Bending and symmetric pinching of pressurized tubes

Abstract Two experiments quantified the forces necessary for large deformation of an inflated cylindrical tube made of a material with a high elastic modulus. In the first experiment, the end force required to maintain a buckled cylinder at a given kink angle was determined. In the second experiment, the lateral force required to pinch the membrane symmetrically between two flat blades was measured. An approximate theory is used, based on the observation that during deformation the membrane conserves its initial zero Gaussian curvature in regions free of wrinkling. The novel feature is a simple approximation for the cross-sectional shape. This permits the volume of the deformed cylinder to be quickly calculated. For walls that have negligible extensional and bending energy, the potential energy consists of only the pressure multiplied by the volume and the work of the prescribed load. Minimization of this potential energy yields results for the indentation and buckling problems that are in reasonable agreement with the experimental measurements. For small displacements in the blade pinching experiment, the volume approximation overestimates the force. It is found that a local solution analogous to the Hertzian contact problem provides a better approximation. For the kinked tube with end loading, an interesting feature is a decrease in the load when the fold from one side contacts the opposite side of the tube. The calculations indicate that a minimum potential energy exists with the fold straight. For slightly larger kink angles, however, the fold buckles out of the plane of symmetry. The moment at the single kink, due to the end loads, remains between bounds from the analysis of a pressurized elastic tube with nonpositive stresses.