In the search of new active materials, Ni-Mn-Ga ferromagnetic shape memory alloys have a prominent position thanks to their capability to rapidly develop a very important strain. This particular behavior is in fact due to variant structure rearrangement of twinned martensitic platelets (5M, 7M or TNM) at constant temperature. To predict this strain induced by an applied magnetic field and/or an applied stress, the authors have proposed a magneto-mechanical model based on phenomenology, thermodynamics of irreversible processes and changing of scale (or homogenization). More exactly, this model has been developed and validated for uniaxial magnetic field (in an fixed direction), but, for multiaxial stress in a single crystal with 5M and 7M twinned martensite.
In this paper, an extension of this model is proposed in order to predict the effect of biaxial magnetic field in single crystal. For sake of simplicity, no demagnetizing field is considered. A Representative Elementary Volume is classically introduced with different microstructural parameters, i.e. volume fractions of martensitic bands, magnetization rotations, width ratios of two consecutive magnetic domains. It must be noticed that these variables are linked to physical phenomenon, for example, the movements of 180 magnetic domains corresponds to the evolution of width ratios. On the contrary to what is done usually, the movements of magnetic domain walls between martensitic bands are dissociated. The driving force acting on twin boundaries is written. Some yield surfaces of rearrangement are deduced under applied biaxial magnetic field, showing the non influence of initial volume fraction of martensitic bands and the existence of directions (at ±45 in respect to c axis) in which the rearrangement under magnetic field is hard or impossible. These results are fully compatible with the experiments of Müllner et al describing the action of a rotating magnetic field.

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