Shape and topology optimization by the level set method. Application to damage evolution modeling

The level set method applied to shape and topology optimization has recently proven its efficiency and its ability to deal with various models and objective functions. We have extended the classical level set method in order to allow 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. Following the ideas developped for example in ² in the context of structural topology optimization, the interface is modeled by a level set function which is advected by the energy gradient issued from a shape derivation. The efficiency of this approach will be demonstrated at the conference through several numerical examples in 2d and 3d.