Mathematical Modeling and Computational Sciences

A general modeling framework has been developed to analyze the dy-namics of multivariant phase transformation in three-dimensional samples of shape memory materials. In this paper we analyze the properties of the coupling between the microscopic phase kinetics due to crystal transforma-tion and the nonlinearity in the continuum thermoelasticity. The model is based on a systematic representation of the Gibbs free energy in stress, temperature and n-dimensional order parameter space. Here n indicates the number of martensitic variants (M). Landau theory has earlier been successfully applied to solve the problem of phase-field evolution in phase transforming solids (see e.g. the works by Artemev et al. [1] and Ichit-subo et al. [2] and the references therein). In the context of diffusion-less transformation in solid described by the Landau theory of first-order kinet-ics, the order parameters are the scaled ensemble average of the atomic order variables [3]. The diffusion kinetics based on the time-dependen