A microstructural damage model for highly entangled multi-network hydrogels

Building on our recently proposed network-refinement strategy, we fabricated a single-component multi-network (MN) hydrogel via repeated swelling-curing cycles, where dense topological entanglements simultaneously enhance toughness, strength, and elasticity. These MN hydrogels exhibit an unusual mechanical behavior: pronounced hysteresis emerges only at large deformations, while the initial elastic modulus remains unchanged. This unique decoupling, where large-deformation dissipation is independent of small-stretch response, cannot be captured by existing constitutive models. To address this gap, we develop a new micromechanically motivated constitutive framework to MN hydrogels. Cyclic tensile tests and swelling anisotropy measurements reveal a deformation-dependent behavior consistent with entangled polymer chains transitioning from mobile slip-links to topologically locked, load-bearing elements under stretching. Guided by this mechanistic insight, we construct a constitutive model that couples an Arruda–Boyce representation of the chemical network with a tube model to explicitly capture topological constraints. The damage evolution function is identified from macroscopic hysteresis energy, ensuring thermodynamic consistency and quantitatively linking dissipation to microstructural evolution. The model accurately predicts both monotonic and cyclic tensile responses across varying network densities. Implemented in finite element simulations, the framework also captures damage localization in pre-notched specimens under pure-shear loading, showing qualitative agreement with experimental birefringence observations. Consequently, this work provides a robust predictive tool for characterizing internal network-damage evolution and guiding the microstructural design of highly entangled, dissipative hydrogels.