@article {663, title = {Grains3D, a flexible DEM approach for particles of arbitrary convex shape{\textemdash}Part III: extension to non-convex particles modelled as glued convex particles}, journal = {Computational Particle Mechanics}, volume = {106}, year = {2019}, month = {Jan-2019}, pages = {55 - 84}, abstract = {

Large-scale numerical simulation using the discrete element method (DEM) contributes to improving our understanding of granular flow dynamics involved in many industrial processes and geophysical flows. In industry, it leads to an enhanced design and an overall optimization of the corresponding equipment and process. Most of the DEM simulations in the literature have been performed using spherical particles. A limited number of studies dealt with non-spherical particles, even less with non-convex particles. Even convex bodies do not always represent the real shape of certain particles. In fact, more complex-shaped particles are found in many industrial applications, for example, catalytic pellets in chemical reactors or crushed glass debris in recycling processes. In Grains3D-Part I (Wachs et al. in Powder Technol 224:374-389, 2012), we addressed the problem of convex shape in granular simulations, while in Grains3D-Part II (Rakotonirina and Wachs in Powder Technol 324:18-35, 2018), we suggested a simple though efficient parallel strategy to compute systems with up to a few hundreds of millions of particles. The aim of the present study is to extend even further the modelling capabilities of Grains3D towards non-convex shapes, as a tool to examine the flow dynamics of granular media made of non-convex particles. Our strategy is based on decomposing a non-convex-shaped particle into a set of convex bodies, called elementary components. We call our method glued or clumped convex method, as an extension of the popular glued sphere method. Essentially, a non-convex particle is constructed as a cluster of convex particles, called elementary components. At the level of these elementary components of a glued convex particle, we employ the same contact detection strategy based on a Gilbert-Johnson-Keerthi algorithm and a linked-cell spatial sorting that accelerates the resolution of the contact, that we introduced in [39]. Our glued convex model is implemented as a new module of our code Grains3D and is therefore automatically fully parallel. We illustrate the new modelling capabilities of Grains3D in two test cases: (1) the filling of a container and (2) the flow dynamics in a rotating drum.

}, keywords = {Granular flow; Discrete element method; Non-convex shape; GJK algorithm; Glued convex}, issn = {2196-4378}, doi = {10.1007/s40571-018-0198-3}, url = {http://link.springer.com/10.1007/s40571-018-0198-3}, author = {Rakotonirina, Andriarimina Daniel and Jean-Yves Delenne and Farhang Radja{\"\i} and Wachs, Anthony} } @article {667, title = {Parallel implicit contact algorithm for soft particle systems}, journal = {Computer Physics Communications}, volume = {237}, year = {2019}, month = {Apr-01-2019}, pages = {17 - 25}, abstract = {

This paper presents a numerical technique to model soft particle materials in which the particles can undergo large deformations. It combines an implicit finite strain formalism of the Material Point Method and the Contact Dynamics method. In this framework, the large deformations of individual particles as well as their collective interactions are treated consistently. In order to reduce the computational cost, this method is parallelised using the Message Passing Interface (MPI) strategy. Using this approach, we investigate the uniaxial compaction of 2D packings composed of particles governed by a Neo-Hookean material behaviour. We consider compressibility rates ranging from fully compressible to incompressible particles. The packing deformation mechanism is a combination of both particle rearrangements and large deformations, and leads to high packing fractions beyond the jamming state. We show that the packing strength declines when the particle compressibility decreases, and the packing can deform considerably. We also discuss the evolution of the connectivity of the particles and particle deformation distributions in the packing. (C) 2018 Elsevier B.V. All rights reserved.

}, issn = {00104655}, doi = {10.1016/j.cpc.2018.10.030}, url = {https://linkinghub.elsevier.com/retrieve/pii/S0010465518303904}, author = {Saeid Nezamabadi and Frank, Xavier and Jean-Yves Delenne and Julien Averseng and Farhang Radja{\"\i}} } @article {533, title = {Mechanical strength of wet particle agglomerates}, journal = {Mechanics Research Communications}, volume = {92}, year = {2018}, month = {Sep-2018}, pages = {1 - 7}, abstract = {

Using particle dynamics simulations, we investigate the strength and microstructure of agglomerates of wet frictional particles subjected to axial compression. The numerical model accounts for the cohesive and viscous effects of the binding liquid up to a debonding distance with the liquid assumed to be distributed homogeneously inside the agglomerate. We show that wet agglomerates undergo plastic deformation due to the rearrangements of primary particles during compression. The compressive strength is thus characterized by the plastic threshold before the onset of failure by the irreversible loss of wet contacts between primary particles. We find that the agglomerate plastic threshold is proportional to the characteristic cohesive stress defined from the liquid-vapor surface tension and the mean diameter of primary particles, with a prefactor that is a nearly linear function of the debonding distance and increases with size span. We analyze the agglomerate microstructure and, considering only the cohesive capillary forces at all bonds between primary particles, we propose an expression of the plastic strength as a function of the texture parameters such as the wet coordination number and packing fraction. This expression is shown to be consistent with our simulations up to a multiplicative factor reflecting the distribution of the capillary bridges. (C) 2018 Published by Elsevier Ltd.

Fig. 1. Schematic drawing of the forces acting on particle i by a contacting particle j{\textellipsis}

Fig. 2. Schematic representation of diametrical compression test (a), and snapshots of{\textellipsis}

Fig. 3. Snapshot of a granule under diametrical compression for α=1

Fig. 4. Vertical strength σzz normalized by the reference stress σc for different{\textellipsis}

Fig. 5. Normalized plastic strength of the granule for several values of the debonding{\textellipsis}

Fig. 6. Normalized plastic strength σp/σc of the granules for different values of the{\textellipsis}

Fig. 7. The initial wet coordination number Z0 of the granules for different values of{\textellipsis}

Fig. 8. The prefactor η in Eq

Fig. 9. The ZΦs in Eq

}, issn = {00936413}, doi = {10.1016/j.mechrescom.2018.07.003}, url = {https://www-sciencedirect-com.libproxy.mit.edu/science/article/pii/S0093641318301216}, author = {Vo, Thanh-Trung and Patrick Mutabaruka and Saeid Nezamabadi and Jean-Yves Delenne and Izard, Edouard and Roland Jean-Marc Pellenq and Farhang Radja{\"\i}} } @article {627, title = {Multiscale modeling for bioresources and bioproducts}, journal = {Innovative Food Science \& Emerging Technologies}, volume = {46}, year = {2018}, month = {Avr-2018}, pages = {41 - 53}, abstract = {

Designing and processing complex matter and materials are key objectives of bioresource and bioproduct research. Modeling approaches targeting such systems have to account for their two main sources of complexity: their intrinsic multi-scale nature; and the variability and heterogeneity inherent to all living systems. Here we provide insight into methods developed at the Food \& Bioproduct Engineering division (CEPIA) of the French National Institute of Agricultural Research (INRA). This brief survey focuses on innovative research lines that tackle complexity by mobilizing different approaches with complementary objectives. On one hand cognitive approaches aim to uncover the basic mechanisms and laws underlying the emerging collective properties and macroscopic behavior of soft-matter and granular systems, using numerical and experimental methods borrowed from physics and mechanics. The corresponding case studies are dedicated to the structuring and phase behavior of biopolymers, powders and granular materials, and to the evolution of these structures caused by external constraints. On the other hand machine learning approaches can deal with process optimizations and outcome predictions by extracting useful information and correlations from huge datasets built from experiments at different length scales and in heterogeneous conditions. These predictive methods are illustrated in the context of cheese ripening, grape maturity prediction and bacterial production.

}, issn = {14668564}, doi = {10.1016/j.ifset.2017.09.015}, url = {https://linkinghub.elsevier.com/retrieve/pii/S1466856417302230}, author = {Barnabe, M. and Blanc, Nicolas and Chabin, T. and Jean-Yves Delenne and Duri, A. and Frank, Xavier and Hugouvieux, V. and Lutton, E. and Mabille, F. and Saeid Nezamabadi and Perrot, N. and Farhang Radja{\"\i} and Ruiz, T. and Tonda, A.} } @article {633, title = {Two-dimensional numerical simulation of chimney fluidization in a granular medium using a combination of discrete element and lattice Boltzmann methods}, journal = {Physical Review E}, volume = {97}, year = {2018}, month = {May-10-2018}, pages = { Article Number 052902 }, abstract = {

We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.

