Peculiar geometry and mechanics of weaves, knits and braids

Textile architectures such as weaves, knits, and braids exhibit remarkable geometrical and mechanical peculiarities, where global form and local deformation are intertwined through the topology of interlacing filaments. In this work, we present a unified exploration of woven, knitted, and braided systems that reveals how geometry alone can dictate curvature, stiffness, and multistability. We begin with weaves, showing that three-dimensional curved surfaces can be generated from initially flat ribbons by tailoring their in-plane curvature. This geometry-driven approach enables continuous tuning of Gaussian curvature and the inverse design of woven shells that approximate arbitrary freeform surfaces. Extending these ideas, knitted fabrics are modeled through a multi-level framework that bridges yarn-scale finite element analysis with homogenized strain energy formulations, allowing rapid and accurate prediction of macroscopic behavior, including heterogeneous regions and transitions. When implemented in 3D printing, these models yield volumetric knits whose interlooped topology endows programmable anisotropy, nonlinearity, and mechanical hysteresis. Finally, we demonstrate multi-stable braids composed of curved ribbons woven in pentagonal or triaxial patterns that display rich indentation mechanics—featuring force maxima, snap-through inversion, and tunable stable states. Across these systems, geometry supersedes material: curvature, topology, and contact define behavior. Together, these studies outline a pathway toward architected textiles that merge form and function—where weaving, knitting, and braiding become geometric operations for encoding elasticity, stability, and adaptability in entangled matter.