Quasistatic isothermal evolution of shape memory alloys

This paper focuses on a three-dimensional phenomenological model for the isothermal evolution of a polycrystalline shape memory alloy. The model, originally proposed by Auricchio, Taylor, and Lubliner in 1997, is thermodynamically consistent and reproduces the crucial martensitic reorientation effect as well as the tension-compression asymmetric behavior of the material. We prove the existence of a weak solution of the corresponding quasistatic evolution problem by passing to the limit within a time-discretization procedure.