A procedure to join the force and volume ensemble statistical descriptions of granular media

United States

Granular media consist of a large number of discrete particles interacting mostly through contact forces that, being dissipative, jeopardizes a classical statistical equilibrium approach based on energy. Instead, two independent equilibrium statistical descriptions have been proposed: the Volume Ensemble and the Force Network Ensemble. Hereby, we propose a procedure to join them into a single description, using Discrete Element simulations of a granular medium of monodisperse spheres in the limit state of isotropic compression as testing ground. By classifying grains according to the number of faces of the Voronoï cells around them, our analysis establishes an empirical relationship between that number of faces and the number of contacts on the grain. In addition, a linear relationship between the number of faces of each Voronoï cell and the number of elementary cells proposed by T. Aste and T. Di Matteo in 2007 is found. From those two relations, an expression for the total entropy (volumes plus forces) is written in terms of the contact number, an entropy that, when maximized, gives an equation of state connecting angoricity (the temperature-like variable for the force network ensemble) and compactivity (the temperature-like variable for the volume ensemble). So, the procedure establishes a microscopic connection between geometry and mechanics and, constitutes a further step towards building a complete statistical theory for granular media in equilibrium.

Powders &amp; Grains 2021

[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

. Magnetic beads attract each other forming rather stable chains. We consider such chains formed by
magnetic beads and push them into a Hele-Shaw cell either from the boundary or from the center. When such
a chain is pushed into a cavity, it bends and folds spontaneously forming interesting unreported patterns. These
patterns are self-similar and an effective fractal dimension can be defined. As found experimentally and with
numerical simulations, the numbers of beads, loops and contacts follow power laws as a function of packing
fraction and, depending on the injection procedure, even energetically less favorable triangular configurations
can be stabilized

Patterns formed by chains of magnetic beads

A Contact Dynamics algorithm is applied to simulate the failure of 2-dimensional granular steps. Focussing on one single value for both the adhesive force threshold and the contact friction, we track the signature of the failure in the cumulative displacement of the grains. The introduction of a displacement threshold allows for the identification of the onset of a rapid failure and the formation of the corresponding shear band. The latter gives access to an estimation of the failure orientation. 
The robustness of the measure thus performed for one single run is assessed by carrying out a series of 10 additional simulations, showing a fairly reproducible behaviour.

Capturing the failure of a cohesive granular step

Particle segregation in geophysical and industrial granular flows is typically driven by gravity and shear. While gravity-induced segregation is relatively well understood, shear-induced segregation is not. In par- ticular, what controls segregation in the absence of gravity and the interplay between shear- and gravity-driven segregation remain unclear. Here, we explore the shear-induced segregation force on an intruder particle in controlled-velocity granular flows where the shear profile is systematically varied. The shear-induced segrega- tion force is found to be proportional to the shear rate gradient, which effectively pushes the large intruder from lower to higher shear rate regions. A scaling law is developed for the segregation force that is accurate over a wide range of overburden pressures and shear rates, and hence inertial numbers.

Exploring shear-induced segregation in controlled-velocity granular flows

The outflow characteristics of hard grains from containers with narrow basal openings have been extensively studied. Recently, it was shown that soft, low-frictional grains can behave qualitatively different from rigid grains. We compare experimentally the discharge of monodisperse hard spheres, soft spheres and mixtures of both from a quasi-twodimensional (2D) silo. The experiments
demonstrate their remarkable differences in discharge behavior and clogging statistics. The flow field of a 50/50 mixture is already very similar to a pure hard bead system, while its clogging behaviour is fill height dependent, like in a pure low friction soft particle system.

