In 2018, a team of French physicists developed rudimentary mathematical model Describes common knit transformations. their work Co-author Frédéric Lecheneau was inspired when he watched his pregnant wife knit baby boots and blankets and noticed how those items could be stretched and then return to their original shape. I got it. Together with several colleagues, he was able to boil down the mechanism into a few simple equations that could be adapted to a variety of stitch patterns. It all depends on three things: the “bend” of the thread, the length of the thread, and the number of points crossed in each stitch.
simpler stitches
A simplified model showing how threads interact
Credit: J. Crassous/University of Rennes
One of the co-authors of the 2018 paper, Samuel Pointcru from Aoyama Gakuin University in Japan, along with two other colleagues, Jérôme Crassou (University of Rennes, France) and Audrey Steinberger (University of Lyon) and co-author of this latest study. This time, Pointcreux was interested in the knotty problem of predicting the remaining shape of a knitted fabric, taking into account the length of the yarn in each stitch. This unanswered question dates back to at least 1990. 1959 paper.
The complex geometry of all the contact zones that create friction between thin elastic fibers makes such systems very difficult to model accurately. This is because the contact zone can rotate and change shape as the fabric moves. Pointecreux and his colleagues devised their own, more simplified model.
The research team conducted the experiment using jersey stitch knit (also known as stockinette). This is a widely used simple knit consisting of a single thread (in this case a nylon thread) forming interlocking loops. We also performed numerical simulations modeling individual elastic rods combined with dry contacts with specific friction coefficients to form a mesh.
Results: Even when no external stress was applied to the fabric, the friction between the threads acted as a stabilizing factor. And the resting state equilibrium form of the knit sweater was not single. Rather, multiple metastable states existed that depended on the fabric’s history, the different ways in which it was folded, stretched, and crumpled. In short, “contrary to relatively common belief in the textile literature, knitted fabrics do not assume a unique shape when no force is applied.” Crassus said.
DOI: Physical Review Letters, 2024. 10.1103/PhysRevLett.133.248201 (About DOI).
