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Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses

Richard, Franck and Chakrabarti, Aditi and Audoly, Basile and Pomeau, Yves and Mora, Serge (2018) Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 474 (2216). Art. No. 20180242. ISSN 1364-5021. https://resolver.caltech.edu/CaltechAUTHORS:20180919-164643802

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Abstract

An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1098/rspa.2018.0242DOIArticle
ORCID:
AuthorORCID
Audoly, Basile0000-0002-0534-1467
Mora, Serge0000-0003-3255-2259
Additional Information:© 2018 The Author(s) http://royalsocietypublishing.org/licence. Published by the Royal Society. Received April 9, 2018. Accepted August 1, 2018. Data accessibility: This article has no additional data. Authors' contributions: Theory and calculations have been developed by A.C., B.A., Y.P. and S.M. F.R. and S.M. implemented and performed the simulations. The authors have no competing interests. No funding has been received for this article.
Subject Keywords:beams and columnsstability and bifurcationasymptotic analysis
Issue or Number:2216
Record Number:CaltechAUTHORS:20180919-164643802
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180919-164643802
Official Citation:Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses Franck Richard, Aditi Chakrabarti, Basile Audoly, Yves Pomeau, Serge Mora Proc. R. Soc. A 2018 474 20180242; DOI: 10.1098/rspa.2018.0242. Published 29 August 2018
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89771
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Sep 2018 14:34
Last Modified:09 Mar 2020 13:18

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