Collapse of thin-walled elliptical tubes for high values of major-to-minor axis ratio

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse's ellipticity k(o), defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure pl. For p < pl, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and pl are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).