Dynamics of shape memory alloys patches

A two-dimensional mathematical model is constructed in the present paper, which includes the nonlinear coupling of thermal and mechanical fields. The model is based on a two-dimensional approximation to the dynamics of cubic-to-tetragonal and tetragonal-to-orthorhombic phase transformations in shape memory alloys (SMA). It is shown that the Falk model in the one-dimensional case is a special case of the formulated model. Computational experiments are carried out to analyze thermomechanical wave interactions in a thin long strip by applying the finite volume method, while a laminated microstructure in the patch is simulated by using a genetic algorithm.