A constitutive model for multi network elastomers pre-stretched by swelling

Abstract 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.