Mathematical Rules Underlie The Ancient Art of Knitting

Came into existence from more than 3000 years, knitting is an ancient form of manufacturing but Elisabetta Matsumoto of the Georgia Institute of Technology in Atlanta believes that understanding how stitch types guide shape and stretchiness will be invaluable for designing new "tunable" materials. For example, tissue like flexible material could be manufactured to replace biological tissues, such as torn ligaments, with stretchiness and sizing personalized to fit each individual. This week at the American Physical Society March Meeting in Boston, Matsumoto will present her work on the rules of mathematics which underlie knitting. "By picking a stitch you are not only choosing the geometry but the elastic properties, and that means you can build in the right mechanical properties for anything from aerospace engineering to tissue scaffolding materials," said Matsumoto. Matsumoto loved knitting as a child and later when she became interested in mathematics and physics, she designed a new appreciation for her hobby. She said she realized that there is just a large amount of math and materials science that goes into textiles, but that's taken for granted an awful lot. She also added that every type of stitch has a different level of elasticity, and if we figure out everything possible then we could design and craft things which are rigid in a certain place using a certain type of stitch, and use a different type of stitch in another place for getting different functionality.

Matsumoto group members are starting to delve through the complex math which encodes mechanical properties. These properties are within the interlocking series of slip knots of material. But applying the pure mathematics of knot theory to the large catalog of knit patterns is a tricky process for Shashank Markande, a Matsumoto's graduate student.

He said that stitches have some very strange and unique constraints. He told an example according to which a question arises that if he needs to be able to make it with two needles and one piece of yarn, how do we translate that into math?

But he is starting to make the knit algebra into larger and more complex patterns. He feeds this into the elastic modeling of simple and easy lattice like knits, which his post-doc, Michael Dimitriyev is developing.

The fabric behavior of Dimitriyev solving code is showcasing potential beyond material design, in the realm of computer game graphics.

He said that fabric and cloth tend to look a little strange in computer games because they use simple bead and spring elasticity models. Therefore, if we can come up with a simple and easy set-up of differential equations, it may make things to look better. The Matsumoto group for the moment is focusing on very simple stitch patterns and curves in knitted lattices; however, soon they hope to understand how knits behave in 3D. But as they tease out the math between the stitches, Matsumoto makes sure they keep their eyes on how these patterns come together by arranging the occasional crafting session with the origami group next door.

By: Preeti Narula

Content: https://www.sciencedaily.com/releases/2019/03/190306081827.htm