Computational aspects of one-dimensional shape memory alloy modeling with phase diagrams Original Research Article

A constitutive model for martensitic solid—solid phase transformations is developed. Specifically, we investigate and model the one-dimensional behavior of shape memory alloys, with the purpose of capturing both the shape memory effect and the pseudoelasticity effect which are uniquely exhibited by this class of alloys. The model is of the popular phase space type and an appropriate numerical approximation of the constitution is developed which robustly handles arbitrary one-dimensional thermomechanical loading. Heuristics are provided for treating two types of non-uniqueness issues that have been identified to arise with such models. Representative simulations demonstrate the ability of the formulation to capture the essential macroscopic behavior of shape memory alloys. In particular, examples are shown solving truss bar and beam finite element problems.