 
Summary: Localized buckling of a floating Elastica
B. Audoly
CNRS, UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F75005 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 nonlinear amplitude equation is derived for the envelope of
the pattern. These results provide a simple interpretation to the wrinkletofold transition reported
by Pocivavsek et al. (Science, 2008). An analogy with the classical problem of the localized buckling
of a strut on an nonlinear 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 freestanding
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
