We investigate a second-order Modica-Mortola functional modeling solid--solid phase transitions in heterogeneous media. We neglect the assumption of frame indifference in the elastic energy density W while allowing for space-dependent, pointwise-compatible wells. Under suitable assumptions on W and regularity conditions on the associated rank-one connection, we prove that Gamma-convergence of the energies to a local interfacial functional defined for suitable laminate-type configurations.
This is joint work with Jakob Deutsch, Manuel Friedrich, and Kerrek Stinson