In this report, we have modeled the shape memory alloy using the three-dimensional crystal mechanics based model. In martensitic transformation, austenite undergoes transformation to form different variants of martensite under thermomechanical loading. The formation of variants of martensite in the material is governed by coherency conditions occurring by a just a position of both austenite phases as well as martensite. Formation of simple natural configurations containing both austenite-martensite phases formed by a simple shear transformations are determined and are assumed to be equivalent to the slip system which are crystal structure dependent. The constitutive equations are derived by taking recourse to the principles of thermodynamics and assuming a form for the Helmholtz potential. Solutions of these constitutive equations are carried out using an explicit elastic predictor - plastic corrector algorithm. Both manifestations of superelasticity: stress-strain response at a fixed temperature and strain-temperature response at fixed stress is successfully simulated by this model. The phase diagram has also been simulated using this model.


The rate effects are brought up in this model by deriving a power balance which consists of latent heat, specific heat, convective heat and the driving force terms and solving this equation with the constitutive equations developed earlier. Further, polycrystalline simulations have been carried out by using a Taylor-type model. The inner hysteresis loops which are crucial in actuator applications have also been simulated.