Journal
JOURNAL OF ELASTICITY
Volume 113, Issue 2, Pages 251-264Publisher
SPRINGER
DOI: 10.1007/s10659-012-9420-3
Keywords
d-Cone; Thin elastic sheets; Energy scaling laws
Funding
- NSF Mathematical Sciences Postdoctoral Research Fellowship
- NSF [DMS-0807347, OISE-0967140, DMS-1201370]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0807347] Funding Source: National Science Foundation
- Office Of The Director
- Office Of Internatl Science &Engineering [967140] Funding Source: National Science Foundation
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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 ha parts per thousand(a)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.
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