A gradient regularized model for shape memory alloys

Abstract

In this work a transformation strain gradient enhancement is introduced into a phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys. The constitutive model is able to capture several unique features of the constitutive response of these materials during the transformation between austenite and martensite during the pseudoelastic response. These features include the asymmetry in the initial transformation stresses in tension versus compression, the asymmetry in the transformation strains in tension and compression, and finally the asymmetry in the hardening behavior in tension and compression. In fact, experiments have shown that untrained NiTi exhibits hardening during its transformation in compression, but softening for tensile loading. It is this softening behavior that motivates the need for the introduction of the transformation strain gradient into the constitutive modeling. Transformation strain gradient effects are introduced via a phase variable that describes the extent of transformation. The free energy of the material then depends on gradients of the phase variable, which introduces a material length scale into the theory. The governing equation for the phase variable is developed from a microforce balance and continuum thermodynamics analysis. The model is implemented in the commercial finite element software Abaqus through user defined subroutines and several numerical simulations are performed to illustrate the model response and lack of numerical mesh-dependency of the results.