Variational modeling of shape memory alloys - An overview

Shape memory alloys can be described in a uniform way relying on energetic considerations only. We present micromechanically motivated models for single and polycrystals. The approach studied here is based on energy minimization and includes hysteretic effects via a simple dissipation ansatz. It is capable of reproducing important aspects of the material behavior such as pseudoelasticity and pseudoplasticity. The influence of anisotropies in the crystalline texture as well as in the elastic constants of the austenite and the martensitic variants is also discussed. Furthermore, regularization is applied in order to receive localized but still mesh independent results for phase distributions in a finite element implementation. The entire presentation emphasizes the usage of variational methods leading to the notion of relaxed potentials. Interrelations to various other applications of these concepts will be highlighted.