOUN
azojete-1	358	11	of	of	ADP
azojete-1	358	12	non	non	ADJ
azojete-1	358	13	linear	linear	ADJ
azojete-1	358	14	composite	composite	ADJ
azojete-1	358	15	materials	material	NOUN
azojete-1	358	16	.	.	PUNCT
azojete-1	359	1	journal	journal	PROPN
azojete-1	359	2	of	of	ADP
azojete-1	359	3	mechanics	mechanic	NOUN
azojete-1	359	4	and	and	CCONJ
azojete-1	359	5	physics	physics	NOUN
azojete-1	359	6	solids	solid	NOUN
azojete-1	359	7	,	,	PUNCT
azojete-1	359	8	44	44	NUM
azojete-1	359	9	:	:	SYM
azojete-1	359	10	827	827	NUM
azojete-1	359	11	-	-	SYM
azojete-1	359	12	862	862	NUM
azojete-1	359	13	.	.	PUNCT
azojete-1	360	1	petracca	petracca	NOUN
azojete-1	360	2	,	,	PUNCT
azojete-1	360	3	m.	m.	NOUN
azojete-1	360	4	,	,	PUNCT
azojete-1	360	5	pela	pela	PROPN
azojete-1	360	6	.	.	PUNCT
azojete-1	361	1	luca	luca	PROPN
azojete-1	361	2	,	,	PUNCT
azojete-1	361	3	rossi	rossi	ADJ
azojete-1	361	4	,	,	PUNCT
azojete-1	361	5	riccardo	riccardo	PROPN
azojete-1	361	6	,	,	PUNCT
azojete-1	361	7	oller	oller	NOUN
azojete-1	361	8	.	.	PUNCT
azojete-1	362	1	s.	s.	PROPN
azojete-1	362	2	,	,	PUNCT
azojete-1	362	3	camata	camata	PROPN
azojete-1	362	4	,	,	PUNCT
azojete-1	362	5	s.	s.	PROPN
azojete-1	362	6	,	,	PUNCT
azojete-1	362	7	spacone	spacone	NOUN
azojete-1	362	8	,	,	PUNCT
azojete-1	362	9	e.	e.	PROPN
azojete-1	362	10	2016	2016	NUM
azojete-1	362	11	.	.	PUNCT
azojete-1	363	1	regularization	regularization	NOUN
azojete-1	363	2	of	of	ADP
azojete-1	363	3	first	first	ADJ
azojete-1	363	4	order	order	NOUN
azojete-1	363	5	computational	computational	ADJ
azojete-1	363	6	homogenization	homogenization	NOUN
azojete-1	363	7	for	for	ADP
azojete-1	363	8	multiscale	multiscale	ADJ
azojete-1	363	9	analysis	analysis	NOUN
azojete-1	363	10	of	of	ADP
azojete-1	363	11	masonry	masonry	NOUN
azojete-1	363	12	structures	structure	NOUN
azojete-1	363	13	.	.	PUNCT
azojete-1	364	1	springer	springer	NOUN
azojete-1	364	2	2	2	NUM
azojete-1	364	3	(	(	PUNCT
azojete-1	364	4	57	57	NUM
azojete-1	364	5	):	):	PUNCT
azojete-1	364	6	257	257	NUM
azojete-1	364	7	-	-	SYM
azojete-1	364	8	276	276	NUM
azojete-1	364	9	.	.	PUNCT
azojete-1	365	1	ponte	ponte	PROPN
azojete-1	365	2	castan	castan	PROPN
azojete-1	365	3	eda	eda	PROPN
azojete-1	365	4	,	,	PUNCT
azojete-1	365	5	p.	p.	NOUN
azojete-1	365	6	1997	1997	NUM
azojete-1	365	7	.	.	PUNCT
azojete-1	366	1	non	non	ADJ
azojete-1	366	2	linear	linear	ADJ
azojete-1	366	3	composite	composite	ADJ
azojete-1	366	4	materials	material	NOUN
azojete-1	366	5	:	:	PUNCT
