The physics of knitting

A new theory could help engineers to create materials for use as smart textiles, artificial tissue and even the aerodynamic contours in jet turbines – by knitting them.

The oldest known example of knitting is from Egypt over a thousand years ago, yet until now scientists did not fully understand how a non-stretchy yarn could be entangled into such a stretchy fabric.

The new study, published in the journal Physical Review X, boils knitwear properties down to three parameters – yarn bendiness, the length of yarn, and the number of crossing points in each stitch.

The simplicity of the model will enable scientists to begin designing knitted materials with custom shapes and properties, says lead author of the paper, Samuel Poincloux from the Ecole Normale Superiore in Paris, France.

“If you understand it well, you can tune your structure to have the properties that you want,” he says.

Poincloux’s analysis found that the primary source of a knitted fabric’s stretchiness came from the loop created as the yarn in one row of stitches weaves through the row above and the row below. When the fabric is pulled, it is able to stretch because the loops become distorted. The energy to do so comes from bending the yarn.

The way the loop can stretch is also limited by the number of times the yarn crosses with neighbouring stitches, and the total length of the yarn in the fabric.

The analysis found yarn bendiness, crossing points and total yarn length were enough parameters to accurately deduce the properties of the material. Poincloux says this should provide a theoretical basis for material designers looking a much more efficient way to create new materials, compared to the current trial and error methods used in industry.

“When I discussed with industry they said they do not have a good fundamental bottom-up design model,” Poincloux explains.

The work originated when Pouncloux’s PhD supervisor, Frédérick Lechenault, watched his wife knit clothes for their unborn child. Lechenault marvelled at the way she could create three-dimensional shapes, such as booties, that would return to their shape even after being stretched significantly.

Lechenault was at the time studying origami, investigating how structure created by folds could alter the properties of a paper object. The one-dimensional nature of yarn suggested the challenge would not be too complex, so he set Poincloux to work analysing knitting stitches.

To get his head around the task Poincloux visited the knitting workshop at the École Nationale Supérieure des Arts Décoratifs across the road from his lab, and learned some stitches.

“Discussing with artists and designers is very interesting, they have a different point of view and a very deep knowledge of what you can do, which can inspire you to design new stuff,” Poincloux says.

“Knits have interesting three-dimensional shapes that appear naturally by changing the stitch pattern. The composite industry can use knitting because it’s quite stretchable and they can fit it to a complex shape, for example in an aeroplane engine turbine.”

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