Existence and non-existence for the full thermomechanical Souza-Auricchio model of shape memory wires

We provide an existence theory for the full thermomechanical quasi-static evolution of a shape memory wire described by the Souza-Auricchio constitutive model. The analysis requires some mild restriction on the choice of the thermomechanical coupling term in the expression on the free energy of the material. This restriction slightly deviates from the original Souza-Auricchio modeling frame, while still being compatible with real situations. We additionally show that, by imposing no such restriction, the original Souza-Auricchio model is ill-posed.