A 3-species model for shape memory alloys
A thermodynamically consistent three species (austenite, plus-martensite & minus-martensite) model for shape memory alloys (SMA) is proposed. The uniaxial model proposed has been formulated with capabilities of simulating the characteristic response under general thermo-mechanical loading conditions. It is shown that a minimal set of model variables, essentially, the volume fractions of the three species, describing the one dimensional state of the polycrystal SMA, is enough to capture its characteristic features including the pseudoelastic and the shape memory effects. Primarily, two back stresses are defined within a dissipative setting - one to take care of polycrystalline nature of SMA and the other for the moving interfaces of the species within the sub grains. The connection between the physical response of the material and the choice of the material parameters is illustrated using different conditions of the material and of the loading. Simulation results exemplify the potential of the proposed model in predicting the characteristic behavior under loading paths such as isothermal, iso-stress and cyclic thermomechanical loading, that are typical in the applications.