A polynomial constitutive model of shape memory alloys based on kinematic hardening

This paper describes the derivation of a phenomenological model for shape memory alloys under the framework of classical plasticity theory. The proposed model combines the Souza constitutive approach with kinematic hardening; the model requires solving only one nonlinear equation rather than several nonlinear ones, therefore increasing the computational efficiency and convergence. Moreover, the original Souza model is improved by adding an odd polynomial function to describe the phase transformation of the shape memory alloys, making it possible to use a lower number of parameters for the inverse identification of the constitutive properties of SMAs from simple tensile tests. A tangent stiffness formulation is also derived to simulate the variation of the elastic modulus during the phase transformation. The tangent stiffness formulation proposed here extends the one used in classical plasticity and improves the convergence of the proposed model. The reliability and fidelity of the model described in this work are benchmarked against experimental data and other models. The numerical results show that the proposed phenomenological approach can describe well the pseudoelasticity and shape memory effect of shape memory alloys. The formulation described in this paper can be readily generalized to finite strains and other formulations based on existing formulations related to classical plasticity theory.