Thin elastic plates: On the core of developable cones

¹ Laboratoire de Physique Statistique de l'ENS 24, rue Lhomond, 75231 Paris Cedex 05, France
² MIT, Department of Mathematics - 77 Massachusetts Avenue Cambridge MA 02139-4307, USA

Corresponding author: boudaoud@lps.ens.fr

Received: 13 December 2001
Accepted: 11 April 2002

Abstract

Large deformations of thin elastic plates lead generally to the focusing of deformations around almost singular structures which are either linear (curved and straight ridges) or point-like (developable cones), as can be observed for crumpled paper. An experiment has been devised to study the core of a developable cone. An initially bent plate is loaded at its center. It is either drilled with two holes or made of metal. The experimental results are used to measure the energy of the core for both elastic and plastic deformations. It is shown that the behaviour of a plate when plastic deformations occur, as in practical applications, can be deduced from its behaviour when deformations are perfectly elastic. This result demonstrates that studies on large deformations of perfectly elastic plates may be used for applications.