Bending of inflated curved hyperelastic tubes

We discuss large flexure of an inflated curved thin-walled tube within the framework of the nonlinear theory of elastic membranes. Wrinkling of the membrane is taken into account by using a relaxed strain energy density derived from a strain energy function of incompressible hyperelastic material. We consider curved tubes with elliptical cross-section and analyze the influence of a cross-section shape and initial curvature of the tube at its deformation. Dependence of the bending moment on the tube curvature is obtained and discussed. In particular, the comparison with the pure bending of a cylindrical tube same material is made. We study the fact that the curving of the curved tube under in-plane bending might be realized in two directions. Depending on the flexure direction the behavior of a curved tube can be similar or significantly different from the behavior of a cylindrical tube.