azojete-1	366	6	e⒐ective	e⒐ective	ADJ
azojete-1	366	7	constitutive	constitutive	ADJ
azojete-1	366	8	behaviour	behaviour	NOUN
azojete-1	366	9	and	and	CCONJ
azojete-1	366	10	microstructure	microstructure	ADJ
azojete-1	366	11	evolution䇅	evolution䇅	NOUN
azojete-1	366	12	in	in	ADP
azojete-1	366	13	:	:	PUNCT
azojete-1	366	14	suquet	suquet	VERB
azojete-1	366	15	,	,	PUNCT
azojete-1	366	16	p.	p.	NOUN
azojete-1	366	17	(	(	PUNCT
azojete-1	366	18	ed	ed	NOUN
azojete-1	366	19	)	)	PUNCT
azojete-1	366	20	continuum	continuum	ADJ
azojete-1	366	21	micromechanics	micromechanic	NOUN
azojete-1	366	22	cism	cism	NOUN
azojete-1	366	23	courses	course	NOUN
azojete-1	366	24	and	and	CCONJ
azojete-1	366	25	lectures	lecture	NOUN
azojete-1	366	26	.	.	PUNCT
azojete-1	367	1	337	337	NUM
azojete-1	367	2	:	:	PUNCT
azojete-1	367	3	188	188	NUM
azojete-1	367	4	-	-	SYM
azojete-1	367	5	195	195	NUM
azojete-1	367	6	ed	ed	NOUN
azojete-1	367	7	.	.	PUNCT
azojete-1	368	1	new	new	PROPN
azojete-1	368	2	york	york	PROPN
azojete-1	368	3	:	:	PUNCT
azojete-1	368	4	spinger	spinger	NOUN
azojete-1	368	5	.	.	PUNCT
azojete-1	369	1	ponte	ponte	NOUN
azojete-1	369	2	castenda	castenda	ADV
azojete-1	369	3	,	,	PUNCT
azojete-1	369	4	p.	p.	NOUN
azojete-1	369	5	and	and	CCONJ
azojete-1	369	6	suquet	suquet	PROPN
azojete-1	369	7	,	,	PUNCT
azojete-1	369	8	p.	p.	NOUN
azojete-1	369	9	1998	1998	NUM
azojete-1	369	10	.	.	PUNCT
azojete-1	370	1	nonlinear	nonlinear	ADJ
azojete-1	370	2	composites	composite	NOUN
azojete-1	370	3	.	.	PUNCT
azojete-1	371	1	advanced	advanced	ADJ
azojete-1	371	2	applied	apply	VERB
azojete-1	371	3	mechanics	mechanic	NOUN
azojete-1	371	4	,	,	PUNCT
azojete-1	371	5	34	34	NUM
azojete-1	371	6	:	:	SYM
azojete-1	371	7	171	171	NUM
azojete-1	371	8	-	-	SYM
azojete-1	371	9	301	301	NUM
azojete-1	371	10	.	.	PUNCT
azojete-1	372	1	reuss	reuss	NOUN
azojete-1	372	2	,	,	PUNCT
azojete-1	372	3	a.	a.	NOUN
azojete-1	372	4	1929	1929	NUM
azojete-1	372	5	.	.	PUNCT
azojete-1	373	1	berechnung	berechnung	PROPN
azojete-1	373	2	del	del	PROPN
azojete-1	373	3	fliessgrenze	fliessgrenze	PROPN
azojete-1	373	4	von	von	PROPN
azojete-1	373	5	mis	mis	PROPN
azojete-1	373	6	-	-	PUNCT
azojete-1	373	7	chkristallen	chkristallen	VERB
azojete-1	373	8	auf	auf	PROPN
azojete-1	373	9	grund	grund	PROPN
azojete-1	373	10	der	der	ADJ
azojete-1	373	11	plastizitätbedingung	plastizitätbedingung	PROPN
azojete-1	373	12	für	für	PROPN
azojete-1	373	13	einkristalle	einkristalle	VERB
azojete-1	373	14	.	.	PUNCT
