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Knitting is not only a mere art and craft hobby but also a thousand year oldtechnology. Unlike weaving, it can produce loose yet extremely stretchablefabrics with almost vanishing rigidity, a desirable property exhibited byhardly any bulk material. It also enables the engineering of arbitrarily shapedtwo and three-dimensional objects with tunable mechanical response. In contrastwith the extensive body of related empirical knowledge and despite a growingindustrial interest, the physical ingredients underlying these intriguingmechanical properties remain poorly understood. To make some progress in thisdirection, we study a model tricot made of a single elastic thread knitted intothe common pattern called \textit{stockinette}. On the one hand, weexperimentally investigate its tensile response and measure local displacementsof the stitches during deformation. On the other hand, we derive afirst-principle mechanical model for the displacement field based on the yarnbending energy, the conservation of its total length and the topologicalconstraints on the constitutive stitches. Our model solves both the shape andmechanical response of the knit and agrees quantitatively with ourmeasurements. This study thus provides a fundamental framework for theunderstanding of knitted fabrics, paving the way to thread-based smartmaterials.

Geometry and elasticity of a knitted fabric