Gradient damage models for heterogeneous materials

TL;DR

This paper investigates the asymptotic behavior of phase-field functionals in gradient damage models for heterogeneous materials, providing a Gamma-convergence characterization of their effective behavior under various oscillation regimes.

Contribution

It offers a rigorous Gamma-convergence analysis of phase-field damage models with small-scale oscillations, advancing understanding of their effective behavior in heterogeneous materials.

Findings

Gamma-convergence characterization of the models

Effective behavior depends on oscillation and approximation rates

Provides insights into static gradient damage models for heterogeneity

Abstract

In this paper we study the asymptotic behaviour of phase-field functionals of Am brosio 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 heterogeneous materials. Depending on the mutual vanishing rate of the approximation and of the oscillation parameters, the effective behaviour of the model is fully characterised by means of Gamma-convergence.