Unravelling the Mechanics of Knitted Fabrics Through Hierarchical Geometric Representation

TL;DR

Knitted fabrics are hierarchical, with mechanics driven by yarn-scale dynamics; the work formulates a yarn-based model to capture nonlinear extensibility and anisotropy arising from geometric rearrangements, using a centerline representation by cubic B-splines with $N$ segments. The dynamics follow a Lagrangian framework with kinetic energy $T$, potential energy $V=V^{s}+V^{b}+V^{g}$, and damping $D$, and include yarn-yarn contact modeled by discrete-sphere envelopes. Validation against uniaxial tests on jersey, garter, rib, and seed samples shows a characteristic two-stage J-shape response and topology-dependent anisotropy; the model also reveals that yarn rearrangements dominate the initial compliant regime. This computational approach enables design of mechanically programmable fabrics and 2D/3D textiles compatible with manufacturing for wearable devices and soft robotics.

Abstract

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organisation 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. Fabric anisotropy originates from observed yarn-yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides a design space of knitted fabrics to embed functionalities by varying geometric configuration and material property in instructed procedures compatible to machine manufacturing. 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.

Figures (16)

• Figure 1: Illustration of basic weft-knitted fabric patterns composed of two by two contacts with varying topology (each contact can either be purl (P) or knit (K)): (A) jersey, (B) garter 1 by 1, (C) rib 1 by 1 and (D) seed 1 by 1.
• Figure .1: Parametric study on the effects on a jersey knitted sample subjected to external tension along fabric warp: (A) from damping mass, $k_g$ (units of g/s) (B) from contact repulsion constant, $k$, (units of g/cm.s^2) (C) from tangential frictional coefficient $k_{dt}$ (units of g/cm^2.s) and (D) from normal frictional coefficient $k_{dn}$ (units of g/cm^2.s).
• Figure 2: The assembly of a representative weft-knitted fabric (jersey). (A) At the microscale: a loop discretised with evenly spaced control points along fixed cubic basis functions. (B) At the mesoscale: each row of yarn formed along fabric weft and translated along fabric warp based on the topological description of representative structure (We present jersey as an example here and the same assembly process is generalised for other patterns, such as garter, rib and seed). (C) At the macroscale: a fabric with ends of each row connected and additional spiral yarns attached to the bottom ("casting on" in textile terminology) and top boundary ("binding off" in textile terminology) to prevent fabric from unravelling.
• Figure .2: (A) Demonstration of the capability of our model to simulate three braided structures each consisting of three yarns with open ends. (B) Simulation of a woven structure consisting of 12 yarns with open ends in parallel and one additional yarn to connect the ends of stress-free boundaries. In both (A) and (B) each yarn is specified with the same material property. However, we colour-code each yarn in a different colour, as to show the capability of specifying different yarn-wise material properties if one may wish to design such braided and woven structures compromising stiff and soft yarns into the same textile structure.
• Figure 3: Deformation profiles from simulation (top) and experiment (bottom) at 0% strain and 80% strain respectively for (A) garter 1 by 1 when subjected to uniaxial tension along warp direction, (B) rib 1 by 1 when subjected to uniaxial tension along warp direction, (C) garter 1 by 1 when subjected to uniaxial tension along weft direction, (D) rib 1 by 1 when subjected to uniaxial tension along weft direction. Note that free ends of the fabrics with the same pattern and loading condition are marked with the same curves to provide a visual comparison between simulation and experiment on the deformation profiles.