A combined numerical and theoretical study on the strengthening and toughening mechanisms of double network hydrogels

Double network (DN) hydrogels, comprising two interpenetrating networks, exhibit superior mechanical strength and toughness compared to single-network hydrogels. Experimental studies attribute their enhanced performance to the sacrificial bonds of the first network. However, a quantitative mechanistic understanding through computational modeling remains insufficient. This study developed a coarse-grained computational model utilizing Langevin dynamics to unravel the strengthening and toughening mechanisms of the DN hydrogels. Simulation results reveal three-stage tensile deformation (pre-necking, necking, and strain-stiffening stages) with yield and fracture stresses (~0.5 MPa and ~ 0.9 MPa, respectively) aligning with experimental data. The first network functions as sacrificial bonds, fracturing into small clusters under stretching, while polymer chains in both component networks progressively align with deformation direction, enhancing energy dissipation. We also proposed a concise one-dimensional viscoelastic theoretical model, capturing key mechanical behaviors and corroborating simulations and experiments. The critical parametric analysis highlights the roles of network stiffness and inter-network interactions: a higher first network increases yield stress, and stronger inter-network interaction elevates stress plateau. These findings quantitatively link sacrificial bonds rupture, chain orientation, and inter-network interactions to DN hydrogel mechanics, bridging computational, theoretical, and experimental insights. This work may advance the design of robust hydrogels through tunable network parameters.