A constitutive model for shape memory polymers with application to torsion of prismatic bars

In this article, satisfying the second law of thermodynamics, we present a 3D constitutive model for shape memory polymers. The model is based on an additive decomposition of the strain into four parts. Also, evolution laws for internal variables during both cooling and heating processes are proposed. Since temperature has considerable effect on the shape memory polymer behavior, for simulation of a shape memory polymer-based structure, it is required to perform a heat-transfer analysis. Commonly, an experimentally observed temperature rate-dependent behavior of shape memory polymers is justified by a rate-dependent glassy temperature, but using the heat-transfer analysis, it is shown that the glassy temperature could be considered as a constant material parameter. To this end, implementing the constitutive model within a nonlinear finite element code, we simulate torsion of a shape memory polymer rectangular bar and a circular tube. Moreover, we compare the predicted results with experimental data recently reported in the literature, which shows a good agreement.