United States

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and di↵raction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.

Powders &amp; Grains 2021

Stress and force measurement uncertainties in 3D granular materials

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

technical paper

Fluid-driven grain flow through a confined channel filled with non-buoyant grains is herein observed to exist in three regimes according to total imposed flow rate. (1) At low imposed flow rates, no grain flow occurs as the fluid stress is insufficient to mobilise the grains and Darcy flow is observed. (2) At a sufficient imposed flow rate, grains begin to flow at the top of the channel with self-similar Gaussian velocity profiles that become faster and encroach deeper into the channel with increased flow rate. (3) At high flow rates, significant grain flow occurs at the base of the channel, distorting the Gaussian profile, resulting in a gradual transition towards a more symmetric, full-channel flow. Each regime, and the transitions between them, is discussed in relation to experimental grain velocity measurements.

From Darcy to Gaussian to fully mobilised grain flow in a confined channel

Granular packings exhibit significant changes in rheological and structural properties when the rotational symmetry of spherical or circular particles is broken. Here, we report on experiments exploring the differences in dynamics of a grain-scale intruder driven through a packing of either disks or pentagons, where the presence of edges and vertices on grains introduces the possibility of rotational constraints at edge-edge contacts, as well as differences in grain-scale dynamics and stress transmission through the granular material. We observe that the intruder’s stick-slip dynamics are comparable between the disk packing near the frictional jamming fraction and the pentagonal packing at significantly lower packing fractions. We connect this stark contrast in packing fraction with the average speed, rotation, and vorticity fields of grains during slip events, finding that rotation of pentagons is limited and the flow of pentagonal grains is largely confined in front of the intruder, whereas disks rotate more on average and circulate around the intruder to fill the open channel behind it. We lastly observe that the packing of pentagons does not transmit stresses as far around the system as does the packing of disks, even at comparable applied forces from the intruder, and that disks transmit back-bending stress chains more frequently and with greater spatial extent than pentagons. Measures of spatial extent of stress transmission collapse when packing fraction is rescaled with respect to the packing fraction of open channel formation, though intruder dynamics do not collapse. Our results indicate that grain-scale rotation constraints significantly modify collective motion of grains on mesoscopic scales and correspondingly enhance resistance to penetration of a local intruder.

Particle dynamics in two-dimensional point-loaded granular media composed of circular or pentagonal grains

Granular asteroids are naturally occurring gravitational aggregates (rubble piles) bound together by gravitational forces. For this reason, it is reasonable to use the theoretical concepts and numerical tools developed for granular media to study them. In this paper, we extend the field of applicability of the Contact Dynamic (CD) method, a class of non-smooth discrete element approach, for the simulation of three-dimensional granular asteroids. The CD method is particularly relevant to address the study of dense granular assemblies of a large number of particles of complex shape and broad particles size distribution since it does not introduces numerical artefacts due to contact stiffness. We describe how the open-source software LMGC90, interfaced with an external library for the calculation of self-gravity, is used to model the accretion process of spherical and irregular polyhedral particles.

A Contact Dynamics open source code for the simulation of granular asteroid with realistic regolith shapes. Application to the accretion process

Experiments on the discharge of a silo with an inclined outlet are performed using flattened seeds in order to evaluate the validity of a previous theoretical formulation developed in our work group [1]. In that description, funnel flow regime is assumed to be based on a free fall parabolic arc. The shape of this arc is described with a parameter which is the only one involved in the flow rate formulation. An experimental analysis of the behavior of this parameter is carried out based on the geometry and shape of the grains within the silo. Also, video analysis of the silo discharge is performed in order to investigate the velocity profiles at the outlet
of the hopper for these non-spherical particles. Experiments are contrasted with analytical predictions derived from the proposed formulation in order to assess and discuss its validity for the case of flattened particles.

Silo fischarge: influence of the particle shape on the velocity profiles

Through numerical simulations, we investigate impact generated seismic wave transmission in gran-ular media under extremely low pressure. This mimics the conditions in the interior of asteroids and other smallplanetary bodies. We find a dependency not only on the overburden pressure on the medium, but also on thevelocity of the impact that generates the wave. This is, at extremely low values of overburden pressure, the wavespeed depends no only on the imposed pressure, but also on the increment in pressure created by the passingof the wave. We study crystalline and random packings and find very similar behaviour though with differentwave speeds as expected. We then relate our results to different mission-related events on asteroids.

Seismic waves in the asteroid environment

In this work, we present an alternative methodology to solve the particle-fluid interaction in the
resolved CFDEM
R coupling framework. This numerical approach consists of coupling a Discrete Element
Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles
in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when
computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction
computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark,
we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the
ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the
new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study
the settling terminal velocity of a sphere under confined conditions.

Modeling particle-fluid interaction in a coupled CFD-DEM framework

We revisit the Critical State (CS) in a dynamic perspective at a mesoscopic scale to enrich the classical view of the critical state as a steady state. The dynamics of mesostructures has been characterized by recording generating and vanishing processes in discrete element simulations. Our results suggest that mesostructures have a short but regular lifespan at the critical state along a biaxial compression loading path.

Dynamic view of critical state regime in granular materials: a mesoscale perspective

We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

We investigate numerically high speed granular flows down an incline and focus our attention on the influence of the restitution coefficient e of binary collisions on the nature of the flow regimes. We show in particular that e plays a major role in rapid flows. Decreasing e leads in general to denser flows but also quicker flows. The increase of the mean flow velocity with decreasing e is explained as the result of the clustering instability which produces a dense and cold core moving very fast as a plug.

Effect of dissipation in rapid-gravitational granular flows

Granular assemblies can experience complex failure patterns along a given loading path, with adistribution of ephemeral inertial events marked by local outbursts in kinetic energy. However, investigatingsuch mechanisms appears to be necessary to understand how a certain failure mode develops in a granularmaterial. Using a discrete element method, this study highlights several microstructure reorganizationsbefore the specimen reaches a proper failure state. Meso structures have proven to be efficient to understand the elementary mechanisms responsible for these outbursts in kinetic energy. Strain–like and stress-like quantities are thus defined at a mesoscale and they are used to characterize the nucleation and propagation of these local microstructural events.

Stress and force measurement uncertainties in 3D granular materials

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From Darcy to Gaussian to fully mobilised grain flow in a confined channel

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