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How a physicist is unraveling the math of the mesh

Physicist Elisabetta Matsumoto is an avid tutor and has been a fan since she was a child. During college at the University of Pennsylvania in 2009, Matsumoto came across an unusually knotted stitch while making a pattern for a Japanese red dragon. “I have books with thousands of different stitch patterns, but the one hanging from the red dragon wall was one I had never seen,” he says. That led her to think about dot geometry and eventually led her to study mesh mathematics.

There are about a hundred basic points, Matsumoto says. By varying the stitch combinations, a knitting machine can alter the elasticity, mechanical strength, and 3D structure of the resulting fabric. The yarn alone is not very elastic. But when knitted, the yarn gives rise to a fabric that can stretch more than twice its length while the yarn itself barely stretches.

Matsumoto, now at the Georgia Institute of Technology in Atlanta, is mocking the mathematical rules that dictate how stitches impart such unique properties to fabrics. She hopes to develop a catalog of stitch types, their combinations, and the resulting properties of the fabric. He said meshes, scientists and manufacturers could benefit from a mesh dictionary.

Elisabetta Matsumoto, a physicist at the Georgia Institute of Technology in Atlanta, hopes to create a mesh dictionary that can be used to manipulate the physical properties of materials.Courtesy of Elisabetta Matsumoto

Matsumoto's research is based on the theory of nodes (SN: 31/10/08), a set of mathematical principles that define how nodes are formed. These principles have helped to explain how DNA folds and develops and how the composition and distribution of a molecule in space gives it physical and chemical characteristics (SN: 23/05/08; SN: 27/08/18). Matsumoto is using knot theory to understand how each point tangles with its neighbors. “The types of stitches, the differences in their geometries, as well as the order in which you put the stitches together in a fabric can determine the properties (of the fabric),” she says.

Making small changes, such as changing a couple of crosses at a knot, can have a huge impact on textile mechanics. For example, a fabric made with only one stitch, such as a stitch or a stitch, tends to curl at the edges. But it combines the two types of stitches in alternating rows or columns and the fabric stays flat. And despite looking almost identical, the fabrics have varying degrees of stretch, Matsumoto and graduate student Shashank Markande reported in July at the Bridges 2020 conference proceedings.

Matsumoto’s team is now training a computer to think like a weaver. Using yarn properties, mathematical stitch details, and end point structures as inputs, a program can predict the mechanical properties of fabrics. These forecasts could one day help to adapt materials for specific applications, from scaffolding for human tissue growth to smart wearable clothing (SN: 6/1/18), and perhaps solve complicated problems of daily life.

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