A non-local implicit gradient-enhanced model for unstable behaviors of pseudoelastic shape memory alloys in tensile loading

• A nonlocal gradient model is developed to predict unstable behaviors of SMAs.
• Effectiveness of the model is examined by experimental data.
• The model can predict stress drop and deviation of local strain from global strain.
• The model is used to simulate material instabilities without mesh dependency.

In this paper, a gradient-enhanced 3-D phenomenological model for shape memory alloys using the non-local theory is developed based on a 1-D constitutive model. The method utilizes a non-local field variable in its constitutive framework with an implicit gradient formulation in order to achieve results independent of the finite element discretization. An efficient numerical approach to implement the non-local gradient-enhanced model in finite element codes is proposed. The model is used to simulate stress drop at the onset of transformation, and its performance is evaluated using different experimental data. The potential of the presented numerical approach for behavior of shape memory alloys in eliminating mesh-dependent simulations is validated by conducting various localization problems. The numerical results show that the developed model can simulate the observed unstable behaviors such as stress drop and deviation of local strain from global strain during nucleation and propagation of martensitic phase.