Micro-to-Meso Scale Limit for Shape-Memory-Alloy Models with Thermal Coupling

Modeling of shape-memory alloys represents a multiscale problem due to occurrence of martensite/austenite phase transformation and a microstructure in the deformation gradient typical for martensitic phase. Inspired by relaxation in static situation, a limit passage between two modeling scales, called microand meso-scales, is performed for the corresponding evolution variants with considering activated phase transformation and even thermodynamically consistent thermal coupling. The mesoscopic model captures possible fine spatial oscillations of the deformation gradient by means of gradient Young measures. In particular, the mesoscopic model is justified as a limit from the microscopic scale and existence of its solutions is proved.