Influence of network topology on sound propagation in granular materials

Abstract

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves. During the past 15 years, techniques from areas of physics such as statistical mechanics and nonlinear dynamics have been used to make important advances in studying networks across myriad disciplines [1]. Conversely, the perspective of networks can also play important roles in physical problems, as there is a large class of heterogeneous systems such as foams, emulsions, and granular materials [2,3] for which the connectivity of the constituent elements is an important factor in the deviation of their behavior from continuum models. In fact, the discontinuous nature of granular materials led to the early idea of a fabric structure governing the anisotropic behavior of such materials [4][5][6].We investigate whether studying the rich and complex dynamics of granular materials [7] using network analysis can provide new insights into the underlying physics. This treatment is a natural one, because granular materials can be represented as spatially-embedded networks [8] composed of nodes (particles) and edges (contacts between particles) with definite locations in Euclidean space [9,10]. In Fig. 1, we show a quasi-two-dimensional (quasi-2D) granular system composed of photoelastic disks that permits the determination of both the contact network and the interparticle forces. The forces between particles in these systems are non-homogeneous, and they form a network of chain-like structures that span the system (see Fig. 1B). This force chain network has the same topology as the contact network but contains edges that are weighted...

Stretch-induced network reconfiguration of collagen fibres in the human facet capsular ligament

“…Community detection techniques are highly applicable to studying properties of non-biological materials [24][25][26] and their use may be expanded in the future to quantitatively investigate physical interactions between material components at intermediate length scales and over time [59][60][61]. As such, this study provides an advanced framework with quantitative formalisms to investigate dynamic network reorganization that may be applicable to a wide range of complex biological and non-biological materials whose structure may affect bulk material properties and function.…”

“…System components are represented as network nodes and their relationships with one another are represented as network edges [20,21]. In many biological [19,22,23] and material [24,25] systems, this formalism reveals important organizational changes that impact the system's underlying structure and resulting function. For example, network-based tools known as community detection techniques can be used to characterize the presence and organization of local geographical domains in non-biological materials [24][25][26] which are referred to as network communities or modules.…”

“…For example, network-based tools known as community detection techniques can be used to characterize the presence and organization of local geographical domains in non-biological materials [24][25][26] which are referred to as network communities or modules. These domains constrain sensitivity to mechanical perturbations in the form of acoustic signals [24] and track alterations in material topology as a function of applied force (pressure) [25], indicating their broad sensitivity to material microstructure.…”

Granular Impact

“…as used by a number of researchers [21,[23][24][25][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. The important feature associated with particles made from a photoelastic material is that they yield particle-scale force information.…”

Tapped granular packings described as complex networks

“…At this point, let us note that any static granular system can be considered in terms of nodes (the grains) and edges (the contacts between grains). This approach has been recently applied to address a wide variety of granular phenomena such as porosity [21], force distribution [22], rheology [23], signal propagation [24] and jamming transition [25,26].…”