A three-dimensional non-isothermal Ginzburg-Landau phase-field model for shape memory alloys

In this paper, a macroscopic three-dimensional non-isothermal model is proposed for describing hysteresis phenomena and phase transformations in shape memory alloys (SMAs). The model is of phase-field type and is based on the Ginzburg-Landau theory. The hysteresis and phase transformations are governed by the kinetic phase evolution equation using the scalar order parameter, laws of conservation of the momentum and energy and a nonlinear coupling of the stress, the strain and the order parameter in a differential form. One of the important features of the model is that the phase transformation is governed by the stress tensor, as opposed to the transformation strain tensor typically used in the literature. The model takes into account different properties of austenite and martensite phases based on the compliance tensor as a function of the order parameter and stress. Representative numerical simulations on an SMA specimen reproduce hysteretic behaviors observed experimentally in the literature.