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Geometry of crumpled paper.

Daniel L Blair1, Arshad Kudrolli

  • 1Department of Physics, Clark University, Worcester, Massachusetts 01610, USA.

Physical Review Letters
|May 21, 2005
PubMed
Summary

Researchers used laser topography to study crumpled paper geometry. They found fold curvature scales with force and ridge networks are less connected than expected, challenging previous self-affinity findings.

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Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Surface Geometry

Background:

  • Crumpled paper exhibits complex geometric and statistical properties.
  • Understanding the mechanics of folds and ridges is crucial for predicting material behavior.
  • Previous studies suggested specific self-affinity characteristics in crumpled surfaces.

Purpose of the Study:

  • To quantitatively measure the geometry of a crumpled paper sheet.
  • To analyze the statistical properties of its surface, folds, and ridges.
  • To compare experimental findings with existing theoretical models and previous results.

Main Methods:

  • Utilized laser-aided topography for high-resolution surface measurements.
  • Analyzed curvature distribution and ridge length distribution.
  • Calculated the Hurst exponent to characterize surface self-affinity.

Main Results:

  • Observed a linear scaling relationship between elastoplastic fold curvature and applied force.
  • Found that ridge length distribution aligns with a hierarchical ridge breaking model.
  • Determined a Hurst exponent of 0.71+/-0.01, indicating significant surface self-affinity, contrasting prior research.

Conclusions:

  • The study provides detailed geometric insights into crumpled paper structures.
  • Ridge network analysis reveals incomplete connectedness, differing from expectations.
  • The measured self-affinity exponent challenges previous characterizations of crumpled surfaces.

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