Developable Cones and Crumpled Paper: An Experimental Point of View

Abstract

In this paper we present an experimental study of an isolated developable cone (d-cone). From profile measurements we found that a d-cone made of a copper sheet is not equivalent to a the one obtained theoretically in a study of the Föppl-von Kármán equations (M. Ben Amar and Y. Pomeau, Proc. R. Soc. Lond. A, 453, 729 (1996)). We investigated local curvature and found two regimes depending on the deformation experienced by the plate. From ridge local curvature measurements, we characterized the transition to the plastic deformation. Finally, we performed an experimental study of a more complicated situation where more than a d-cone appear. By buckling a cylindrical panel, a crease or a series of creases appear as a collection of d-cones. We measured crease length, maximum deflection and critical force at the crease nucleation as a function of the panel geometrical parameters. From creases profile measurements, we also showed that the crease local curvature varies like the one of a singular d-cone near the plastic deformation.