A Microstructural Damage Model toward Simulating the Mullins Effect in Double-Network Hydrogels

The damage models based on the eight-chain model and the affine full-chain network model are not adequate to describe the damage behaviors in double-network (DN) hydrogels. To overcome this limitation, we propose a combined chain stretch model with new damage flow rules. It is demonstrated that the new proposed micro-chain stretch is a reduced form of the complete representation for the transversely isotropic tensor function. As a result, the damage models based on the eight-chain model and the affine model are incorporated as special cases. The effects of chain affineness and network entangling are simultaneously involved in the new model, while only one of these two effects can be characterized in either the eight-chain model or the affine model. It is further shown that the new model can effectively capture the Mullins features of the DN hydrogels and achieve better agreement with the experimental data than the affine model and the eight-chain model.