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.