Knitting is not only a mere art and craft hobby but also a thousand year old technology. Unlike weaving, it can produce loose yet extremely stretchable fabrics with almost vanishing rigidity, a desirable property exhibited by hardly any bulk material. It also enables the engineering of arbitrarily shaped two and three-dimensional objects with tunable mechanical response. In contrast with the extensive body of related empirical knowledge and despite a growing industrial interest, the physical ingredients underlying these intriguing mechanical properties remain poorly understood. To make some progress in this direction, we study a model tricot made of a single elastic thread knitted into the common pattern called stockinette. On the one hand, we experimentally investigate its tensile response and measure local displacements of the stitches during deformation. On the other hand, we derive a first-principle mechanical model for the displacement field based on the yarn bending energy, the conservation of its total length and the topological constraints on the constitutive stitches. Our model solves both the shape and mechanical response of the knit and agrees quantitatively with our measurements. This study thus provides a fundamental framework for the understanding of knitted fabrics, paving the way to thread-based smart materials.Due to the wide range of applications, the advancement in knitting technology as well as the availability of high performance fibers, knitted materials are commonly employed in various innovative areas. For instance, they are intensively utilized in textile industry [1], advanced engineering [2], biomedical and biomimetic applications [3,4]. A basic knit consists in a single yarn which is topologically constrained to form intertwined loops, or stitches, from which originates its effective dimensionality. While the topological properties of a knitted fabric are usually unaltered, the stitches can undergo large deformations due to their curved nature and the fact that the yarn can slide from one stitch into the neighbouring ones. Those properties manifest also in the outstanding drapability of the resultant knitted fabrics allowing for the shaping of complex curved composite components. Moreover, while the constituent yarn shows significant resistance to elongation, a knitted fabric can endure large strains in response to small applied tractions. Pulling on a typical scarf can easily produce deformations of the order of 100% while the same force applied on the yarn itself would only deform it by a few percent. A stretched knit also exhibits a characteristic catenary shape similarly to incompressible bulk materials.Although most of the efforts have been focusing on woven fabrics, the peculiar properties of knitted materials have induced increasing interest in modelling their mechanical behavior. Several early studies have addressed the fact that a knit is comprised of a discrete network of repetitive stitches characterized by a given topology. On the one hand, geometrical models have focused o...
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