Knitting has been around for thousands of years, but this researcher believes it can pave the way for a novel class of materials.

Hand-knitted stockinette fabric. Image via Wikipedia.

Elisabetta Matsumoto enjoyed knitting since she was a child. But when she developed a passion for mathematics and physics at the Georgia Institute of Technology in Atlanta, she developed a whole 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.

Knitting is a process in which yarn (or another filament material) is shaped in space to form a fabric, an essentially sheet-like material, via stitching together a lattice of slip-knots.

Essentially, it involves using a 1D material to fill a 2D sheet, and then covering a 3D material like our head or body. Although this process can be traced back to the 11th century BCE, the theory behind it is much more complex than the actual practice. However, we rarely think about the complexity of knitted fabrics. Knitted textiles have become ubiquitous as they are easy and cheap to create, lightweight, portable, flexible and stretchy.

The key to their outstanding properties, however, lies in its microstructure.

A schematic diagram of a knit fabric (in stockinette pattern) — even the simplest knitting patterns are very difficult to describe mathematically. Image in public domain.

Unlike woven fabrics, where strands usually run straight horizontally and vertically, knitting follows a looped path along its row — there is no single straight line of yarn anywhere in the pattern. Regardless of the technique or material used, knitters need to have a good understanding of the material properties they are working with, as well as the fabric geometry they are producing.

By changing these two complex parameters, a wide array of material properties can be developed.

“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.

Developing a mathematical framework for knitting, however, is no easy feat. What grandmas have been doing almost intuitively for centuries is extremely difficult to describe algebraically — but Matsumoto’s graduate student, Shashank Markande is doing just that: developing a catalog of knit patterns and the different resulting geometrical and material properties.

It’s definitely not an easy task, especially considering the thousands of different patterns described in knitting books.

“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.

Five fabrics (a) stockinette, (b) reverse stockinette, (c) garter, (d) 1×1 ribbing and (e) seed made from knits and purls. Each of these are doubly periodic – with unit cell outlined by a dashed box. Image credits: Elisabetta Matsumoto.

Meanwhile, Michael Dimitriyev, a post-doc working in Matsumoto’s lab, is taking the catalog developed by Markande and using it to generate computer models which predict material properties. In addition to actually using this to produce novel materials, this can be applied to another different field: computer graphics.

“Fabric and cloth tends to look a little strange in computer games because they use simple bead and spring elasticity models, so if we can come up with a simple set up of differential equations it may help things to look better,” said Matsumoto.

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

Speaking at the American Physical Society March Meeting in Boston this week, Matsumoto will be presenting her team’s results and how the seemingly monotonous process of knitting can be used to develop a whole new class of materials, taking advantage of the particularities of knitting patterns.

“To this end, we have developed a geometric framework for relating the yarn path to the emergent surface geometry of the fabric. The generality of our approach allows for a systematic coarse-graining of yarn degrees of freedom, without a priori specification of a model of yarn elasticity. Thus, we are able to arrive at a stitch pattern-dependent, continuum elastic model of knits by assuming a simple phenomenological model of yarn, whilst allowing for the possibility of including more realistic yarn mechanics and experimental comparison,” the abstract reads.

For the moment, the team is focusing on the simplest stitch patterns and curves in knitted lattices. They hope to soon move on to more complex patterns and study how knits behave in 3D.

 

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