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 modelling of shape memory alloys. Computational experiments are carried out to study the thermo-mechanical wave interactions in a shape memory alloy rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a one-dimensional structure are successfully simulated with the developed methodology. In the two-dimensional case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.
@article{arxiv.cs/0702167,
title = {Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys},
author = {Linxiang X. Wang and Roderick V. N. Melnik},
journal= {arXiv preprint arXiv:cs/0702167},
year = {2025}
}