Hyperelastic Swelling of Stiff Hydrogels.

Hydrogels are swollen polymer networks where elastic deformation is coupled to nanoscale fluid flow. As a consequence, hydrogels can withstand large strains and exhibit nonlinear, hyperelastic properties. Previous studies have shown that low-modulus hydrogels and semiflexible biopolymer networks universally contract when sheared on timescales much longer than the poroelastic relaxation timescale. Using rheological and tribological measurements, we find that stiff polyacrylamide and polyacrylic acid hydrogels, with moduli of order ∼10-100  kPa, exclusively swell (dilate) when sheared. Poroelastic relaxation was examined using strain-controlled compression, indicating a volumetric diffusion constant of order 10^{-9} m^{2}/s. Upon shearing, we observed an increase in normal stress that varied quadratically with shear strain, which persisted for hours. Moreover, we show that this dilatant behavior manifests as swelling during tribological sliding, imbibing the hydrogel with fluid. We suggest that this inherent, hyperelastic dilatancy is an important feature in all stiff hydrogels, and may explain rehydration and mechanical rejuvenation in biological tissues such as cartilage.