Modeling of Shape Memory Polymer Behavior Using Generalized Maxwell Model with Time-Temperature Superposition: Experiments, Parameter Identification, and Finite Element Validation

The modeling of the mechanical behavior of shape memory polymers (SMPs) is crucial for their engineering applications. This paper proposes a viscoelastic constitutive model based on the Generalized Maxwell Model combined with the Time-Temperature Superposition Principle (TTSP) to quantitatively predict the thermomechanical response of SMPs throughout the full shape memory cycle (loading–cooling–unloading–recovery). By decoupling the instantaneous elastic modulus and the normalized relaxation modulus, and considering the effect of temperature on the instantaneous modulus as well as the scaling of relaxation times, the model effectively resolves the simulation of stress increase during cooling caused by the growth of elastic modulus. The parameters of the Generalized Maxwell Model at different temperatures were determined through stress relaxation experiments, and the time-scaling factors were fitted using the Williams-Landel-Ferry (WLF) equation. Based on the fitted parameters, a three-dimensional constitutive model was implemented in ABAQUS, and finite element simulations of the full shape memory cycle under both uniaxial tension and bending deformation were conducted. Results demonstrate that the model accurately captures the stress growth due to increased elastic modulus during cooling, the shape fixity effect after unloading at low temperature, and the release of viscoelastic strain during the heating recovery process. The simulation results for both uniaxial and bending deformations are consistent with expected phenomena, validating the model's applicability under complex stress states. This study provides an efficient and reliable numerical tool for the intelligent structural design and controllable deformation analysis of SMPs.