azojete-1	374	1	z	z	PROPN
azojete-1	374	2	angew	angew	PROPN
azojete-1	374	3	math	math	PROPN
azojete-1	374	4	mech	mech	NOUN
azojete-1	374	5	,	,	PUNCT
azojete-1	374	6	9	9	NUM
azojete-1	374	7	:	:	SYM
azojete-1	374	8	49	49	NUM
azojete-1	374	9	-	-	SYM
azojete-1	374	10	58	58	NUM
azojete-1	374	11	.	.	PUNCT
azojete-1	375	1	suquet	suquet	NOUN
azojete-1	375	2	,	,	PUNCT
azojete-1	375	3	p.	p.	NOUN
azojete-1	375	4	1993	1993	NUM
azojete-1	375	5	.	.	PUNCT
azojete-1	376	1	overall	overall	ADJ
azojete-1	376	2	potential	potential	ADJ
azojete-1	376	3	and	and	CCONJ
azojete-1	376	4	external	external	ADJ
azojete-1	376	5	surfaces	surface	NOUN
azojete-1	376	6	of	of	ADP
azojete-1	376	7	power	power	NOUN
azojete-1	376	8	law	law	NOUN
azojete-1	376	9	or	or	CCONJ
azojete-1	376	10	ideally	ideally	ADV
azojete-1	376	11	plastic	plastic	ADJ
azojete-1	376	12	composite	composite	NOUN
azojete-1	376	13	.	.	PUNCT
azojete-1	377	1	journal	journal	PROPN
azojete-1	377	2	of	of	ADP
azojete-1	377	3	mechanics	mechanic	NOUN
azojete-1	377	4	and	and	CCONJ
azojete-1	377	5	physics	physics	NOUN
azojete-1	377	6	solids	solid	NOUN
azojete-1	377	7	,	,	PUNCT
azojete-1	377	8	41	41	NUM
azojete-1	377	9	:	:	PUNCT
azojete-1	377	10	981	981	NUM
azojete-1	377	11	-	-	SYM
azojete-1	377	12	1002	1002	NUM
azojete-1	377	13	.	.	PUNCT
azojete-1	378	1	http://www.azojete.com.ng	http://www.azojete.com.ng	ADV
azojete-1	378	2	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	PROPN
azojete-1	378	3	arid	arid	NOUN
azojete-1	378	4	zone	zone	NOUN
azojete-1	378	5	journal	journal	NOUN
azojete-1	378	6	of	of	ADP
azojete-1	378	7	engineering	engineering	NOUN
azojete-1	378	8	,	,	PUNCT
azojete-1	378	9	technology	technology	NOUN
azojete-1	378	10	and	and	CCONJ
azojete-1	378	11	environment	environment	NOUN
azojete-1	378	12	,	,	PUNCT
azojete-1	378	13	september	september	PROPN
azojete-1	378	14	,	,	PUNCT
azojete-1	378	15	2019	2019	NUM
azojete-1	378	16	;	;	PUNCT
azojete-1	378	17	vol	vol	NOUN
azojete-1	378	18	.	.	PUNCT
azojete-1	379	1	15(3):488	15(3):488	NUM
azojete-1	379	2	-	-	PUNCT
azojete-1	379	3	509	509	NUM
azojete-1	379	4	.	.	PUNCT
azojete-1	380	1	issn	issn	PROPN
azojete-1	380	2	1596	1596	NUM
azojete-1	380	3	-	-	SYM
azojete-1	380	4	2490	2490	NUM
azojete-1	380	5	;	;	PUNCT
azojete-1	380	6	e	e	X
azojete-1	380	7	-	-	NOUN
azojete-1	380	8	issn	issn	VERB
azojete-1	380	9	2545	2545	NUM
azojete-1	380	10	-	-	SYM
azojete-1	380	11	5818	5818	NUM
azojete-1	380	12	;	;	PUNCT
