Smooth triaxial weaving with naturally curved ribbons

TL;DR

This paper introduces a method to create smoothly curved triaxial woven structures by tuning ribbon curvature, enabling continuous Gaussian curvature variation and the design of complex smooth shapes like spheres and tori.

Contribution

It demonstrates that in-plane ribbon curvature controls the weave's Gaussian curvature, allowing for smooth, continuous curved structures without relying on topological defects or elasticity.

Findings

Continuous variation of Gaussian curvature through ribbon curvature tuning

Shape of unit cells determined solely by in-plane geometry

Design of smooth spherical, ellipsoidal, and toroidal structures

Abstract

Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of the ribbons, the integrated Gaussian curvature of the weave can be varied continuously, which is not feasible using traditional techniques. Further, we reveal that the shape of the physical unit cells is dictated solely by the in-plane geometry of the ribbons, not elasticity. Finally, we leverage the geometry-driven nature of triaxial weaving to design a set of ribbon profiles to weave smooth spherical, ellipsoidal, and toroidal structures.