The Geometry of Crumpled Paper

Abstract

We measure the geometry of a crumpled sheet of paper with laser-aided topography and discuss its statistical properties. The curvature of an elasto-plastic fold scales linearly with applied force. The curvature distribution follows an exponential form with regions of high curvature localized along ridges. The measured ridge length distribution is consistent with a hierarchical model for ridge breaking during crumpling. A large fraction of the ridges are observed to terminate without bifurcating and the ridge network connectedness is not as complete as anticipated. The self-affinity of the surface is characterized by a Hurst exponent of $0.72\pm 0.01$ in contrast with previous results.

arXiv comment4 pages, 5 figures, uses revtex 4

References in corpus (6)

• Crackling Noise
• Properties of Ridges in Elastic Membranes
• Acoustic Emission from crumpling paper
• Stress condensation in crushed elastic manifolds
• Universal Power Law in the Noise from a Crumpled Elastic Sheet
• Anomalous strength of membranes with elastic ridges

Cited by in corpus (47)

• On relaxations and aging of various glasses
• Algorithm to estimate the Hurst exponent of high-dimensional fractals
• The Statistics of Crumpled Paper
• A comparative study of crumpling and folding of thin sheets
• 3-dimensional structure of a sheet crumpled into a ball
• Memory from coupled instabilities in unfolded crumpled sheets
• Packing of elastic wires in spherical cavities
• Morphogenesis of filaments growing in flexible confinements
• Morphological Phases of Crumpled Wire
• Ridge Network in Crumpled Paper
• Entropic rigidity of a crumpling network in a randomly folded thin sheet
• Curvature condensation and bifurcation in an elastic shell
• Subdivision Shell Elements with Anisotropic Growth
• Logarithmic aging via instability cascades in disordered systems
• Crumpling under an ambient pressure
• X-ray tomography of a crumpled plastoelastic thin sheet
• Compaction of Quasi One-Dimensional Elastoplastic Materials
• Condensation of elastic energy in two-dimensional packing of wire
• A model for the fragmentation kinetics of crumpled thin sheets
• Tension-dependent transverse buckles and wrinkles in twisted elastic sheets
• Energy distributions and effective temperatures in the packing of elastic sheets
• Crumpling for Energy: Modeling Generated Power from the Crumpling of Polymer Piezoelectric Foils for Wearable Electronics
• Statistical distributions in the folding of elastic structures
• A shapeable material without plastic deformation
• Power law scaling of lateral deformations with universal Poissons index for randomly folded thin sheets
• Extreme Contractility and Torsional Compliance of Soft Ribbons under High Twist
• Furrows in the wake of propagating d-cones
• Topological crossovers in the forced folding of self-avoiding matter
• Tensional twist-folding of sheets into multilayered scrolled yarns
• Crumpling wires in two dimensions
• Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth
• Crumples as a generic stress-focusing instability in confined sheets
• Birth and decay of tensional wrinkles in hyperelastic sheets
• Bistability and equilibria of creased annular sheets and strips
• Plastic Deformation of 2D Crumpled Wires
• Simulation of crumpled sheets via alternating quasistatic and dynamic representations
• Effect of Ridge-Ridge Interactions in Crumpled Thin Sheets
• Topological field theory of dynamical systems. II
• A relaxation constant in the folding of thin viscoelastic sheets
• Topological field theory of dynamical systems
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• Rim curvature anomaly in thin conical sheets revisited
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Interplay of gross and fine structures in strongly-curved sheets
• Crumple-Origami Transition for Twisting Cylindrical Shells
• Memory in cyclically crumpled sheets