A constitutive model for hydrogels with coupled volumetric and entanglement effects

Abstract The unique mechanical behaviour of hydrogels is governed by solvent–polymer interactions as well as network topology. Classical rubber elasticity models, which typically ignore volumetric compressibility and entanglement effects, are often inadequate for describing hydrogels under large deformations. This study presents a new constitutive framework that integrates the Flory–Huggins lattice theory with affine network and tube models. The proposed free energy formulation embodies the mechanisms of solvent-induced volumetric change and entanglement-induced stiffening. Model validation was validated against experimental data of polyvinyl alcohol (PVA) hydrogels under uniaxial compression and NaSS-co-DMAEA-Q polyampholyte hydrogels under uniaxial tension. Our results reveal a decrease in compressive modulus with water content and an increase in tensile stiffness with cross-linker concentration, both owing to intensified entanglements. It is noteworthy that the volumetric contribution, though passive, is non-negligible under shear-dominated conditions. Ultimately, this study yields a thermodynamically consistent and experimentally validated model that advances our understanding of hydrogel structure–property relationships.