Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys

This article documents a new implementation of a three dimensional constitutive model that describes evolution of elastic and transformation strains during thermo-mechanical shape memory alloy loading events assuming a symmetric, isotropic material response. In achieving this implementation, improvements were made to the original formulation of the constitutive model. These improvements allow for robust three-dimensional calculations over a greater range of thermo-mechanical loadings. Furthermore, a new explicit scheme for solving the model equations was derived. This scheme removed the need for user calibration of the numerical integration parameters and greatly reduced the sensitivity of this explicit finite element implementation of a rate independent model to mass scaling. Studies were performed that quantified both simulation times and convergence of the new scheme along with the original solution scheme of Panico and Brinson for single element and multi-element simulations. The effectiveness of the new scheme is apparent in 6 and 30 times reductions in computation expense for selected single and multi element simulations, respectively.