  We propose a sharp-interface model for a hyperelastic material consisting of
two phases. In this model, phase interfaces are treated in the deformed
configuration, resulting in a fully Eulerian interfacial energy. In order to
penalize large curvature of the interface, we include a geometric term
featuring a curvature varifold. Equilibrium solutions are proved to exist via
minimization. We then utilize this model in an Eulerian topology optimization
problem that incorporates a curvature penalization.
