Gradient damage models for periodically heterogeneous media

In this seminar we will study the asymptotic behaviour of phase-field functionals of Ambrosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be interpreted as an instance of a static gradient damage model for periodically heterogeneous materials. Depending on the mutual vanishing rate of the phase-field parameter and the oscillation parameter, the effective behaviour of the model will be fully characterised by means of Γ-convergence.

This is joint work with T. Esposito, R. Marziani, and C. I. Zeppieri (Münster).