Coupled thermomechanical simulation of shape memory alloys

A general formulation for coupled thermomechanical shape memory alloys is presented in the context of the finite element method. An internal variable formalism is adopted for the evolution of the martensite fraction at the microstrutural level. In particular the response of material under partial loading/unloading conditions at various temperature ranges is modeled. An isothermal fractional-step method is utilized for the solution of the coupled problem, in which the development and implementation of the mechanical and thermal parts of the problem ate discussed. In this report our attention is restricted to the area of geometrically linear quasi-static problems. Specifically: me investigate the proposed formulation in the setting of a truss element and show its extenstion to multiple dimensions. Representative numerical simulations of full and partial load cycles show favorable performance of the formulation, for all admissible regions in stress-temperature space.