From creases to conical deflections in a buckled thin sheet: stress focusing vs singularities in strong deformations of a thin elastic sheet

Abstract

The localization of deformation is a simple consequence of the fact that bending a thin sheet is energetically cheaper than stretching it. Thus, on examining a crumpled piece of paper, we find that it is made of nearly-planar or cylindrically curved regions folded along line-like stretched ridges or point-like conical singularities. Since the real crumpled paper problem is fairly difficult to deal with, we investigate two simple model experiments where one or two singularities are isolated and studied. When a cylindrical panel is axially compressed, a crease terminated by two conical type singularities appears. The length of this crease is selected by the width of the panel when the length and the thickness of the panel are kept constant. We study also a single conical singularity. This is achieved by pushing a thin sheet into a hollow cylinder similar to pushing coffee-filter paper in a funnel. We measured the singularity energy of the plate, or the work required to form a scar in the sheet. A simple model is proposed to understand the energetics of the crease formation.