Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces

Abstract: "This paper develops a thermomechanics of two-phase heat conductors in which the interface between phases is fully faceted. The theory is based on balance of forces, balance of energy, and growth of entropy in conjunction with constitutive equations for the interface; and the chief result is a free-boundary problem of Stefan type in which the classical interface condition u = O is replaced by a condition relating the integral of u over each facet to the normal velocity of that facet."