Inflation of a Cylindrical Membrane Partially Stretched over a Rigid Cylinder

We consider the problem of a contact between an initially cylindrical hyperelastic membrane and a rigid rough cylinder. One end of the cylindrical membrane is partially stretched over the rigid cylinder. A uniform internal pressure is applied on that part of the membrane which is not in contact with the cylinder. The membrane is in equilibrium and does not slide off the rigid cylinder due to a friction in the contact area. Is assumed to hold on the contact surface Coulomb’s law of friction is assumed to hold in the contact area. The membrane is composed of an incompressible homogeneous, isotropic elastic material possessing a strain energy function. The problem is formulated for arbitrary form of the strain energy function. For the particular case of the Bartenev–Khazanovich (Varga) material, the exact solution is obtained.