Phase-field models for transition phenomena in materials with hysteresis

Non-isothermal phase-field models of transition phenomena in materials with hysteresis are considered within the framework of the Ginzburg-Landau theory. Our attempt is to capture the relation between phase-transition and hysteresis (either mechanical or magnetic). All models are required to be compatible with thermodynamics and to fit well the shape of the major hysteresis loop. Focusing on uniform cyclic processes, numerical simulations at different temperatures are performed.