3-dimensional structure of a sheet crumpled into a ball

TL;DR

This study uses X-ray microtomography to analyze the internal 3D structure of crumpled sheets, revealing isotropic geometry with localized nematic ordering that intensifies with compression.

Contribution

It provides the first detailed 3D structural characterization of crumpled sheets, highlighting isotropic internal geometry and localized nematic layering.

Findings

Internal geometry is largely isotropic and homogeneous.

Local nematic ordering forms parallel stacks.

Layering increases with degree of compression.

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.