A WKB Analysis of the Buckling of an Everted Neo-Hookean Cylindrical Tube

Author:

Fu Y. B.1,Lin Y. P.2

Affiliation:

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

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

Abstract

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.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Cited by 14 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. WKB analysis of the bifurcation for a three-dimensional neo-Hookean cylindrical tube under restricted compression;International Journal of Engineering Science;2024-01

2. Asymptotic solutions on the circumferential wrinkling of growing tubular tissues;International Journal of Engineering Science;2018-07

3. An approach for verification of finite-element analysis in nonlinear elasticity under large strains;IOP Conference Series: Materials Science and Engineering;2016-11

4. Evaluation of the Buckling Modes of a Rotating Neo-Hookean Cylinder by WKB Method;Iranian Journal of Science and Technology, Transactions A: Science;2016-10-27

5. Higher-order asymptotic result for the wrinkling of an everted Varga spherical shell;Zeitschrift für angewandte Mathematik und Physik;2014-11-06

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