Calculus of Variations and Geometric Measure Theory

A. Chambolle - V. Crismale

Phase-field approximation for a class of cohesive fracture energies with an activation threshold

created by crismale on 21 Feb 2019
modified on 30 Jan 2021


Published Paper

Inserted: 21 feb 2019
Last Updated: 30 jan 2021

Journal: Adv. Calc. Var.
Year: 2020
Doi: 10.1515/acv-2019-0018

ArXiv: 1812.05301 PDF

Published online


We study the $\Gamma$-limit of Ambrosio-Tortorelli-type functionals $D_\varepsilon(u,v)$, whose dependence on the symmetrised gradient $e(u)$ is different in $\mathbb{A} u$ and in $e(u)-\mathbb{A} u$, for a $\mathbb{C}$-elliptic symmetric operator $\mathbb{A}$, in terms of the prefactor depending on the phase-field variable $v$. This is intermediate between an approximation for the Griffith brittle fracture energy and the one for a cohesive energy by Focardi and Iurlano. In particular we prove that $G(S)BD$ functions with bounded $\mathbb{A}$-variation are $(S)BD$.