Double network hydrogels (DN hydrogels) are a class of reinforced hydrogels that benefit from significant high stretchability and toughness. They have high water content and are extremely soft and mostly biocompatible. These excellent properties make them a great candidate for load bearing in biomedical applications. Although recent advances in the process and characterization of the gels have led to significant improvements in their properties, our understanding of the load transfer mechanism within them has remained sparse and inconclusive. In this study, a physically motivated constitutive model of DN gel in quasi-static deformation is developed, which can be particularly used to elucidate the inelastic features such as permanent damage during deformation. The proposed model enables us to describe the damage and its influences on the microstructure of the gel. The model is validated against the experimental tests. DN hydrogels demonstrate J-type and S-type nonlinear behaviors under large deformations, with an inelastic feature similar to the history-dependent stress softening of the filled rubbers, generally referred to as the Mullins effect. This damage may result from the rupture of cross-linking, as no fillers are present in a DN hydrogel matrix. Therefore, irreversible chain detachment and decomposition of the first network due to its highly cross-linked structure are explored as the underlying reasons for the nonlinear inelastic phenomenon. The continuum damage approach based on the thermodynamic representation of the network evolution theory and the concept of integration over the unit sphere is utilized to describe the constitutive behaviour of the material. The model contains a few numbers of material constants and shows a good agreement with cyclic uni-axial tensile test data.