A micromechanical model for martensitic phase‐transformations in shape‐memory alloys based on energy‐relaxation

Abstract

Abstract We develop a micromechanical model for single‐crystalline materials undergoing diffusionless solid‐to‐solid phase transitions. It is based on the specification of laminated microstructures on the materials' microscale and hence is designed to approximate the rank‐1‐convex hull of the underlying energy‐density for the phase‐mixture. In order to capture the hysteretic behavior of such materials like shape‐memory‐alloys we also account for dissipation by means of evolution equations for the inelastic internal variables. In this context, we derive different evolution‐laws from inelastic potentials via least‐action principles. Several material‐point computations emphasize the characteristics of the presented model.