  In this paper, a macroscopic three dimensional non-isothermal model is
proposed to describe 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,
conservation laws of momentum and energy, and a non-linear coupling between
stress, 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 a SMA
specimen reproduce hysteretic behaviors observed experimentally in the
literature.
