Unravelling the Mechanics of Knitted Fabrics Through Hierarchical Geometric Representation

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organization of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. We identify the dictating factors of the mechanics of knitted fabrics, highlighting the previously overlooked but critical effect of pre-tension. Fabric anisotropy originates from observed yarn--yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides design flexibility of knitted fabrics to embed functionalities by allowing variation in both geometric configuration and material property. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.