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We present a numerical implementation of an active inclusion in a granular material submitted to a biaxial test. We discuss the dependence of the response to this perturbation on two parameters: the intra-granular friction coefficient on one hand, the degree of the loading on the other hand. We compare the numerical results to theoretical predictions taking into account the change of volume of the inclusion as well as the anisotropy of the elastic matrix.

We have performed a simulation study of 3D cohesionless granular flows down an inclined chute. We find that the oscillations observed in [L.E. Silbert, Phys. Rev. Lett., 94, 098002 (2005)] near the angle of repose are harmonic vibrations of the lowest normal mode. Their frequencies depend on the contact stiffness as well as on the depth of the flow. Could these oscillations account for the phenomena of "booming sand"? We estimate an effective contact stiffness from the Hertz law, but this leads to frequencies several times higher than observed. However, the Hertz law also predicts interpenetrations of a few nanometers, indicating that the oscillations frequencies are governed by the surface stiffness, which can be much lower than the bulk one. This is in agreement with previous studies ascribing the ability to sing to the presence of a soft coating on the grain surface., Comment: accepted for publication in Physical Review E http://pre.aps.org; Physical Review E (2012) to be published

We study numerical simulations of large (N~10^4) two-dimensional quasi-static granular assemblies subjected to a slowly increasing deviator stress. We report some peculiarities in the behavior of these packings that have not yet been adressed. The number of sliding contacts is not necessarily related to stability: first the number of sliding contacts rises linearly and smoothly with the applied stress. Then, at approximately half the peak stress, the increase slows down, a plateau develops, and a decrease follows.

We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. % with transform boundaries. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent on particle shape and in good agreement with the Gutenberg-Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omori's law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy., Comment: 10 pages, 12 figures

We present a detailed analysis of the bounds on the integration step in Discrete Element Method (DEM) for simulating collisions and shearing of granular assemblies. We show that, in the numerical scheme, the upper limit for the integration step, usually taken from the average time $t_c$ of one contact, is in fact not sufficiently small to guarantee numerical convergence of the system during relaxation. In particular, we study in detail how the kinetic energy decays during the relaxation stage and compute the correct upper limits for the integration step, which are significantly smaller than the ones commonly used. In addition, we introduce an alternative approach, based on simple relations to compute the frictional forces, that converges even for integration steps above the upper limit., Comment: 16 page, 10 figures, submitted to Acta Mechanica, Special Issue to Honour J.D Goddard

We report two-dimensional simulations of strongly vibrated granular materials without gravity. The coefficient of restitution depends on the impact velocity between particles by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. Use of this model of restitution coefficient leads to new unexpected behaviors. When the number of particles N is large, a loose cluster appears near the fixed wall, opposite the vibrating wall. The pressure exerted on the walls becomes independent of N, and linear in the vibration velocity V, quite as the granular temperature. The collision frequency at the vibrating wall becomes independent of both N and V, whereas at the fixed wall, it is linear in both N and V. These behaviors arise because the velocity-dependent restitution coefficient introduces a new time scale related to the collision velocity near the cross over from viscoelastic to plastic deformation., Comment: Final version - To be published in Powder Technology

Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying properties of the solved particles and the solvents, one has to choose the simulation method properly in order to use the available compute resources most effectively with resolving the system as well as needed. Various techniques for the simulation of particle suspensions have been implemented at the Institute for Computational Physics allowing us to study the properties of clay-like systems, where Brownian motion is important, more macroscopic particles like glass spheres or fibers solved in liquids, or even the pneumatic transport of powders in pipes. In this paper we will present the various methods we applied and developed and discuss their individual advantages., Comment: 31 pages, 11 figures, to appear in Lecture Notes in Applied and Computational Mechanics, Springer (2006)

We report numerical simulations of strongly vibrated granular materials designed to mimic recent experiments performed both in presence or absence of gravity. The coefficient of restitution used here depends on the impact velocity by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. We show that this model with impact velocity dependent restitution coefficient reproduce results that agree with experiments. We measure the scaling exponents of the granular temperature, collision frequency, impulse, and pressure with the vibrating piston velocity as the particle number increases. As the system changes from a homogeneous gas state at low density to a clustered state at high density, these exponents are all found to decrease continuously with the particle number. All these results differ significantly from classical inelastic hard sphere kinetic theory and previous simulations, both based on a constant restitution coefficient., Comment: to be published in Phys. Rev. E

Plug conveying along a horizontal tube has been investigated through simulation, using a discrete element simulation approach for the granulate particles and a pressure field approach for the gas. The result is compared with the simulation of the vertical plug conveying. The dynamics of a slug are described by porosity, velocity and force profiles. Their dependence on simulation parameters provides an overall picture of slug conveying., Comment: 13 pages, 23 figures, to be published in Granular Matter

