A level set method for the numerical simulation of damage evolution

Abstract

This paper is devoted to the numerical simulation of the evolution of damage in brittle materials following the Francfort–Marigo model. This model is based on a Griffith energy criterion for the competition between the two phases, healthy and damaged, separated by a sharp interface. In a quasi-static and irreversible framework, the damage configuration is obtained by minimizing a total energy using a gradient descent method. The interface is modeled by a level set function which is advected by the energy gradient issued from a shape derivation. The nucleation of the damaged zone is obtained by using the so-called topological derivative. Several numerical examples in 2-d and 3-d are discussed.