A gradient approach for the macroscopic modeling of superelasticity in softening shape memory alloys. (1st January 2015) - León Baldelli, A.A.; Maurini, C.; Pham, K.
Abstract: This paper presents a gradient approach for the quasi-static macroscopic modeling of superelasticity in softening shape memory alloys bars. The model is assumed to be rate-independent and to depend on a single internal variable. Regularization of the model is achieved through the free energy by assuming a quadratic dependance with respect to the gradient of the internal variable. The quasi-static evolution is then formulated in terms of two physical principles: a stability criterion which consists in selecting the local minima of the total energy of the system and an energy balance condition. Both homogeneous and non-homogeneous evolutions are investigated analytically for a family of material parameters. Non-homogeneous evolutions can be divided into three stages: the localized martensite nucleation followed by the propagation of the localized phase transformation front and finally the annihilation of the austenite phase. For each stage, the local phase field profile as well as the global stress–strain response are derived in closed-form. Due to the presence of an internal length related to the regularization, size effects are inherent with such non-local model. We show that for sufficiently long bars, snap-backs occur at the onset of localized phase transformation, leading to a time discontinuity in the quasi-static evolution.