A phase-field approach to Eulerian interfacial energies

TL;DR

This paper develops a phase-field model for two-phase materials with Eulerian interfacial energies, proving convergence to the sharp-interface limit and analyzing admissible configurations.

Contribution

It introduces a phase-field approximation for an Eulerian interfacial energy model and establishes its convergence and existence results.

Findings

Proved Γ-convergence to the sharp-interface model.

Established existence of phase-field minimizers.

Provided detailed analysis of admissible sharp-interface configurations.

Abstract

We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by M. Silhavy [32, 33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is defined on the deformed configuration. We discuss a functional frame allowing for existence of phase- field minimizers and {\Gamma}-convergence to the sharp-interface limit. As a by-product, we provide additional detail on the admissible sharp-interface configurations with respect to the analysis in [32, 33].