Inserted: 24 may 2022
Last Updated: 26 jan 2023
Journal: Siam J. Math. Anal.
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