Volume changes in hydrogels subjected to finite deformations

• A constitutive model is developed in finite elasticity of hydrogels.
• Adjustable parameters are found by fitting observations on two types of hydrogels.
• Evolution of osmotic Poisson's ratio under tension is examined by simulation.

Constitutive equations are derived for the elastic response of hydrogels under an arbitrary deformation with finite strains. An expression is proposed for the free energy density of a hydrogel based on the Flory concept of a network of flexible chains with constrained junctions whose reference configuration differs from the initial configuration of a fully swollen gel. Adjustable parameters in the stress–strain relations are found by fitting observations on poly(acrylamide) and gellan hydrogels under uniaxial tension and compression. The effect of elongation ratio on osmotic Poisson's ratio is examined numerically.