标题： 关于理解随机纤维网络的结构-功能关系的研究进展 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众多生物组织和工程材料的结构基础。从力学的角度来看，理解随机纤维网络的结构-功能关系尤其有趣，因为当外力施加到这些网络上时，只有小部分纤维会承担大部分载荷。具体而言，这些承载载荷的纤维通过网络形成载荷路径，也称为力链。然而，纤维网络几何结构、力链与随机纤维网络整体力学行为之间的关系仍然知之甚少。 为此，我们构建了一个具有几何精确梁单元的随机纤维网络有限元模型，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，我们探讨了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分析方法，仅基于结构信息来预测纤维网络的力学特性。 关键发现包括对单根纤维链以及由Voronoi图生成的纤维网络的临界应变硬化转变点的洞察，以及力链与将纤维网络视为空间图结构时出现的距离加权图最短路径之间的联系。这项工作标志着在绘制经历大变形的随机纤维网络结构-功能关系方面迈出了重要一步。 此外，由于我们的代码以开源许可证分发，我们希望未来的研究人员能够直接在此基础上开展工作，解决超出此处定义范围的相关问题。 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.