Crossover behavior in stress relaxations of poroelastic and viscoelastic dominant hydrogels

The mechanical response and relaxation behavior of hydrogels are crucial to their diverse functions and applications. However, understanding how stress relaxation depends on the material properties of hydrogels and accurately modeling relaxation behavior at multiple time scales remains a challenge for soft matter mechanics and soft material design. While a crossover phenomenon in stress relaxation has been observed in hydrogels, living cells, and tissues, little is known about how the crossover behavior and characteristic crossover time depend on material properties. In this study, we conducted systematic atomic-force-microscopy (AFM) measurements of stress relaxation in agarose hydrogels with varying types, indentation depths, and concentrations. Our findings show that the stress relaxation of these hydrogels features a crossover from short-time poroelastic relaxation to long-time power-law viscoelastic relaxation at the micron scale. The crossover time for a poroelastic-dominant hydrogel is determined by the length scale of the contact and diffusion coefficient of the solvent inside the gel network. In contrast, for a viscoelastic-dominant hydrogel, the crossover time is closely related to the shortest relaxation time of the disordered network. We also compared the stress relaxation and crossover behavior of hydrogels with those of living cells and tissues. Our experimental results provide insights into the dependence of crossover time on poroelastic and viscoelastic properties and demonstrate that hydrogels can serve as model systems for studying a wide range of mechanical behaviors and emergent properties in biomaterials, living cells, and tissues.