Inserted: 14 jun 2021
Last Updated: 8 jan 2022
Journal: AWM Volume - Research in the Mathematics of Materials Science
In this note we study the relative impact of fine-scale heterogeneities and singular perturbations in a one-dimensional phase-field model of Ambrosio-Tortorelli type. We show that the limit functional is always of Mumford-Shah type, with a surface term depending on the mutual converging rate of the oscillation and the perturbation parameter.
Keywords: $\Gamma$-convergence, singular perturbations, homogenisation