Tension-dependent transverse buckles and wrinkles in twisted elastic sheets

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 T λ and critical twist angle η tr , 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 L B and a clamp length L C (< L B ). In the stiff regime ( L > L B ), we find that mode n =1 develops above η tr ≡ η S ∼( t / W ) T −1/2 , independent of L . In the bendable regime L C < L < L B , n =1 as well as n >1 occur above η tr ≡ η B ∼ t / L T − 1 / 4 . Here, we find the wavelength λ B ∼ L t T − 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 < L C ), we find that η tr is higher compared to η B due to additional stiffening induced by the clamped boundary conditions.