Modélisation de la transmission des forces dans les matériaux granulaires

International audienceThe probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.La densité de probabilité des forces de contact dans les matériaux granulaires représente une signature remarquable de la microstructure granulaire et, à ce titre, elle a fait l'objet de nombreuses études et d'efforts de modélisation. Nous allons analyser le rôle fondamental des environnementaux locaux des particules pour la transmission des forces et les effets des contraintes stériques par rapport à l'équilibre des forces. Cette analyse permet de montrer qu'une force de contact met en jeu des forces supérieures et inférieures à cette force dans des proportions qui sont contrôlées par les effets stériques. Cette idée simple conduit à un modèle général qui prédit une expression analytique de la densité des forces avec un seul paramètre libre. Ce paramètre coïncide avec le degré d'homogénéité des forces et peut dépendre de l'anisotropie du réseau des contacts ou des formes et distributions des tailles des particules. Cette expression ajuste bien les données numériques et prédit d'une manière générique la décroissance exponentielle des forces fortes, un petit pic en dessous de la force moyenne et une densité de probabilité non nulle pour les forces très petites

Multi-periodic boundary conditions and the Contact Dynamics method

International audienceFor investigating the mechanical behavior of granular materials by means of the discrete element approach, it is desirable to be able to simulate representative volume elements with macroscopically homogeneous deformations. This can be achieved by means of fully periodic boundary conditions such that stresses or displacements can be applied in all space directions. We present a general framework for periodic boundary conditions in granular materials and its implementation more specifically in the Contact Dynamics method

An equation of state for granular media at the limit state of isotropic compression

International audienceIt is well believed that the volumetric entropy of Edwards captures part of the physics of granular media, but it is still unclear whether it can be applied to granular systems under mechanical stress. By working out a recent proposal by Aste, Di Matteo et al. to measure Edwards' compactivity from the volume distribution of Voronoıör Delaunay tessellations (Phys. Rev. E, 77 (2008) 021309), and assuming that the total volume divides into elementary cells of fixed minimal volume, we derive an equation of state relating the compactivity to the packing fraction, and we show by extensive molecular-dynamics simulations that this equation and its underlying assumption describe well the volumetric aspects of both the limit state of isotropic compression and the limit state of shear (also called critical state in soil mechanics) for three-dimensional ensembles of mono-disperse spheres, for a broad range of the sliding and rolling friction coefficients. In addition, by using the limit state of isotropic compression as testing ground, we find that the compactivity, the entropy per elementary cell and the number of elementary cells per grain computed by this method are the same within statistical precision, either by using Vorono¨ı, Delaunay, or centroidal Voronoı¨tessellations Voronoı¨tessellations, allowing thus for an objective definition. This means that not only Aste's cell method is robust and suitable to measure Edwards' compactivity of granular systems under mechanical stress but also the actual nature of the elementary cells might be unimportant

Liquid clustering and capillary pressure in granular media

International audienceBy 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

Internal friction and absence of dilatancy of packings of frictionless polygons

International audienceBy means of numerical simulations, we show that assemblies of frictionless rigid pentagons in slow shear flow possess an internal friction coefficient (equalto0.183±0.008 with our choice of moderately polydisperse grains) but no macroscopic dilatancy. In other words, despite side-side contacts tending to hinder relative particle rotations, the solidfraction under quasistatic shear coincides with that of isotropic random close packings of pentagonal particles. Properties of polygonal grains are thus similar to those of disks in that respect. We argue that continuous reshuffling of the force-bearing network leads to frequent collapsing events at the microscale, thereby causing the macroscopic dilatancy to vanish. Despite such rearrangements, the shear flow favors an anisotropic structure that is at the origin of the ability of the system to sustain shear stress

Comparison of the effects of rolling resistance and angularity in sheared granular media

International audienceIn this paper, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. For this purpose, we use contact dynamics simulations. By means of a simple shear numerical device, we investigate the mechanical behavior of these materials in the steady state in terms of shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. We find that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape

Structuration des écoulements granulaires

Nous analysons les propriétés microstructurales de systèmes granulaires cisaillés par simulations numériques discrètes. Les lois rhéologiques décrivant les écoulements de grains (i.e. relations entre contraintes normales, tangentielles, vitesse de cisaillement et compacité) peuvent être formulées à l’aide d’un nombre sans dimension I défini comme le rapport du temps inertiel par le temps de cisaillement. Les systèmes analysés sont dans un état quasi-statique, d’écoulement dense et collisionnel (ou gazeux), respectivement, en fonction de I. Nos données numériques, appuyées par des données expérimentales extraites de la littérature, montrent que la transition entre les régimes est caractérisée par une variation rapide de l’angle de frottement. Considérant un critère énergétique, nous montrons que la transition entre le régime d’écoulement dense et le régime collisionnel peut être identifié explicitement par un nombre inertiel critique I_0. De manière remarquable, nous montrons que la transition entre les régimes quasi-statique et d’écoulement dense se produit exactement à I_0^2, qui correspond au point où l’énergie cinétique injectée équilibre l’énergie potentielle du système. En analysant les corrélations spatiales entre particules flottantes (particules ne portant pas de contacts) nous montrons que des zones « fluidisées » se créent dans le régime d’écoulement dense. La taille de ces zones augmente avec I et diverge à l’approche de la transition vers le régime collisionel révélant ainsi la percolation des zones fluidisées. Par une décomposition additive du tenseur de contrainte basée sur une approximation harmonique des orientations moyennes des contacts et des forces, nous mettons en évidence que la variation de l’angle de frottement se déduit de celle de l’anisotropie structurelle elle-même liée à l’évolution de la connectivité moyenne des particules dans chaque régime. La diminution de l’anisotropie des forces normales en fonction du nombre d'inertie (due à l’inhomogénéité grandissante des forces normales) est compensée par l’augmentation de l’anisotropie tangentielle (mobilisation du frottement)

Effect of size polydispersity versus particle shape in dense granular media

International audienceWe present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles.We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail.We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The sideside contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size

Friction vs Texture at the Approach of a Granular Avalanche

We perform a novel analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilisation in a simulated two-dimensional packing. In this way, we recover the bimodal character of granular texture, and the coexistence of weak and strong phases in the sense of distinct contacts populations. Moreover, we show the existence of a well-defined subset of contacts within the weak contact network. These contacts are characterized by their important friction, and form a highly coherent population in terms of fabric. They play an antagonistic role with respect to force chains. We are thus able to discriminate between incoherent contacts and coherent contacts in the weak phase, and to specify the role that the latter plays in the destabilisation process.Comment: 4 pages, 6 figure