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

B. A. DiDonna, T. A. Witten, Shankar C Venkataramani, E. M. Kramer

Research output: Contribution to journalArticle

31 Citations (Scopus)

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 languageEnglish (US)
Article number016603
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number1
DOIs
StatePublished - Jan 2002
Externally publishedYes

Fingerprint

Scaling
Singularity
Condensation
scaling
elastic sheets
condensation
Energy
Ridge
energy
ridges
Energy Functional
Singular Point
rigidity
Energy Density
embedding
Rigidity
Three-dimension
cones
apexes
Cone

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 65, No. 1, 016603, 01.2002.

Research output: Contribution to journalArticle

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