The Science of Knitting: Understanding How Stitch Types Govern Shape

a) Knitting is a periodic structure of slip knots. b) Textiles with intricate patterns are knit by combining slipknots in specific combinations. Credit: Elisabetta Matsumoto

Dating back more than 3,000 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 govern shape and stretchiness will be invaluable for designing new “tunable” materials. For instance, tissuelike flexible material could be manufactured to replace biological tissues, such as torn ligaments, with stretchiness and sizing personalized to fit each individual.

At the American Physical Society March Meeting in Boston, Matsumoto presented her work on the mathematical rules that 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 enjoyed knitting as a child and when she later became interested in mathematics and physics, she developed a new appreciation for her hobby.

“I realized that there is just a huge amount of math and materials science that goes into textiles, but that is taken for granted an awful lot,” said Matsumoto.

“Every type of stitch has a different elasticity, and if we figure out everything possible then we could create things that are rigid in a certain place using a certain type of stitch, and use a different type of stitch in another place to get different functionality.”

Topological defects in the square can shape the (a) out-of-plane and (b) in-plane deformations of knitted textiles. Credit: Elisabetta Matsumoto

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

“Stitches have some very strange constraints; for instance, I need to be able to make it with two needles and one piece of yarn —how do you translate that into math?” said Matsumoto.