The Next Generation of Shape Memory Alloy FEA Models: Development of a User Material for Improved Simulation of Transformation-Plasticity Coupling Effects

An anisotropic shape memory alloy material model with coupled transformation-plasticity constitutive behavior is implemented as a user subroutine (UMAT) in the commercial finite element code Abaqus. This material model properly handles anisotropic thermal-mechanical loading, which lends itself to analyzing complex problems like low temperature compression, e.g., cold crimp, stress-ratcheting, and fatigue; and is a significant improvement in capability from other industry-standard shape memory alloy material models. Micromechanical material behavior is extended by introducing a transformation-plasticity coupling hypersurface directly in the free energy equation. Anisotropic superelastic initiation and saturation transformation is evaluated using a new implicit, triclinic, asymmetric, and pressure sensitive yield criterion. The fully differentiable form of this yield criterion allows for more precise gradient descent when solving the fundamental minimization problem. The incremental stress tangent required by an implicit solver utilizes an approximation to avoid inefficient numerical perturbation of the stress function. The material model is demonstrated within Abaqus under complex loading and is assessed against literature data.