The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. It is found that for both normal and oblique impacts the crack patterns are the same and depend solely on the normal component of the impact velocity. Analysing the pattern of breakage, amount of damage, fragment masses and velocities, we show the existence of a critical velocity which separates two regimes of the impact process: below the critical point only a damage cone is formed at the impact site (damage), cleaving of the particle occurs at the critical point, while above the critical velocity the disc breaks into several pieces (fragmentation). In the limit of very high impact velocities the disc suffers complete disintegration (shattering) into many small fragments. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc., Comment: submitted to J. Phys: Condensed Matter special issue on Granular Media

Plug conveying along a vertical tube has been investigated through simulation, using a discrete element simulation approach for the granulate particles and a pressure field approach for the gas. The result is compared with an experiment. The dynamics of a plug are described by porosity, velocity and force profiles. Their dependence on simulation parameters provides an overall picture of plug conveying., Comment: 27 pages, 18 Postscript figures, uses elsart.cls, Powder Technology (in review)

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 figures

Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector in a high-dimensional space enable us to show that the set of all possible contact forces is convex, facilitating its numerical exploration. It is also found that the boundary of the set is connected with the presence of sliding contacts, suggesting that a stable packing should not have more than 2M-3N sliding contacts in two dimensions, where M is the number of contacts and N is the number of particles. These results were used to analyze packings generated in different ways by either molecular dynamics or contact dynamics simulations. The dimension of the set of possible forces and the number of sliding contacts agrees with the theoretical expectations. The indeterminacy of each component of the contact forces are found, as well as the an estimate for the diameter of the set of possible contact forces. We also show that contacts with high indeterminacy are located on force chains. The question of whether the simulation methods can represent a packing's memory of its formation is addressed., Comment: 12 pages, 13 figures, submitted to Phys Rev E

The fragmentation of a two-dimensional circular disc by lateral impact is investigated using a cell model of brittle solid. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. We found that the fragment mass distribution follows a power law with an exponent close to 2 independent of the system size. We also observed two types of crack patterns: radial cracks starting from the impact point and cracks perpendicular to the radial ones. Simulations revealed that there exists a critical projectile energy, above which the target breaks into numerous smaller pieces, and below which it suffers only damage in the form of cracks. Our theoretical results are in a reasonable agreement with recent experimental findings on the fragmentation of discs., Comment: 7 pages, 9 figures included

We report numerical simulations of strongly vibrated granular materials designed to mimic recent experiments performed both in presence [1] or absence [2] of gravity. We show that a model with impact velocity dependent restitution coefficient is necessary to bring the simulations into agreement with experiments. We measure the scaling exponents of the granular temperature, collision frequency, impulse and pressure with the vibrating piston velocity. As the system changes from a homogeneous gas state at low density to a clustered state at high density, these exponents are all found to decrease continuously with the particle number. In absence of gravity, a loose cluster appears near the upper wall, opposite the piston, and acts as a buffer for fastest particles leading to unexpected non-extensive scaling exponents ; whereas in presence of gravity, the cluster bounces as a single inelastic body. All these results differ significantly from classical inelastic hard sphere kinetic theory and previous simulations, both based on a constant restitution coefficient., Comment: In: T. Poeschel, N.V. Brilliantov (eds.) "Granular Gas Dynamics", Lecture Notes in Physics Vol. 624, Springer (Berlin, 2003), p. 131-162

The inelastic hard sphere model of granular material is simple, easily accessible to theory and simulation, and captures much of the physics of granular media. It has three drawbacks, all related to the approximation that collisions are instantaneous: 1) The number of collisions per unit time can diverge, i.e. the ``inelastic collapse'' can occur. 2) All interactions are binary, multiparticle contacts cannot occur and 3) no static limit exists. We extend the inelastic hard sphere model by defining a duration of contact t_c such that dissipation is allowed only if the time between contacts is larger than t_c. We name this generalized model the ``TC model'' and discuss it using examples of dynamic and static systems. The contact duration used here does not change the instantaneous nature of the hard sphere contacts, but accounts for a reduced dissipation during ``multiparticle contacts''. Kinetic and elastic energies are defined as well as forces and stresses in the system. Finally, we present event-driven numerical simulations of situations far beyond the inelastic collapse, possible only with the TC model., Comment: 15 pages, Latex, 14 bw.ps figures + 2 col.ps figures, to be published in Granular Matter 1(3) 1998

We study the power input of a vibrating wall into a fluidized granular medium, using event driven simulations of a model granular system. The system consists of inelastic hard disks contained between a stationary and a vibrating elastic wall, in the absence of gravity. Two scaling relations for the power input are found, both involving the pressure. The transition between the two occurs when waves generated at the moving wall can propagate across the system. Choosing an appropriate waveform for the vibrating wall removes one of these scalings and renders the second very simple., Comment: 5 pages, revtex, 7 postscript figures