Rate-independent evolution in shape memory alloys at finite strains

We discuss the modeling of shape memory alloys through a finite strain-version of the Souza-Auricchio model. By assuming an isotropic elastic response, a convenient formulation in terms of the Green-St-Venant transformation strain tensor can be established. A rate-independent inelastic constitutive relation is assumed, which is coupled to a quasi-static hyper-elastic energy with an additional regularizing interface-energy; the global existence of energetic solutions (i.e. a kind of variational evolution) to the corresponding boundary value problem is proven. In this framework, a rigorous linearization limit of the model at small strain can be established by means of the evolutive Γ-convergence for rate independent processes. A similar finite-strain approach is applied to provide a model for the magnetoelastic evolution in magnetic shape-memory materials.