Thermodynamics of deformation and swelling of crosslinked polymers under small deformations

A system of equations and physical relationships that show the quasi-static processes of deformation and swelling of crosslinked polymers in solvents under small deformations of the polymer matrix is proposed. The system is obtained via linearization of the respective equations of the nonlinear theory. This makes it possible to reveal the relationship between the constants of the linear theory and the parameters that characterize the elastic and thermodynamic properties of a solvent-swollen crosslinked polymer under finite deformations. Different types of problems that describe the stress-strain state of inhomogeneously swollen crosslinked polymers, as well as the thermodynamics of their deformation and swelling in a solvent medium, are discussed in terms of the linear theory.