Nonlocal modelling of superelastic behavior of shape memory alloys

Abstract
Recently, various constitutive laws based on phenomenological or micromechanical approaches have been developed to describe the behavior of shape memory alloys (SMA). They are particularly well adapted for modelling the effects of phase transformation and martensite reorientation on the thermomechanical behavior of the bulk material.
Nevertheless, these models fail to describe phenomena such as transformation localisation or size effects which may appear in wires and thin films. Indeed, to describe such phenomena, the influence of the neighbouring area of the material point should be taken into account. This can be achieved through a nonlocal formulation of the constitutive equations.
In the present work, we propose a nonlocal modelling of the superelastic behavior of SMA. It uses for the martensite volume fraction, besides the usual local variable, a corresponding nonlocal contribution. This latter is governed by a partial differential equation defined on an influence zone whose size is dependant on an internal length parameter of the material.
Based on this formulation, a 1D specifc element is developped where the nonlocal variable is an additional degree of freedom. Simulations are performed to study the influence of the internal length parameter and nonlocality on the mechanical response during superelastic loadings.