A Constrained Model for MSMA

Abstract

A mathematical description of transformation processes in magnetic shape memory alloys (MSMA) under applied stresses and external magnetic fields needs a combination of micromagnetics and continuum elasticity theory. In this note, we discuss the so-called constrained theories, i.e., models where the state described by the pair (linear strain, magnetization) is at every point of the sample constrained to assume one of only finitely many values (that reflect the material symmetries). Furthermore, we focus on large body limits, i.e., models that are formulated in terms of (local) averages of a microstructured state, as the one proposed by DeSimone and James. We argue that the effect of an interfacial energy associated with the twin boundaries survives on the level of the large body limit in form of a (local) rigidity of twins. This leads to an alternative (i.e., with respect to reference 1) large body limit. The new model has the advantage of qualitatively explaining the occurrence of a microstructure with charged magnetic walls, as observed in SPP experiments in reference 2.