Multi network elastomers (MNEs), composed of a single sacrificial network and other matrix networks, exhibit appealing mechanical properties. In this paper, we develop a constitutive model for MNEs prepared by multiple swellings. Firstly, the swelling process is analyzed. The free energy of a swollen elastomer consists of the strain energy of deformed polymer chains and the energy of mixing. We analyze the mechanical equilibrium and chemical potential equilibrium during the swelling of MNEs. The degree of swelling of MNEs is affected by the preparation conditions, like the component of the solution, as well as the microscopic physical quantities, such as the chain length and density of polymer chains of the networks. Secondly, the free energy of the completed MNE subjected to external loading is composed of the strain energy of each network. The chains of the sacrificial network (first network) can be destroyed gradually when the applied load increases. We adopt the network alteration theory to describe the above progressive damage of the sacrificial network. In addition, the matrix networks are fully elastic. We verify this model using the experimental data including stress–stretch curves of elastomers with double and triple networks, as well as the step cycle curves of triple network elastomers (TNEs). This model predicts well for the swelling-induced pre-stretches of each network under specified preparation conditions. It relates the stress to the stretch of MNEs under external loading, and indicates the stress contribution of each network, and the damage evolution of the sacrificial network. Our model is instructive for designing MNEs with desired mechanical properties.

由单个牺牲性网络和其他矩阵网络组成的多网络弹性体（MNE）具有吸引人的机械性能。在本文中，我们开发了由多重溶胀制备的跨国公司的本构模型。首先，分析了膨胀过程。溶胀的弹性体的自由能由变形的聚合物链的应变能和混合能组成。我们分析了跨国公司膨胀期间的机械平衡和化学势平衡。MNE的溶胀程度受制备条件（如溶液的成分）以及微观物理量（如网络的链长和聚合物链的密度）的影响。其次，完整的MNE承受外部载荷的自由能由每个网络的应变能组成。当施加的负载增加时，牺牲网络（第一网络）的链可以逐渐被破坏。我们采用网络变更理论来描述上述牺牲网络的渐进式破坏。另外，矩阵网络是完全弹性的。我们使用包括双网和三网的弹性体的应力-拉伸曲线以及三网的弹性体（TNEs）的阶跃循环曲线的实验数据验证了该模型。该模型可以很好地预测在指定的准备条件下每个网络的膨胀诱发的预拉伸。它将应力与外部负载下的MNE的拉伸相关联，并指示每个网络的应力贡献以及牺牲网络的损伤演化。我们的模型对于设计具有所需机械性能的MNE具有指导意义。