The finite inflation of a curved elastic tube

Abstract

The problem of the inflation of a curved tube for large elastic strains using a nonlinear membrane theory is investigated. This problem is the special case of a pure bending. The boundary-value problem reduces to a system of ordinary differential equations with periodical boundary conditions. Tubes with an elliptical cross-section are considered. To describe mechanical properties of tubes a neo-Hookean incompressible material model is used. The dependence between the pressure and the curvature of the deformed curved tube is obtained. The influence of the cross-section on this dependence is analyzed.