Development of the network alteration theory for the Mullins softening of double-network hydrogels

Double-network hydrogels (DN gels) with excellent mechanical properties have great application prospects as an innovative soft material. The Mullins effect originally discovered in rubber materials is also observed in this material. The network alteration theories have achieved many successes in capturing this stress-softening behavior of DN gels and exploring the underlying damage mechanisms. In this paper, we develop a network alteration theory to account for the softening behaviors of DN gels under both uniaxial tension and pure shear and simultaneously explore more about the damage origins. The advantage of the use of worm-like chain model for DN gels is illustrated. New network evolutions of the network alteration parameters are further developed on a basis of an existing network alteration theory. The model predictions of the new model for the experimental results of DN gels under both uniaxial tension and pure shear are compared with those of the old one. The results demonstrate that the new model is more physically sound and offers much better predictive capabilities. It is found that the dangling chains, chain disentanglements and the degradation of the interactions between the two networks during deformation play significant roles in the Mullins softening of DN gels. This paper gives new insights into the microdamage origins of DN gels and significantly improve the network alteration theory for DN gels.