Twisted Structure of Multifilament Bundles and Sheets*

We will report on an experimental investigation of the shapes and strength of elastic multifilament bundles and sheets as a function of applied end-to-end twists in the limit of low tension. Two complementary geometries will be discussed. One consists of a set of filaments that are mounted parallel on linear clamps and then twisted, and compared with a twisted sheet with the same aspect ratio. In the other, the filaments are mounted corresponding to a cylindrical surface in circular end-clamps and then twisted axially to compare with a sheet which is rolled into a cylinder and then twisted. While the filaments deform corresponding to a hyperbolic hyperboloid before contact, deviations are observed from these shapes in the case of sheets even at vanishing twist. In both cases, a bundle forms at the center as the filaments come in contact with a cross section which evolves with an applied twist. We will discuss the analysis of the shapes and torques required in terms of the Geometric yarn model [1], and by generalizing the energetics derived for twisted two filament bundles [2] noting the important contributions of stretching, bending, and contact, besides twist.

[1]: Tensional twist-folding of sheets into multilayered scrolled yarns, J Chopin, A Kudrolli - Science Advances, 8, eabi8818 (2022).

[2]: Energetics of twisted elastic filament pairs, J Chopin, A Biswas, and A Kudrolli, arXiv preprint arXiv:2309.11344 (2023).