Hyperelastic models for the swelling of soft material plugs in confined spaces

By incorporating local volume change as a parametric constraint into the conventional theory of hyperelasticity it is possible to model a variety of swelling affects. Here we examine the finite strain swelling of a soft solid plug within a rigid tube of circular cross section. The eventual channel wall contact as the swelling proceeds generates a confinement pressure that increases as the plug expands. The contact problem for a solid cylinder plug is one of homogeneous deformation, allowing the pressure-swelling response of classical hyperelastic models to be contrasted with hyperelastic models that display limited chain extensibility. We then examine a cylindrical plug that itself contains an internal channel. Wall contact now gives a deformation in which swelling combines axial lengthening with internal channel narrowing. Of particular interest is the closing behavior as the swelling proceeds. Treating the associated boundary value problem provides asymptotic expressions for the channel radius closing and the contact pressure in the large swelling regime.