标题： 走向理解随机纤维网络中的结构-功能关系 显示英文标题

标题： Towards understanding structure-function relationships in random fiber networks

摘要： 随机纤维网络构成了许多生物组织和工程材料的结构基础。 从力学角度来看，理解随机纤维网络的结构-功能关系特别有趣，因为当外部力作用于这些网络时，只有少数纤维实际上会承载大部分负载。 具体来说，这些承载负荷的纤维通过网络传播形成负荷路径，也称为力链。 然而，纤维网络几何结构、力链以及随机纤维网络结构整体力学行为之间的关系仍然不明确。 为此，我们采用几何精确的梁单元实现了随机纤维网络的有限元模型，并利用该模型探索随机纤维网络的力学行为。 我们的研究重点有两个方面。 首先，我们研究单根纤维链和随机纤维网络的力学行为。 其次，我们提出并验证了一种可解释的解析方法，仅从结构信息预测纤维网络的力学行为。 关键发现包括对由Voronoi图生成的单根纤维链和纤维网络的关键应变硬化转变点的洞察，以及将力链与通过将纤维网络视为空间图结构而产生的距离加权图最短路径之间的联系。 这项工作标志着在映射经历大变形的随机纤维网络的结构-功能关系方面迈出了重要的一步。 此外，由于我们的代码在开源许可下发布，我们希望未来的研究人员可以直接基于我们的工作来解决此处定义范围之外的相关问题。 显示英文摘要

摘要： Random fiber networks form the structural foundation of numerous biological tissues and engineered materials. From a mechanics perspective, understanding the structure-function relationships of random fiber networks is particularly interesting because when external force is applied to these networks, only a small subset of fibers will actually carry the majority of the load. Specifically, these load-bearing fibers propagate through the network to form load paths, also called force chains. However, the relationship between fiber network geometric structure, force chains, and the overall mechanical behavior of random fiber network structures remains poorly understood. To this end, we implement a finite element model of random fiber networks with geometrically exact beam elements, and use this model to explore random fiber network mechanical behavior. Our focus is twofold. First, we explore the mechanical behavior of single fiber chains and random fiber networks. Second, we propose and validate an interpretable analytical approach to predicting fiber network mechanics from structural information alone. Key findings include insight into the critical strain-stiffening transition point for single fiber chains and fiber networks generated from a Voronoi diagram, and a connection between force chains and the distance-weighted graph shortest paths that arise by treating fiber networks as spatial graph structures. This work marks an important step towards mapping the structure-function relationships of random fiber networks undergoing large deformations. Additionally, with our code distributed under open-source licenses, we hope that future researchers can directly build on our work to address related problems beyond the scope defined here.