A Phase-Field Approach to Eulerian Interfacial Energies

We analyze a phase-field approximation of a sharp-interface model for two-phase materials proposed by Šilhavý (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, pp 233–244, Springer, Dordrecht, 2010; J Elast 105:271–303, 2011). 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 the existence of phase-field minimizers and Γ-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 Šilhavý (2010, 2011).