A visco-poroelastic theory for polymeric gels

A polymeric gel can imbibe solvent and swell. Besides the dilatational mode of deformation, which involves long-range solvent migration, a gel may also undergo volume-conserved deformation. For a macroscopic gel with covalent cross-links, the volume-conserved deformation is usually much faster. However, these two modes are coupled for deformation at the microscopic level and for gels containing physical cross-links or large solvent molecules. In this paper, we seek to formulate a unified theoretical framework for the transient behaviour of polymeric gels to account for both solvent migration and viscoelastic deformation. Under this framework, we further develop a simple material model, and implement it into a finite-element code for numerical calculations. By simultaneously tracking the solvent migration and motion of polymer network, we evolve the inhomogeneous fields of stress and chemical potential. Several initial-boundary-value problems are solved as illustrative examples. For macroscopic gels with low viscosity, the time scales for viscoelasticity and poroelasticity are separated, and the long-term behaviour is just as that predicted by a poroelastic model. For structures or processes involving sizes comparable to the intrinsic length of a material, the viscoelasticity and poroelasticity must be considered simultaneously, especially when studying impact responses.