An extension of a shape memory alloy model for large deformations based on an exactly integrable Eulerian rate formulation with changing elastic properties

Abstract

A small-displacement, phenomenological 3D model for shape memory alloys is expanded for large deformations. The Eulerian rate type formulation from the large deformation theory is used, with an additive decomposition of the stretching tensor. The expansion is performed by introducing, in the first stage, a thermodynamic frame for an isotropic material with logarithmic strains and scalar-valued internal state variables. The rate type characterisation of the elasticity is derived from the free energy. The relation is exactly integrable to define a free energy-based elastic relation. The formulation presented extends the previously presented ideas to possibly characterise changing elastic behaviours as a result of a phase transformation or other inelastic mechanisms. In the second part, a thermodynamic framework is used to derive the SMA constitutive equations by introducing large deformation counterparts in the small displacement theory for the Gibbs free energy, the transformation flow rule and the criteria for transformation. Then, a compatible integration algorithm is derived and implemented in Abaqus Standard FE software. The simulations presented demonstrate both a path-independent description of the elasticity and the model applicability to describe the unique properties of shape memory alloys.