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 fabric free of external forces. This is 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 metastable states is obtained by varying the braid inclination while contact forces remain on the friction cone.
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