# 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

#### Paper Mentions

#### 156 Citations

Dynamics of singularities in a constrained elastic plate

- Physics, Medicine
- Nature
- 2000

This work studies a generic situation in which a plate is initially bent in one direction into a cylindrical arch, then deformed in the other direction by a load applied at its centre, and induces the generation of pairs of singularities. Expand

in a constrained elastic plate

- Mathematics
- 2000

have also shown that a large number of singularities are generated by successive instabilities. Here we study, experimentally and numerically, a generic situa- tion in which a plate is initially bent… Expand

The effect of plasticity in crumpling of thin sheets.

- Materials Science, Medicine
- Nature materials
- 2009

A numerical model that can be purely elastic or elasto-plastic is introduced and evidence is found of Dpl not being universal but dependent on the plastic yield point of the material. Expand

Scaling of the buckling transition of ridges in thin sheets.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

This work considers the buckling of a single ridge under the action of inward forcing applied at its ends and demonstrates a simple scaling relation for the response of the ridge to the force prior to buckling and finds that ridges buckle when the authors' forcing increases their elastic energy by 20% over their resting state value. Expand

Three-dimensional structure of a sheet crumpled into a ball

- Physics, Medicine
- Proceedings of the National Academy of Sciences
- 2011

The authors' X-ray microtomography experiments reveal that the internal three-dimensional geometry of a crumpled ball is in many respects isotropic and homogeneous, and crumpling recapitulates other classic nonequilibrium problems such as turbulence. Expand

Curvature in compressed thin cylindrical shells approaching the isometric limit

- 2020

The ability to manipulate surface elastic instabilities finds many applications in engineering smart interfaces, e.g. in fluid-structure interaction and micro-fabrication. We study the buckling of a… Expand

The Shape of Helically Creased Cylinders

- Materials Science
- 2013

Creasing in thin shells admits large deformation by concentrating curvatures while relieving stretching strains over the bulk of the shell: after unloading, the creases remain as narrow ridges and… Expand

Buckling of geometrically confined shells.

- Physics, Materials Science
- Soft matter
- 2019

One geometric parameter captures the wave number through a wide range of radial and transverse confinement, connecting the shell shape to the shape of the boundary that confines it, and is applicable to the design of shape-shifting materials and the swelling and growth of soft structures. Expand

Direct observation of the temporal and spatial dynamics during crumpling.

- Physics, Medicine
- Nature materials
- 2010

Direct measurements of the configurations of a fully elastic sheet evolving during the dynamic process of crumpling under isotropic confinement are presented and the formation of a network of ridges and vertices into which the energy is localized is observed. Expand

Furrows in the wake of propagating d-cones.

- Physics, Medicine
- Nature communications
- 2015

It is shown that rather than merely being the consequence of folding, plasticity can act as its instigator and form a different type of crease that is inherently plastic and is formed by the propagation of a single point defect. Expand

#### References

SHOWING 1-10 OF 36 REFERENCES

Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet

- Materials Science
- Science
- 1995

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 numerically… Expand

Crumpled paper

- 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 a… Expand

Properties of ridges in elastic membranes

- Physics
- 1997

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. A… Expand

Conical Surfaces and Crescent Singularities in Crumpled Sheets

- Physics
- 1998

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 analytical… Expand

The complex buckling of flexible sheet materials—Part I. Theoretical approach

- Materials Science
- 1986

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 little… Expand

Theory of Shell Structures

- Computer Science
- 1983

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

- Mathematics
- 1982

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 quadrilateral… Expand

Acoustic emission from crumpling paper.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

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

- Engineering
- 1986

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.

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

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