}, issn = {2470-0045}, doi = {10.1103/PhysRevE.97.052902}, url = {https://link.aps.org/doi/10.1103/PhysRevE.97.052902}, author = {Jeff Ngoma and Pierre Philippe and St{\'e}phane Bonelli and Farhang Radja{\"\i} and Jean-Yves Delenne} } @article {600, title = {Cohesive strength of iron ore granules}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 08020}, abstract = {

We present an experimental and numerical investigation of the mechanical strength of crude iron ore (Hematite) granules in which capillary bonds between primary particles are the source of internal cohesion. The strength is measured by subjecting the granules to vertical compression between two plates. We show that the behavior of the granules is ductile with a well-defined plastic threshold which increases with the amount of water. It is found that the compressive strength scales with capillary cohesion with a pre-factor that is nearly independent of size polydispersity for the investigated range of parameters but increases with friction coefficient between primary particles. This weak dependence may be attributed to the class of fine particles which, due to their large number, behaves as a cohesive matrix that controls the strength of the granule.

}, doi = {10.1051/epjconf/201714008020}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714008020}, author = {Contreras, Rafael Jaimes and Berger, Nicolas and Izard, Edouard and Douce, Jean-Fran{\c c}ois and Koltsov, Alexey and Jean-Yves Delenne and Emilien Az{\'e}ma and Saeid Nezamabadi and van Loo, Fr{\'e}d{\'e}ric and Roland Jean-Marc Pellenq and Farhang Radja{\"\i}}, editor = {Luding, S.} } @article {602, title = {Compaction of granular materials composed of deformable particles}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 05013}, abstract = {

In soft particle materials such as metallic powders the particles can undergo large deformations without rupture. The large elastic or plastic deformations of the particles are expected to strongly affect the mechanical properties of these materials compared to hard particle materials more often considered in research on granular materials. Herein, two numerical approaches are proposed for the simulation of soft granular systems: (i) an implicit formulation of the Material Point Method (MPM) combined with the Contact Dynamics (CD) method to deal with contact interactions, and (i) Bonded Particle Model (BPM), in which each deformable particle is modeled as an aggregate of rigid primary particles using the CD method. These two approaches allow us to simulate the compaction of an assembly of elastic or plastic particles. By analyzing the uniaxial compaction of 2D soft particle packings, we investigate the effects of particle shape change on the stress-strain relationship and volume change behavior as well as the evolution of the microstructure.

}, doi = {10.1051/epjconf/201714005013}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714005013}, author = {Thanh Hai Nguyen and Saeid Nezamabadi and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Luding, S.} } @article {601, title = {Effect of particle size distribution on 3D packings of spherical particles}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 02030}, abstract = {

We use molecular dynamics simulations of frictionless spherical particles to investigate a class of polydisperse granular materials in which the particle size distribution is uniform in particle volumes. The particles are assembled in a box by uniaxial compaction under the action of a constant stress. Due to the absence of friction and the nature of size distribution, the generated packings have the highest packing fraction at a given size span, defined as the ratio of the largest size to the smallest size. We find that, up to = 5, the packing fraction is a nearly linear function of . While the coordination number is nearly constant due to the isostatic nature of the packings, we show that the connectivity of the particles evolves with . In particular, the proportion of particles with 4 contacts represents the largest proportion of particles mostly of small size. We argue that this particular class of particles occurs as a result of the high stability of local configurations in which a small particle is stuck by four larger particles.

}, doi = {10.1051/epjconf/201714002030}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714002030}, author = {Taiebat, Mahdi and Patrick Mutabaruka and Roland Jean-Marc Pellenq and Farhang Radja{\"\i}}, editor = {Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {606, title = {Modeling root growth in granular soils: effects of root stiffness and packing fraction}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 14013}, abstract = {

We use molecular dynamics simulations to investigate the effects of root bending stiffness and packing fraction on the path followed by a growing root in 2D packings of grains representing a soil. The root is modeled as a chain of elements that can grow in length and change their direction depending on the forces exerted by soil grains. We show that the root shape is mainly controlled by the bending stiffness of its apex. At low stiffness, the root randomly explores the pore space whereas at sufficiently high stiffness, of the order of soil hardness multiplied by mean grain size, the root follows a straight path across the soil. Between these two limits, the root shape can be characterized by the standard deviation of its re-directions at the scale of soil grains. We find that this shape parameter varies as a power-law function of the normalized bending stiffness.

}, doi = {10.1051/epjconf/201714014013}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714014013}, author = {Fakih, Mahmoud and Jean-Yves Delenne and Farhang Radja{\"\i} and Fourcaud, Thierry}, editor = {Saeid Nezamabadi and Luding, S.} } @article {265, title = {Modeling soft granular materials}, journal = {Granular Matter}, volume = {19}, year = {2017}, month = {Jun-17-2017}, pages = {Article Number: 8}, abstract = {

Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.

}, issn = {1434-5021}, doi = {10.1007/s10035-016-0689-y}, author = {Saeid Nezamabadi and Thanh Hai Nguyen and Jean-Yves Delenne and Farhang Radja{\"\i}} } @proceedings {336, title = {Modelling Transient Dynamics of Granular Slopes: MPM and DEM}, journal = {PROCEEDINGS OF THE 1ST INTERNATIONAL CONFERENCE ON THE MATERIAL POINT METHOD (MPM 2017) Book Series: Procedia Engineering }, volume = {175}, year = {2017}, month = {Jul-17-2017}, pages = {94 - 101}, publisher = {Elsevier Ltd.}, address = {JAN 10-13, 2017, Delft, NETHERLANDS}, abstract = {

Transient granular flows, such as rock falls, debris flows, and aerial and submarine avalanches, occur very often in nature. In the geotechnical context, transient movements of large granular slopes are a substantial factor of risk due to their destructive force and the transformations the y may produce in the landscape. This paper investigates the ability of MPM, a continuum approach, to reproduce the evolution of a granular slope destabilised by an external energy source. In particular, a central issue is whether the power-law dependence of run-out distance and time observed with respect to the initial geometry or energy can be reproduced by a simple Mohr-Coulomb plastic behaviour. The effect of base friction on the run-out kinematics is studied by comparing the data obtained from the DEM and MPM simulations. The mechanism of energy dissipation is primarily through friction and the MPM is able to predict the run-out response in good agreement with the DEM simulations. At very low excitation energies, the DEM simulations show longer run-out in comparison to the MPM due to local destabilization at the flow front. At low input energies, a larger fraction of the energy is consumed in the destabilisation process, hence the amount energy available for flow is less. However, at higher input energy, where most of the energy is dissipated during the spreading phase, the run-out distance has a weak dependence on the distribution of velocity in the granular mass.

}, issn = {18777058}, doi = {10.1016/j.proeng.2017.01.032}, author = {Krishna Kumar and Kenichi Soga and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Rohe, A and Kenichi Soga and Teunissen, H} } @proceedings {337, title = {MPM with Frictional Contact for Application to Soft Particulate Materials}, journal = {PROCEEDINGS OF THE 1ST INTERNATIONAL CONFERENCE ON THE MATERIAL POINT METHOD (MPM 2017) Book Series: Procedia Engineering }, volume = {175}, year = {2017}, month = {Mar-23-2017}, pages = {141 - 147}, publisher = {Elsevier Ltd.}, address = {JAN 10-13, 2017, Delft, NETHERLANDS}, abstract = {

Soft particle materials are composed of discrete particles that can undergo large deformations without rupture. Most food products, many powders, colloidal pastes, vesicles and biological cells are soft particle systems. In order to model such materials, we present an efficient numerical approach combining an implicit formulation of the Material Point Method (MPM) and Contact Dynamics (CD) method. The MPM deals with bulk variables of an individual particle by discretizing it as a collection of material points, whereas the CD allows for the treatment of frictional contacts between particles. This model is applied for the simulation of the uniaxial compression of 2D soft-particle packings. The compaction is a nonlinear process in which new contacts are formed between particles and the contact areas increase. The change of particle shapes allows these materials to reach high packing fraction. We find that the contact specific surface, the orientation anisotropy and the aspect ratio of particles increase as a function of the packing fraction but at different rates. We also evidence the effect of friction, which favors strong stress chains and thus the elongation of particles, leading to larger values of the orientation anisotropy and the aspect ratio at a given level of packing fraction as compared to a frictionless particle packing.

