Variational brittle fracture: evolution, branching and approximation

First, we propose to briefly recall the basic principles of classical brittle fracture, and the link between that theory and the variational theory. After reviewing the main results and drawbacks of the variational approach, we will discuss the approximation techniques used in the computation of the obtained variational evolutions and the challenging mathematical issues that arise in attempting any kind of implementation.

We will conclude with very recent and still incomplete results on crack branching.