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Geometry and Ordering in Crumpled Sheets
Graphene membranes, cabbage leaves, and even the Himalayas are all examples of thin sheets : objects with a thickness much smaller than their length and width. Despite their differences in size and in material composition, similar patterns emerge when sheets are crumpled or forced into a small three-dimensional space. As the compaction progresses, the deformations focus into increasingly sharper features that look like the network of peaks and creases found on the surface of a balled up piece of paper. In this regime, external forces are straining the membrane, causing the elastic energy to localize while leaving most of the surface smooth and undeformed. In addition to forming a collection of deformations and smooth facets, various sections of the sheet come into contact and thus, a description of the interior configuration of the packed sheet is necessary for a complete understanding of the internal structure and how it can resist external compression while maintaining a low volume fraction. In my presentation, I will discuss our investigations of highly confined sheets composed of two materials with varying elasticity : Aluminum and Polydimethylsiloxane (PDMS). I will describe how we quantified elements of the inner geometry and the spontaneous ordering within the structure of a crumpled sheet.