Post Buckling Behavior of Elastic Tubes and Rings with Opposite Sides in Contact

Abstract

An elastic tube of circular cross section or an elastic ring can buckle if p, the outside pressure minus the inside pressure, exceeds the buckling pressure $p_{b2} $. As p increases above $p_{b2} $ the cross section becomes somewhat elliptical. Ultimately opposite sides touch at one point at the contact pressure $p_{c2} $ . As p increases above $p_{c2} $ the curvature of the cross section at the points of contact decreases until it becomes zero at $p_{02} $. For $p> p_{02}$ contact occurs along a straight-line segment which increases in length as p increases. The pressures $p_{b2} $, $p_{c2} $ and $p_{02} $ are determined numerically, and the shape of the cross section is found for various values of p. Graphs of the results are shown. Above $p_{b2} $ a similarity solution is found. Analogous results are obtained for the nth buckling mode, $n > 2$. The flux of an incompressible viscous fluid through the buckled tube is also determined as a function of p. The results may be applicable to the collapse of veins and the flow of blood through them.