Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

[+] Author and Article Information
C. Ribreau, S. Naili

Laboratoire de Mécanique Physique, Université Paris Val de Marne, Av. du Général De Gaulle, 94010 Creteil Cedex, France

M. Bonis

Division Systèmes Mécaniques, Université de Technologie de Compiègne, 60206 Compiegne, France

A. Langlet

Laboratoire de Mécanique Physique, Université Paris Val de Marne, Av. du Général De Gaulle, 94010 Créteil Cedex, France

J Biomech Eng 115(4A), 432-440 (Nov 01, 1993) (9 pages) doi:10.1115/1.2895508 History: Received October 15, 1991; Revised December 06, 1992; Online March 17, 2008


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 ko , 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 p c . If p is lowered beneath p c , 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 p1 . For p <p1 , the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 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).

Copyright © 1993 by The American Society of Mechanical Engineers
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