  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.
