Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organisation of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. Fabric anisotropy originates from observed yarn-yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides a design space of knitted fabrics to embed functionalities by varying geometric configuration and material property in instructed procedures compatible to machine manufacturing. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.

翻译：针织将一维纱线互锁成三维织物，使其表现出超越其构成材料的行为。纱线如何通过分层组织形成针织织物的可扩展性和各向异性，长期以来一直未得到解决。我们通过开发一种基于纱线的动力学模型，试图揭示纱线层面的拉伸力学、组装和动力学对织物非线性的力学作用。这一经过物理验证的模型捕捉了针织织物的基本力学响应，类似于柔性超材料和生物纤维网络，这是由于此类分层系统内的几何非线性所致。织物的各向异性源于在排列动力学过程中观察到的纱线-纱线重排，并且依赖于拓扑结构。这种基于纱线的模型还为针织织物提供了一个设计空间，通过在与机器制造兼容的指导程序中改变几何配置和材料属性来嵌入功能。我们这种通过计算构建针织织物的分层方法，使这一古老工艺现代化，并代表了在广泛的工程应用中实现针织织物力学可编程性的第一步。