A level set method for the numerical simulation of damage evolution

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.