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Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability

Chakrabarti, Aditi and Mora, Serge and Richard, Franck and Phou, Ty and Fromental, Jean-Marc and Pomeau, Yves and Audoly, Basile (2018) Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability. Journal of the Mechanics and Physics of Solids, 121 . pp. 234-257. ISSN 0022-5096. http://resolver.caltech.edu/CaltechAUTHORS:20180731-113100932

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Abstract

We investigate the non-linear buckling patterns produced by the elastic Rayleigh-Taylor instability in a hyper-elastic slab hanging below a rigid horizontal plane, using a combination of experiments, weakly non-linear expansions and numerical simulations. Our experiments reveal the formation of hexagonal patterns through a discontinuous transition. As the unbuckled state is transversely isotropic, a continuum of linear modes become critical at the first bifurcation load: the critical wavevectors form a circle contained in a horizontal plane. Using a weakly non-linear post-bifurcation expansion, we investigate how these linear modes cooperate to produce buckling patterns: by a mechanism documented in other transversely isotropic structures, three-modes coupling make the unbuckled configuration unstable with respect to hexagonal patterns by a transcritical bifurcation. Stripe and square patterns are solutions of the post-bifurcation expansion as well but they are unstable near the threshold. These analytical results are confirmed and complemented by numerical simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jmps.2018.07.024DOIArticle
Additional Information:© 2018 Published by Elsevier Ltd. Received 13 February 2018, Revised 30 July 2018, Accepted 30 July 2018, Available online 31 July 2018. This paper was prepared using the TeXmacs typesetting system (van der Hoeven et al., 2013); we are grateful to the developers for making this outstanding tool freely available. We are also grateful to the anonymous reviewers for their valuable comments on the initial version of this manuscript.
Subject Keywords:A. Buckling; B. Elastic material; B. Finite strain; B. Plates; C. Stability and bifurcation
Record Number:CaltechAUTHORS:20180731-113100932
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180731-113100932
Official Citation:Aditi Chakrabarti, Serge Mora, Franck Richard, Ty Phou, Jean-Marc Fromental, Yves Pomeau, Basile Audoly, Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability, Journal of the Mechanics and Physics of Solids, Volume 121, 2018, Pages 234-257, ISSN 0022-5096, https://doi.org/10.1016/j.jmps.2018.07.024. (http://www.sciencedirect.com/science/article/pii/S0022509618301339)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88378
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Jul 2018 18:37
Last Modified:20 Aug 2018 16:08

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