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Crescent singularities in crumpled sheets.

Tao Liang1, Thomas A Witten

  • 1The James Franck Institute, Department of Physics, The University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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Researchers studied the crescent singularity of a developable cone, finding that core size scales with sheet thickness and container radius. This provides numerical evidence for a proposed scaling law.

Area of Science:

  • Physics of deformable materials
  • Geometric mechanics
  • Solid mechanics

Background:

  • The behavior of developable cones under stress is complex.
  • Previous studies, such as Cerda et al. (1999), have explored cone singularities.

Purpose of the Study:

  • To analyze the crescent singularity of a developable cone.
  • To investigate the relationship between stretching, bending, and stress distribution.
  • To determine the scaling laws governing the core region size.

Main Methods:

  • Numerical simulations and direct geometrical measurements were employed.
  • Analysis of stress distribution in the outer and core regions.
  • Estimation of cone energies.

Main Results:

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  • Stretching is concentrated in a core region near the pushing tip.
  • Bending dominates the outer region with distinct stress scaling.
  • Core size (Rc) scales as approximately h(1/3)R(2/3), where h is sheet thickness and R is container radius.

Conclusions:

  • The observed scaling law for core size is supported by numerical evidence.
  • Arguments are presented that this scaling may not be asymptotic.
  • Further numerical studies confirm the analysis of other cone properties.