Chiral yarn and a twist on the symmetries of knitted fabric

Textiles such as knitted fabric are mechanical metamaterials whose properties depend on the topology and symmetries of the underlying microstructure. The basic slipknot construction of knitted fabrics gives rise to mirror symmetries, allowing the fabric to adopt its regular "V-patterned" texture and the fabric boundaries to remain rectangular. This depends on the use of "balanced yarn" where any internal torques that remain from the spinning process are either relaxed or counter-balanced by a plied bundle structure, and it is known that the use of twisted or unbalanced yarn can cause the fabric to become skewed, adopting a sheared state that breaks its mirror symmetries. We consider this phenomenon in the context of a plectoneme or ``twist-to-writhe'' instability and use a Kirchhoff model of yarn mechanics with soft contact interactions to study the mechanism of chirality transfer across scales: from yarn twist, to stitch structure, to fabric shear. In doing so, we find conditions under which symmetry breaking is confined to stitch morphology without large changes in fabric shape. We further examine the coupling between yarn twist, stitch symmetry, and "fabric crystallography" by considering patterns beyond plain knit, establishing a new route to designing symmetry in textile metamaterials.