Finite element analysis of pseudoelastic behavior of shape memory alloys using a micromechanics based constitutive model
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In this paper, we describe the finite element formulation and implementation of a micromechanics based constitutive model of pseudoelasticity. The constitutive model describes the behavior of SMA's through a constitutive element (CE) consisting of several grains. A volume average over the CE provides the macroscopic continuum response. The remarkable feature of this model is its strong similarity to the incremental stress-strain relations of elastoplasticity and the internal variable approach. The martensitic transformations are described through the evolution of martensite volume fraction over the CE. The model accounts for behavior similar to isotropic and kinematic hardening of elastoplasticity. The finite element formulation involves the linearization of the weak form, computation of the tangent stiffness, and a stress update based on the operator split method. A numerical result is presented to illustrate the accuracy of the finite element formulation with respect to the theoretical model.