Tension-dependent transverse buckles and wrinkles in twisted elastic sheets

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 ≡ 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 ≡ 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.