azojete-1	380	13	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	380	14	corresponding	correspond	VERB
azojete-1	380	15	author	author	NOUN
azojete-1	380	16	’s	’s	PART
azojete-1	380	17	e	e	NOUN
azojete-1	380	18	-	-	NOUN
azojete-1	380	19	mail	mail	NOUN
azojete-1	380	20	address	address	NOUN
azojete-1	380	21	:	:	PUNCT
azojete-1	380	22	ohunene.hafsa@fubk.edu.ng	ohunene.hafsa@fubk.edu.ng	NOUN
azojete-1	380	23	509	509	NUM
azojete-1	380	24	talbot	talbot	PROPN
azojete-1	380	25	,	,	PUNCT
azojete-1	380	26	drs	drs	PROPN
azojete-1	380	27	.	.	PROPN
azojete-1	380	28	and	and	CCONJ
azojete-1	380	29	willis	willis	PROPN
azojete-1	380	30	,	,	PUNCT
azojete-1	380	31	jr	jr	PROPN
azojete-1	380	32	.	.	PROPN
azojete-1	380	33	1985	1985	NUM
azojete-1	380	34	.	.	PUNCT
azojete-1	381	1	variational	variational	ADJ
azojete-1	381	2	principles	principle	NOUN
azojete-1	381	3	of	of	ADP
azojete-1	381	4	inhomogeneous	inhomogeneous	ADJ
azojete-1	381	5	non	non	ADJ
azojete-1	381	6	-	-	ADJ
azojete-1	381	7	linear	linear	ADJ
azojete-1	381	8	media	medium	NOUN
azojete-1	381	9	.	.	PUNCT
azojete-1	382	1	journal	journal	NOUN
azojete-1	382	2	of	of	ADP
azojete-1	382	3	applied	apply	VERB
azojete-1	382	4	math	math	NOUN
azojete-1	382	5	,	,	PUNCT
azojete-1	382	6	35	35	NUM
azojete-1	382	7	:	:	SYM
azojete-1	382	8	39	39	NUM
azojete-1	382	9	-	-	SYM
azojete-1	382	10	54	54	NUM
azojete-1	382	11	.	.	PUNCT
azojete-1	383	1	talbot	talbot	PROPN
azojete-1	383	2	,	,	PUNCT
azojete-1	383	3	drs	drs	PROPN
azojete-1	383	4	.	.	PROPN
azojete-1	384	1	and	and	CCONJ
azojete-1	384	2	willis	willis	PROPN
azojete-1	384	3	,	,	PUNCT
azojete-1	384	4	jr	jr	PROPN
azojete-1	384	5	.	.	PROPN
azojete-1	384	6	1992	1992	NUM
azojete-1	384	7	.	.	PUNCT
azojete-1	385	1	some	some	DET
azojete-1	385	2	explicit	explicit	ADJ
azojete-1	385	3	bounds	bound	NOUN
azojete-1	385	4	for	for	ADP
azojete-1	385	5	the	the	DET
azojete-1	385	6	overall	overall	ADJ
azojete-1	385	7	behaviour	behaviour	NOUN
azojete-1	385	8	of	of	ADP
azojete-1	385	9	nonlinear	nonlinear	ADJ
azojete-1	385	10	composites	composite	NOUN
azojete-1	385	11	.	.	PUNCT
azojete-1	386	1	international	international	ADJ
azojete-1	386	2	journal	journal	PROPN
azojete-1	386	3	for	for	ADP
azojete-1	386	4	structures	structure	NOUN
azojete-1	386	5	,	,	PUNCT
azojete-1	386	6	29	29	NUM
azojete-1	386	7	:	:	SYM
azojete-1	386	8	1981	1981	NUM
azojete-1	386	9	-	-	SYM
azojete-1	386	10	1987	1987	NUM
azojete-1	386	11	.	.	PUNCT
azojete-1	387	1	torquato	torquato	PROPN
