Dynamics of singularities in a constrained elastic plate

Arezki Boudaoud (), Pedro Patrício, Yves Couder and Martine Ben Amar
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Arezki Boudaoud: Laboratoire de Physique Statistique de l'ENS (associated with CNRS and the universities Paris VI and Paris VII)
Pedro Patrício: Centro de Física da Matéria Condensada, Universidade de Lisboa Av. Prof. Gama Pinto 2
Yves Couder: Laboratoire de Physique Statistique de l'ENS (associated with CNRS and the universities Paris VI and Paris VII)
Martine Ben Amar: Laboratoire de Physique Statistique de l'ENS (associated with CNRS and the universities Paris VI and Paris VII)

Nature, 2000, vol. 407, issue 6805, 718-720

Abstract: Abstract Large deformations of thin elastic plates usually lead to the formation of singular structures which are either linear1,2,3,4 (ridges) or pointlike5,6,7,8 (developable cones). These structures are thought to be generic for crumpled plates3,5, although they have been investigated quantitatively only in simplified geometries1,2,3,4,6,7,8. Previous studies9,10,11 have also shown that a large number of singularities are generated by successive instabilities. Here we study, experimentally and numerically, a generic situation in which a plate is initially bent in one direction into a cylindrical arch, then deformed in the other direction by a load applied at its centre. This induces the generation of pairs of singularities; we study their position, their dynamics and the corresponding resistance of the plate to deformation. We solve numerically the equations describing large deformations of plates; developable cones are predicted, in quantitative agreement with the experiments. We use geometrical arguments to predict the observed patterns, assuming that the energy of the plate is given by the energy of the singularities.

Date: 2000
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DOI: 10.1038/35037535

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