A visco-hyperelastic constitutive model of hydrogel considering the coupling effect between segment motion and interchain slippage

Segment motion induces interchain slippage, leading to a complex coupling between hyperelastic and viscoelastic behaviors in hydrogels. Traditional models, which treat these behaviors separately and introduce a coupling free energy, struggle to capture this visco-hyperelastic coupling mechanism accurately. In this work, we develop a visco-hyperelastic constitutive model incorporating viscoelastic contributions into the general hyperelastic free energy to capture the coupling mechanism. The model introduces both the end-to-end distance and the envelope radius to describe the three-dimensional chain conformation. A joint probability distribution of these two parameters is used to capture the relationship between the chain conformation and the chain distribution. We also propose a two-level macro-micro transition framework to link the evolution of end-to-end distance and envelope radius to macroscopic deformations. In the first level of such macro-micro transition, the elongation of individual chains in various directions within the network is mapped to the overall chain elongation. In the second level, both interchain slippage and total chain elongation are incorporated into the overall deformation of the polymer network. A comparison between our predicted results with our experimental data demonstrates the predictability of the new model. Finally, the modeling results show that the interchain slippage always involves two sequential stages, i.e., orientation and relative slippage; and the increasing strain rate enhances the asynchronous responses between segment motion and relative slippage due to multichain interactions, making the viscoelastic responses of hydrogel more obvious.