Variational methods applied to discrete and evolutionary brittle damage models

During this talk, I will first recall a brittle damage model of a linearly elastic material, introduced by Francfort and Marigo, and its applications to the study of concentration and elastic degeneracy of weak material phenomena. I will explain the two main directions we intended to investigate during my thesis and the resulting research projects I wish to carry out.

I will then explain in further detail the study of a static model which is based on the Gamma-convergence of brittle damage total energies to the Griffith functional. This first joint work with my director, Jean-François Babadjian, is the content of an article we submitted. The preprint is available on ArXiv (arXiv:2202.12152).

If time allows it, I will finally present the convergence of a quasi-static brittle damage evolution, introduced by Francfort and Garroni, to a model of quasi-static perfect plasticity in the one dimensional setting.