Approximation in multiscale modelling of microstructure evolution in shape-memory alloys

Various models of microstructure in deformation gradient and its evolution arising in martensitic mechanically-induced isothermal phase transformation are surveyed and scrutinized, focusing on over-bridging of various scales of the problem and its numerical approximation. In particular, numerically efficient model of a relaxed problem is shown to be approximated by conventional but computationally less efficient model based on standard partial differential inequalities.