Equilibrium for multiphase solids with Eulerian interfaces

We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and $Gamma$-convergence of diffuse-interface approximations to the sharp-interface limit.