}, issn = {18777058}, doi = {10.1016/j.proeng.2017.01.044}, author = {Saeid Nezamabadi and Thanh Hai Nguyen and Jean-Yves Delenne and Julien Averseng and Frank, Xavier and Farhang Radja{\"\i}}, editor = {Rohe, A and Kenichi Soga and Teunissen, H} } @article {623, title = {Nano-granular texture of cement hydrates}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 15027}, abstract = {

Mechanical behavior of concrete crucially depends on cement hydrates, the \“glue\” of cement. The design of high performance and more environmentally friendly cements demands a deeper understanding of the formation of the multiscale structure of cement hydrates, when they precipitate and densify. We investigate the precipitation and setting of nano-grains of cement hydrates using a combination of Monte Carlo and Molecular Dynamics numerical simulations and study their texture from nano up to the micron scale. We characterize the texture of cement hydrates using the local volume fraction distribution, the pore size distribution, the scattering intensity and the chord length distribution and we compare them with experiments. Our nano-granular model provides cement structure with realistic texture and mechanics and can be further used to investigate degradation mechanisms.

}, doi = {10.1051/epjconf/201714015027}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714015027}, author = {Katerina Ioannidou and Franz-Josef Ulm and Pierre E. Levitz and Emanuela Del Gado and Roland Jean-Marc Pellenq}, editor = {Farhang Radja{\"\i} and Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {604, title = {Numerical insight into the micromechanics of jet erosion of a cohesive granular material}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 15017}, abstract = {

Here we investigate the physical mechanisms behind the surface erosion of a cohesive granular soil induced by an impinging jet by means of numerical simulations coupling fluid and grains at the microscale. The 2D numerical model combines the Discrete Element and Lattice Boltzmann methods (DEM-LBM) and accounts for the granular cohesion with a contact model featuring a paraboloidal yield surface. Here we review first the hydrodynamical conditions imposed by the fluid jet on a solid granular packing, turning then the attention to the impact of cohesion on the erosion kinetics. Finally, the use of an additional subcritical debonding damage model based on the work of Silvani and co-workers provides a novel insight into the internal solicitation of the cohesive granular sample by the impinging jet.

}, doi = {10.1051/epjconf/201714015017}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714015017}, author = {Cuellar, Pablo and Benseghier, Zeyd and Luu, Li-Hua and St{\'e}phane Bonelli and Jean-Yves Delenne and Farhang Radja{\"\i} and Pierre Philippe}, editor = {Saeid Nezamabadi and Luding, S.} } @article {608, title = {Numerical modeling of the tensile strength of a biological granular aggregate: Effect of the particle size distribution}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 08013}, abstract = {

Wheat grains can be considered as a natural cemented granular material. They are milled under high forces to produce food products such as flour. The major part of the grain is the so-called starchy endosperm. It contains stiff starch granules, which show a multi-modal size distribution, and a softer protein matrix that surrounds the granules. Experimental milling studies and numerical simulations are going hand in hand to better understand the fragmentation behavior of this biological material and to improve milling performance. We present a numerical study of the effect of granule size distribution on the strength of such a cemented granular material. Samples of bi-modal starch granule size distribution were created and submitted to uniaxial tension, using a peridynamics method. We show that, when compared to the effects of starch-protein interface adhesion and voids, the granule size distribution has a limited effect on the samples\’ yield stress.

}, doi = {10.1051/epjconf/201714008013}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714008013}, author = {Heinze, Karsta and Frank, Xavier and Val{\'e}rie Lullien-Pellerina and George, Matthieu and Farhang Radja{\"\i} and Jean-Yves Delenne}, editor = {Saeid Nezamabadi and Luding, S.} } @article {603, title = {Numerical study of the failure of materials embedding soft to hard particles}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 02029}, abstract = {

In this study, we use a bond-based peridynamic approach to investigate the mechanical strength and cracking of composite materials with spherical inclusions. The total volume fraction of particles and the particle-matrix toughness ratio were varied to cover a range of soft to hard inclusions. The mean particle damage was characterized together with crack patterns at a sub-particle scale. Three types of crack patterns are identified depending on the toughness ratio.

}, doi = {10.1051/epjconf/201714002029}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714002029}, author = {Frank, Xavier and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Saeid Nezamabadi and Luding, S.} } @article {597, title = {Peridynamics simulation of the comminution of particles containing microcraks}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 07018}, abstract = {

In this study, we rely on a \’bond-based\’ peridynamic approach to investigate the strength and failure of 2D particles containing a collection of 1D microcracks. The mechanical tests were performed on disks under diametral compression. In an extensive parametric study, the distribution of microcracks was varied for different particle sizes. The evolution of yield stress with diameter and the probability of failure in terms of Weibull distributions are investigated in detail. Finally, by means of a floodfill algorithm, we analyze the variation of the mean fragment size as a function of the density of defects.

}, doi = {10.1051/epjconf/201714007018}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714007018}, author = {Blanc, Nicolas and Frank, Xavier and Mayer-Laigle, Claire and Farhang Radja{\"\i} and Jean-Yves Delenne}, editor = {Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {622, title = {The Potential of Mean Force concept for bridging (length and time) scales in the modeling of complex porous materials}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 01009}, abstract = {

We introduce the concept of Potential of Mean Force, PMF, as a way to implement upscaling modeling from the nano-scale to micron-scale. A PMF is a free energy function representing in an effective way the interactions between objects (cement hydrates, clay platelets, etc.) at thermodynamics conditions. The PMF is therefore the key piece of information allowing to coarse-grained Physical-Chemistry information in a meso-scale model formulation. The use of PMF offers a huge computational advantage as it allows a straight up-scaling to the meso-scale while keeping essential interactions information that are the hallmark of Physical-Chemistry processes. Such a coarse-grained modeling integrates atomistic response into inter-particle potentials that fully propagate molecular scale information all the way to the meso-scale.

}, doi = {10.1051/epjconf/201714001009}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714001009}, author = {Katerina Ioannidou and Benoit Carrier and Matthieu Vandamme and Roland Jean-Marc Pellenq}, editor = {Farhang Radja{\"\i} and Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {607, title = {Scaling behavior of immersed granular flows}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 09044}, abstract = {

The shear behavior of granular materials immersed in a viscous fluid depends on fluid properties (viscosity, density), particle properties (size, density) and boundary conditions (shear rate, confining pressure). Using computational fluid dynamics simulations coupled with molecular dynamics for granular flow, and exploring a broad range of the values of parameters, we show that the parameter space can be reduced to a single parameter that controls the packing fraction and effective friction coefficient. This control parameter is a modified inertial number that incorporates viscous effects.

}, doi = {10.1051/epjconf/201714009044}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714009044}, author = {L. Amarsid and Jean-Yves Delenne and Patrick Mutabaruka and Yann Monerie and Perales, F. and Farhang Radja{\"\i}}, editor = {Saeid Nezamabadi and Luding, S.} } @article {605, title = {Small solar system bodies as granular systems}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 14011}, abstract = {

Asteroids and other Small Solar System Bodies (SSSBs) are currently of great scientific and even industrial interest. Asteroids exist as the permanent record of the formation of the Solar System and therefore hold many clues to its understanding as a whole, as well as insights into the formation of planetary bodies. Additionally, SSSBs are being investigated in the context of impact risks for the Earth, space situational awareness and their possible industrial exploitation (asteroid mining). In all these aspects, the knowledge of the geophysical characteristics of SSSB surface and internal structure are of great importance. Given their size, constitution, and the evidence that many SSSBs are not simple monoliths, these bodies should be studied and modelled as self-gravitating granular systems in general, or as granular systems in micro-gravity environments in particular contexts. As such, the study of the geophysical characteristics of SSSBs is a multi-disciplinary effort that lies at the crossroads between Granular Mechanics, Celestial Mechanics, Soil Mechanics, Aerospace Engineering and Computer Sciences.

}, doi = {10.1051/epjconf/201714014011}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714014011}, author = {Hestroffer, Daniel and Adriano Campo Bagat{\'\i}n and Losert, Wolfgang and Opsomer, Eric and S{\'a}nchez, Paul and Scheeres, Daniel J. and Staron, Lydie and Taberlet, Nicolas and Yano, Hajime and Eggl, Siegfried and Lecomte, Charles-Edouard and Murdoch, Naomi and Farhang Radja{\"\i} and Richardson, Derek C. and Salazar, Marcos and Schwartz, Stephen R. and Tanga, Paolo}, editor = {Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {599, title = {Strength of wet agglomerates of spherical particles: effects of friction and size distribution}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 08021}, abstract = {

We investigate the mechanical behavior of wet granular agglomerates composed of spherical particles by means of molecular dynamics simulations. The capillary cohesion force is modeled as an attraction force at the contact between two particles and expressed as an explicit function of the gap and volume of the liquid bridge. We are interested in the effect of the friction coefficient between primary particles. The agglomerates are subjected to diametrical compression tests. We find that the deformation is ductile involving particle rearrangements. However, a well-defined stress peak is observed and the peak stress is used as a measure of the compressive strength of the agglomerate. The strength increases with friction coefficient but levels off at friction coefficients above 0.4. Furthermore, the compressive strength is an increasing function of particle size span.

