A finite-strain finite element model for the pseudoelastic behavior of shape memory alloys

This paper presents a finite deformation finite element model for the pseudoelastic response of shape memory alloys under stress loading-unloading conditions at constant temperature. A local multiplicative decomposition of the deformation gradient into volumetric-elastic and isochoric-inelastic components is assumed, where the inelastic component is associated with phase transformation and defines an additional intermediate configuration. Strain measure defined on the intermediate configuration is the Hencky strain. The constitutive equations are cast in the framework of generalized plasticity and the two-way phase transformation is modeled via a Kuhn-Tucker type transformation criteria for the rate-independent shape memory behavior. These equations are able to predict the stress-induced phase transformations during complete loading-unloading cycles, and can also predict the correct material behavior when incomplete transformations take place. The resulting nonlinear system of equations is solved for updated stress variables via the radial return algorithm embedded in the Newton-Raphson iteration scheme. Numerical results are presented to show the performance of the model.