基于社区检测的颗粒材料力链网络结构提取
Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection
摘要：
力链形成的非均匀物理结构可以限制颗粒介质的力学稳定性和声波传播。然而，尽管它们的相关性预测材料的散装性能，有没有一个力链的定量描述协议。因此，很难比较不同材料或实验条件下的力链结构。为了解决这一挑战，我们把颗粒材料作为空间嵌入式网络，其中节点（颗粒）由代表接触力的加权边连接。我们使用来自社区检测的技术，这是一种聚类，以找到紧密连接的粒子集。通过使用受粒子接触网络约束的地理零模型，我们提取了类似于力链的链状结构。我们提出了三种诊断来测量这些链状结构，我们证明了这些诊断的实用性，用于识别和表征各种材料中的力链网络架构。为了说明我们的方法，我们描述了力链结构如何依赖于两种非常不同类型的填料的压力：（1）来自实验室实验和（2）来自理想化的，数值生成的无摩擦填料。通过解析单个力链，我们量化了力链形状和强度的统计特性，这可能是对本体特性（包括材料稳定性）的关键诊断。这些方法便于不同颗粒系统之间的定量比较，无论它们是实验测量还是数值测量。
英文摘要：
Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.
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