Modelling and numerical simulation of martensitic transformation

Abstract

We consider the time evolution of martensite-austenite phase transformations in shape memory alloys. The process is modelled on a microscopical, continuum mechanical level by partial differential equations. Here the stored energy density is used, which is a rotationally invariant and nonconvex function of the transformation gradient with minima at several wells. The energy dissipation observed in physical experiments is modelled by an additional homogeneous degree-1 dissipation potential for rate-independent phase transformations. Furthermore, viscous and capillarity-like effects are handled by nonlocal terms of higher order.

We discuss the existence of solutions of this model and derive its energetic properties. Its discretization and implementation is described. Special care is taken to handle the nonlocal terms efficiently using wavelet techniques. Finally we present numerical experiments for an Indium-Thallium alloy under various loading regimes.