Modeling of unstable behaviors of shape memory alloys during localization and propagation of phase transformation using a gradient-enhanced model

In this article, a multi-dimensional gradient-enhanced constitutive model of shape memory alloys is developed. The model is developed to capture unstable behaviors of shape memory alloys during both the forward and reverse phase transformations. Also, influence of loading history on the start of the phase transformation during both forward and reverse transformations is considered in the model by introducing new transformation limits and phase fraction formulations. The model is implemented in a finite element code, and using a numerical framework, effects of loading, boundary condition, inhomogeneous deformations, imperfection, and geometry on the unstable behaviors of different shape memory alloy samples during nucleation and phase transformation are investigated. The obtained results are compared with the available experimental and numerical results in the literature. The obtained results show that the gradient enhancement removes pathological localization effects which would typically result from the softening influence. In addition, the numerical study proves that the mode can capture the basic features of phase transformation front patterns and their evolution during transformations.