The mechanical behavior and elastic response of a non-uniformly swollen cylindrical sample of polymer gel with axisymmetrical distribution of a solvent

The nonlinear boundary-value problem of the mechanical equilibrium of a cylindrical sample of polymer gel with non-uniform distribution of a solvent under uniaxial tension is considered. An exact solution, describing the stress-strain state of the cylinder caused by the non-uniform distribution of the solvent and external mechanical load, has been obtained. On the basis of the obtained solution, the deformation behavior of polymer gels and elastomers, non-uniformly swelling in a solvent, is studied.