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In this paper we introduce a 3D phenomenological model for shape memorybehavior, accounting for: martensite reorientation, asymmetric response of thematerial to tension/compression, different kinetics between forward and reversephase transformation. We combine two modeling approaches using scalar andtensorial internal variables. Indeed, we use volume proportions of differentconfigurations of the crystal lattice (austenite and two variants ofmartensite) as scalar internal variables and the preferred direction ofstress-induced martensite as tensorial internal variable. Then, we deriveevolution 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 ensuringdifferent evolution laws during forward and reverse transformation of theoriented martensite.

A new 3D macroscopic model for shape memory alloys describing martensite reorientation