A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys

Abstract

We formulate a model describing rate-independent hysteretic response of shape-memory alloys under slow external forcing. Under natural assumptions we prove that this model has a solution. The microstructure is treated on a "mesoscopic" level, described by volume fractions of particular phases in terms of Young measures. The whole formulation is based on energetic functionals for energy storage and energy dissipation. The latter is built into the model by a dissipation distance between different values of these volume fractions.