Calculus of Variations and Geometric Measure Theory

A. Giacomini

Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures

created by giacomini on 05 Jan 2006


Published Paper

Inserted: 5 jan 2006

Journal: Calc. Var. Partial Differential Equations
Volume: 22
Pages: 129-172
Year: 2005


We define a notion of quasistatic evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi static growth of brittle fractures in linearly elastic bodies.

Keywords: variational models, quasi-static evolution, Crack propagation, energy minimization