Cylindrical membrane partially stretched on a rigid cylinder

• A contact problem of a thin-walled elastic tube stretched on a rigid cylinder is studied.
• The non-linear theory of elastic membranes under large strains is used to model the tube.
• A contact between the membrane and the rigid cylinder is with a dry friction.
• The analytical solution for Bartenev–Khazanovich (Varga) material is presented.

We consider the equilibrium problem of a hyperelastic thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder. We assume that the deformation of the tube is finite and axisymmetric. The tube is modeled by a cylindrical membrane. The membrane is composed of an incompressible, homogeneous, isotropic elastic material. We use Bartenev–Khazanovich (Varga) strain energy function. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by a friction and at a sufficient contact area. The friction is described by Coulomb's law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to the equilibrium of the membrane.