Elastic behavior in Contact Dynamics of rigid particles

The systematic errors due to the practical implementation of the Contact Dynamics method for simulation of dense granular media are examined. It is shown that, using the usual iterative solver to simulate a chain of rigid particles, effective elasticity and sound propagation with a finite velocity occur. The characteristics of these phenomena are investigated analytically and numerically in order to assess the limits of applicability of this simulation method and to compare it with soft particle molecular dynamics.Comment: submitted to PRE, 7 pages, 6 figure

Dynamic Rearrangements and Packing Regimes in Randomly Deposited Two-Dimensional Granular Beds

We study the structural properties of two-dimensional granular packings prepared by random deposition from a source line. We consider a class of random ballistic deposition models based on single-particle relaxation rules controlled by a critical angle, and we show that these local rules can be formulated as rolling friction in the framework of dynamic methods for the simulation of granular materials. We find that a packing prepared by random deposition models is generically unstable, and undergoes dynamic rearrangements. As a result, the dynamic method leads systematically to a higher solid fraction than the geometrical model for the same critical angle. We characterize the structure of the packings generated by both methods in terms of solid fraction, contact connectivity and anisotropy. Our analysis provides evidence for four packing regimes as a function of solid fraction, the mechanisms of packing growth being different in each regime.Comment: 36 pages, 17 figures to be published in Phys.Rev E. September 200

Multiscale Analysis of the Stress State in a Granular Slope in Transition to Failure

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted towards its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This transition coincides with the onset of dilatation in the packing. We map this transition into a percolation transition of the overloaded grains, and we argue that in the presence of long-range correlations above the transition angle, the granular slope is metastable.Comment: 11 pages, 14 Fig, submitted to PR

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

Shearing behavior of polydisperse media

We study the shearing of polydisperse and bidisperse media with a size ratio of 10. Simulations are performed with a the two dimensional shear cell using contact dynamics. With a truncated power law for the polydisperse media we find that they show a stronger dilatancy and greater resistance to shearing than bidisperse mixtures. Motivated by the practical problem of reducing the energy needed to shear granular media, we introduce "point-like particles" representing charged particles in the distribution. Even though changing the kinematic behavior very little, they reduce the force necessary to maintain a fixed shearing velocity.Comment: 17 pages, 15 figure

Self-stresses and Crack Formation by Particle Swelling in Cohesive Granular Media

We present a molecular dynamics study of force patterns, tensile strength and crack formation in a cohesive granular model where the particles are subjected to swelling or shrinkage gradients. Non-uniform particle size change generates self-equilibrated forces that lead to crack initiation as soon as strongest tensile contacts begin to fail. We find that the coarse-grained stresses are correctly predicted by an elastic model that incorporates particle size change as metric evolution. The tensile strength is found to be well below the theoretical strength as a result of inhomogeneous force transmission in granular media. The cracks propagate either inward from the edge upon shrinkage and outward from the center upon swelling

Rearrangements and Dilatancy for Sheared Dense Materials

Constitutive equations are proposed for dense materials, based on the identification of two types of free-volume activated rearrangements associated to shear and compaction. Two situations are studied: the case of an amorphous solid in a stress-strain test, and the case of a lubricant in tribology test. Varying parameters, strain softening, shear thinning, and stick-slip motion can be observed.Comment: 4 pages, 3 figure

Comment on "Mechanical analog of temperature for the description of force distribution in static granular packings"

It has been proposed by Ngan [Phys. Rev. E 68, 011301 (2003)] that the granular contact force distribution may be analytically derived by minimizing the analog of a thermodynamic free energy, in this case consisting of the total potential energy stored in the compressed contacts minus a particular form of entropy weighted by a parameter. The parameter is identified as a mechanical temperature. I argue that the particular form of entropy cannot be correct and as a result the proposed method produces increasingly errant results for increasing grain rigidity. This trend is evidenced in Ngan's published results and in other numerical simulations and experiments.Comment: 4 pages, 1 figure, minor editorial correction