Force cycles and force chains

Abstract

We examine the coevolution of N cycles and force chains as part of a broader study which is designed to quantitatively characterize the role of the laterally supporting contact network to the evolution of force chains. Here, we elucidate the rheological function of these coexisting structures, especially in the lead up to failure. In analogy to force chains, we introduce the concept of force cycles: N cycles whose contacts each bear above average force. We examine their evolution around force chains in a discrete element simulation of a dense granular material under quasistatic biaxial loading. Three-force cycles are shown to be stabilizing structures that inhibit relative particle rotations and provide strong lateral support to force chains. These exhibit distinct behavior from other cycles. Their population decreases rapidly during the initial stages of the strain-hardening regime-a trend that is suddenly interrupted and reversed upon commencement of force chain buckling prior to peak shear stress. Results suggest that the three-force cycles are called upon for reinforcements to ward off failure via shear banding. Ultimately though, the resistance to buckling proves futile; buckling wins under the combined effects of dilatation and increasing compressive load. The sudden increase in three-force cycles may thus be viewed as an indicator of imminent failure via shear bands.

Extraction of force-chain network architecture in granular materials using community detection

“…The values of pressure, which we report in units of the elastic modulus E (recall that the configuration is two-dimensional), are 2.7 × 10 −4 E, 4.1 × 10 −4 E, 6.7 × 10 −4 E, 1.1 × 10 −3 E, 2.2 × 10 −3 E, 3.8 × 10 −3 E, and 5.9 × 10 −3 E. Particles are constrained by vertical walls to prevent deformation due to these pressures from occurring in the direction perpendicular to the loading direction. Such constraints on deformation can influence the shape of force chains, which tend to form in the direction of the major principal stress [6,26,37]. See Refs.…”

“…Network approaches in granular materials have already had several success in describing the dynamics of granular materials. For example, prior studies have investigated spatial patterns in the breaking of edges in a (binary) contact network under shear [25][26][27][28] and the influence of network topology on acoustic propagation [29]. The latter study established the importance of using weighted contact networks to take into account the strength of interparticle forces.…”

Minimum cut and shear bands

“…Not surprisingly, the characterisation of fabric has been the focus of numerous investigations into a broad gamut of particulate matter encountered in both industry and nature (e.g. [1,3,4,5]). Our interest here lies in the evolution of granular fabric as it relates to force transmission in the large strain, so-called critical state regime.…”

“…This regime is especially compelling since the material embodies a unique fabric that is the outcome of a process of self-organization during the sample's preceding loading history (e.g. [4,5]). In the critical state, the material displays a near steady mechanical response at the macroscopic level (i.e.…”

Topological analysis of tapped granular media using persistent homology

“…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. Related with failure is the process of buckling of force chains studied in [13], where the importance of the presence of loops of contacts in the network was revealed. These loops were also proven to be crucial in the stability of other granular systems [14,15].…”