azojete-1	387	2	,	,	PUNCT
azojete-1	387	3	s.	s.	PROPN
azojete-1	387	4	2001	2001	NUM
azojete-1	387	5	.	.	PUNCT
azojete-1	388	1	random	random	ADJ
azojete-1	388	2	heterogenous	heterogenous	ADJ
azojete-1	388	3	materials.new	materials.new	PROPN
azojete-1	388	4	york	york	PROPN
azojete-1	388	5	:	:	PUNCT
azojete-1	388	6	springer	springer	NOUN
azojete-1	388	7	torquato	torquato	PROPN
azojete-1	388	8	,	,	PUNCT
azojete-1	388	9	s.	s.	PROPN
azojete-1	388	10	2013	2013	NUM
azojete-1	388	11	.	.	PUNCT
azojete-1	389	1	random	random	ADJ
azojete-1	389	2	heterogenous	heterogenous	ADJ
azojete-1	389	3	materials.new	materials.new	PROPN
azojete-1	389	4	york	york	PROPN
azojete-1	389	5	:	:	PUNCT
azojete-1	389	6	springer	springer	NOUN
azojete-1	389	7	:	:	PUNCT
azojete-1	390	1	5	5	X
azojete-1	390	2	.	.	X
azojete-1	390	3	van	van	PROPN
azojete-1	390	4	der	der	PROPN
azojete-1	390	5	sluis	sluis	PROPN
azojete-1	390	6	,	,	PUNCT
azojete-1	390	7	o.	o.	PROPN
azojete-1	390	8	,	,	PUNCT
azojete-1	390	9	schreurs	schreur	NOUN
azojete-1	390	10	,	,	PUNCT
azojete-1	390	11	pjg	pjg	PROPN
azojete-1	390	12	.	.	PROPN
azojete-1	390	13	,	,	PUNCT
azojete-1	390	14	brekelemans	brekelemans	PROPN
azojete-1	390	15	,	,	PUNCT
azojete-1	390	16	wam	wam	PROPN
azojete-1	390	17	.	.	PROPN
azojete-1	390	18	,	,	PUNCT
azojete-1	390	19	and	and	CCONJ
azojete-1	390	20	meijer	meijer	NOUN
azojete-1	390	21	,	,	PUNCT
azojete-1	390	22	heh	heh	NOUN
azojete-1	390	23	.	.	PROPN
azojete-1	390	24	2000	2000	NUM
azojete-1	390	25	.	.	PUNCT
azojete-1	391	1	overall	overall	ADJ
azojete-1	391	2	behaviour	behaviour	NOUN
azojete-1	391	3	of	of	ADP
azojete-1	391	4	heterogenous	heterogenous	ADJ
azojete-1	391	5	elastoviscoplastic	elastoviscoplastic	ADJ
azojete-1	391	6	materials	material	NOUN
azojete-1	391	7	:	:	PUNCT
azojete-1	391	8	effect	effect	NOUN
azojete-1	391	9	of	of	ADP
azojete-1	391	10	microstructural	microstructural	ADJ
azojete-1	391	11	modelling	modelling	NOUN
azojete-1	391	12	.	.	PUNCT
azojete-1	392	1	mechanics	mechanic	NOUN
azojete-1	392	2	of	of	ADP
azojete-1	392	3	materials	material	NOUN
azojete-1	392	4	,	,	PUNCT
azojete-1	392	5	32(8	32(8	NUM
azojete-1	392	6	):	):	PUNCT
azojete-1	392	7	449	449	NUM
azojete-1	392	8	-	-	SYM
azojete-1	392	9	462	462	PROPN
azojete-1	392	10	.	.	PUNCT
azojete-1	393	1	voigt	voigt	PROPN
azojete-1	393	2	,	,	PUNCT
azojete-1	393	3	w.	w.	PROPN
azojete-1	393	4	1889	1889	NUM
azojete-1	393	5	.	.	PUNCT
azojete-1	394	1	über	über	PROPN
azojete-1	394	2	die	die	PROPN
