拓扑在研究开孔固体力学的标度律中的作用：超越经典Gibson-Ashby标度
Role of topology in scaling laws for studying mechanics in open-porous solids: Moving beyond classical Gibson-Ashby scaling
AI总结：
该研究提出拓扑感知框架，分离无序多孔材料模量标度的本征与结构贡献，发现拓扑变化会改变表观标度指数，为理解异常模量标度提供基础。
AI中文摘要：
多孔材料的弹性模量通常用与相对密度相关的幂律标度关系描述，其中标度指数常被用来解释潜在的变形机制。然而，在高度无序的多孔网络中，密度变化通常伴随网络拓扑的改变，这会显著改变表观标度行为。本文提出一种拓扑感知的框架，将本征力学贡献与网络结构的影响分离开来。研究考虑了三个代表性拓扑描述符：平均配位数、承重主链的占比以及载荷路径的曲折度。针对每种情况，推导并分析了对应于表观模量标度指数的密度依赖贡献。结果表明，连通性、固相的力学参与度以及载荷路径效率的变化，均可导致表观标度指数超过与局部变形机制相关的本征指数，这些效应在低相对密度下尤为显著，此时网络拓扑演化最为剧烈。该框架为理解无序多孔材料中异常的模量-密度标度提供了具有物理可解释性的基础，并强调需将拓扑与相对密度一同明确考虑。
英文摘要：
The elastic modulus of porous materials is commonly described using power-law scaling relations with relative density, where the scaling exponent is often interpreted in terms of the underlying deformation mechanism. However, in highly disordered porous networks, changes in density are generally accompanied by changes in network topology, which can substantially modify the apparent scaling behavior. In this paper, we propose a topology-informed framework that separates the intrinsic mechanical contribution from the effects of network structure. Three representative topological descriptors are considered: the mean coordination number, the fraction of the load-bearing backbone, and the tortuosity of the load paths. For each case, the corresponding density-dependent contribution to the apparent modulus-scaling exponent is derived and analyzed. The results show that variations in connectivity, mechanical participation of the solid phase, and load-path efficiency can all lead to apparent scaling exponents exceeding the intrinsic exponent associated with the local deformation mechanism. These effects are particularly pronounced at low relative densities, where network topology evolves most strongly. The framework provides a physically interpretable basis for understanding anomalous modulus-density scaling in disordered porous materials and highlights the need to consider topology explicitly alongside relative density.
