Deformation behavior of polymer networks containing or interacting with a solvent

General formalism to describe both equilibrium and nonequilibrium states of polymer networks containing a solvent or interacting with the solvent medium is proposed. Two classes of problems have been formulated. It is necessary to determine the stress-strain state of an inhomogeneously swollen material in one case and that of a statically loaded material occurring in thermodynamic equilibrium with the solvent in the other case. The state of the swollen material is characterized in terms of the global mechanical stress tensor and the solvent chemical potential. In the case of incompressible material and liquid, an osmotic stress tensor is introduced. A method for deriving physical expressions for the mechanical stress tensor, the chemical potential, and the osmotic stress tensor is proposed on the basis of the known free energy relations that follow from different theories of rubber elasticity. The efficacy of the general formalism is demonstrated using particular examples in which the deformation behavior and the equilibrium swelling of mechanically loaded polymer networks are considered.