azojete-1	394	3	beziehung	beziehung	PROPN
azojete-1	394	4	zwischen	zwischen	PROPN
azojete-1	394	5	den	den	PROPN
azojete-1	394	6	beiden	beiden	ADJ
azojete-1	394	7	elastizitätskonstanten	elastizitätskonstanten	PROPN
azojete-1	394	8	isotroper	isotroper	NOUN
azojete-1	394	9	körper	körper	NOUN
azojete-1	394	10	.	.	PUNCT
azojete-1	395	1	wied	wied	PROPN
azojete-1	395	2	ann	ann	PROPN
azojete-1	395	3	,	,	PUNCT
azojete-1	395	4	38	38	NUM
azojete-1	395	5	:	:	PUNCT
azojete-1	395	6	573–587	573–587	NUM
azojete-1	395	7	.	.	PUNCT
azojete-1	396	1	weinan	weinan	PROPN
azojete-1	396	2	,	,	PUNCT
azojete-1	396	3	e.	e.	PROPN
azojete-1	396	4	,	,	PUNCT
azojete-1	396	5	engquist	engquist	PROPN
azojete-1	396	6	,	,	PUNCT
azojete-1	396	7	b.	b.	PROPN
azojete-1	396	8	,	,	PUNCT
azojete-1	396	9	li	li	PROPN
azojete-1	396	10	,	,	PUNCT
azojete-1	396	11	x.	x.	PROPN
azojete-1	396	12	,	,	PUNCT
azojete-1	396	13	ren	ren	PROPN
azojete-1	396	14	,	,	PUNCT
azojete-1	396	15	w.	w.	PROPN
azojete-1	396	16	,	,	PUNCT
azojete-1	396	17	and	and	CCONJ
azojete-1	396	18	vanden	vanden	NOUN
azojete-1	396	19	-	-	PUNCT
azojete-1	396	20	eijnden	eijnden	NOUN
azojete-1	396	21	,	,	PUNCT
azojete-1	396	22	e.	e.	PROPN
azojete-1	396	23	2007	2007	NUM
azojete-1	396	24	.	.	PUNCT
azojete-1	397	1	heterogeneous	heterogeneous	ADJ
azojete-1	397	2	multiscale	multiscale	ADJ
azojete-1	397	3	methods	method	NOUN
azojete-1	397	4	:	:	PUNCT
azojete-1	397	5	a	a	DET
azojete-1	397	6	review	review	NOUN
azojete-1	397	7	.	.	PUNCT
azojete-1	398	1	community	community	NOUN
azojete-1	398	2	of	of	ADP
azojete-1	398	3	computational	computational	ADJ
azojete-1	398	4	physics	physic	NOUN
azojete-1	398	5	,	,	PUNCT
azojete-1	398	6	2	2	NUM
azojete-1	398	7	:	:	PUNCT
azojete-1	398	8	367	367	NUM
azojete-1	398	9	-	-	SYM
azojete-1	398	10	450	450	NUM
azojete-1	398	11	.	.	PUNCT
azojete-1	399	1	weinan	weinan	PROPN
azojete-1	399	2	,	,	PUNCT
azojete-1	399	3	e.	e.	PROPN
azojete-1	399	4	and	and	CCONJ
azojete-1	399	5	jianfeng	jianfeng	PROPN
azojete-1	399	6	,	,	PUNCT
azojete-1	399	7	l.	l.	PROPN
azojete-1	399	8	2011	2011	NUM
azojete-1	399	9	.	.	PUNCT
azojete-1	400	1	䇅mulitiscale	䇅mulitiscale	NOUN
azojete-1	400	2	modelling䇅	modelling䇅	NOUN
azojete-1	400	3	.	.	PUNCT
azojete-1	401	1	scholarpedia	scholarpedia	PROPN
azojete-1	401	2	,	,	PUNCT
azojete-1	401	3	6(10	6(10	NUM
azojete-1	401	4	)	)	PUNCT
azojete-1	401	5	,	,	PUNCT
azojete-1	401	6	pp	pp	PROPN
azojete-1	401	7	.	.	PUNCT
azojete-1	401	8	11527	11527	NUM
