The investigator extends the analysis and the numerical implementation of a Free-Discontinuity approach to brittle fracture mechanics proposed by G. Francfort and J-J. Marigo. This formulation departs from the classical Griffith theory while preserving its essence, the competition between surface and bulk terms. Doing so, it allows to address the issues of crack path determination, creation of new cracks, and interactions between cracks. Its numerical implementation is based on a Gamma-convergence approximation, which gives a natural way to consider global minimizations over all possible crack sets. The investigator extends the existing model to account for the propagation of cracks under thermal loads and in heterogeneous media and conduct numerical experiments in these areas. He builds a robust numerical algorithm avoiding most local minimizers, and studies the link between Gamma-convergence and local minimizers for this model. He implements an overlapping domain decomposition method on supercomputers and studies the relation between discretization and regularization parameters.
Fracture mechanics is a very active area of research, with vital applications. In recent years, the unexpected collapse of terminal 2F at Charles de Gaulle airport in France, the disintegration the Columbia space shuttle upon re-entry, and the crash of American Airlines Flight 582 over Queens, NY were all linked to unpredicted and unexplained fracture. In the area of brittle fracture (which encompasses materials as diverse as ceramics, glass, and concrete), most commonly accepted theories are based on Griffith's criterion and are limited to the propagation of an isolated, pre-existing crack along a given path. The investigator extends the analysis and the numerical implementation of a generalization of Griffith's theory, proposed by G. Francfort and J.J. Marigo, that eliminates these restrictions. He extends the current model to account for more general problems (thermal loads, heterogeneous materials), and improves the current numerical implementation on supercomputers.
