Chiral Analogues of Knit Stitches Designed Using Chiral Topology

Abstract: Fabrics are flexible thin structures made of entangled yarn or fibers, yet the topological bases of their mechanics remain poorly understood. For weft knitted fabrics, we describe how the entanglement of adjacent stitches contributes to the flexibility of the fabric. Interpreting heterogeneous stitch pairs as domain boundaries reveals that the step between pairs of neighboring stitches is responsible for direction-specific flexibility. In typical knitted fabrics, anisotropic flexibility can be attributed to latticed domain boundaries. The intersections between domain boundaries result in point defects that induce frustration that resembles the impossible Penrose stairs. We identify these by a chiral characteristic, defined summing the ascending or descending steps in a cycle surrounding the defect. Remarkably, seed fabric, a knit with high flexibility in both course and wale directions, is characterized as a racemic crystal of these chiral point defects.