A non-local implicit gradient-enhanced model for thermomechanical behavior of shape memory alloys

A three-dimensional, implicit gradient-enhanced, fully coupled thermomechanical constitutive model is developed within the framework of thermodynamic principles for NiTi shape memory alloys. This work focuses on unstable behaviors of NiTi samples under different thermomechanical loading conditions. Temperature variation and its coupling effect on non-local behavior of a shape memory alloy during a loading–unloading cycle at different strain rates are considered. The proposed constitutive equations are implemented into the finite element software ABAQUS, and the numerical investigations indicate that the used procedure is an effective computational tool for simulation of several behaviors of NiTi samples including phase front nucleation and propagation, stress–strain–temperature responses, and transformation-induced stress relaxation. The obtained results are shown to be in a good agreement with available experimental and numerical findings in the literature. The effectiveness of the model in removing mesh sensitivity is evaluated by investigating the mesh-dependence issue for the low strain rate problems through numerical examples.