Three-dimensional thermo-mechanical viscoelastic model for shape memory polymers with binding factor

Shape memory polymers show high promise in the area of morphing structures. Thermally activated shape memory polymers will exhibit shape memory effect under appropriate loading and thermal configurations. In this article, the steps in which a one-dimensional thermo-mechanical viscoelastic model is expanded into three-dimensional form are fully described. For the one-dimensional constitutive model, the standard linear viscoelastic arm is in series with a thermal and storage element. The three-dimensional translation is initiated by transforming Young’s modulus into bulk and shear modulus. Also, the compliance and stiffness matrix for correlating elements are defined and applied into the model. A binding factor is defined by the authors in the one-dimensional model in order to account for the storage strain energy within the polymer. To program the three-dimensional model into finite element analysis software, it was rendered into a time discrete form. The time discrete form was used to develop a UMAT subroutine code within ABAQUS to generate a numerical simulation. Finally, the results of this model are compared to available experiment data and previous model developed by the authors. Numerical simulation results clearly exhibit the thermo-mechanical properties of the polymer which include shape fixity, shape recovery, and recovery stress.