Hyperelastic swelling of tough hydrogels

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 tough polyacrylamide and polyacrylic acid hydrogels, with moduli of order  10-100 kPa, exclusively exhibit dilatancy when sheared. The poroelastic relaxation process was examined using strain-controlled compression, indicating a diffusion constant of order 10^-9 m^2/s. On short timescales (minutes), an applied shear stress induced an increase in normal stress that varied quadratically with shear strain. At long timescales (hours), creep experiments revealed that tough hydrogels can “remember” the initial direction of applied shear, suggesting an evolution of the polymer network. 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 tough hydrogels, and may explain rehydration and mechanical rejuvenation in biological tissues such as cartilage.