Physicists decode the mathematics of knitting to make bespoke materials
Physicists are decoding math-y secrets of knitting to make bespoke materials

          
          
An avid knitter since childhood, Matsumoto started pondering the underlying mathematics when she went into science and developed a new appreciation for all the math and materials physics behind her hobby. "There's this huge wealth of knowledge in the knitting community that hasn't been translated into a quantitative model yet," she said. "We're trying to take that knowledge and bring it into the physics world, where we can study these as materials and look at elasticity and other emergent properties."
In essence, knitted fabrics are composed of an interlocking series of slip knots composed of a single thread hooking back and forth on itself. (Woven fabrics, in contrast, are composed of multiple threads crossing each other.) To make a knitted stitch, you pull the slip knot through the front of the fabric; to make a purl stitch, you pull it through the back of the fabric. Experienced knitters know how to combine those stitches in many different ways, playing with the topology and creating intricate new shapes—including elaborate 3D shapes, like a stuffed rabbit. And changing the topology will also change the emergent properties (like elasticity).

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

          
  
        
            

"There are hundreds of books with thousands of patterns of stitches, with seemingly unbounded complexity," said Matsumoto. "And every type of stitch has a different elasticity. 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."
Matsumoto isn't the only physicist intrigued by the remarkable complexity of this ancient craft. Just last year, a team of French physicists developed a rudimentary mathematical model to describe the deformation of a common type of knit. Their work was inspired when co-author Frédéric Lechenault watched his pregnant wife knitting baby booties and blankets, and he noted how the items would return to their original shape even after being stretched. With a few colleagues, he was able to boil the mechanics down to a few simple equations, adaptable to different stitch patterns.

          
                  