3-dimensional structure of a sheet crumpled into a ball

Abstract

When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not necessarily amenable to a statistical description in which the parameters of the initially flat sheet and the final confinement fully specify the resulting crumpled state. Instead, the internal geometry and mechanical properties of the crumpled ball may reflect the history of its preparation. Our X-ray microtomography experiments reveal that the internal 3-dimensional geometry of a crumpled ball is in many respects isotropic and homogeneous. In these respects, crumpling recapitulates other classic nonequilibrium problems such as turbulence, where a system driven by long-wavelength, low-symmetry, forcing shows only rather subtle fingerprints of the forcing mechanism. However, we find local nematic ordering of the sheet into parallel stacks. The layering proceeds radially inwards from the outer surface. The extent of this layering increases with the volume fraction, or degree of compression.

Accepted by the PNAS Editorial Board July 16, 2011 (received for review December 20, 2010)

References in corpus (10)

• The Geometry of Soft Materials: A Primer
• The Geometry of Crumpled Paper
• Properties of Ridges in Elastic Membranes
• Anomalous strength of membranes with elastic ridges
• The spontaneous emergence of ordered phases in crumpled sheets
• X-ray tomography of a crumpled plastoelastic thin sheet
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• Energy distributions and effective temperatures in the packing of elastic sheets
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• Self-Ordering of Buckling, Bending, Bumping Beams
• Cutting holes in bistable folds
• Furrows in the wake of propagating d-cones
• Complex Memory Formation in Frictional Granular Media
• Crumples as a generic stress-focusing instability in confined sheets
• Effect of Ridge-Ridge Interactions in Crumpled Thin Sheets
• Simulation of crumpled sheets via alternating quasistatic and dynamic representations
• Plastic deformation of a permanently bonded network: stress relaxation by pleats
• Packing of elastic rings with friction
• Transition to stress focusing for locally curved sheets
• Memory in cyclically crumpled sheets
• Elasticity and Stability of Shape Changing Structures