Mechanical behavior of double-network (DN) gels with covalent and non-covalent bonds under multi-cycle loading depends strongly on time, strain rate and deformation program. A model is developed for the viscoelastic and viscoplastic responses of a polymer network with permanent and temporary junctions. Viscoelasticity is modeled as breakage and reformation of temporary bonds driven by thermal fluctuations. Viscoplasticity is treated as sliding of permanent junctions with respect to their initial positions in the network. Slippage occurs when a junction becomes unbalanced due to transition of a chain linked by this junction from its active state into the dangling state. Analysis of observations in tensile tests with various strain rates, relaxation tests, loading-unloading tests, and multi-cycle tests with various deformation programs on a series of DN gels shows that the experimental stress–strain diagrams are described correctly by the governing equations, material parameters evolve consistently with experimental conditions, and predictions of the model are in quantitative (where sufficient data are provided) and qualitative agreement with experimental data. In particular, numerical simulation demonstrates the ability of the model to describe the Mullins effect in DN gels.

具有多价负载的具有共价键和非共价键的双网络（DN）凝胶的机械行为在很大程度上取决于时间，应变率和变形程序。针对具有永久和临时连接的聚合物网络的粘弹性和粘塑性响应，开发了一个模型。粘弹性建模为由热波动驱动的临时键的断裂和再形成。粘塑性被视为永久性接头相对于其在网络中的初始位置的滑动。当一个结由于该结所连接的链从其活动状态过渡到悬空状态而变得不平衡时，就会发生滑移。分析各种应变率下的拉伸试验，松弛试验，装卸试验，一系列DN凝胶的各种变形程序进行的多周期测试表明，控制方程正确地描述了实验应力-应变图，材料参数随实验条件的变化而变化，模型的预测是定量的（在足够的情况下）数据）和实验数据的定性一致。尤其是，数值模拟证明了该模型能够描述DN凝胶中的Mullins效应。