Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses

Dynamic imaging of force chains in 3D granular media

Granular media constitute the most abundant form of solid matter on Earth and beyond. When external forces are applied to a granular medium, the forces are transmitted through it via chains of contacts among grains-force chains. Understanding the spatial structure and temporal evolution of force chains constitutes a fundamental goal of granular mechanics. Here, we introduce an experimental technique, interference optical projection tomography, to study force chains in three-dimensional (3D) granular packs under triaxial shear loads and illustrate the technique with random assemblies of spheres and icosahedra. We find that, in response to an increasing vertical load, the pack of spheres forms intensifying vertical force chains, while the pack of icosahedra forms more interconnected force-chain networks. This provides microscopic insights into why particles with more angularity are more resistant to shear failure-the interconnected force-chain network is stronger (that is, more resilient to topological collapse) than the isolated force chains in round particles. The longer force chains with less branching in the pack of round particles are more likely to buckle, which leads to the macroscopic failure of the pack. This work paves the way for understanding the grain-scale underpinning of localized failure of 3D granular media, such as shear localization in landslides and stick-slip frictional motion in tectonic and induced earthquakes.

X-ray 3D imaging-based microunderstanding of granular mixtures: Stiffness enhancement by adding small fractions of soft particles

This research focuses on performing ultrasound propagation measurements and micro-X-ray computed tomography (µXRCT) imaging on prestressed granular packings prepared with biphasic mixtures of monodisperse glass and rubber particles at different compositions/fractions. Ultrasound experiments employing piezoelectric transducers, mounted in an oedometric cell (complementing earlier triaxial cell experiments), are used to excite and detect longitudinal ultrasound waves through randomly prepared mixtures of monodisperse stiff/soft particles. While the fraction of the soft particles is increasing linearly from zero, the effective macroscopic stiffness of the granular packings transits nonlinearly and nonmonotonically toward the soft limit, remarkably via an interesting stiffer regime for small rubber fractions between 0.1 ≲ ν ≲ 0.2. The contact network of dense packings, as accessed from µXRCT, plays a key role in understanding this phenomenon, considering the structure of the network, the chain length, the grain contacts, and the particle coordination. While the maximum stiffness is due to surprisingly shortened chains, the sudden drop in elastic stiffness of the mixture packings, at ν ≈ 0.4, is associated with chains of particles that include both glass and rubber particles (soft chains); for ν ≲ 0.3, the dominant chains include only glass particles (hard chains). At the drop, ν ≈ 0.4, the coordination number of glass and rubber networks is approximately four and three, respectively, i.e., neither of the networks are jammed, and the chains need to include particles from another species to propagate information.

Force inference in granular materials: Uncertainty analysis and application to three-dimensional experiment design

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be "recovered" through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.