In this work, we focus our attention to the case of the commercially most successful SMA, NiTi. The downside of this material with respect to micromechanical modeling is the elevated number of 17 different variants of cubic austenite, monoclinic martensite, and the intermediate rhombohedral R-phase. Compared to the formation or re-orientation of martensite, a transformation between austenite and R-phase or between different variants of the latter implies a relatively small change in crystal structure. It is therefore assumed that austenite and R-phase may transform spontaneously and without losing energy, whereas a dissipation ansatz homogeneous of first order is assumed for the evolution of martensite.
Sample computations and comparison with experimental data show that using this approach leads to a realistic estimate of the material behavior of NiTi. Especially, modeling the stress-strain relation for a tensile test exhibits the typical slope reduction before the onset of the stress plateau.