A 3D finite-strain-based constitutive model for shape memory alloys accounting for thermomechanical coupling and martensite reorientation

The paper presents a finite-strain constitutive model for shape memory alloys (SMAs) that accounts for thermomechanical coupling and martensite reorientation. The finite-strain formulation is based on a two-tier, multiplicative decomposition of the deformation gradient into thermal, elastic, and inelastic parts, where the inelastic deformation is further split into phase transformation and martensite reorientation components. A time-discrete formulation of the constitutive equations is proposed and a numerical integration algorithm is presented featuring proper symmetrization of the tensor variables and explicit formulation of the material and spatial tangent operators involved. The algorithm is used for finite element analysis of SMA components subjected to various loading conditions, including uniaxial, non-proportional, isothermal and adiabatic loading cases. The analysis is carried out using the FEA software Abaqus by means of a user-defined material subroutine, which is then utilized to simulate a SMA archwire undergoing large strains and rotations.