Tension of a cylindrical membrane partially stretched over a rigid cylinder

We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to another end. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a semi-infinity cylindrical membrane. The axial force tends to a constant value at large distances from the inclusion. The membrane is made of an incompressible, homogeneous, isotropic elastic material. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by 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 hold the membrane on the rigid cylinder. We obtain an explicit solution for the Bartenev-Khazanovich (Varga) strain-energy function and numerical results for the Mooney-Rivlin and Fung models.