Elastic–Plastic Analysis of a Circular Pipe Turned Inside Out

Abstract

The article presents an analytical solution for the problem of a circular pipe turning inside out in a rigid gasket. Formulas for the magnitude of the radial stress, which is responsible for the adhesion between the pipe and the gasket, have been obtained. The solution is obtained for an arbitrary incompressible hyperelastic material with a hyperelastic potential that depends only on the first invariant of the left Cauchy–Green deformation tensor (various generalizations of the neo-Hookean solid) or on the second invariant of the logarithmic Hencky strain tensor (various generalizations of the incompressible Hencky material). The solution considers the occurrence of plastic flow in areas adjacent to the lateral surfaces of the pipe. Both ideally plastic and isotropically hardening materials of a general type are considered. For the latter, a solution scheme is given; in the particular case of a linearly hardening material, a closed-form solution is obtained. For the perfect plasticity model, a closed-form solution was obtained for the neo-Hookean solid, for an incompressible Hencky material, and for the Gent material.