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A WKB analysis of the buckling of an everted neo-Hookean cylindrical tube. (English) Zbl 1072.74027
Summary: 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.

MSC:
74G60 Bifurcation and buckling
74B20 Nonlinear elasticity
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
Software:
Mathematica
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