用简化模型精准模拟编织材料的几何力学行为,计算快且原理清晰。
A Reduced Order Model for Emergent Mechanics in Woven Systems

- 通过节点与四类物理元件建模编织单元,捕捉轴向、剪切、松紧等变形机制。
- 在不同宽度间距下,弯曲与剪切实验误差小于5%,验证精度高。
- 适合需要快速设计可编程机械性能的编织材料研究人员使用。
编织结构展现出各向异性刚度、剪切锁紧和屈曲互换等丰富力学行为,这些现象仅由纤维几何排布引起,而非材料本身属性。现有模型或过度均质化,或计算成本过高。本文提出一种降阶模型,将单根纤维相互作用表示为节点系统及四类具有物理意义的刚度元件:轴向变形、平面去屈曲、纤维间剪切与摩擦滑移。对单元胞进行特征值分析表明,最低能量变形模式直接对应已知的编织特有现象,且每类元件均不可或缺。刚度参数通过三点弯曲与剪切实测数据校准,在不同纤维宽度与间距下误差均控制在5%以内。模型成功拓展了连续介质方法无法实现的能力:揭示屈曲互换引发的非平凡泊松响应、逐步拉出纤维时的阶梯式力下降、三种撕裂构型下的应力集中,以及通过空间梯度纤维刚度实现可编程机械各向异性。该框架兼具物理透明性与计算高效性,适用于可编程力学响应编织结构材料的设计与分析。
原文摘要 · Abstract (English)
Woven structures exhibit rich mechanical behaviors including anisotropic stiffness, shear-induced locking, and crimp interchange that emerge purely from the geometric arrangement of individual weavers rather than from constituent material properties. Existing models either homogenize these interactions or resolve them at prohibitive computational cost. We introduce a reduced-order model that bridges this gap by representing individual weaver interactions through a system of nodes and four physically interpretable stiffness elements capturing axial deformation, in-plane uncrimping, inter-weaver shear, and frictional slip. Eigenvalue analysis of the unit cell confirms that the lowest-energy deformation modes correspond directly to known weave-specific phenomena, and that each element is necessary for a complete kinematic and mechanistic description. Element stiffness parameters are calibrated against empirical three-point bending and shear data, achieving agreement within 5% across varied weaver widths and spacings. The validated model is then applied to demonstrate capabilities beyond the reach of continuum approaches including: the emergent Poisson's response arising from crimp interchange, stepwise force reduction during progressive weaver pullout, stress localization under three distinct tearing configurations, and programmable mechanical anisotropy through spatially graded weaver stiffness. The physical transparency and computational efficiency of the framework position it as a practical tool for the analysis and design of woven architected materials with programmable mechanical response.
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