Mathematics

In this talk I discuss about mathematical models of dynamic brittle fracture based on Griffith's criterion. In particular I focus on the phase-field ones, which rely on the Ambrosio-Tortorelli approximation. In these models the crack is aprroximated by a function $v \in \left[ 0,1 \right]$ (called phase-field) which takes values close to $0$ in a small neighborhood of the crack set, and values close to $1$ far from it. By adapting a time discretization scheme, I prove the existence of a solution for a phase-field model in which the dissipative effects due to the crack tips speed are taken into account. Finally I show that this evolution satisfies an energy dissipation balance according to Griffith's criterion.