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Summary: Localized buckling of a floating Elastica
B. Audoly
CNRS, UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris
(Dated: June 7, 2011)
We study the buckling of a 2D Elastica floating on a bath of dense fluid, subjected to axial
compression. The sinusoidal pattern predicted by the analysis of linear stability is shown to become
localized above the buckling threshold. A non-linear amplitude equation is derived for the envelope of
the pattern. These results provide a simple interpretation to the wrinkle-to-fold transition reported
by Pocivavsek et al. (Science, 2008). An analogy with the classical problem of the localized buckling
of a strut on an non-linear elastic foundation is presented.
I. INTRODUCTION
The buckling of an elastic rod resting on an elastic
foundation is a classical problem in structural engineer-
ing. While the critical load and wavelength are set by
the size of the system in the case of Euler's free-standing
Elastica, an intrinsic length scale appears in the presence
of a foundation. This scale determines a critical load and
wavelength that are independent of the size of the sys-
tem, provided it is large enough.
This classical problem and its variants have received
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