Physics
Tension-dependent transverse buckles and wrinkles in twisted elastic sheets
Document Type
Article
Abstract
We investigate with experiments the twist-induced transverse buckling instabilities of an elastic sheet of length L, width W and thickness t, that is clamped at two opposite ends while held under a tension T. Above a critical tension Tλ and critical twist angle ηtr, we find that the sheet buckles with a mode number n ≥ 1 transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable and stiff are identified, by introducing a bendability length LB and a clamp length LC(< LB). In the stiff regime (L > LB), we find that mode n = 1 develops above ηtr ζ ηS ∼ (t/W)T-1/2, independent of L. In the bendable regime LC < L < LB, n = 1 as well as n > 1 occur above ηtr ζ ηB ∼ √t/LT-1/4. Here, we find the wavelength λB ∼ √LtT-1/4, when n > 1. These scalings agree with those derived from a covariant form of the Föppl-von Kármán equations, however, we find that the n = 1 mode also occurs over a surprisingly large range of L in the bendable regime. Finally, in the clamp-dominated regime (L < Lc), we find that ηtr is higher compared to ηB due to additional stiffening induced by the clamped boundary conditions.
Publication Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publication Date
6-2018
Volume
474
Issue
2214
ISSN
1364-5021
DOI
10.1098/rspa.2018.0062
Keywords
buckling, elastic instability, ribbon, thin sheet, twist, wrinkling
Repository Citation
Kudrolli, A. and Chopin, J., "Tension-dependent transverse buckles and wrinkles in twisted elastic sheets" (2018). Physics. 96.
https://commons.clarku.edu/faculty_physics/96
