Double network (DN) elastomers are a class of reinforced gels that benefit from a significantly high stretch-ability and toughness. However, DN gels lose their toughness due to the accumulation of damage under cyclic loading during their lifetime. While recent advances in the process and characterization of the DN gels have led to significant improvements in their properties, our understandings of the accumulated damage mechanisms within the material remain sparse and inconclusive. Here, a physically motivated constitutive model is presented for DN gels subjected to a high number of cyclic deformations, which will eventually approach a steady-state after thousands of cycles. The model can be particularly used to elucidate the inelastic features, such as permanent damage during deformation of each cycle. The observed damage may be induced from the chain scission, chain slippage, or polymer relaxation. 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 stress softening phenomenon. The model is validated against the experimental tests. The model contains a few numbers of material constants and shows good agreement with cyclic uni-axial tensile test data.

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