Abstract
This paper describes a phase-field model of solid-liquid phase transitions with inhomogeneous temperature in one-component systems. Our model includes fluid flow and non-linear elasticity in solids: plastic deformations take place at large elastic strains. We present two numerical results of melting in two dimensions. First, a solid domain is placed in a warmer liquid under shear flow. The solid melts gradually, preserving circular shape due to elasticity. Cooling of the surrounding liquid is accelerated by external shear flow. Second, a solid rod is under uniaxial compression in liquid. Slips appear from the solid-liquid interface, leading to plastic deformation. Melting starts in the slips, leading to the fracture of the rod into pieces.
