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 \textit{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.
University of California, Berkeley（加州大学伯克利分校）；University of Duisburg-Essen（杜伊斯堡-埃森大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics
Tohoku University（东北大学）；RIKEN, Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心（iTHEMS））；Hiroshima University（广岛大学）；University of California, Berkeley（加州大学伯克利分校）；Texas A&M University（德克萨斯农工大学）
Textiles: from twisted yarn to topology and mechanics
University of California, Berkeley（加州大学伯克利分校）；Tohoku University（东北大学）；RIKEN（理化学研究所）；Hiroshima University（广岛大学）；Drexel University（德雷塞尔大学）；University of Pennsylvania（宾夕法尼亚大学）；Aoyama Gakuin University（青山学院大学）；Rice University（莱斯大学）；Texas A&M University（德州农工大学）
