A phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys

Shape memory alloys (SMAs) possess the distinctive ability to recover large mechanically-induced inelastic strains upon unloading, which is known as the pseudoelastic behavior. This paper deals with an extension of the phenomenological viscoplasticity theory, which has been developed by the author to depict the negative strain rate sensitivity, to model the macroscopic behavior of the phase transformation. Unlike most phenomenological models for the pseudoelasticity, the proposed model does not employ a kinetic law describing the evolution of the martensitic volume fraction and the transformation loading and unloading conditions but introduces two internal state variables concerned with the evolution of the elastic modulus and the back stress. The applicability of the constitutive model to SMAs is validated by comparing simulation results with experimental data on uniaxial and torsional loading reported in the literature. And then it is demonstrated that the same constitutive equations can be applied to model the highly nonlinear unloading behavior of solid polymer.