Statistical Knitting and the Resulting Macroscopic Emergent Behavior*

Knitted fabrics are programmable materials whose elastic properties stem from the spatial arrangement of stitches. The most common fabrics are simple periodic patterns of the two most elementary stitches, the knit stitch and the purl stitch. Our previous studies have shown that one can introduce soft deformation modes to a pattern by alternating between knit and purl stitches. This motivates the question: how does alternating between these stitches on different lengthscales control macroscopic elastic behavior of the fabric? We systematically study the mechanics of disordered, uncorrelated arrangements of knits and purls and gradually introduce correlations. To do this we model a collection of knits and purls as a binary mixture undergoing phase separation. Following Cahn-Hilliard dynamics, we track the development of knits and purls into domains and manufacture the resulting pattern at different stages of coarsening. We expect that the macroscopic mechanical behavior of each generated fabric will depend on the collective response of correlated structures over a variety of lengthscales, and we wish to understand the role of soft elasticity on macroscopic emergent behavior. This statistical mechanics-motivated study is an unexplored design space for fabrics.