Discharge of soft and hard grains and their mixtures from 2D silos

Swelling of grains due to water absorption is ubiquitous in many natural materials and industrial products. Hence, a thorough understanding of grain swelling is of great scientific importance. An experimental investigation can only provide limited information, whereas great insight could be gained from numerical modelling, rigorous numerical models for describing particle swelling are essential. Thus, the objective of this study is to develop and validate a discrete element method (DEM) model for swelling of grains. A first order kinetic model was introduced to describe the swelling of a single grain, and subsequently implemented into the DEM code LIGGGHTS. Model validation was performed by comparing the time evolution of the expansion of a packed bed made of super absorbent polymer (SAP) particles obtained numerically and experimentally. It was demonstrated that the developed model can accurately predict the bed expansion. The validated model was then used to investigate the effect of material properties on the swelling behaviour using rice and SAP as the model materials. It is shown that the swelling depends significantly on material properties, as expected; the expansion of the powder bed made of rice is much lower than that of SAP. The developed model could be further advanced to study consequences of swelling phenomena in granular materials, such as segregation and heat generation.

DEM modelling of swelling of grains

The paper describes a micromechanical approach that explores the anisotropic nature of the capillary stress tensor and its evolution in pendular granular materials via Discrete Element Modeling (DEM) simulations. Dimensionless parameters are used to address the conditions under which the contribution of capillarity (or cohesive interparticle forces) to the stress transmission within a Representative Elementary Volume (REV) is expected to be considerable. From a series of suction-controlled conventional triaxial tests, numerical results show that the significance of the capillary stress and the relative magnitude of its mean to deviatoric components is directly connected to the characteristic particle size and applied stress. In addition, it is shown that the anisotropic character of the capillary stress tensor intensifies with increasing suction. Furthermore, a simple shear test is conducted at constant mean stress to reveal the development of deviatoric capillary stresses in the absence of any change in mean stress, which cannot be captured by the commonly used Bishop’s stress expression.

Anisotropic nature of the capillary stress tensor

It is well recognised that particle breakage in granular materials is affected by stress level, stress path, initial density, and particle size distribution (PSD), amongst others. Furthermore, it has been shown that breakage has a significant influence on the stress-strain behaviour of soils. This paper compares a commonly used breakage parameter with grading entropy coordinates. Such coordinates enable for the representation of any PSD as a single point in a Cartesian coordinate plane. Hence, the evolution of PSD changes may be easily tracked. This paper aims to demonstrate that grading entropy coordinates are as (or more) effective than other breakage parameters, whilst providing additional insight. On the basis of limited data it is shown that grading entropy coordinates are able to capture the dependence of breakage on stress level, stress path and initial PSD.

Revisiting Hardin’s parameters for the quantification of particle breakage – A statistical entropy approach

Inthepresenceofviscousandcohesiveinteractionsbetweenparticles,agranularflowisgoverned by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, e↵ective viscosities). In this paper, we revisit and extend the scaling arguments used previously for dry cohesionless granular flows and suspensions. We show that the rheology can be in principle described by a single dimensionless control parameter that includes all characteristic times. We also briefly present simulation results for 2D sheared suspensions and 3D wet granular flows where the e↵ective friction coecient and packing fraction are consistently described as functions of this unique control parameter.

Time scales and rheology of visco-cohesive granular flows

Granular-slurry rheology and asphalt compaction

A spiral jet mill was simulated using Discrete Element Method modelling and Computational
Fluid Dynamics. The particle behavior and fluid motion were analysed as a function of hold-up and
grinding pressure. The particle collision energy was predicted to be prevalent along the bed surface and in front
of the grinding jets, as shown through the collision data recorded. The bed itself affects the fluid flow field,
as momentum is transferred to the particles. Increasing the grinding pressure does not result in a proportional
increase in the kinetic energy of the particle system, as the high-pressure jets begin to penetrate the bed with
greater ease. The particle bed moves as ‘plug-flow’, with the layers of the bed closest to the chamber wall.

A procedure to join the force and volume ensemble statistical descriptions of granular media

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A procedure to join the force and volume ensemble statistical descriptions of granular media

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Next from Powders & Grains 2021

Patterns formed by chains of magnetic beads

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