TY  - EJOU
AU  - Yongxing	Shen, 

TI  - Energy	Relations	in	the	Phase	Field	Approach to	Fracture
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2023
VL  - 25
IS  - 4
SN  - 1933-2815

AB  - The	phase	field	approach	to	fracture	originates	from	the	variational	formulation	of	brittle	fracture	proposed	
by	Francfort	and	Marigo.	The	regularized	version	of	the	latter	formulation	by	Bourdin	et	al.	is	also	dubbed	
the	 phase	 field	 approach	 to	 fracture.	 Compared	with	 explicit	 crack	methods such	 as	 the	 extended	 finite	
element	 method,	 the	 phase	 field	 approach	 to	 fracture	 does	 not	 require	 additional	 criteria	 for	 crack	
simulation	 and	 can	 naturally	 simulate	 complex	 fracture	 behaviors	 such	 as	 crack	initiation,	 propagation,	
branching	 and	 merging	 with	 a	 fixed	 mesh	 and	 fixed	 shape	 functions.	 This	 work	 examines	 the	 energy	
relations	in	the	phase	field	approach	to	fracture.	First,	the	relation	of	the	elastic	potential	energy	and	the	
fracture	energy	is	revisited	 from	 the	Γ-convergence	point	of	view.	Second,	 the	energy	balance	relation	is	
carefully	investigated	from	the	thermodynamic	perspective.	For	this	both	the	first	law	of	thermodynamics	
and	 the	second	law	of	 thermodynamics	are	considered,	and	 the	role	of	 the	degradation	 function	and	 the	
asymmetric	 relation	 for	distinguishing	 tension	and	 compression	will	 be	 reviewed.	 Finally,	 some	existing	
phase	field	models	for	fracture	are	evaluated	based	on	the	energy	relations.	Some	popular	models	will	be	
shown	not	 to	always	obey	 thermodynamic	laws.	With	 this	opportunity,	some	of	 the	recent	works	of	our	
research	group	are	showcased	from	the	energy	perspective.
KW  - Phase	field	approach	to	fracture;	energy	relations

DO  - 10.32604/icces.2023.09314