Internal variable model for magneto-mechanical behaviour of ferromagnetic shape memory alloys Ni-Mn-Ga

In this paper, a predictive model of field-induced strain in Ferromagnetic Shape Memory Alloy (FSMA) is proposed. This phenomenological scalar magneto-mechanical model is built in the frame of thermodynamic of irreversible process. The strain mechanism corresponds to the reorientation process of twinned martensite platelets at constant temperature. In this model, physical microstructure parameters are chosen as variables: volume fraction z of one martensite variant and ratio a of magnetic domain width. Pure mechanical behaviour of FSMA is supposed to be decomposed in reversible (or anhysteretic) part and irreversible one. From dissipation, a yield function written in terms of energy, has been introduced to determine when reorientation of twinned martensite platelets (via internal variable z) could occur. Pure magnetic behaviour is supposed to be non-linear reversible. The coupling between magnetism and mechanics is introduced in the expression of magnetisation via microstructure parameters z and a. The good prediction capability of the proposed model is shown by an identification made on experiments performed by O'Handley & Murray: simulations of strain induced by pure mechanical loading or by applied magnetic field under constant compressive stress, are presented and compared with these experiments. These first results are very promising.