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

Numerical simulations of granular media composed with irregular polyhedral particles: effect of particles’ angularity

We use contact dynamic simulations to perform a systematic investigation of the effects of particles shape angularity on mechanicals response in sheared granular materials. The particles are irregular polyhedra with varying numbers of face from spheres to “double pyramid” shape with a constant aspect ratio. We study the quasi-static behavior, structural and force anisotropies of several packings subjected to triaxial compression. An interesting finding is that the shear strength first increases with angularity up to a maximum value and then saturates as the particles become more angular. Analyzing the anisotropies induced by the angular distributions of contacts and forces orientations, we show that the saturation of the shear strength at higher angularities is a consequence of fall-off of the texture anisotropies compensated by an increase of the tangential force anisotropy. This is attributed to the fact that at higher angularity, particles are better connected (or surrounded) leading to an increase of friction mobilization in order to achieve the deformation. Moreover, the most angular particles also have very few sides so that, this effect is enhanced by the increase of the proportion of face-side and side-side contacts with angularity

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

Creep behaviour of confined layers of polyhedral grains

By means of contact dynamics simulations, we investigate the creep deformation of a thin granular layer composed of irregular polyhedral particles under the action of a constant vertical overload applied on a horizontal wall on top of the layer. We show that the total deformation induced by the overload increases with the ratio between the vertical and confining horizontal stresses and the aspect ratio of the sample. The effect of the aspect ratio is a consequence of the mobilized wall-grain friction forces at the top and bottom boundaries, that lead to enhanced strength by stabilizing strong force chains at the center of the sample. We also evidence the influence of loading history due to strain-induced fabric change or inertial effects resulting from the instant application of the overload. The topology of the contact network evolves in close correlation with creep. In particular, the face/face contacts between polyhedral particles concentrate largest force chains and their number is an increasing function of creep. A crucial feature of a confined granular system is the statistical variability of the mechanical response that we analyzed for creep deformations by performing a large number of simulations for independent initial configurations. Our data indicate that the distribution of fluctuations with respect to the mean creep falls off exponentially

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

Granular slumping in a fluid : focus on runout distances

We investigate the effect of an ambient fluid on the dynamics of collapse and spread of a granular column simulated by means of a recently developed model which takes into account both fluid forces that act on each grain and contacts between grains. The model couples the contact dynamics method for discrete element modeling of the grains and their interactions with the finite element method for the integration of Navier-Stokes equations in 2D. The coupling is based on the fictitious domain approach in which the fluid domain is extended to that of grains, and the rigid-body motion of the grains is imposed by means of distributed Lagrange multipliers. As in similar numerical and experimental works with dry grains, we focus here on the run-out distances and avalanche durations for different column aspect ratios (height vs width). We consider three options for the surrounding fluid: 1) no fluid, 2) water and 3) a viscous fluid that allows us to perform our simulations in the grain-inertial, fluid-inertial and viscous regimes, respectively. The run-out distance is found to increase as a power law with the aspect ratio of the column, and surprisingly, for a given aspect ratio and packing fraction, it may be similar in the grain-inertial regime and fluid inertial regimes but with considerably longer duration in the latter case. We show that the effect of the fluid in viscous and fluid-inertial regimes is both to reduce the kinetic energy during the collapse and enhance the flow by lubrication during the spread. Hence, the run-out distance in a fluid may be below or equal to that in the absence of fluid due to compensation between those effects

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