}, doi = {10.1051/epjconf/201714008021}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714008021}, author = {Vo, Thanh-Trung and Patrick Mutabaruka and Jean-Yves Delenne and Saeid Nezamabadi and Farhang Radja{\"\i}}, editor = {Luding, S.} } @article {263, title = {Viscoinertial regime of immersed granular flows}, journal = {Physical Review E}, volume = {96}, year = {2017}, month = {Oct-10-2017}, pages = {Article Number: 012901}, abstract = {

By means of extensive coupled molecular dynamics\–lattice Boltzmann simulations, accounting for grain dynamics and subparticle resolution of the fluid phase, we analyze steady inertial granular flows sheared by a viscous fluid. We show that, for a broad range of system parameters (shear rate, confining stress, fluid viscosity, and relative fluid-grain density), the frictional strength and packing fraction can be described by a modified inertial number incorporating the fluid effect. In a dual viscous description, the effective viscosity diverges as the inverse square of the difference between the packing fraction and its jamming value, as observed in experiments. We also find that the fabric and force anisotropies extracted from the contact network are well described by the modified inertial number, thus providing clear evidence for the role of these key structural parameters in dense suspensions.

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}, issn = {2470-0045}, doi = {10.1103/PhysRevE.96.012901}, author = {L. Amarsid and Jean-Yves Delenne and Patrick Mutabaruka and Yann Monerie and Perales, F. and Farhang Radja{\"\i}} } @article {598, title = {Wall roughness and nonlinear velocity profiles in granular shear flows}, journal = {EPJ Web of Conferences}, volume = {140}, year = {2017}, month = {Jun-30-2017}, pages = {Article Number 03090}, abstract = {

Inhomogeneous velocity profiles in granular flows are well known from both experiments and simulations, and considered as a hallmark of nonlocal behavior. By means of extensive contact dynamics simulations, we show that the sigmoidal velocity profiles in 2D flows of rigid disks are controlled by the roughness of driving boundary walls. We find that the velocity profile becomes linear for a critical value of wall roughness up to an exponential decay close to the walls with a characteristic length that does not depend on the flow thickness and rate. We describe the velocity profiles by introducing a state parameter that carries wall perturbation. By assuming that the local shear rate is a linear function of the state parameter, we obtain an analytical expression that fits velocity profiles. In this model, the nonlinear velocity profiles are explained in terms of the effects of wall roughness as boundary condition for the state parameter.

}, doi = {10.1051/epjconf/201714003090}, url = {http://www.epj-conferences.org/10.1051/epjconf/201714003090}, author = {Schuhmacher, Paul and Farhang Radja{\"\i} and St{\'e}phane Roux}, editor = {Saeid Nezamabadi and Luding, S. and Jean-Yves Delenne} } @article {267, title = {Bottom-up model for understanding the effects of wheat endosperm microstructure on its mechanical strength}, journal = {Journal of Food Engineering}, volume = {190}, year = {2016}, month = {Dec-2016}, pages = {40 - 47}, abstract = {

Wheat flours are essential ingredients of daily food products like bread, cookies or pastries. Their quality depends on the milling process and mechanical strength of wheat grains. Although it is well known that the strength and rupture of grains are strongly controlled by the endosperm microstructure, the respective roles of the starch and polymer volume fractions and their adhesion are not yet fully understood. This typical biological microstructure can be modeled as a cemented granular material, where the two size populations of starch granules (large:A-type, small:B-type) are the particles, and the protein matrix, which partially fills the space between granules, plays the role of a cement. This structural model of wheat endosperm is used, together with mechanical characteristics of starch and proteins obtained by means of Atomic Force Microscopy (AFM) measurements, to simulate the mechanical behavior and breakage of wheat endosperm in milling process. We find that the porosity outweighs the effect of other parameters for the elastic modulus, which declines as a nearly linear function of porosity. We also show that the tensile strength is an increasing function of the amount and connectivity of starch granules with increasing concentration of stresses along chains of granules. This effect is more significant at low porosity where stress distribution is mainly controlled by the contact network between starch granules. This effect explains why the protein content is not fully correlated to vitreousness, and samples of similar protein content can be different in vitreosity. Finally, we find that the starch-granule adhesion strongly affects the tensile strength whereas the effect of starch volume fraction appears mainly at high interface adhesion, which is the case of hard type wheat grains.

Fig.1. (a) Scanning Electron Micrograph of the fracture surface of a soft wheat{\textellipsis}

Fig.2. Illustration of the lattice approach for one step: (1) Initial lattice state{\textellipsis}

Fig.3. (a) Bidisperse granular sample generated with DEM for the highest starch volume{\textellipsis}

Fig.4. Example of samples submitted to tensile tests: (a) Maps of vertical stress{\textellipsis}

Fig.5. Stress-strain plots showing the effect of different values of the starch{\textellipsis}

Fig.6. Effective Young{\textquoteright}s modulus as a function of (a) protein volume fraction ρp and{\textellipsis}

}, issn = {02608774}, doi = {10.1016/j.jfoodeng.2016.06.009}, author = {Chichti, Emna and Val{\'e}rie Lullien-Pellerina and George, Matthieu and Farhang Radja{\"\i} and Rafik Aff{\`e}s and Jean-Yves Delenne} } @proceedings {338, title = {Contribution of mechanical factors to the variability of root architecture: Quantifying the past history of interaction forces between growing roots and soil grains}, journal = {2016 IEEE INTERNATIONAL CONFERENCE ON FUNCTIONAL-STRUCTURAL PLANT GROWTH MODELING, SIMULATION, VISUALIZATION AND APPLICATIONS (FSPMA)}, year = {2016}, month = {Nov-11-2016}, pages = {52-60}, publisher = {I E E E}, address = {NOV 07-11, 2016, Qingdao, PEOPLES R CHINA }, abstract = {

The relation between a growing root and the soil movement has often been under-estimated. The present work aims to determine how grains in granular soils are reorganized by the action of growing roots, and in turn how the resulting forces acting on root tips modify their development. For this purpose, we have developed a 2D Discrete Element Model (DEM) able to compute a numerical growth of a single root inside a granular medium, taking into account the grain-grain and the root-grain contact forces during the growth. First in silico simulations were carried out in order to : 1-quantify the influence of the granular structure (grain diameter distribution and gaps) and root mechanical properties (root bending stiffness) on the evolution of reaction forces applied to a single root during its growth; 2-highlight \“group effects\”, e.g. how the reorganization of grains and their interaction forces due to a given growing root can affect the mechanical signal perceived by its near neighbours; 3-investigate how the presence of initial channels within the granular medium can effect the growth trajectory and minimize the resistance to penetration. All simulations were carried out assuming that root growth direction was only driven by external forces. Simlation results allowed the extraction of general physical laws that will be used further to provide mechanoperceptive indicators and analyze experimental data provided by phenotyping platforms. The final objective will be to quantify the response of plants to mechanical stresses in terms of root elongation rate, root straightness and ramification.

}, doi = {10.1109/FSPMA.2016.7818288}, author = {Fakih, Mahmoud and Jean-Yves Delenne and Farhang Radja{\"\i} and Fourcaud, Thierry} } @article {266, title = {Lattice Boltzmann modelling of liquid distribution in unsaturated granular media}, journal = {Computers and Geotechnics}, volume = {80}, year = {2016}, month = {Dec-2016}, pages = {353 - 359}, abstract = {

We use capillary condensation simulated by a multiphase Lattice Boltzmann model as a means to generate homogeneous distributions of liquid clusters in 2D granular media. Liquid droplets condense from the vapour phase between and on the grains, and they transform into capillary bonds and liquid clusters as thermodynamic equilibrium is approached. As the amount of condensed liquid is increased, liquid clusters of increasing connectivity are formed and the distribution of liquid undergoes topological transitions until the whole pore space is filled by the liquid. We investigate the cluster statistics and local grain environments. From extensive simulations, we also obtain the mean Laplace pressure as a function of the amount of liquid, which is found to be quite similar to the well-known experimental retention curve in soil mechanics. The tensile stress carried by the grains increases as a function of the amount of condensed liquid up to a peak in the funicular state beyond which the stress falls off as a result of pressure drop inside the merging clusters.

