Calculus of Variations and Geometric Measure Theory

A. Bach - T. Esposito - R. Marziani - C. I. Zeppieri

Gradient damage models for heterogeneous materials

created by bach on 24 May 2022
modified on 26 Jan 2023


Accepted Paper

Inserted: 24 may 2022
Last Updated: 26 jan 2023

Journal: Siam J. Math. Anal.
Year: 2022


In this paper we 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 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.

Keywords: gradient damage model, phase-field functionals, homogenisation, $\Gamma$-convergence, elliptic approximation, free-discontinuity functionals