A double network (DN) gel consists of interpenetrating networks of a cross-linked polyelectrolyte (the 1st network) and a neutral polymer (the 2nd network). The partial fracture of the 1st network is believed to be the main cause of the high toughness of a DN gel. In order to carry out further analysis, a quantitative material model is necessary. In this paper, we introduce two continuous internal variables to describe the gradual damage in a DN gel, and incorporate it in the free-energy function through which the constitutive relation can be derived. Using the model, the pseudo-elasticity of a DN gel in large deformation is analyzed for both uniaxial and biaxial loading cases. The model captures the Mullins effect as well as the stable necking phenomenon of a DN gel under tension. Both the Mullins effect and the necking propagation dissipate a significant amount of energy, and are directly related to the fracture toughness of a DN gel.
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