Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys

Abstract

Shape memory alloys, notably NiTi, often exhibit softening pseudoelastic response that results in formation and propagation of Lüders-like bands upon loading, for instance, in uniaxial tension. A common approach to modelling softening and strain localization is to resort to gradient-enhanced formulations that are capable of restoring well-posedness of the boundary-value problem. This approach is also followed in the present paper by introducing a gradient-enhancement into a simple one-dimensional model of pseudoelasticity. In order to facilitate computational treatment, a micromorphic-type regularization of the gradient-enhanced model is subsequently performed. The formulation employs the incremental energy minimization framework that is combined with the augmented Lagrangian treatment of the resulting non-smooth minimization problem. A thermomechanically coupled model is also formulated and implemented in a finite-element code. The effect of the loading rate on the localization pattern in a NiTi wire under tension is studied, and the features predicted by the model show a good agreement with the experimental observations. Additionally, an analytical solution is provided for a propagating interface (macroscopic transformation front) both for the gradient-enhanced model and for its micromorphic version.