Geometry and Elasticity of a Knitted Fabric
Résumé
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 threedimensional 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 a 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.
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...