Upcycling plastic sheets by scrolling yarns guided by Schläffli origami*

We discuss a new tensional twist-folding framework for hyperelastic sheets leading to re-deployable yarns with intricate crossectional structures. Our experiments demonstrate that applied tension drives the folding of stretchable sheets as opposed to traditional compression-induced folding methods in origami with bendable sheets, generating new fabrication strategies. Using microfocus x-ray imaging, we show that tensional twist-folding is surprisingly ordered and can be used to transform thin elastic sheets into delicate nested multilayered structures. We find spiral accordion folded sheets can be algorithmically generated using rigid origami kinematics represented by Schläfli symbols. We uncover the key role of the sheet geometry and elasticity to set the fold number and organize the folding into tightly scrolled yarns. Further, guided by the twisting of two filaments into a rope, we develop a geometric yarn model to explain the growth of yarns with twist. Because of the great control of the internal yarn structure, tensional twist-folded offers a promising avenue for waste upcycling and functional yarns with optimized mechanical strength and energy storage capacity.