Abstract
We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet's center is of order h|logh|, where hâ‰1 is the thickness of the sheet, we establish matching upper and lower bounds of order h 2|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.
Original language | English (US) |
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Pages (from-to) | 251-264 |
Number of pages | 14 |
Journal | Journal of Elasticity |
Volume | 113 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2013 |
Keywords
- Energy scaling laws
- Thin elastic sheets
- d-Cone
ASJC Scopus subject areas
- General Materials Science
- Mechanics of Materials
- Mechanical Engineering