Stress–strain relations for hydrogels under multiaxial deformation

Constitutive equations are derived for the elastic response of swollen elastomers and hydrogels under an arbitrary deformation with finite strains. An expression is developed for the free energy density of a polymer network based on the Flory concept of flexible chains with constrained junctions and solvent-dependent reference configuration. The importance of introduction of a reference configuration evolving under swelling is confirmed by the analysis of experimental data on nanocomposite hydrogels subjected to swelling and drying. Adjustable parameters in the stress–strain relations are found by fitting observations on swollen elastomers, chemical gels (linked by covalent bonds and sliding cross-links), and physical gels under uniaxial stretching, equi-biaxial tension, and pure shear. Good agreement is demonstrated between the observations and results of numerical simulation. A pronounced difference is revealed between the effect of solvent content on elastic moduli of chemical and physical gels.