Necking of double-network gels: Constitutive modeling with microstructural insight

In this study, a constitutive model is proposed to describe the necking behavior of double network (DN) gels based on statistical micromechanics of interpenetrating polymer networks. Accordingly, the constitutive response of DN gels in large deformations has been divided into three zones, i.e., prenecking, necking, and postnecking. The behavior of the DN gel is dominated by the behavior of the first and the second networks in each stage. In a previous study, we described how the destruction of the first network can govern the inelastic effects during the prenecking stage. Here, we elucidate the role of the second network to govern the material behavior in the necking and postnecking stages. To incorporate the effect of necking, the material behavior at each zone is described through the competition of three mechanisms that control the rearrangement of the two networks. Here, we challenge a general simplifying assumption in the modeling of DN gels, which considers the second network to be fully elastic. The recent experimental observations show the reduction of energy dissipation in the first network after necking initiation due to the localization of the damage in an active zone. Thus, we assumed that the chains of the second network contribute to the energy dissipation of the matrix by keeping the connection between the fragments of the first network. The proposed model has been validated in all three stages against different sets of experimental data on the uniaxial cyclic tensile behavior of DN gels. Moreover, the initiation and propagation of necking instability have been comprehensively illustrated through a finite-element implementation of the proposed model.