Phase mixtures in dynamics of pseudoelasticity

We give a numerical treatment of phase mixtures in pseudoelasticity from a purely mathematical point of view. It is based on a surprising result that the approximate solution may consist of persistent oscillations in strain which resemble the experimentally observed interface patterns. Such a solution is obtained from a sequence of solutions for a rate-type viscoelastic problem with a non-monotone equilibrium stress-strain relation, for which in the limit as the viscosity tends to infinity the viscoelastic problem reduces to the rate-independent elastic problem describing phase transitions. In this manner, it seems to give yet another perspective for the phase mixture from dynamic point of view as the evolution of an unstable state, in contrast to the traditional treatment from stability analysis for phase equilibrium.