Time-dependent response of hydrogels under multiaxial deformation accompanied by swelling

Constitutive equations are developed for the time-dependent behavior of a covalently cross-linked gel under an arbitrary deformation accompanied by swelling. Analysis of experimental data on poly(acrylamide) (PAAm) gels demonstrates that a modified Mooney–Rivlin expression for the strain energy density of the polymer network ensures an adequate description of observations in short-term (diffusion of water is disregarded) and long-term (transport of water molecules is taken into account) mechanical tests on sheets subjected to uniaxial tension, equi-biaxial tension, biaxial tension and shear. Numerical simulation shows that the cooperative diffusion coefficient is weakly influenced by chemical composition and preparation conditions for PAAm gels, whereas mechanically induced water uptake is strongly affected by deformation mode and conditions of loading (constant stresses versus constant elongation ratios).