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Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities of K rapidly deviate from predictions standing on a small-strain framework or the, so-called, Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution of K as a function of the sample’s solid fraction and a reference state as the applied pressure P-&gt; 0. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction on K’s evolution and how our model easily adapts to such a mechanical constraint.

Powders &amp; Grains 2021

Bulk modulus of soft particle assemblies under compression

[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.

Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities of K rapidly deviate from predictions standing on a small-strain framework or the, so-called, Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution of K as a function of the sample’s solid fraction and a reference state as the applied pressure P-> 0. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction on K’s evolution and how our model easily adapts to such a mechanical constraint.

poster

Earthquakes happen with frictional sliding, by releasing all the stresses accumulated in the pre-stressed surrounding medium. The geological fault gouge, coming from the wear of previous slips, acts on friction stability and plays a key role in this sudden energy release. A large part of slip mechanisms is influenced, if not controlled, by the characteristics and environment of this tribological “third body”. A 2D granular fault (mm scale) is implemented with Discrete Element Modelling (DEM). A displacement-driven model with dry contact is studied to observe kinematics and properties of the slipping zone. Changing the percentage of infill material (as matrix particles) within the granular media modifies the kinematic of the gouge and Riedel shears evolution. Low-angle Riedel shear bands are mostly observed. Their number increases with the inter-particle friction coefficient (which also influences shear bands formation in their orientation angle) and reduces with an increase in shear modulus.

Shear bands in dense fault gouge

During industrial air preparation, one of the most important issues is the proper moisture content. In vehicle brake systems, compressed air is commonly used, where condensate in the system can lead to serious problems as corrosion, frosting, etc. For avoiding malfunctions, the relative humidity of the media must decrease to 20-40%, by adsorbing its moisture content. To achieve this, air dryer units filled with desiccant granular media is commonly used in railway industry. The compressed air flows through the dryer, thus the particles can bind the water vapour. If the packing density of the desiccant can increase, the efficiency of the dryer can improve. In this paper an interesting method for container filling, the snowstorm technique was investigated and optimized by applying discrete element method. Essence of the device is a rod system placed below the filler bin, which ensures even distribution of the particles. By the numerical analysis it was revealed, the particles’ lateral velocity is increased because of the snowstorm system, but with non-optimal arrangement, the particle flow can be significantly blocked. Based on our systematic analysis, optimal geometry of the particle distribution system was found, which ensures settling more particles by 9.5% into the dryer reservoir.

Numerical investigation of snowstorm filling

The shape of the particles and local friction, separately, are known to strongly affect the macroscopic properties of an assembly of grains. But the combined effects of these two parameters still remain poorly described. By means of extensive two dimensional contact dynamics simulations, we perform a systematic analysis of the interplay between friction and shape on strength properties of granular systems.
The shape of the particles is varied from disks to triangles, while the friction is varied from 0 to 0.7. We find that the macroscopic friction first increases with angularity, but it may decline (for low friction values), saturate (for intermediates friction values), or continue to increase (for large friction values) for the most angular shapes. In other words, the effect of the particle's angularity on the shear strength depends on the level of sliding friction. In contrast, the effect of local friction on the shear strength does not depend on the specific properties of shape. The results presented here highlight the subtle coupling existing between shape and friction effects.

Shape or friction? Which of these characteristics drives the shear strength in granular systems?

We investigate numerically the statistics of the stresses, defined for cells - the irreducible loops surrounded by particles in contact - in two-dimensional granular solids and the relation between these cell stresses and cell structures. We prepared a number of mechanically stable granular assemblies at various packing fractions and mean coordination numbers, and measured the stress statistics on each cell. We find the following. (1) The mean cell stress agrees with the bulk external pressure; (2) the probability density function of the normalised cell stress ratio collapses into a master curve; (3) the mean stress ratio increases with increasing intergranular friction; (4) the mean stress ratio per cell order decreases with increasing cell order because of their reduced stability; (5) the maximum cell stress direction correlates well with the cell’s long axis. These results are strong evidence that the cell structure and the stress field self-organise together and reveal the co-evolving correlations between the two.

