In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modeling of shape memory alloys (SMA). Computational experiments are carried out to study the thermo-mechanical wave interactions in a SMA rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a 1D structure are successfully simulated with the developed methodology. In the 2D case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.
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