• Multiscale chain-based FE framework for double-network gel mechanics • Coupled damage and viscoelasticity drive path-dependent anisotropy • Predicts hysteresis, damage localization, and crack initiation • Energy-based formulation captures fracture resistance evolution • Physics-informed framework for designing tough soft materials Double-network (DN) gels exhibit an exceptional combination of stretchability, toughness, and energy dissipation, making them promising materials for soft robotics, biomedical devices, and flexible electronics. These outstanding properties arise from the interplay between a brittle, sacrificial primary network and a ductile, extensible secondary network. However, capturing the complex, anisotropic, and path-dependent mechanical response of DN gels - especially under multiaxial and non-uniform loading - remains a major modeling challenge. This work introduces a three-dimensional multiscale constitutive model that integrates progressive chain scission, anisotropic damage, viscoelastic relaxation, and inter-network interactions. The primary network is modeled as an entropic assembly of chains with stochastic lengths undergoing irreversible damage, upscaled via microsphere integration to capture directionality. The secondary network follows a generalized Maxwell formulation to reproduce rate-dependent dissipation. Energy coupling between the two networks enables the model to reflect microstructural rearrangement, directional softening, and residual anisotropy. The model is implemented as a UMAT in ABAQUS/Standard and validated against experimental data under both homogeneous and non-uniform loading conditions. It accurately captures nonlinear stress-strain behavior, hysteresis, and anisotropic softening resulting from prior deformation. In pre-notched specimens under pure shear, simulations reproduce force-displacement response, stress localization, and damage evolution up to crack initiation. An energy-based analysis highlights the roles of reversible and dissipated energy, with predicted critical energy release rates closely matching experiments across pre-stretch levels. The model offers a predictive, physically grounded framework for understanding and engineering tough, damage-resistant DN gels.
Ogouari et al. (Sun,) studied this question.