Simplifications and comparisons of shape memory alloy constitutive models

Here we will present a simplification of the form of one popular shape memory alloy (SMA) constitutive model. This simplification allows a more compact written form and hence easier calculations with the one-dimensional SMA constitutive law first developed by Tanaka, later modified by Liang and Rogers, and again by Brinson. In addition, a new derivation of the model will be given based on micromechanics. In this context, comparisons between the Tanaka and two other models will be presented and implications discussed. It will be shown that the constitutive models are in fact quite similar, and that the important distinction between these SMA models is primarily in the formulation of the transformation kinetics. Several examples will be presented utilizing the models.