Hyperelastic swelling of stiff hydrogels

Abstract: Hydrogels are biphasic, 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. For low-modulus hydrogel and semiflexible biopolymer networks, previous studies have shown that these materials 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. The poroelastic relaxation process 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, and 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.