A new 3D macroscopic model for shape memory alloys describing martensite   reorientation
  In this paper we introduce a 3D phenomenological model for shape memory behavior, accounting for: martensite reorientation, asymmetric response of the material to tension/compression, different kinetics between forward and reverse phase transformation. We combine two modeling approaches using scalar and tensorial internal variables. Indeed, we use volume proportions of different configurations of the crystal lattice (austenite and two variants of martensite) as scalar internal variables and the preferred direction of stress-induced martensite as tensorial internal variable. Then, we derive evolution equations by a generalization of the principle of virtual powers, including microforces and micromovements responsible for phase transformation. In addition, we prescribe an evolution law for phase proportions ensuring different evolution laws during forward and reverse transformation of the oriented martensite. 
Ferdinando Auricchio and Elena Bonetti
math.AP