In 2018, a team of French physicists developed a rudimentary mathematical model to describe the deformation of a common type of knitting. Their work was inspired when co-author Frédéric Lechenault watched his pregnant wife knit baby booties and blankets, and he noticed how the items would return to their original shape even after being stretched. With a few colleagues he managed to reduce the mechanics to a few simple equations, adaptable to different stitch patterns. It all comes down to three factors: the “bendiness” of the yarn, the length of the yarn, and the number of intersections in each stitch.
A simpler stitch
A simplified model of how yarns interact
Credit: J. Crassous/University of Rennes
One of the co-authors of that 2018 paper, Samuel Poincloux of Aoyama Gakuin University in Japan, also co-authored this latest study with two other colleagues, Jérôme Crassous (University of Rennes in France) and Audrey Steinberger ( University of Lyon). This time, Poincloux was interested in the knotty problem of predicting the residual shape of a knitted fabric given the length of yarn per stitch—an open question that dates back at least to a 1959 paper.
It is the complex geometry of all the friction-producing contact zones between the thin elastic fibers that makes such a system too difficult to model accurately, because the contact zones can rotate or change shape as the fabric moves. Poincloux and his cohorts came up with their own, simpler model.
The team conducted experiments with a jersey stitch knit (also called stockinette stitch), a common and simple knit consisting of a single yarn (in this case a nylon thread) that forms interlocking loops. They also performed numerical simulations modeled on discrete elastic rods in combination with dry contacts with a specific friction coefficient to form meshes.
The results: Even when no external stresses were applied to the fabric, the friction between the threads served as a stabilizing factor. And there was no kind of balance to the rest form of a knitted sweater; rather, there were multiple metastable states that depended on the history of the substance: the different ways it had been folded, stretched, or crumpled. In short: “Knitted fabrics do not have a unique shape if no forces are applied to them, contrary to relatively common belief in the textile literature,” says Crassous.
DOI: Physical Review Letters, 2024. 10.1103/PhysRevLett.133.248201 (About DOIs).
