This work advances the modeling of complex polymer systems by developing physically based constitutive frameworks capable of predicting the nonlinear, anisotropic, and history-dependent mechanical behavior of multi-network materials such as double-network hydrogels and filled elastomers [1-2]. These soft materials exhibit remarkable toughness and resilience due to intricate energy dissipation mechanisms involving chain scission, interfacial sliding, filler debonding, and viscoelastic relaxation. A multiscale modeling approach is proposed, combining molecular-level statistical mechanics with homogenization techniques to link microscale deformation mechanisms to macroscopic responses. The resulting models account for anisotropic softening, directional damage, and the influence of deformation history, achieving excellent agreement with multiaxial experimental observations. For filled elastomers, the framework incorporates visco-hyperelastic effects by representing the material as coupled elastic-viscous networks subjected to strain amplification from the filler phase. This description captures key phenomena such as the Mullins effect, hysteresis, and the evolution of anisotropy under cyclic loading. A comprehensive formulation is also proposed to explicitly represent the interaction between polymer and filler subnetworks, integrating mechanisms like chain-cluster debonding and interfacial viscous sliding. The finite element implementation of the hydrogel model demonstrates its robustness for simulating heterogeneous deformation fields. Altogether, this research establishes a unified and predictive basis for the design of architectured polymer materials, opening pathways toward multiphysics extensions coupling mechanical, electrical, or thermal effects for advanced functional applications.

References:

1. Ogouari, L., Guo, Q., Zaïri, F., Mai, T.-T., Gong, J.P., Urayama, K., 2024. A multiscale model for the multiaxial anisotropic damage of double-network gels. Mechanics of Materials 105058.
2. Ogouari, L., Guo, Q., Zaïri, F., Mai, T.-T., Urayama, K., 2024. An anisotropic damage visco-hyperelastic model for multiaxial stress-strain response and energy dissipation in filled rubber. International Journal of Plasticity 182, 104111.