Calculus of Variations and Geometric Measure Theory

D. Grandi - M. Kruzik - E. Mainini - U. Stefanelli

A phase-field approach to Eulerian interfacial energies

created by mainini on 28 May 2018
modified on 03 May 2019


Published Paper

Inserted: 28 may 2018
Last Updated: 3 may 2019

Journal: Arch. Ration. Mech. Anal.
Year: 2019
Doi: 10.1007/s00205-019-01391-8


We analyze a phase-field approximation of a sharp-interface model for two-phase materials proposed by M. Silhavy $[$41, 42$]$. 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 $[$41, 42$]$.