A 3D finite deformation constitutive model for amorphous shape memory polymers: A multi-branch modeling approach for nonequilibrium relaxation processes

Shape memory polymers (SMPs) are materials that can recover a large pre-deformed shape in response to environmental stimuli. For a thermally activated amorphous SMP, the pre-deformation and recovery of the shape require the SMP to traverse its glass transition temperature (T_g) to complete the shape memory (SM) cycle. As a result, the recovery behavior of SMPs shows strong dependency on both the pre-deforming temperature and recovery temperature. Generally, to capture the multitude of relaxation processes, multi-branch models (similar to the 1D generalized viscoelastic model or Prony series) are used to model the time-dependent behaviors of polymers. This approach often requires an arbitrary (usually numerous) number of branches to capture the material behavior, which results in a substantial number of material parameters. In this paper, a multi-branch model is developed to capture the SM effect by considering the complex thermomechanical properties of amorphous SMPs as the temperature crosses T_g. The model utilizes two sets of nonequilibrium branches for fundamentally different modes of relaxation: the glassy mode and Rouse modes. This leads to a significant reduction in the number of material parameters. Model simulation comparisons with a range of thermomechanical experiments conducted on a tert-butyl acrylate-based SMP show very good agreement. The model is further utilized to explore the intrinsic recovery behavior of an SMP and the size effects on the free recovery characteristics of a magneto-sensitive SMP composite.