}, issn = {0266352X}, doi = {10.1016/j.compgeo.2016.02.017}, author = {Vincent Richefeu and Farhang Radja{\"\i} and Jean-Yves Delenne} } @article {271, title = {Implicit frictional-contact model for soft particle systems}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {83}, year = {2015}, month = {Oct-2015}, pages = {72 - 87}, abstract = {

We introduce a novel numerical approach for the simulation of soft particles interacting via frictional contacts. This approach is based on an implicit formulation of the Material Point Method, allowing for large particle deformations, combined with the Contact Dynamics method for the treatment of unilateral frictional contacts between particles. This approach is both precise due to the treatment of contacts with no regularization and artificial damping parameters, and robust due to implicit time integration of both bulk degrees of freedom and relative contact velocities at the nodes representing the contact points. By construction, our algorithm is capable of handling arbitrary particle shapes and deformations. We illustrate this approach by two simple 2D examples: a Hertz contact and a rolling particle on an inclined plane. We also investigate the compaction of a packing of circular particles up to a solid fraction well above the jamming limit of hard particles. We find that, for the same level of deformation, the solid fraction in a packing of frictional particles is above that of a packing of frictionless particles as a result of larger particle shape change.

}, issn = {00225096}, doi = {10.1016/j.jmps.2015.06.007}, author = {Saeid Nezamabadi and Farhang Radja{\"\i} and Julien Averseng and Jean-Yves Delenne} } @article {156, title = {Liquid clustering and capillary pressure in granular media}, journal = {Journal of Fluid Mechanics}, volume = {762}, year = {2015}, month = {Jan-2015}, pages = {Article Number: R5}, abstract = {

By means of extensive lattice Boltzmann simulations, we investigate the process of growth and coalescence of liquid clusters in a granular material as the amount of liquid increases. A homogeneous grain\–liquid mixture is obtained by means of capillary condensation, thus providing meaningful statistics on the liquid distribution inside the granular material. The tensile stress carried by the grains as a function of the amount of condensed liquid reveals four distinct states, with a peak stress occurring at the transition from a primary coalescence process, where the cohesive strength is carried mostly by the grains, to a secondary process governed by the increase of the liquid cluster volumes. We show that the evolution of capillary states is correctly captured by a simple model accounting for the competing effects of the Laplace pressure and grain\–liquid interface.

}, issn = {0022-1120}, doi = {10.1017/jfm.2014.676}, author = {Jean-Yves Delenne and Vincent Richefeu and Farhang Radja{\"\i}} } @proceedings {358, title = {Micromechanical analysis of the surface erosion of a cohesive soil by means of a coupled LBM-DEM model}, journal = {IV International Conference on Particle-based Methods (PARTICLES 2015)}, volume = {PARTICLE-BASED METHODS IV-FUNDAMENTALS AND APPLICATIONS}, year = {2015}, month = {sept-30-2015}, pages = {519-528}, publisher = {International Center for Numerical Methods in Engineering (CIMNE)}, address = {SEP 28-30 2015 Barcelona, SPAIN}, abstract = {

The elementary mechanisms driving the ubiquitous surface erosion of cohesive geomaterials can be analysed from a micromechanical perspective combining well-known numerical techniques. Here, a coupled model combining the Discrete Element and Lattice Boltzmann methods (DEM-LBM) provides an insight into the solid-fluid interaction during the transient erosion caused by a vertical fluid jet impinging on the surface of a granular assembly. The brittle cementation providing cohesion between the solid grains is described here by means of a simple bond model with a single-parameter yield surface. The initial topology of the surface erosion tends to mimic the profile of fluid velocity directly above the soil surface. We find that both the rate of erosion and the magnitude of eroded mass depend directly on the micromechanical strength of the single solid bonds.

}, keywords = {Cohesion, DEM, LBM, Surface erosion}, url = {https://hal.archives-ouvertes.fr/hal-01269324}, author = {Cuellar, Pablo and Pierre Philippe and St{\'e}phane Bonelli and Benahmed, Nadia and Brunier-Coulin, Florian and Jeff Ngoma and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Onate, E and Bischoff, M and Owen, DRJ} } @article {152, title = {Transient dynamics of a 2D granular pile}, journal = {The European Physical Journal E}, volume = {38}, year = {2015}, month = {May-26-2015}, pages = {Article Number: 47}, abstract = {

We investigate by means of Contact Dynamics simulations the transient dynamics of a 2D granular pile set into motion by applying shear velocity during a short time interval to all particles. The spreading dynamics is directly controlled by the input energy whereas in recent studies of column collapse the dynamics scales with the initial potential energy of the column. As in column collapse, we observe a power-law dependence of the runout distance with respect to the input energy with nontrivial exponents. This suggests that the power-law behavior is a generic feature of granular dynamics, and the values of the exponents reflect the distribution of kinetic energy inside the material. We observe two regimes with different values of the exponents: the low-energy regime reflects the destabilization of the pile by the impact with a runout time independent of the input energy whereas the high-energy regime is governed by the input energy. We show that the evolution of the pile in the high-energy regime can be described by a characteristic decay time and the available energy after the pile is destabilized.

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}, issn = {1292-8941}, doi = {10.1140/epje/i2015-15047-x}, author = {Patrick Mutabaruka and Krishna Kumar and Kenichi Soga and Farhang Radja{\"\i} and Jean-Yves Delenne} } @proceedings {359, title = {Transient regime to fluidized chimney within a granular bed by means of a 2D DEM/LBM modeling}, journal = {IV International Conference on Particle-based Methods (PARTICLES 2015)}, volume = {PARTICLE-BASED METHODS IV-FUNDAMENTALS AND APPLICATIONS}, year = {2015}, month = {sept-30-2015}, pages = {558-566}, publisher = {International Center for Numerical Methods in Engineering (CIMNE)}, address = {SEP 28-30 2015 Barcelona, SPAIN}, abstract = {

Beyond a given threshold, an upward fluid flow at constant flowrate, injected through a small size section, is able to generate a fluidization along a vertical chimney over the entire height of a granular assembly. Fluidization is first initiated in the immediate vicinity of the injection hole and then the fluidized zone grows gradually until reaching the upper surface of the granular packing. In this work, we present numerical results on the kinetics of chimney fluidization in an immersed granular bed produced with two-dimensional simulations coupling the Discrete Element and Lattice Boltzmann Methods (DEM-LBM). A parametric study is carried out with 11 different sets of physical parameters and analyzed based on spatio-temporal diagrams. Then a dimensional analysis allows finding general scaling laws for both threshold and growth rate of the fluidized zone by use of two dimensionless numbers, namely Reynolds and Archimedes numbers, while quite simple empirical relationships can also be proposed.

}, keywords = {DEM, Fluidization, Granular Materials, LBM}, url = {https://hal.archives-ouvertes.fr/hal-01269325}, author = {Jeff Ngoma and Pierre Philippe and St{\'e}phane Bonelli and Cuellar, Pablo and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Onate, E and Bischoff, M and Owen, DRJ} } @proceedings {346, title = {Geomechanics from Micro to MacroInteraction between two localized fluidization cavities in granular media : Experiments and numerical simulation}, journal = {3rd International Symposium on Geomechanics from Micro to Macro}, volume = {Geomechanics from Micro to Macro}, year = {2014}, month = {Sep-2014}, pages = {1571 - 1576}, publisher = {CRC Press}, address = {SEP 01-03-2014 Univ Cambridge, Cambridge, ENGLAND}, abstract = {

In this work, we present experimental and numerical results on the interaction between two localized fluidization cavities in an immersed granular packing. According to the gap between the two locally injected upward fluid flows, each fluidized cavity will evolve independently of the another, or conversely, the two cavities can interact with each other: they merge and eventually behave like a single cavity. Combined optical techniques are used for visualization of particle motion inside the granular media (Refractive Index-Matching between liquid and beads and Planar Laser-Induced Fluorescence), the experimental results are compared to a two-dimensional simulation based on coupled Discrete Element and Lattice Boltzmann Methods (DEM-LBM).

