The effect of inflating pressure on the finite pure bending of hyperelastic tubes

The problem of nonlinear bending of a curved tube made of incompressible rubber-like material is considered. The tube shaped like a portion of a thin-walled toroidal shell between two radial planes is inflated by pressure and then subjected to in-plane bending moments. To investigate nonlinear response and stability of the tube under these loading conditions, a finite-element approach is proposed. A special shell finite element is formulated under the assumption of uniform deformation along the tube length. The effect of wrinkling on nonlinear response of the tube is described using the tension-field theory. A change in the inflating pressure resulting from deformation of the tube due to bending is taken into account in the formulation of the governing equations. The effect of pressure on the bending stiffness, stability, and deformations of a curved tube is examined and discussed.