Gel Mechanics: A Thermo-mechanically Coupled Theory for Fluid Permeation in Elastomeric Materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent, and certain gels can undergo large reversible volume changes as they are cycled about a critical temperature. We have developed a continuum-level theory to describe the coupled mechanical deformation, fluid permeation, and heat transfer of such thermally-responsive gels. In discussing special constitutive equations we limit our attention to isotropic materials, 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. We have numerically implemented our theory in a finite element program. We have shown that our theory is capable of simulating swelling, squeezing of fluid by applied mechanical forces, and thermally-responsive swelling/deswelling of such materials.