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.

中文翻译：

---

考虑链段运动与链间滑移耦合效应的水凝胶粘超弹性本构模型


段运动会引起链间滑移，导致水凝胶中的超弹性和粘弹性行为之间产生复杂的耦合。传统模型单独处理这些行为并引入耦合自由能，难以准确捕捉这种粘-超弹性耦合机制。在这项工作中，我们开发了一个粘-超弹性本构模型，将粘弹性贡献纳入一般的超弹性自由能中，以捕获耦合机制。该模型引入了端到端距离和包络半径来描述三维链构象。这两个参数的联合概率分布用于捕获链构象和链分布之间的关系。我们还提出了一个两级宏观-微观过渡框架，将端到端距离和包络半径的演变与宏观变形联系起来。在这种宏观-微观过渡的第一级中，网络内各个链在各个方向上的伸长被映射到整个链的伸长。在第二级中，链间滑移和总链伸长率都被纳入聚合物网络的整体变形中。我们的预测结果与实验数据之间的比较证明了新模型的可预测性。最后，建模结果表明，链间滑点总是涉及两个连续阶段，即方向滑点和相对滑点;应变速率的增加增强了链段运动与多链相互作用引起的相对滑移之间的异步响应，使水凝胶的粘弹性响应更加明显。