Beex, Lars

Bordas, Stéphane

Rappel, Hussein

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Identifying	material	parameter	distributions	of	fibers	with	extremely	limited	experimental	efforts		Hussein	Rappela,b,	Lars	A.A.	Beexa,	Stephane	P.A.	Bordasa,c		a University of Luxembourg, Institute of Computational Engineering, Luxembourg b	University	of	Liege,	Aerospace	and	Mechanical	Engineering	Department,	Liege,	Belgium	c	Cardiff	University,	Architectural,	Civil	&	Environmental	Engineering,	Wales,	UK		Numerous	materials	are	essentially	discrete	networks	of	fibers,	yarns	or	struts	at	length	scales	substantially	smaller	than	the	application	scale.	Some	examples	of	these	materials	are	foams,	paper	materials,	printed	lattices	and	textiles.	Besides	the	possible	geometrical	randomness,	many	of	these	materials	are	characterized	by	the	fact	that	each	fiber,	yarn	or	strut	has	its	own	set	of	material	parameters.	Incorporating	this	randomness	in	discrete	mechanical	models	can	substantially	influence	the	predictions,	compared	to	those	of	mechanical	models	in	which	no	randomness	of	material	parameters	is	included.			If	we	assume	that	the	material	parameters	of	each	discrete	constituent	are	realisations	from	a	distribution,	the	parameters	of	this	probability	density	function	(PDF)	must	be	identified.	The	most	conventional	manner	of	identifying	the	parameters	of	such	a	distribution	is	to	experimentally	identify	the	material	parameters	of	hundreds	of	fibers,	yarns	or	struts	and	subsequently,	use	these	material	parameters	to	identify	the	parameters	of	the	distribution.		This	entails	an	enormous	amount	of	experimental	efforts,	which	is	the	reason	that	hardly	anybody	will	go	through	these	efforts.		As	an	alternative	to	testing	hundreds	of	fibers,	yarns	of	struts,	we	will	present	an	approach	that	requires	testing	only	a	few	fibers.	We	will	use	Bayes’	theorem	for	this	purpose,	which	entails	the	proposition	of	the	shape	of	PDF,	as	well	as	a	proposition	of	the	possible	values	of	this	PDF	(albeit	as	distributions	as	well).	For	each	set	of	material	parameters,	we	then	assess	how	likely	it	is	that	it	is	a	realisation	from	the	proposed	PDF	and	its	proposed	parameters	and	we	update	the	PDF’s	proposed	parameters	such	that	the	likelihood	that	the	set	is	a	realization	of	this	PDF	increases.		In	order	to	explain	the	approach	as	gently	as	possible,	we	will	not	directly	deal	with	the	PDF’s	parameters	as	parameters	that	also	originate	from	a	PDF.	Instead,	we	will	first	focus	the	PDF’s	parameters	as	deterministic	variables	[1].			[1]	Rappel	H,	Beex	LAA,	Bordas	SPA,	‘Bayesian	inference	to	identify	parameters	in	viscoelasticity’,	Mechanics	of	Time-Dependent	Materials,	2017,	In	press.					

Identifying material parameter distributions of fibers with extremely limited experimental efforts

http://orbilu.uni.lu/bitstream/10993/36494/1/Beex_abstract.pdf

Identifying material parameter distributions of fibers with extremely limited experimental efforts

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