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Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet
Abstract
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 demonstrated by an examination of the ridges joining pairs of sharp points in a range of simple geometries of variable size. As the linear size X increases sufficiently, the deformation energy grows as X 1/3 and consists of similar amounts of bending and stretching energy. The deformation energy becomes concentrated in a fraction of the sheet that decreases as X 1/3 . Despite this concentration, the local strain in the ridge decreases as X 2/3 . Nearly all the deformation energy in thin, crumpled elastic sheets was found to be concentrated in ridges that obey these scaling laws.
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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.
“We note that stretching energy in thin sheets scales the same way with ρface as bending energy due to a virial theorem3435, but is expected to be considerably smaller3435. Further, for thin sheets, bending strain is much larger than stretching strain in low-energy configurations3435.”
From Self-folding origami at any energy scale (2017) · cites this paper as [34]
Bending stress is localized to a furrow along the diagonal, a result expected for thin sheets.
“we see that the bending stress is localized to a furrow along the diagonal, a result expected for thin sheets34”
From Self-folding origami at any energy scale (2017) · cites this paper as [34]
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Self-citation
Metadata
- Authors
- Lobkovsky, A., Gentges, S., Li, H., Morse, D., & Witten, T. A.
- Affiliations
- University of Chicago (US)
- University of California, Santa Barbara (US)
- Corresponding author
- Li, Hao
- Witten, T. A.
- Venue
- Science
- Published
- 1995-12
- Volume
- 270
- Issue
- 5241
- Pages
- 1482-1485
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2048290375
- Cited by
- 392
- References
- 0
- Citations by year
- 2026: 6 · 2025: 10 · 2024: 13 · 2023: 13 · 2022: 13 · 2021: 12 · 2020: 15 · 2019: 17 · 2018: 8 · 2017: 12 · 2016: 8 · 2015: 12 · 2014: 15 · 2013: 11 · 2012: 8
- FWCI
- 38.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Engineering › Mechanics of Materials › Elasticity and Wave Propagation
- Keywords
- scaling laws, strain energy, energy concentration, bending energy, stretching energy, strain localization, thin sheets
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