  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.