}, isbn = {978-1-138-02707-7}, doi = {10.1201/b17395-286}, author = {Jeff Ngoma and Pierre Philippe and St{\'e}phane Bonelli and Jean-Yves Delenne and Farhang Radja{\"\i}}, editor = {Kenichi Soga and Krishna Kumar and Giovanna Biscontin and Kuo, Matthew} } @article {275, title = {Initiation of immersed granular avalanches}, journal = {Physical Review E}, volume = {89}, year = {2014}, month = {May-09-2014}, pages = {Article Number: 052203}, abstract = {

By means of coupled molecular dynamics-computational fluid dynamics simulations, we analyze the initiation of avalanches in a granular bed of spherical particles immersed in a viscous fluid and inclined above its angle of repose. In quantitative agreement with experiments, we find that the bed is unstable for a packing fraction below 0.59 but is stabilized above this packing fraction by negative excess pore pressure induced by the effect of dilatancy. From detailed numerical data, we explore the time evolution of shear strain, packing fraction, excess pore pressures, and granular microstructure in this creeplike pressure redistribution regime, and we show that they scale excellently with a characteristic time extracted from a model based on the balance of granular stresses in the presence of a negative excess pressure and its interplay with dilatancy. The cumulative shear strain at failure is found to be ≃ 0.2, in close agreement with the experiments, irrespective of the initial packing fraction and inclination angle. Remarkably, the avalanche is triggered when dilatancy vanishes instantly as a result of fluctuations while the average dilatancy is still positive (expanding bed) with a packing fraction that declines with the initial packing fraction. Another nontrivial feature of this creeplike regime is that, in contrast to dry granular materials, the internal friction angle of the bed at failure is independent of dilatancy but depends on the inclination angle, leading therefore to a nonlinear dependence of the excess pore pressure on the inclination angle. We show that this behavior may be described in terms of the contact network anisotropy, which increases with a nearly constant connectivity and levels off at a value (critical state) that increases with the inclination angle. These features suggest that the behavior of immersed granular materials is controlled not only directly by hydrodynamic forces acting on the particles but also by the influence of the fluid on the granular microstructure.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.89.052203}, author = {Patrick Mutabaruka and Jean-Yves Delenne and Kenichi Soga and Farhang Radja{\"\i}} } @proceedings {344, title = {Lattice Boltzmann modeling of liquid clusters in granular media}, journal = {3rd International Symposium on Geomechanics from Micro to Macro}, volume = {Geomechanics from Micro to Macro}, year = {2014}, month = {Dec-03-2014}, pages = {461 - 466}, publisher = {CRC Press}, address = {SEP 01-03-2014 Univ Cambridge, Cambridge, ENGLAND}, abstract = {

We use capillary condensation simulated by a multiphase Lattice Boltzmann model as a means to generate homogeneous distributions of liquid clusters in 2D granular media. Liquid droplets condense from the vapor phase between and on the grains, and they transform into capillary bonds and liquid clusters as thermodynamic equilibrium is approached. As the amount of condensed liquid is increased, liquid clusters of increasing connectivity are formed and the distribution of liquid undergoes topological transitions until the whole pore space is filled by the liquid. We investigate the cluster statistics and local grain environments. From extensive simulations, we also obtain the mean Laplace pressure as a function of the amount of liquid, which is found to be quite similar to the well-known experimental retention curve in soil mechanics.

}, isbn = {978-1-138-02707-7}, doi = {10.1201/b1739510.1201/b17395-83}, author = {Jean-Yves Delenne and Vincent Richefeu and Farhang Radja{\"\i}}, editor = {Kenichi Soga and Krishna Kumar and Giovanna Biscontin and Kuo, Matthew} } @proceedings {345, title = {Shear flow of dense granular suspensions by computer simulations}, journal = {3rd International Symposium on Geomechanics from Micro to Macro}, volume = {Geomechanics from Micro to Macro}, year = {2014}, month = {Apr-2014}, pages = {467-472}, publisher = {CRC Press}, address = {SEP 01-03-2014 Univ Cambridge, Cambridge, ENGLAND}, abstract = {

We analyze the shear flow of dense granular materials composed of circular particles immersed in a viscous fluid by means of Molecular Dynamics simulations interfaced with the Lattice Boltzmann Method. A homogeneous flow of the suspension is obtained through periodic boundary conditions and by directly applying a confining pressure on the granular phase and shearing the fluid phase. The stead-state rheology can be described in terms of effective friction coefficient and packing fraction of the suspension as a function of the ratio of viscous shear stress to confining pressure (frictional description), on one hand, and in terms of normal and shear viscosities of the suspension as a function of the packing fraction (viscous description), on the other hand. We show that the simulation data are consistent with both descriptions and in close agreement with the corresponding scaling laws observed in recent experiments.

}, url = {http://prodinra.inra.fr/record/369542}, author = {L. Amarsid and Patrick Mutabaruka and Jean-Yves Delenne}, editor = {Kenichi Soga and Krishna Kumar and Giovanna Biscontin} } @proceedings {367, title = {A benchmark for particle shape dependence}, journal = {7th International Conference on Micromechanics of Granular Media (Powders and Grains)}, volume = {Book Series: AIP Conference Proceedings POWDERS AND GRAINS 2013}, year = {2013}, month = {Jun-18-2013}, pages = {883-886}, publisher = {AIP}, address = {JUL 08-12 2013 Sydney, AUSTRALIA}, abstract = {

Particle shape is a major parameter for the space-filling and strength properties of granular materials. For a systematic investigation of shape effect, a numerical benchmark test was set up within a collaborative group using different numerical methods and particles of various shape characteristics such as elongation, angularity and nonconvexity. Extensive 2D shear simulations were performed in this framework and the shear strength and packing fraction were compared for different shapes. We show that the results may be analyzed in terms of a low-order shape parameter \η describing the degree of distortion from a perfectly circular shape. In particular, the shear strength is an increasing function of \η with nearly the same trend for all shapes, the differences being of second order compared to \η. We also observe a nontrivial behavior of packing fraction which, for all our simulated shapes, increases with \η from the random close packing fraction for disks, reaches a peak considerably higher than that for disks, and subsequently declines as \η is further increased. Finally, the analysis of contact forces for the same value of \η leads to very similar statistics regardless of our specific particle shapes.

}, doi = {10.1063/1.4812073}, author = {Gael Combe and C{\'e}cile Nouguier-Lehon and Emilien Az{\'e}ma and Krzysztof Szarf and Baptiste Saint-Cyr and Marie Chaze and Farhang Radja{\"\i} and Pascal Villard and Jean-Yves Delenne and Vincent Richefeu and Philippe Sornay and Charles Voivret and CEGEO Group}, editor = {Yu, A and Dong, K and Yang, R} } @proceedings {369, title = {Capillary states of granular materials in the funicular state}, journal = {7th International Conference on Micromechanics of Granular Media (Powders and Grains)}, volume = {Book Series: AIP Conference Proceedings POWDERS AND GRAINS 2013}, year = {2013}, month = {Jun-18-2013}, pages = {1023-1026}, publisher = {AIP}, address = {JUL 08-12 2013 Sydney, AUSTRALIA}, abstract = {

Using a multi-phase lattice Boltzmann model, we investigate the capillary states of a 2D granular packing gradually saturated by condensation from a homogeneously injected vapor phase. The internal stresses induced by surface tension and Laplace pressure are directly calculated from the forces acting on the grains with increasing amount of liquid. The evolution of cohesive strength with the amount of liquid reveals four different states reflecting the connectivity of the liquid phase and local grain environments. It increases in the pendular state, characterized by binary liquid bridges holding the grains together, and within the funicular state with an increasing number of liquid clusters connected to several grains. Beyond 40\% of saturation, the cohesive strength falls off due to a decreasing Laplace pressure of liquid clusters.

}, doi = {10.1063/1.4812108}, author = {Jean-Yves Delenne and Vincent Richefeu and Farhang Radja{\"\i}}, editor = {Yu, A and Dong, K and Yang, R} } @article {281, title = {Cohesive granular materials composed of nonconvex particles}, journal = {Physical Review E}, volume = {87}, year = {2013}, month = {May-28-2013}, pages = {Article Number: 052207}, abstract = {

The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.052207}, author = {Baptiste Saint-Cyr and Farhang Radja{\"\i} and Jean-Yves Delenne and Philippe Sornay} } @article {284, title = {An interdisciplinary approach towards improved understanding of soil deformation during compaction}, journal = {Soil and Tillage Research}, volume = {128}, year = {2013}, month = {Apr-2013}, pages = {61 - 80}, abstract = {

Soil compaction not only reduces available pore volume in which fluids are stored, but it alters the arrangement of soil constituents and pore geometry, thereby adversely impacting fluid transport and a range of soil ecological functions. Quantitative understanding of stress transmission and deformation processes in arable soils remains limited. Yet such knowledge is essential for better predictions of effects of soil management practices such as agricultural field traffic on soil functioning. Concepts and theory used in agricultural soil mechanics (soil compaction and soil tillage) are often adopted from conventional soil mechanics (e.g. foundation engineering). However, in contrast with standard geotechnical applications, undesired stresses applied by agricultural tyres/tracks are highly dynamic and last for very short times. Moreover, arable soils are typically unsaturated and contain important secondary structures (e.g. aggregates), factors important for affecting their soil mechanical behaviour. Mechanical processes in porous media are not only of concern in soil mechanics, but also in other fields including geophysics and granular material science. Despite similarity of basic mechanical processes, theoretical frameworks often differ and reflect disciplinary focus. We review concepts from different but complementary fields concerned with porous media mechanics and highlight opportunities for synergistic advances in understanding deformation and compaction of arable soils. We highlight the important role of technological advances in non-destructive measurement methods at pore (X-ray tomography) and soil profile (seismic) scales that not only offer new insights into soil architecture and enable visualization of soil deformation, but are becoming instrumental in the development and validation of new soil compaction models. The integration of concepts underlying dynamic processes that modify soil pore spaces and bulk properties will improve the understanding of how soil management affect vital soil mechanical, hydraulic and ecological functions supporting plant growth.

