Two-phase deformations within the framework of phase transition zones

A. B. Freidin, E. N. Vilchevskaya, L. L. Sharipova

We analyze conditions on the equilibrium interface and develop the concept of phase transition zones (PTZ) formed in strain-space by all deformations which can exist on the equilibrium interface. The importance of the PTZ construction follows from the fact that deformations outside the PTZ cannot exist on the interface, whatever the loading conditions. The PTZ boundary acts as a phase diagram or yield surface in strain-space. We develop a general procedure for the PTZ construction and give examples for various nonlinear elastic materials and in a case of small strains. We study orientations of the interface and jumps of strains on the interface and demonstrate that various points of the PTZ correspond to different types of strain localization due to phase transformations on different loading path.