Book excerpt: Double network (DN) hydrogels are hydrogels consist of two different networks to make them both tough and extensible. This thesis focuses on understanding the time-dependent mechanical behavior of DN hydrogels through constitutive modeling and numerical simulation. We start by working with a poly(vinyl alcohol) (PVA) gel which is chemically cross-linked by glutaraldehyde and physically cross-linked by Borax ions. This PVA gel serves as a model system because of its well-defined simple chemical structure. Based on the steady state breaking and healing kinetics of the temporary (physical) cross-links, a time-dependent large deformation constitutive model for this model system is developed. This constitutive model is compared against a large set of experimental data, including uniaxial tension tests of loading-holding-unloading at different rates, and torsional rheology tests at temperatures ranging from 13 to 50 degrees Celsius; all results agree very well. A standard procedure for determining the material parameters is also presented. Using the steady state constitutive model, an asymptotic analysis for the dominant stress and strain fields near the tip of a plane stress crack is carried out. This model is then implemented into a commercial finite element (FE) software, ABAQUS, through a user defined material subroutine (UMAT) with a novel time integration scheme. This enables us to run numerical simulations with complex geometries and loading conditions. Currently we are able to numerically simulate the PVA gel with undamaged polymer chains that follow Gaussian chain statistics. A possible way to incorporate strain hardening into ABAQUS using polynomial strain energy density functions is also discussed. Model prediction, FE simulation, and experimental data are compared for samples with high stress and strain concentrations (cracked or notched samples). Comparisons range from full field responses to local singularities as well as 3D and 2D simulations; all results agree very well. However, a limitation of the PVA model system is that the bond breaking and healing kinetics are independent of stress, while bond dissociations in most polymeric materials are stress-induced. A more general constitutive model for a polyampholyte (PA) gel that considers stress-dependent breaking kinetics for the temporary cross-links is investigated. Physical meanings of each material parameter and how to fit for them are presented. Using this stress-dependent model along with the steady state model, differences between nonlinear and linear viscoelasticity are discussed, and two cases with stress concentrations as analogs of crack problems are examined to study the role of nonlinear viscoelasticity at crack tip fields.