}, issn = {01671987}, doi = {10.1016/j.still.2012.10.004}, author = {Keller, T. and Lamand, M. and Peth, S. and Berli, M. and Jean-Yves Delenne and Baumgarten, W. and Rabbel, W. and Farhang Radja{\"\i} and Rajchenbach, J. and Selvadurai, A.P.S. and Or, D.} } @article {279, title = {Nano-mechanical properties of starch and gluten biopolymers from atomic force microscopy}, journal = {European Polymer Journal}, volume = {49}, year = {2013}, month = {Dec-2013}, pages = {3788 - 3795}, abstract = {

An original method based on atomic force microscopy (AFM) in contact mode was developed to abrade progressively the surface of tablets made of starch or gluten polymers isolated from wheat. The volume of the material removed by the tip was estimated from the analysis of successive topographic images of the surface, and the shear force was measured by keeping a constant normal force. Our data together with a simple tribological model provide clear evidence for a higher hardness and shear strength of starch compared to gluten. Gluten appears to have mechanical properties close to soft materials, such as talc, whereas starch displays higher hardness close to calcite. Our results are in a better agreement with structural properties of gluten (complex protein network) and starch (granular and semi-cristalline structure) than earlier studies by micro-indentation. This work shows that the AFM scratching method is relevant for the characterization of any polymer surface, in particular in application to materials made of different polymers at the nano-scale.

Graphical abstract

Unlabelled figure
}, issn = {00143057}, doi = {10.1016/j.eurpolymj.2013.08.024}, author = {Chichti, Emna and George, Matthieu and Jean-Yves Delenne and Farhang Radja{\"\i} and Val{\'e}rie Lullien-Pellerina} } @article {282, title = {Rheology of three-dimensional packings of aggregates: Microstructure and effects of nonconvexity}, journal = {Physical Review E}, volume = {87}, year = {2013}, month = {May-22-2013}, pages = {Article Number: 052205}, abstract = {

We use 3D contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with nonconvexity. In contrast, the packing fraction increases first to a maximum value but declines as nonconvexity further increases. At high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as friction mobilization are enhanced by multiple contacts between aggregates and interlocking, revealing thus the mechanical and geometrical origins of shear strength.

}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.052205}, author = {Emilien Az{\'e}ma and Farhang Radja{\"\i} and Baptiste Saint-Cyr and Jean-Yves Delenne and Philippe Sornay} } @proceedings {350, title = {Effect of Particle Shape non-Convexity on the Rheology of Granular Media : 3D Contact Dynamics Simulations}, journal = {2nd International Conference on Particle-Based Methods - Fundamentals and Applications (Particles)}, volume = {PARTICLE-BASED METHODS II: FUNDAMENTALS AND APPLICATIONS}, year = {2012}, month = {Apr-10-2012}, pages = {427-434}, address = {OCT 26-28 2011 Barcelona, SPAIN}, abstract = {

We analyze the effect of particle shape non-convexity on the quasi-static behavior of granular materials by means of contact dynamics simulations. The particles are regular aggregates of four overlapping spheres described by a nonconvexity parameter depending on the relative positions of the particles. Several packings are first submitted to isotropic compression without friction. We find that, as in 2D, the solid fraction of isotropic packings increases with non-convexity up to a maximum value and then declines to be nearly equal to that of a packing composed of only spheres. It is also remarkable that the coordination number increases quickly and saturates so that the packings composed of grains with a high level of nonconvexity are looser but more strongly connected. Then, the quasi-static behavior, structural and force anisotropies are analyzed by subjecting each packing to a triaxial compression. We find that the shear strength increases with non-convexity. We show that this increase results from the presence of multiple contacts between trimers leading to enhanced frictional interlocking.

}, keywords = {force transmission, Granular Materials, non-convexity, particle shape, texture}, url = {https://hal.archives-ouvertes.fr/hal-00686453}, author = {Baptiste Saint-Cyr and Emilien Az{\'e}ma and Jean-Yves Delenne and Farhang Radja{\"\i} and Philippe Sornay}, editor = {Onate, E and Owen, DRJ} } @article {308, title = {Fabric evolution and accessible geometrical states in granular materials}, journal = {Granular Matter}, volume = {14}, year = {2012}, month = {Mar-02-2012}, pages = {259 - 264}, abstract = {

We analyze the geometrical states of granular materials by means of a fabric tensor involving the coordination number and fabric anisotropy as the lowest-order descriptors of the contact network. In particular, we show that the fabric states in this representation are constrained by steric exclusions and the condition of mechanical equilibrium required in the quasi-static limit. A simple model, supported by numerical data, allows us to characterize the range of accessible fabric states and the joint evolution of fabric parameters. The critical state in this framework appears as a jammed state in the sense of a saturation of contact gain and loss along the principal strain-rate directions.

}, issn = {1434-5021}, doi = {10.1007/s10035-012-0321-8}, author = {Farhang Radja{\"\i} and Jean-Yves Delenne and Emilien Az{\'e}ma and St{\'e}phane Roux} } @article {307, title = {Particle shape dependence in 2D granular media}, journal = {EPL (Europhysics Letters)}, volume = {98}, year = {2012}, month = {Apr-20-2012}, pages = {Article Number: 44008}, abstract = {

Particle shape is a key to the space-filling and strength properties of granular matter. We consider a shape parameter

describing the degree of distortion from a perfectly spherical shape. Encompassing most specific shape characteristics such as elongation, angularity and non-convexity, is a low-order but generic parameter that we used in a numerical benchmark test for a systematic investigation of shape dependence in sheared granular packings composed of particles of different shapes. We find that the shear strength is an increasing function of with nearly the same trend for all shapes, the differences appearing thus to be of second order compared to . We also observe a non-trivial behavior of packing fraction which, for all our simulated shapes, increases with from the random close packing fraction for disks, reaches a peak considerably higher than that for disks, and subsequently declines as is further increased. These findings suggest that a low-order description of particle shape accounts for the principal trends of packing fraction and shear strength. Hence, the effect of second-order shape parameters may be investigated by considering different shapes at the same level of .

}, issn = {0295-5075}, doi = {10.1209/0295-5075/98/44008}, author = {Baptiste Saint-Cyr and Krzysztof Szarf and Charles Voivret and Emilien Az{\'e}ma and Vincent Richefeu and Jean-Yves Delenne and Gael Combe and C{\'e}cile Nouguier-Lehon and Pascal Villard and Philippe Sornay and Marie Chaze and Farhang Radja{\"\i}} } @article {295, title = {Tensile strength and fracture of cemented granular aggregates}, journal = {The European Physical Journal E}, volume = {35}, year = {2012}, month = {Nov-2012}, pages = { Article Number: 117}, abstract = {

Cemented granular aggregates include a broad class of geomaterials such as sedimentary rocks and some biomaterials such as the wheat endosperm. We present a 3D lattice element method for the simulation of such materials, modeled as a jammed assembly of particles bound together by a matrix partially filling the interstitial space. From extensive simulation data, we analyze the mechanical properties of aggregates subjected to tensile loading as a function of matrix volume fraction and particle-matrix adhesion. We observe a linear elastic behavior followed by a brutal failure along a fracture surface. The effective stiffness before failure increases almost linearly with the matrix volume fraction. We show that the tensile strength of the aggregates increases with both the increasing tensile strength at the particle-matrix interface and decreasing stress concentration as a function of matrix volume fraction. The proportion of broken bonds in the particle phase reveals a range of values of the particle-matrix adhesion and matrix volume fraction for which the cracks bypass the particles and hence no particle damage occurs. This limit is shown to depend on the relative toughness of the particle-matrix interface with respect to the particles.