azojete-1	401	9	.	.	PUNCT
azojete-1	402	1	wiechert	wiechert	PROPN
azojete-1	402	2	,	,	PUNCT
azojete-1	402	3	l.	l.	PROPN
azojete-1	402	4	and	and	CCONJ
azojete-1	402	5	wall	wall	PROPN
azojete-1	402	6	,	,	PUNCT
azojete-1	402	7	w.a	w.a	PROPN
azojete-1	402	8	.	.	PROPN
azojete-1	402	9	2010	2010	NUM
azojete-1	402	10	.	.	PUNCT
azojete-1	403	1	a	a	DET
azojete-1	403	2	nested	nested	ADJ
azojete-1	403	3	dynamic	dynamic	ADJ
azojete-1	403	4	multi	multi	ADJ
azojete-1	403	5	-	-	ADJ
azojete-1	403	6	scale	scale	ADJ
azojete-1	403	7	approach	approach	NOUN
azojete-1	403	8	for	for	ADP
azojete-1	403	9	3d	3d	PROPN
azojete-1	403	10	problems	problem	NOUN
azojete-1	403	11	accounting	account	VERB
azojete-1	403	12	for	for	ADP
azojete-1	403	13	micro	micro	ADJ
azojete-1	403	14	-	-	NOUN
azojete-1	403	15	scale	scale	ADJ
azojete-1	403	16	multi	multi	NOUN
azojete-1	403	17	-	-	NOUN
azojete-1	403	18	physics	physics	NOUN
azojete-1	403	19	.	.	PUNCT
azojete-1	404	1	computer	computer	NOUN
azojete-1	404	2	methods	method	NOUN
azojete-1	404	3	in	in	ADP
azojete-1	404	4	applied	applied	ADJ
azojete-1	404	5	mechanics	mechanic	NOUN
azojete-1	404	6	and	and	CCONJ
azojete-1	404	7	engineering	engineering	NOUN
azojete-1	404	8	,	,	PUNCT
azojete-1	404	9	199(21	199(21	NUM
azojete-1	404	10	-	-	SYM
azojete-1	404	11	22	22	NUM
azojete-1	404	12	):	):	PUNCT
azojete-1	404	13	1342	1342	NUM
azojete-1	404	14	-	-	SYM
azojete-1	404	15	1351	1351	NUM
azojete-1	404	16	.	.	PUNCT
azojete-1	405	1	willis	willis	PROPN
azojete-1	405	2	,	,	PUNCT
azojete-1	405	3	j.	j.	PROPN
azojete-1	405	4	1986	1986	NUM
azojete-1	405	5	.	.	PUNCT
azojete-1	406	1	variational	variational	ADJ
azojete-1	406	2	estimates	estimate	NOUN
azojete-1	406	3	for	for	ADP
azojete-1	406	4	the	the	DET
azojete-1	406	5	overall	overall	ADJ
azojete-1	406	6	response	response	NOUN
azojete-1	406	7	of	of	ADP
azojete-1	406	8	an	an	DET
azojete-1	406	9	inhomogeneous	inhomogeneous	ADJ
azojete-1	406	10	nonlinear	nonlinear	ADJ
azojete-1	406	11	dielectric	dielectric	NOUN
azojete-1	406	12	in	in	ADP
azojete-1	406	13	:	:	PUNCT
azojete-1	406	14	ericksen	ericksen	PROPN
azojete-1	406	15	j.l	j.l	PROPN
azojete-1	406	16	.	.	PROPN
azojete-1	406	17	et	et	PROPN
azojete-1	406	18	al	al	PROPN
azojete-1	406	19	(	(	PUNCT
azojete-1	406	20	eds	eds	PROPN
azojete-1	406	21	)	)	PUNCT
azojete-1	406	22	䇅homogeneous	䇅homogeneous	ADJ
azojete-1	406	23	and	and	CCONJ
azojete-1	406	24	effective	effective	ADJ
azojete-1	406	25	moduli	modulus	NOUN
azojete-1	406	26	of	of	ADP
