Masud An internal-variable formalism is developed for a new family of inelastic models that are capable of representing the super-elastic transformations as well as the fully coupled thermo-mechanical phase transformarion is Shape Memory Alloys. These models can show different material response in tension and compression, and can account fof th single-variant-martensite reorientation prcess. The constitutive models are extended to the finite deformation regime by employing a multiplicative split of the deformation gradient. The issue of change in symmetry group because of the multiple natural configurations in SMA's is addressed. An unconditionally stable algorithm is develloped to solve the completed coupled thermo-mechanical system arising is SMA's. Technical issues related to numerical integration of the constitutive equations via the return mapping schemes, and the form of algorithmically consistent tangents needed to achieve higher order convergence are addressed in detail.***
