J. Mech. Phys. Solids 215 (2026) 106701

Keywords:Spatial confinement hydrogels, Directional chain slippage, Crosslinking distance evolution, Hyperelastic-to-viscoelastic transition

Spatial confinement hydrogels (SCHs) exhibit excellent mechanical properties, including en hanced toughness, self-healing capacity, and swelling-induced degradation, all of which stem  from their unique network structures. In these structures, tangential and normal displacements at  crosslinking points govern chain slippage and crosslinking distance evolution, yielding variable  Kuhn segment numbers and non-zero crosslinking distances overlooked in classical models. This  study proposes a micro-macroscopic constitutive model to capture the response of SCHs under  large deformation. We first derive an entropic free energy function for individual chains to ac count for the evolution of the Kuhn segment number. By incorporating finite crosslinking distances  into a micro-macroscopic transition model, we develop a macroscopic continuum model that fea tures non-affine deformation mapping and evolution equations for both the Kuhn segment vector  and the crosslinking distance. Our analysis reveals that directional chain slippage and crosslink ing distance evolution collectively mitigate stress concentrations in SCHs under large strains.  Furthermore, the model characterizes the strain rate-dependent behavior of SCHs, specifically  the transition from a hyperelastic-dominated to a viscoelastic-dominated regime. The proposed  constitutive model provides a valid description of SCH mechanical behavior and may advance  engineering applications for hydrogels.

Yunqiang Hu, Zhaoguo Gao, Fei Jia, Yanju Liu, Jinsong Leng

A micro-macroscopic constitutive model for spatial confinement hydrogels incorporating directional chain slippage and crosslinking distance evolution.pdf