Statistical properties of cell stresses in 2D granular solids

We present a novel numerical model allowing to take the best part of continuum-based and discrete modelling in a single framework. This model is applied to the reproduction of laboratory earthquakes in a high-pressure triaxial cell. It allows to represent most of the relevant phenomena at stake, including elastic stress build-up during loading, fast and slow sliding events, seismic waves emission in the surrounding elastic medium and evolution of fault gouge on the sliding interface. We review here some illustrative results obtained with this model and propose further research avenues.

Reproducing laboratory earthquakes with a discrete-continuum model

The relaxation from a non-equilibrium state to the equilibrium depends on the methodologies and initial conditions. To investigate the microscopic mechanisms of equilibration systematically, we focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous expansion of the simple hard disk systems. Large scale simulations by event-driven molecular dynamics revealed that an anomalous slow equilibration toward the liquid states emerges when starting from the co-existence phase. The origin of the slow decay mechanism is investigated using the probability distribution of local density and orientational order parameter. Their inhomogeneities seem to cause the anomalous slow equilibration.

Non-equilibrium response and slow equilibration in hard disk systems

We study the evolution of shear bands in granular media subjected to very large deformations using the orthogonal cutting geometry. We perform our cutting experiments on Cauvery Delta sand with d50 of 0.45mm. We also capture images of the cutting process which allows us to perform a PIV analysis to determine the deformation in material around the cutting tool. In our experiments we observe that the dynamic angle of repose of the pile that forms in-front of the tool as cutting progresses, approaches the critical state friction angle of the material. We observe a flow bifurcation around the tool as the material begins to slip along planes which are oriented at an angle of π/4 − θ/2, θ being the dynamic angle of repose, to the cutting direction. This leads to formation of shear bands/velocity jumps which contain around 14 particles. A measurement of dilation angle within the shear bands indicate that material is in a critical state of deformation.

An experimental study on shear bands in sand using the orthogonal cutting setup

Particle Size Distribution (PSD) is one of the prime guiding factors of granular media response. Degradation via weathering is a process, which brings about a gradual shift in the PSD. In nature, chemically sensitive material like calcite undergoes chemo-mechanical degradation bringing about variations in their behaviour. In the present study, an experimental investigation is carried out to get insight into the mechanical response during the coupled chemo-mechanical process. The experiments were carried out at two different rates of dissolutions in a custom made 1D compression mould. From the experiments, it is clear that the higher rate of dissolution reduces the lateral earth pressure more than the lower rate. Discrete Element Method (DEM) analyses the micromechanical process behind the observed response from experiments. The results showed a reduction in lateral stress as soon as the dissolution starts. DEM analysis confirms the competing mechanism between grain size reduction and grain rearrangement as the guiding element for the granular media response.

Exploring chemo-mechanics of granular material using DEM

This study aims to assess and analyse the patterns of segregation and stratification in pouring heaps of granular mixtures composed by binary sized and uniformly shaped particles. We present 2D and 3D simulations which respectively build deposits of poured disks and spheres by means of a discrete-element approach known as contact dynamics (CD). In order to identify preferable conditions for segregation and stratification, we try several deposition scenarios varying the pouring flow rate, injection height, heap’s width and mass ratio between large and small grains in our binary samples. Although some authors assert that shape dispersity might not be necessary to obtain stratification, the phenomenon seems hard to seize with mono-shaped granular media as it appears to require a close control on pouring conditions. The introduction of our DEM models and statistical analysis intend to provide examples of what could constitute efficient numerical tools to study the remaining open problems related to heap segregation patterns prediction.

DEM modeling of segregation and stratification in pouring heaps of bidispersed mixtures of rounded particles

In this work, we explore the influence of the grain size distribution (GSD) on density, connectivity and internal forces distributions, for both 2D and 3D granular packings built mechanically. For power law GSDs, we show that there is an exponent for which density and connectivity are optimized, and this exponent is close to those that characterize other well known GSDs such as the Fuller and Thompson distribution and the Appollonian packing. In addition, we studied the distributions of normal forces, finding that these can be well described by a power-law tail, specially for the GSDs with large size span. These results highlight the role of the GSD on internal structure and suggest important consequences on macroscopic properties.

Bulk modulus of soft particle assemblies under compression

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