azojete-1	406	27	materials	material	NOUN
azojete-1	406	28	and	and	CCONJ
azojete-1	406	29	media	medium	NOUN
azojete-1	406	30	.	.	PUNCT
azojete-1	407	1	new	new	PROPN
azojete-1	407	2	york	york	PROPN
azojete-1	407	3	:	:	PUNCT
azojete-1	407	4	springer	springer	NOUN
azojete-1	407	5	.	.	PUNCT
azojete-1	408	1	zohdi	zohdi	PROPN
azojete-1	408	2	,	,	PUNCT
azojete-1	408	3	t.i	t.i	PROPN
azojete-1	408	4	.	.	PROPN
azojete-1	408	5	and	and	CCONJ
azojete-1	408	6	wriggers	wrigger	NOUN
azojete-1	408	7	,	,	PUNCT
azojete-1	408	8	p.	p.	NOUN
azojete-1	408	9	2005.introduction	2005.introduction	NUM
azojete-1	408	10	to	to	ADP
azojete-1	408	11	compuational	compuational	ADJ
azojete-1	408	12	micromechanics	micromechanic	NOUN
azojete-1	408	13	.	.	PUNCT
azojete-1	409	1	1st	1st	PROPN
azojete-1	409	2	edition	edition	PROPN
azojete-1	409	3	berlin	berlin	PROPN
azojete-1	409	4	berlin	berlin	PROPN
azojete-1	409	5	–	–	PUNCT
azojete-1	409	6	verlag	verlag	PROPN
azojete-1	409	7	berling	berling	PROPN
azojete-1	409	8	heidelberg	heidelberg	PROPN
azojete-1	409	9	:	:	PUNCT
azojete-1	409	10	springer	springer	NOUN
azojete-1	409	11	:	:	PUNCT
azojete-1	409	12	springer	springer	NOUN
azojete-1	409	13	.	.	PUNCT
azojete-1	410	1	zohdi	zohdi	PROPN
azojete-1	410	2	,	,	PUNCT
azojete-1	410	3	t.i	t.i	PROPN
azojete-1	410	4	.	.	PROPN
azojete-1	410	5	and	and	CCONJ
azojete-1	410	6	wriggers	wrigger	NOUN
azojete-1	410	7	,	,	PUNCT
azojete-1	410	8	p.	p.	NOUN
azojete-1	410	9	2008.introduction	2008.introduction	NUM
azojete-1	410	10	to	to	ADP
azojete-1	410	11	compuational	compuational	ADJ
azojete-1	410	12	micromechanics	micromechanic	NOUN
azojete-1	410	13	.	.	PUNCT
azojete-1	411	1	p	p	NOUN
azojete-1	411	2	2	2	NUM
azojete-1	411	3	2nd	2nd	NOUN
azojete-1	411	4	edition	edition	NOUN
azojete-1	411	5	,	,	PUNCT
azojete-1	411	6	berlin	berlin	PROPN
azojete-1	411	7	–	–	PUNCT
azojete-1	411	8	verlag	verlag	PROPN
azojete-1	411	9	berling	berling	PROPN
azojete-1	411	10	heidelberg	heidelberg	PROPN
azojete-1	411	11	:	:	PUNCT
azojete-1	411	12	springe	springe	VERB
azojete-1	411	13	file:///c:/users	file:///c:/user	NOUN
azojete-1	411	14	/	/	SYM
azojete-1	411	15	user	user	NOUN
azojete-1	411	16	/	/	SYM
azojete-1	411	17	downloads	download	NOUN
azojete-1	411	18	/	/	SYM
azojete-1	411	19	azojete143	azojete143	PROPN
azojete-1	411	20	/	/	SYM
azojete-1	411	21	www.azojete.com.ng	www.azojete.com.ng	NOUN
azojete-1	411	22	mailto:ohunene.hafsa@fubk.edu.ng	mailto:ohunene.hafsa@fubk.edu.ng	NOUN