Equilibrium Conditions at a Solid-Solid Interface

We derive the thermodynamic conditions necessary for two elasto-plastic solid phases to coexist in equilibrium. Beyond temperature, velocity, and traction continuity, these conditions require continuity of a generalization of the specific Gibbs free energy. We express this quantity in the Eulerian frame, as well as the Lagrangian frame. We also discuss two possible interpretations for the Gibbs free energy, which lead to distinct generalizations, except in the case of inviscid fluids, where they coincide.