Role of topology in scaling laws for studying mechanics in open-porous solids: Moving beyond classical Gibson-Ashby scaling

Abstract

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.