Physicists develop criteria for knit-able patterns
A sock consists of only a single intertwined thread. Researchers now show that the manufacturability of such patterns can be predicted using knot theory.
Knitting is a fascinating craft. From a long thread and two needles, sweaters, scarves, and socks can be made in a wide variety of shapes, colors, and patterns. The earliest European knitted items date back to the 13th century. However, it was previously unclear what criteria a textile pattern must meet to be produced by knitting or crocheting. Using knot theory, researchers have now developed a mathematical criterion that distinguishes knittable from non-knittable textiles. The study was published in the journal "Physical Review X".
The physicists from a total of four Japanese universities consider knitted and crocheted fabrics as so-called mechanical metamaterials. These owe their special properties less to the material used than to the geometric and topological arrangement of their components. Although many textile structures can be made from just a single thread, they exhibit very different mechanical properties. For example, there are textile patterns that, at first glance, resemble knitted fabrics but cannot be produced by the local movements of knitting needles or crochet hooks due to their entanglements.
According to the scientists, so-called topological defects play a key role in identifying knittable patterns. Such disturbances arise, for example, when an entanglement locally unravels. Similar to a dropped stitch, these defects can spread through the fabric and gradually unravel it. It is precisely this defect propagation that, in the researchers' view, reflects the actual manufacturing process, but in reverse.
Based on this behavior, the authors distinguish between "knittable" and "non-knittable" patterns. In real knitted or crocheted structures, the defects can gradually unravel the fabric. This is not possible with non-knittable patterns because the entanglements become increasingly complex as the fabric size increases. Two patterns can look almost identical, similar to how two knots appear the same at first glance. But while one knot can be untied with skillful pulling, the other contains an additional entanglement.
The work also reveals a connection between manufacturing methods and mechanical robustness. Since defects spread more easily in some patterns than in others, topology could be used specifically to design fabrics with defined resistance to damage. This should be particularly interesting for technical textiles that are either intended to deform in a controlled manner or to be particularly robust.
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