Effect of water redistribution on the fracture of hydrogel in mechanochemical equilibrium state

Fluid effect on the fracture of hydrogel is of growing interest to the community of soft matter. In this work, we investigate the effect of water redistribution on the fracture of hydrogel in mechanochemical equilibrium state. The impermeable condition (e.g., in oil) and permeable condition (e.g., in water) are considered, which results in different redistributions of water in hydrogels. Here, we derive the general form of J integral incorporating the chemical potential energy of water, and then obtain the analytical forms of J integral for the fracture of hydrogel in oil and water, respectively. Also, we perform finite element calculations and experiments at an extremely large time scale to verify the theoretical predictions. It is found that the J integral of the hydrogel in oil is the sum of two parts: one part from the area under the stress-stretch curve and the other part from the area in water concentration-chemical potential curve. The J integral in oil is amplified by water redistribution, which is obvious for small deformations but becomes negligible for extremely large deformations. The J integral for the hydrogel in water is determined by the area under stress-stretch curve, which is reduced by water redistribution. This work reveals the effect of water redistribution on the fracture of hydrogel, which is fundamental for understanding fracture of hydrogels.