A Nonlinear Thermo-Visco-Green-Elastic Constitutive Model for Mullins Damage of Shape Memory Polymers under Giant Elongations

In this paper, we introduce a comprehensive 3D finite-deformation constitutive model for shape memory polymers focused on addressing the Mullins effect when subjected to substantial elongation, reaching up to 200 % strain. Considering only four Maxwell branches with nonlinear viscous components integrated with the WLF equation, our modeling framework inherently ensures thermodynamic consistency without imposing excessive constraints, linear (Boltzmann) or phenomenological modeling. This approach allows the study of time- and temperature-dependent behaviors, including stress relaxation, cyclic loadings related to the shape memory effect, shape and force recovery, and damage phenomena in SMPs under large elongations. The model integrates hyperelasticity and stress-softening effects while employing the concept of rational thermodynamics and internal state variables in the realm of the thermo-visco-green-elastic continuum approach. Additionally, we delve into the influence of strain levels on stretch-induced softening effects and their subsequent impact on free-shape recovery behavior. To streamline characterization and calibration, we conducted extensive experimental uniaxial cyclic loading tests across various strain rates and temperatures on a shape memory polymer. The model is compatible with both COMSOL and Abaqus software, enabling robust simulations of complex material responses. Through rigorous comparison against experimental data and extensive finite element multi-physics analysis simulations, we evaluate the model's performance via several multi-physics case studies and validate our proposed algorithm while minimizing both the number of parameters and computational costs.