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Mathematics and Mechanics of Solids
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A WKB Analysis of the Buckling of an Everted Neo-Hookean Cylindrical Tube

Y. B. Fu

Department of Mathematics, Keele University, Staffordshire ST5 5BG, UK

Y. P. Lin

Department of Mathematics, Kunming Institute of Science and Technology, Kunming, China

It is well-known that a circular cylindrical tube may not stay circular cylindrical after eversion and it may prefer to adopt a wrinkled configuration. A linear analysis using the method of adjacent equilibria followed by a numerical computation shows that for a neo-Hookean tube, a wrinkled configuration is possible when the ratio of the inner radius to the outer radius is approximately equal to 0.4232. The wrinkles have a circumferential mode number approximately equal to 14. In this paper the WKB method is used to derive an asymptotic expression for the critical ratio of the inner radius to the outer radius, with the mode number used as a large parameter. A turning point is found to exist in the eigenmodes, and is used to explain the difficulties experienced in previous numerical computations.

Key Words: WKB method • singular perturbation • finite elasticity • eversion of tubes

Mathematics and Mechanics of Solids, Vol. 7, No. 5, 483-501 (2002)
DOI: 10.1177/108128650200700502
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