TY  - EJOU
AU  - Niu, Zongwu 
AU  - Shen, Yongxing 

TI  - A	Hybrid	Asynchronous	Variational	Integrator for	the	Phase	Field	 Approach	to	Dynamic	Fracture
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2023
VL  - 26
IS  - 3
SN  - 1933-2815

AB  - The	phase	field	approach	has	powerful	abilities	to	simulate	complicated	fracture	behaviors.	However,	the	
requirement	of	fine	mesh	near	cracks	leads	to	high	computational	cost,	especially	for	dynamic	cases	in	which	
the	critical	time	step	is	restricted	by	the	smallest	element	size	according	to	the	CFL	stability	condition.	In	
this	work,	the	asynchronous	variational	integrator	(AVI)	is	used	to	alleviate	the	high	computational	cost	in	
the	 case	 of	 dynamic	 brittle	 fracture.	 The	 AVI	 is	 derived	 from	 the	 discrete	 Hamilton’s	 principle	 with	
asynchronous	temporal	discretization,	which	allows	each	element	in	the	mesh	to	have	its	own	local	time	
step	that	is	independent	of	other	elements.	The	asynchrony	allows	the	elements	with	smaller	time	steps	to	
be	more	frequently	updated.	A	hybrid	explicit-implicit	staggered	scheme	is	used	to	solve	the	coupled	multifield	system,	in	which	the	displacement	and	velocity	fields	are	integrated	with	an	explicit	scheme	while	the	
phase	field	is	the	solution	to	an	inequality-constrained	optimization	problem.	In	essence,	the	phase	field	of	
only	one	element	is	solved	implicitly	at	a	time	based	on	elemental	patches,	it	is	very	convenient	to	enforce	
the	 upper	 and	 lower	 bounds	 strictly	 through	 the	 reduced-space	 active	 set	 strategy.	 In	 addition,	 two	
important	 variants	 of	 the	 phase	 field	 approach	 are	 equally	 easily	 implemented.	 The	 results	 of several	
benchmark	problems	show	that	AVI	for	the	phase	field	approach	captures	the	complicated	dynamic	fracture	
behavior	successfully	and	speeds	up	the	computational	efficiency	significantly.
KW  - Asynchronous	variational	integrators; phase	field	approach; dynamic	brittle	fracture; hybrid	scheme

DO  - 10.32604/icces.2023.09037