Complex networks in confined comminution

Abstract

The physical process of confined comminution is investigated within the framework of complex networks. We first characterize the topology of the unweighted contact networks as generated by the confined comminution process. We find this process gives rise to an ultimate contact network which exhibits a scale-free degree distribution and small world properties. In particular, if viewed in the context of networks through which information travels along shortest paths, we find that the global average of the node vulnerability decreases as the comminution process continues, with individual node vulnerability correlating with grain size. A possible application to the design of synthetic networks (e.g., sensor networks) is highlighted. Next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks, where each link is weighted by the inverse magnitude of the normal force acting at the associated contact. We find that the strong forces (i.e., force chains) are transmitted along pathways in the network which are mainly following shortest-path routing protocols, as typically found, for example, in communication systems. Motivated by our earlier studies of the building blocks for self-organization in dense granular systems, we also explore the properties of the minimal contact cycles. The distribution of the contact strain energy intensity of 4-cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale-free distribution with infinite variance, thereby suggesting that 4-cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking.

Asymptotic behaviour of granular materials

“…A number of authors argued that the existence of asymptotic states is directly linked to particle crushing [2,7,8,[43][44][45]65]. Using DEM simulations, the existence of normal compression lines was explained by particle crushing in references [2,7,8,44,65].…”

“…Using DEM simulations, the existence of normal compression lines was explained by particle crushing in references [2,7,8,44,65]. Cheng et al [7,8] predicted both critical states and normal compression lines, using the same parameter sets, creating a more complete picture of the granular material behaviour.…”

A fractal model of contact force distribution and the unified coordination distribution for crushable granular materials under confined compression

“…A systematic review of the DEM applications and findings is presented by Zhu et al [28] and will not be repeated here. The DEM is a more robust tool to capture the contact intensity and visualize the contact network for an individual particle [11][12][13][14][29][30][31][32][33][34][35], particularly when the fracture process is considered [20,[36][37][38][39]]. In addition, particle crushing makes a more complicated and heterogeneous contact system than a simple system under loading.…”

“…1 illustrate the response to effective crushing during confined uniaxial compression in our study using the DEM. Over the past two decades, DEM has been used to investigate crushable particles through two alternative approaches: replacing the breaking particles with new smaller fragments or using a bonded agglomerate [15,20,[37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Different numerical models with their respective advantages and limitations are considered in terms of time efficiency, physical conservation and computing accuracy.…”

Topological analysis of tapped granular media using persistent homology

“…The contact network has been used to study a large variety of global properties of disordered media [6][7][8]. This approach can be also used to analyze the evolution of granular media in dynamic situations [9][10][11]. In [12] the topological properties of the network were related to the * sardanza@unav.es † iker@unav.es process of strain localization, which leads to shear banding and material failure.…”