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 Luders-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 empl…