Linear and nonlinear deformation behavior of hydrogels

Based on a linear theory of deformation coupled with diffusion, the chemomechanical-coupled problems are solved analytically by the separation variable method and airy stress function for the four case studies of hydrogel, including a hydrogel rod subject to uniaxial stress, spherical hydrogel with centrosymmetrical boundary condition and subject to centrosymmetrical loading, and an infinite-long and traction-free hydrogel cylinder with nonaxisymmetric boundary condition subject to a solute concentration distributed in cosine pattern on its cylindrical surface, a thin-wall hydrogel cylinder subject to uniform pressure and its end effect. Using these analytical solutions, the temporal and spatial evolution of concentration and stress is studied in these hydrogel structures. In addition, a Eulerian-based nonlinear coupled chemomechanical model is also developed.