A constitutive model for coupled fluid permeation and large viscoelastic deformation in polymeric gels

A polymeric gel is a cross-linked polymer network swollen with a solvent. Much of the literature concerning the constitutive response of these materials is limited to elasticity coupled with fluid permeation. We have developed a continuum-level theory to describe the coupled fluid permeation and large viscoelastic deformation of polymeric gels. In discussing special constitutive equations we limit our attention to isothermal conditions, isotropic gels, and consider a model based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy-a model which accounts for the limited extensibility of polymer chains, paired with a linear viscosity. We have numerically implemented our theory in a finite element program. We show that our theory is capable of qualitatively reproducing the experimentally observed behavior of a polymeric gel in simple compression and a fixed depth indentation experiment.