X-ray tomography of a crumpled plastoelastic thin sheet.

Three-dimensional x-ray tomography is performed to investigate the internal structure and its evolution of a crumpled aluminum foil ball. The upper and lower bounds of the internal geometric fractal dimension are determined, which increase with the compression. Contrary to the simulation results, we find that the mass distribution changes from being inhomogeneous to uniform. Corroborated with the evidence from previous experiments, these findings support the physical picture that the elastic property precedes the plastic one at dominating the deformation and mechanical response for all crumpled structures. We show that the interior of a crumpled ball at the plastic regime can be mapped to the compact packing of a granular system.

Spontaneous emergence of ordered phases in crumpled sheets.

X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation function along each path is found to decay exponentially with an effective persistence length that shortens as the crumpled ball becomes more compact. In the meantime, we observed ordered domains near the crust, similar to the lamellae phase mixed by the amorphous portion in lyotropic liquid crystals. The size and density of these domains grow with further compaction, and their orientation favors either perpendicular or parallel to the radial direction. Ordering is also identified near the core with an arbitrary orientation, exemplary of the spontaneous symmetry breaking.