Taxonomy of granular rheology from grain property networks

Abstract

We construct complex networks from symbolic time series of particle properties within a dense quasistatically deforming granular assembly subjected to biaxial compression. The structure of the resulting networks embodies the evolving structural rearrangements in the granular material, in both contact forces and contact topologies. These rearrangements are usefully summarized through standard network statistics as well as building block motifs and community structures. Dense granular media respond to applied compression and shear by a process of self-organization to form two cooperatively evolving structures comprising the major load-bearing columnlike force chains, and the lateral trusslike three-cycle triangle topologies. We construct networks summarizing their individual evolution based on relationships between symbolic time series indicating a particle's chronological force chain and three-cycle membership histories. We test which particle membership histories are similar with respect to each other through the information theory-based measure of Hamming distance. The complex networks summarize the essential structural rearrangements, while the community structures within the networks partition the material into distinct zones of deformation, including interlacing subregions of failure inside the shear band. The taxonomy of granular rheology at the mesoscopic scale distills the inelastic structural rearrangements throughout loading history down to its core elements, and should lay bare an objective and physics-based formalism for thermodynamic internal variables and associated evolution laws.

Understanding multi-scale structural evolution in granular systems through gMEMS

“…Here, with respect to the dilatative 7-cycle structures we are finding a similar number of communities -three have significantly higher membership than the others -and the spatial location of the grains in each communities are also codifying the sample into stable regions and more clamourous areas. As seen in the 3-cycle networks of [8], parts of the shear band were predominately jammed; here community 6 shows that parts of the shear band are predominately unjammed (i.e., tend to have consistently high porosity). This relative invariance in taxonomy size across different sensors suggests that internal variable theory formalisms towards a constitutive law may only require a small number of variables to succinctly abbreviate the description of a system with a vast number of individual degrees of freedom.…”

“…In earlier work [8], we have presented the results of codifying granular material's response to applied loads in terms of the structural sensors measuring force chain membership, 3-cycle membership and conjoined evolution of these two structures. We have also introduced the analysis of networks based on displacement and rotational measurements elsewhere [6,9].…”

“…In [8], we reported that with respect to force chain membership this DEM sample can be partitioned into 3 communities consisting of (i) a persistent strong network (ii) a persistent weak network and (iii) the shear band. By considering a conjoined force chain and 3-cycle membership time sensor we found 5 communities, two of which partitioned the shear band into two interlacing zones intimating the jamming-unjamming physics present.…”

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.…”

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].…”