Conical dislocations in crumpling

@article{Cerda1999ConicalDI,
  title={Conical dislocations in crumpling},
  author={E Cerda and Sahraoui Chaieb and Francisco Melo and Lakshminarayanan Mahadevan},
  journal={Nature},
  year={1999},
  volume={401},
  pages={46-49}
}
A crumpled piece of paper is made up of cylindrically curved or nearly planar regions folded along line-like ridges, which themselves pivot about point-like peaks; most of the deformation and energy is focused into these localized objects. Localization of deformation in thin sheets is a diverse phenomenon, and is a consequence of the fact that bending a thin sheet is energetically more favourable than stretching it. Previous studies considered the weakly nonlinear response of peaks and ridges… Expand

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References

SHOWING 1-10 OF 36 REFERENCES
Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet
Strong deformation of a sheet of solid material often leads to a crumpled state having sharp points of high curvature. A scaling property governing the crumpled state has been numericallyExpand
Crumpled paper
  • M. Ben Amar, Y. Pomeau
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1997
The crumpling of a piece of paper leaves permanent scars, showing a focusing of the stress. This is explained by looking at the geometry of the developable surfaces. According to Gauss, such aExpand
Properties of ridges in elastic membranes
When a thin elastic sheet is confined to a region much smaller than its size the morphology of the resulting crumpled membrane is a network of straight ridges or folds that meet at sharp vertices. AExpand
Conical Surfaces and Crescent Singularities in Crumpled Sheets
We analyze the geometry and elasticity of the crescentlike singularity on a crumpled elastic sheet. We give a physical realization of this in terms of a free-boundary contact problem. An analyticalExpand
The complex buckling of flexible sheet materials—Part I. Theoretical approach
Abstract This paper reviews the technological importance of the problems of complex buckling of textile fabrics and other sheet materials and the reasons why conventional shell theory is of littleExpand
Theory of Shell Structures
TLDR
This book tackles the fundamental question of how bending and stretching effects combine and interact in shell structures from a physical point of view; and it shows that this approach leads to an understanding of the structural mechanics of shells in general, and to useful results in particular problems. Expand
Rigidity and energy
Suppose one holds two sticks in the form of a cross in one hand, and places a rubber band in tension around the four ends. When it is released, it comes to rest in the shape of a convex quadrilateralExpand
Acoustic emission from crumpling paper.
  • Houle, Sethna
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
The results suggest that the pulse energy depends only weakly on the size of paper regions responsible for sound production, which is in contrast to previous results suggesting that the energy distribution varied systematically over time or thesize of the sheet. Expand
The complex buckling of flexible sheet materials—Part II. Experimental study of three-fold buckling
Abstract This paper describes the apparatus which has been constructed in order to investigate three-fold buckling in textile fabrics and other sheet materials; includes the method of use,Expand
Universal power law in the noise from a crumpled elastic sheet.
  • Kramer, Lobkovsky
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
Using high-resolution digital recordings, the crackling sound that is emitted from crumpled sheets of Mylar as they are strained is studied, suggesting that the probability distribution of click energies has a power law regime p(E) that is universal. Expand
...
1
2
3
4
...