Metastability of a periodic network of threads: what are the shapes of a knitted fabric ?

Knitted fabrics are metamaterials with remarkable mechanical properties, such as extreme deformability and multiple history-dependent rest shapes. This letter shows that those properties may stem from a continuous set of metastable states for a mechanically relaxed fabric, evidenced through experiments, numerical simulations and analytical developments. Those states arise from the frictional contact forces acting in the braid zone where the threads interlace and follow a line in the configuration space accurately described by a 2D-elastica model. The friction coefficient sets a terminal point along this line, and the continuous set of relaxed states is obtained by varying the braid inclination while contact forces remain on the friction cone.