Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation

The present paper develops a refined and general three-dimensional phenomenological constitutive
model for shape memory alloys (SMAs), along the lines of what recently proposed by Auricchio
and Bonetti (2013) in a more theoretical context. Such an improved model takes into
account several physical phenomena, as martensite reorientation and different kinetics between
forward/reverse phase transformations, including also smooth thermo-mechanical response, lowstress
phase transformations as well as transformation-dependent elastic properties. The model is
treated numerically through an effective and efficient procedure, consisting in the replacement of
the classical set of Kuhn-Tucker inequality conditions by the so-called Fischer-Burmeister complementarity
function. Numerical predictions are compared with experimental results and the finite
element analysis of a SMA-based real device is described to assess the reliability of the proposed
model as well as the effectiveness of its numerical counterpart.