Entanglement-driven responses through multiscale 3D-printed knits

Abstract

Filamentous entanglement underlies the resilience and toughness of systems from polymer networks to textiles, yet most architected materials do not capitalize on this principle. While knitting research across mechanics, architecture, and design has demonstrated that stitch structure governs physical behavior, a quantitative framework linking stitch-level geometry to mechanical response has been lacking. Here we show that 3D printing --- as a topology-agnostic fabrication platform --- enables systematic exploration of entangled architectures, revealing a simple scaling law that unifies the mechanics of traditional and printed knits across materials, geometries, and length scales, from centimeters down to the smallest knit ever fabricated. This framework yields programmable stiffness and dissipation tunable by topology and pre-strain, establishing entanglement as a design primitive for next-generation metamaterials.