### Abstract

The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in two-dimensional elastic sheets embedded in spatial dimensions three or four and three-dimensional elastic sheets embedded in spatial dimensions four and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density falloff away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis, we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

Original language | English (US) |
---|---|

Article number | 016603 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*65*(1), [016603]. https://doi.org/10.1103/PhysRevE.65.016603

**Singularities, structures, and scaling in deformed m-dimensional elastic manifolds.** / DiDonna, B. A.; Witten, T. A.; Venkataramani, Shankar C; Kramer, E. M.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 65, no. 1, 016603. https://doi.org/10.1103/PhysRevE.65.016603

}

TY - JOUR

T1 - Singularities, structures, and scaling in deformed m-dimensional elastic manifolds

AU - DiDonna, B. A.

AU - Witten, T. A.

AU - Venkataramani, Shankar C

AU - Kramer, E. M.

PY - 2002/1

Y1 - 2002/1

N2 - The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in two-dimensional elastic sheets embedded in spatial dimensions three or four and three-dimensional elastic sheets embedded in spatial dimensions four and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density falloff away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis, we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

AB - The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in two-dimensional elastic sheets embedded in spatial dimensions three or four and three-dimensional elastic sheets embedded in spatial dimensions four and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density falloff away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis, we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

UR - http://www.scopus.com/inward/record.url?scp=41349099118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349099118&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.016603

DO - 10.1103/PhysRevE.65.016603

M3 - Article

AN - SCOPUS:41349099118

VL - 65

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 1

M1 - 016603

ER -