Hysteresis phenomena in shape memory alloys by non-isothermal Ginzburg–Landau models

In this paper, we propose the new one- and three- dimensional models for the description of hysteretic phenomena in shape memory alloys (SMAs). These thermodynamic models are non-isothermal and allow to account for the thermo-mechanical material properties of both austenite and martensite phases based on the local phase value of the order parameter. They are based on the Ginzburg–Landau free energy and the phase field theory. The core of the models is a phase evolution governed by the time dependent Ginzburg–Landau (TDGL) equation and the conservation balance laws with nonlinear coupling between stress, strain and the phase order parameter. The models account for the gradient energy and have been tested in the study of material properties evolution under harmonic stress loading for all important practical cases. The representative numerical simulations have been carried out here without the gradient energy term. The developed models account for the phase dependent properties based on the compliance tensor as a function of the order parameter and stress. We also compared the results obtained with these models and observed differences in homogeneous and inhomogeneous situations due to the change in compliance. In this way, the description of quasiplastic and pseudoelastic behaviors in SMA specimens is improved and becomes in an agreement with existing experiments.