The postulate of realizability : formulation and applications to the post-bifurcation behaviour and phase transitions in elastoplastic materials. II

Abstract The extremum principles for the interface are derived using the postulate of realizability. They are used to derive a number of equations for the description of phase transitions (PTs): for jumps of the deformation gradient and the tensors characterizing the mutual orientation of the phases; for the deformation gradient history in the course of PT; for the normal velocity of the interface and the velocity of the relative sliding along the interface; the local criteria for the martensitic PT. The governing extremum principle for the description of a stable post-bifurcation process for a volume of elastoplastic materials with PT is derived. The local PT criteria represent the equations for some parameters across the interface. But even when they can be met, two solutions are possible: first, the solution with fixed interface, second, the solution with the moving one. The more stable solution can be chosen using the extremum principle for the whole volume, which is the global PT criterion and gives the final solution. Some examples are considered. It is shown that in the course of PT, the traction continuity condition is violated across the interface. To remove this contradiction the concept of fluctuating stresses is introduced. These stresses overcome the energy barrier and restore the traction continuity condition.