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Cited by 401Advanced Materials and MechanicsElasticity and Wave PropagationStructural Analysis and Optimization

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Stress focusing in elastic sheets

Witten, T. A.·2007·Reviews of Modern Physics
DOI 10.1103/revmodphys.79.643
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Abstract

This paper reviews recent progress in understanding phenomena such as crumpling, in which elastic membranes or sheets subject to structureless forces develop sharply curved structure over a small fraction of their surface. In the limit of zero thickness, these structures become singular. After reviewing several related phenomena, the paper recalls the physical elements that give rise to the singular behavior: elasticity and the nearly inextensible behavior of thin sheets. This singular behavior has counterparts in higher dimensions. Then the paper discusses the most basic of these singularities, the vertex. The paper recounts mathematical progress in describing the $d$-cone, a simple realization of a vertex. After discussing the size of the core that governs departure from singularity, the paper concludes that fundamental understanding is lacking. It points out further mysterious behavior at the region where a $d$-cone is supported. Next comes a discussion of an emergent singularity that appears when two or more vertices are present: the stretching ridge. The paper offers several explanations of the scale of this singularity, ranging from qualitative scaling arguments to a formal asymptotic analysis. It discusses recent experiments and theories about the interaction of ridges and vertices and reviews evidence that these ridges dominate the mechanics of crumpled sheets.

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  • Stretching energy in thin sheets scales the same way with ρface as bending energy due to a virial theorem, but is expected to be considerably smaller; for thin sheets, bending strain is much larger than stretching strain in low-energy configurations.

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    From Self-folding origami at any energy scale (2017) · cites this paper as [35]

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Metadata

Authors
Witten, T. A.
Affiliations
University of Chicago (US)
Corresponding author
Witten, T. A.
ORCID
Witten, T. A.
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
2007-04-25
Volume
79
Issue
2
Pages
643-675
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.79.643
OpenAlex
W2001032586
Cited by
401
References
0
Citations by year
2026: 11 · 2025: 11 · 2024: 18 · 2023: 16 · 2022: 22 · 2021: 18 · 2020: 17 · 2019: 23 · 2018: 19 · 2017: 19 · 2016: 19 · 2015: 34 · 2014: 21 · 2013: 35 · 2012: 23
FWCI
51.97
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Reviews of Modern Physics (publishedVersion)
Topics
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
  • Physical Sciences › Engineering › Mechanics of Materials › Elasticity and Wave Propagation
  • Physical Sciences › Engineering › Civil and Structural Engineering › Structural Analysis and Optimization
Keywords
elastic sheet, crumpling, vertex singularity, inextensibility, scaling arguments, asymptotic analysis

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