Calculus of Variations and Geometric Measure Theory

M. Negri - D. Knees

Convergence of alternate minimization schemes for phase field fracture and damage

created by negri on 02 Nov 2015
modified by knees on 19 Dec 2017


Published Paper

Inserted: 2 nov 2015
Last Updated: 19 dec 2017

Journal: Mathematical Models and Methods in Applied Sciences (M3AS)
Volume: 27
Number: 9
Pages: 1743-1794
Year: 2017


We consider time-discrete evolutions for a phase field model (for fracture and damage) obtained by alternate minimization schemes. First, we characterize their time-continuous limit in terms of parametrized BV-evolutions, introducing a suitable family of “intrinsic energy norms”. Further, we show that the limit evolution satisfies Griffith’s criterion, for a phase field energy release, and that the irreversibility constraint is thermodynamically consistent.