Many models for twinning-like microstructure and its evolution in crystallic alloys exhibiting shape-memory effects have been proposed worldwide. Various levels of description of microstructure can be distinguished (atomistic, microscopical continuum mechanical, mesoscopical continuum mechanical, or macroscopical), as well as various evolutionar mechanisms (iso- or aniso-thermal, viscous or/and plastic). Two models has been especially developed during past years in series of papers with M.Arndt, M.Griebel, M.Kruzik, P.Plechac, and, last but not least, K.R.Rajagopal. A multiwell stored energy and a degree-1 homogeneous dissipation potential are the main ingredients. The first model is based on rather conventional partial differential inequalities for displacements, while the second one uses Young measures to describe volume fractions of particular phases or phase variants. Mathematical justification is based on a proof of existence of a weak solution of an initial-value problem, as well as (in the first mentioned option) an analysis of a limit of visco-plastic models for vanishing viscosity. Application to simulation of single-crystal laboratory experiments with specific SMAs (e.g. NiMnGa) are available, too.
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