Modelling Stress Softening and Necking Phenomena in Double Network Hydrogels

Double network (DN) gels are three-dimensional polymer matrices formed by interpenetrating networks. In contrast to the conventional single-network gels, DN gels have significant toughness, which makes them a promising material for different biomedical and biological applications. However, DN gels show complicated inelastic behavior including the Mullins effect and necking instability. Despite extensive efforts on modelling different aspects of the damage process in gels, the micro-mechanical modelling of the mechanisms that lead to necking in DN gels remains to be a challenging task. Here, a constitutive model is proposed to understand and describe the mechanical behavior of DN gels based on statistical micro-mechanics of interpenetrating polymer networks. DN gels behavior is divided into three parts including pre-necking, necking, and hardening. The first network is dominant in the response of the gel in the pre-necking stage. The breakage of the first network to smaller network fractions (clusters) induces the stress softening observed in this stage. The interaction of both networks and the second network are also considered as main contributors to the response of gel in necking and hardening stages, respectively. The contribution of clusters decreases during the necking as the second network starts hardening. The numerical results of the proposed model are validated and compared by uni-axial cyclic tensile experimental data of DN gels.