Shear induced loss of saturation in a fluid infused swollen hyperelastic cylinder

We discuss a continuum model for the absorption and redistribution of fluid in swollen elastomers due to mechanical loading; and in particular distinguish between systems that are saturated with liquid and those that are not. To this end we consider a boundary value problem of radial displacement combined with azimuthal shear for an annular cylinder consisting of a fluid infused hyperelastic media. In the absence of load the elastomer deforms by free swelling, giving a homogeneous expansion in which the imbibed fluid is uniformly distributed. This free swelling is described by the theory of Flory and Rehner. We then consider the effect of various boundary displacements and tractions so as to study how this alters the uniform fluid distribution. This problem was previously considered by Wineman and Rajagopal for the case in which the lateral surfaces maintained the radius associated with free swelling. Here we consider certain generalizations in which the lateral surfaces may undergo not only a prescribed relative twist, but also radial displacement. This permits fluid to either enter or exit the cylinder. A numerical method is invoked to solve these boundary value problems using representative material parameters. Certain boundary tractions generate an overall volume increase after the free swelling. If the amount of available fluid is limited, this gives rise to the possibility of complete fluid absorption, whereupon the system is no longer saturated. It is found that the overall mechanical response after loss of saturation is stiffer than it would be if the system had remained saturated.