A Constitutive Model for Isothermal Pseudoelasticity Coupled with Plasticity

In this paper, a new constitutive model for isothermal pseudoelastic shape memory alloys is presented. The model is based upon a kinematic hardening framework that was previously developed for ferroelastic and ferroelectric switching behavior. The basis of the model includes a transformation surface, an associated flow rule for transformation strain, and kinematic hardening with the back stresses represented by a transformation potential that is dependent upon the transformation strain. In contrast to many models that introduce tension/compression asymmetry by devising transformation surfaces in terms of invariants of the stress tensor, this model achieves this capability by means of expressing the transformation potential from which the back stresses are derived as a weighted mix of two potentials that are, respectively, calibrated to measured tensile and compressive responses. Additionally, in this model, plastic deformation is allowed to occur at high stresses by employing a standard \(J_{2}\)-based yield surface with isotropic hardening. Finally, to demonstrate the ability of the constitutive model to perform in highly non-proportional loading states, some finite element simulations on crack tip fields are presented.