Pressure distribution in an elastomer confined by a long thin-walled flexible hollow cylinder under the assumption of a hydrostatic stress state

The stress distribution in a pressurized elastomer confined by a hollow cylinder is of interest in various applications of material testing and manufacturing. A relatively accurate closed form solution for the pressure distribution inside an elastomer confined by a rigid hollow cylinder was presented by Yu et al. (2001). But in many practical applications the assumption of a rigid hollow cylinder is not appropriate, because the cylinder deformations have a significant influence on the stresses inside the elastomer. Thus in this paper a solution for an elastomer confined by a deformable hollow cylinder is derived. Both axial and radial deformations of the hollow cylinder are taken into account, while the bending stiffness of the cylinder wall is neglected, i.e. the cylinder wall is treated according to the membrane theory. The accuracy of the proposed closed form solution is verified by a parametric finite element simulation.