}, issn = {1292-8941}, doi = {10.1140/epje/i2012-12117-7}, author = {Rafik Aff{\`e}s and Jean-Yves Delenne and Yann Monerie and Farhang Radja{\"\i} and Vincent Topin} } @proceedings {356, title = {Compressive strength of an unsaturated granular material during cementation}, journal = {Symposium on Science and Technology of Powders and Sintered Materials (STPMF 2009)}, volume = {POWDER TECHNOLOGY}, year = {2011}, month = {Mar-25-2011}, pages = {308 - 311}, address = {MAY 25-27 2009 Montpellier, FRANCE}, abstract = {

The cohesive behaviour of unsaturated granular materials is due to the presence of cohesive bonds between grains. These bonds can have various physico-chemical characteristics and may evolve with environmental conditions. We study the case of a granular material partially saturated by an aqueous solution. The bonds are thus initially of capillary type and the mechanical strength is weak. At low relative humidity, the phase change of water involves crystallization of the solute at the contact points between grains, generating thus solid bonds. The mechanical strength of the material is then enhanced. An experimental study of the evolution of the mechanical strength during crystallization of the solute shows clearly the transition from capillary regime to cemented regime. This transition is not correlated with the mass of the crystallized solute, but rather with the residual degree of saturation. This behavior is analyzed here in the light of discrete element simulations. We introduce a local cohesion law that accounts for transition from capillary to cemented bonding. This law is formulated in terms of the degree of crystallization as a result of the evaporation of water at the boundary of the sample. The cohesion of the packing is initially of capillary type. A crystallization front then spreads from the sample boundaries to the center of the sample, and the strength increases as a result. Uniaxial compression allows us to determine the strength at different times. The numerical strength agrees well with the experimental data, and reveals strength enhancement as the solute crystallizes, as well as the transition from capillary to cementation regime.

}, issn = {00325910}, doi = {10.1016/j.powtec.2010.08.021}, author = {Jean-Yves Delenne and Souli{\'e}, Fabien and Moulay Sa{\"\i}d El Youssoufi and Farhang Radja{\"\i}} } @article {316, title = {From liquid to solid bonding in cohesive granular media}, journal = {Mechanics of Materials}, volume = {43}, year = {2011}, month = {Oct-2011}, pages = {529 - 537}, abstract = {

We study the transition of a granular packing from liquid to solid bonding in the course of drying. The particles are initially wetted by a liquid brine and the cohesion of the packing is ensured by capillary forces, but the crystallization of the solute transforms the liquid bonds into partially cemented bonds. This transition is evidenced experimentally by measuring the compressive strength of the samples at regular intervals of times. Our experimental data reveal three regimes: (1) Up to a critical degree of saturation, no solid bonds are formed and the cohesion remains practically constant; (2) The onset of cementation occurs at the surface and a front spreads towards the center of the sample with a nonlinear increase of the cohesion; (3) All bonds are partially cemented when the cementation front reaches the center of the sample, but the cohesion increases rapidly due to the strengthening of cemented bonds. We introduce a model based on a parametric cohesion law at the bonds and a bond crystallization parameter. This model predicts correctly the phase transition and the relation between microscopic and macroscopic cohesion.

Fig. 1. (a) Photograph of the sample in the process of drying; (b) The press used for{\textellipsis}

Fig. 2. Compressive yield stress σY, normalized by the yield stress σLY due only to{\textellipsis}

Fig. 3. Photograph of a partially dried sample in the second regime

Fig. 4. Schematic representation of the evolution of bridge: from a liquid to a solid{\textellipsis}

Fig. 5. Evolution of the global crystallization index with time; solid line:{\textellipsis}

Fig. 6. The parametric adhesion law

}, issn = {01676636}, doi = {10.1016/j.mechmat.2011.06.008}, author = {Jean-Yves Delenne and Souli{\'e}, Fabien and Moulay Sa{\"\i}d El Youssoufi and Farhang Radja{\"\i}} } @proceedings {352, title = {Modeling Porous Granular Aggregates}, journal = {9th International Workshop on Buifurcation and Degradation in Geomaterials (IWBDG 2011)}, volume = {Springer Series in Geomechanics and Geoengineering - ADVANCES IN BIFURCATION AND DEGRADATION IN GEOMATERIALS}, year = {2011}, month = {May-28-2011}, pages = {249 - 254}, publisher = {Springer Netherlands}, address = {MAY 23-26 2011 Porquerolles, FRANCE}, abstract = {

We rely on 3D simulations based on the Lattice Element Method (LEM) to analyze the failure of porous granular aggregates under tensile loading. We investigate crack growth by considering the number of broken bonds in the particle phase as a function of the matrix volume fraction and particle-matrix adhesion. Three regimes are evidenced, corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We also show that the probability density of strong stresses falls off exponentially at high particle volume fractions where a percolating network of jammed particles occurs. Decreasing the matrix volume fraction leads to increasingly broader stress distribution and hence a higher stress concentration. Our findings are in agreement with 2D results previously reported in the literature.

}, isbn = {978-94-007-1420-5}, issn = {1866-8755}, doi = {10.1007/978-94-007-1421-2_32}, author = {Rafik Aff{\`e}s and Vincent Topin and Jean-Yves Delenne and Yann Monerie}, editor = {St{\'e}phane Bonelli and Dascalu, Cristian and Fran{\c c}ois Nicot} } @proceedings {353, title = {Onset of Immersed Granular Avalanches by DEM-LBM Approach}, journal = {9th International Workshop on Buifurcation and Degradation in Geomaterials (IWBDG 2011)}, volume = {Springer Series in Geomechanics and Geoengineering - ADVANCES IN BIFURCATION AND DEGRADATION IN GEOMATERIALS}, year = {2011}, month = {May-28-2011}, pages = {109 - 115}, publisher = {Springer Netherlands}, address = {MAY 23-26 2011 Porquerolles, FRANCE}, abstract = {

We present 3D grain-fluid simulations based on the discrete element method interfaced with the lattice Boltzmann method and applied to investigate the initiation of underwater granular flows. We prepare granular beds of 800 spherical grains with different values of the initial solid fraction in a biperiodic rectangular box. In order to trigger an avalanche, the bed is instantaneously tilted to a finite slope angle above the maximum angle of stability. We simulate the dynamics of the transient flow for different solid fractions. In agreement with the experimental work of Iverson (Water Resour Res 36(7):1897\–1910, 2000) and Pailha et\ al. (Phys Fluids 20(11):111701, 2008), we find that the flow onset is controlled by the initial solid fraction.

}, isbn = {978-94-007-1420-5}, issn = {1866-8755}, doi = {10.1007/978-94-007-1421-210.1007/978-94-007-1421-2_14}, author = {Jean-Yves Delenne and Mansouri, M. and Farhang Radja{\"\i} and Moulay Sa{\"\i}d El Youssoufi and Seridi, A.}, editor = {St{\'e}phane Bonelli and Dascalu, Cristian and Fran{\c c}ois Nicot} } @article {315, title = {Rheology of granular materials composed of nonconvex particles}, journal = {Physical Review E}, volume = {84}, year = {2011}, month = {Oct-10-2011}, pages = {Article Number: 041302 Part: 1 }, abstract = {

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

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}, issn = {1539-3755}, doi = {10.1103/PhysRevE.84.041302}, author = {Baptiste Saint-Cyr and Jean-Yves Delenne and Charles Voivret and Farhang Radja{\"\i} and Philippe Sornay} } @proceedings {355, title = {Stress fields in granular solids: Effect of composition}, journal = {Symposium on Science and Technology of Powders and Sintered Materials (STPMF 2009)}, volume = {POWDER TECHNOLOGY}, year = {2011}, month = {Mar-25-2011}, pages = {568 - 573}, address = {MAY 25-27 2009 Montpellier, FRANCE}, abstract = {

We use the lattice element method to investigate stress fields at the sub-particle scale in granular solids composed of particles embedded in a cementing matrix. The stress distributions are found to be similar in 2D and 3D samples subjected to vertical loading with free lateral boundaries. We find that the number of strong forces falls off exponentially at high particle volume fractions where a percolating network of jammed particles occurs. The influence of the matrix volume fraction and particle/matrix stiffness ratio with respect to stress distribution is analyzed in 2D and 3D. We show that both decreasing the matrix volume fraction and increasing the stiffness ratio lead to increasingly broader distributions within a limit beyond which the distribution is independent of one or both of these parameters.

}, issn = {00325910}, doi = {10.1016/j.powtec.2010.08.060}, author = {Vincent Topin and Farhang Radja{\"\i} and Jean-Yves Delenne} }