On infinitesimal and finite deformations in shape memory alloys

Abstract

Two material models for shape memory alloys are developed and are evaluated by comparing and contrasting their predictions in three standard problems involving martensitic transformations. Both models are based on generalized plasticity and comprise a von Mises type of expression for the loading surfaces, a linear evolution law for the material martensite fraction, and a hyperelastic constitutive equation. The first model is an infinitesimal one, based on the usual additive decomposition of the small strain tensor into elastic and inelastic (transformation-induced) parts, while the second is a finite one based on the consistent use of the “physical” (intrinsic material) metric concept. This study reveals that in the first and second problem—uniaxial tension and simple shear—and under small and moderate levels of strain, both models predict almost identical response, while for higher levels of strain the models still predict comparable response, even though their basic kinematical assumptions differ vastly. The third problem, comprising infinitesimal shear with finite rotation, is considered next. In this case, it is shown that while the finite model yields the physically correct response, the infinitesimal model yields completely erroneous results.