Collision-induced friction in the motion of a single particle on a bumpy inclined line

Simulating direct shear tests with the Bullet physics library: A validation study

This study focuses on the possible uses of physics engines, and more specifically the Bullet physics library, to simulate granular systems. Physics engines are employed extensively in the video gaming, animation and movie industries to create physically plausible scenes. They are designed to deliver a fast, stable, and optimal simulation of certain systems such as rigid bodies, soft bodies and fluids. This study focuses exclusively on simulating granular media in the context of rigid body dynamics with the Bullet physics library. The first step was to validate the results of the simulations of direct shear testing on uniform-sized metal beads on the basis of laboratory experiments. The difference in the average angle of mobilized frictions was found to be only 1.0°. In addition, a very close match was found between dilatancy in the laboratory samples and in the simulations. A comprehensive study was then conducted to determine the failure and post-failure mechanism. We conclude with the presentation of a simulation of a direct shear test on real soil which demonstrated that Bullet has all the capabilities needed to be used as software for simulating granular systems.

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.

Rolling friction on a granular medium

We present experimental results for the rolling of spheres on a granular bed. We use two sets of glass and steel spheres with varying diameters and a high-speed camera to follow the motion of the spheres. Despite the complex phenomena occurring during the rolling, the results show a friction coefficient nearly independent of the velocity (0.45-0.5 for glass and 0.6-0.65 for steel). It is found that for a given sphere density, the large spheres reach a longer distance, a result that may also help explain the rock sorting along natural stone accumulations at the foot of mountain slopes.

Transport of a heated granular gas in a washboard potential

We study numerically the motion of a one dimensional array of Brownian particles in a washboard potential, driven by an external stochastic force and interacting via short range repulsive forces. In particular, we investigate the role of instantaneous elastic and inelastic collisions on the system dynamics and transport. The system displays a locked regime, where particles may move only via activated processes and a running regime where particles drift along the direction of the applied field. By tuning the value of the friction parameter controlling the Brownian motion we explore both the overdamped dynamics and the underdamped dynamics. In the two regimes we considered the mobility and the diffusivity of the system as functions of the tilt and other relevant control parameters such as coefficient of restitution, particle size, and total number of particles. We find that while in the overdamped regime the results for the interacting systems present similarities with the known noninteracting case, in the underdamped regime the inelastic collisions determine a rich variety of behaviors among which is an unexpected enhancement of the inelastic diffusion.

Hard-sphere limit of soft-sphere model for granular materials: stiffness dependence of steady granular flow

Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard-sphere limit of the soft-sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard-sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard-sphere limit, although the contact time fraction for the binary collisions tends to zero.

Rolling motion of a bead in a rapid water stream

This paper investigates the two-dimensional rolling motion of a single large particle in a shallow water stream down a steep rough bed from both an experimental and a theoretical point of view. The experiment is prototypal of sediment transport on sloping beds. Two theoretical models are presented. The first model uses the mean kinetic energy balance to deduce the average particle velocity and the bounds of the flow-rate range within which a rolling regime occurs. This range is found to be narrow, which means that the fully rolling regime is a marginal mode of transport between repose and saltation. In the second model, the particle state (resting, rolling, saltating) is considered as a random variable, whose evolution constitutes a jump Markov chain. This makes it possible to deduce the mean particle velocity as a function of the flow conditions without explicit mention of its state. The theoretical results are finally compared to the experimental data. The second model provides correct estimates of the particle velocity and the probability of finding the particle in a given state for various flow conditions (bead material, slope, and roughness).

Gravity-assisted segregation of granular materials of equal mass and size

High-resolution segregation is demonstrated for elastic granular materials of the same mass and size. Each grain starts at a randomly selected position in the entrance facet of a cylinder, accelerates downwards due to gravity, and then bounces against a massive obstacle with a collision cross section that is proportional to the facet size. Bounce dynamics of the falling grain is a function of its relative elasticity with the obstacle. Subsequent collisions of the grain with the wall are assumed to be perfectly elastic. In the absence of interparticle collisions, grain focusing occurs at points along the cylinder axis. In the absence of rotation, focusing occurs regardless of the initial locations and (downward) velocities of the grains at the entrance facet. The focus location depends only on the coefficient of restitution of the falling particle and the obstacle size. Grains arrive at the focus in temporally localized bursts even if released simultaneously from the facet. Efficient segregation is, therefore, achieved without additional mechanical work (e.g., shaking, spinning) on the system configuration.

Saltating motion of a bead in a rapid water stream

This paper experimentally and numerically investigates the two-dimensional saltating motion of a single large particle in a shallow water stream down a steep rough bed. The experiment is prototypical of sediment transport on sloping beds. Similar to the earlier experimental results on fine particles entrained by a turbulent stream, we found that most features of the particle motion were controlled by a dimensionless shear stress (also called the Shields number) N(Sh) defined as the ratio of the bottom shear stress exerted by the water flow to the buoyant weight of the particle (scaled by its cross-sectional area to obtain a stress). We did not observe a clear transition from rest to motion, but on the contrary there was a fairly wide range of N(Sh) (typically 0.001-0.005 for gentle slopes) for which the particle could be set in motion or come to rest. When the particle was set in motion, it systematically began to roll. The rolling regime was marginal in that it occurred for a narrow range of N(Sh) (typically 0.005-0.01 for gentle slopes). For sufficiently high Shields numbers (N(Sh)>0.3), the particle was in saltation. The mean particle velocity was found to vary linearly with the square root of the bottom shear stress and here, surprisingly enough, was a decreasing function of the channel slope. We also performed numerical simulations based on Lagrangian equations of motion. A qualitative agreement was found between the experimental data and numerical simulations but, from a quantitative point of view, the relative deviation was sometimes substantial (as high as 50%). An explanation for the partial agreement is the significant modification in the water flow near the particle.

Dynamics of a grain on a sandpile model

The dynamics of a macroscopic grain rolling on an inclined plane composed of fixed identical grains is investigated both experimentally and theoretically. As real sand, the system exhibits an hysteretic transition between static and dynamical states: for angles smaller than straight phi(d), the roller always stops, for angles larger than straight phi(s), it spontaneously starts rolling down. But for angles between straight phi(d) and straight phi(s), it can be either at rest or in motion with a constant velocity. It is shown that the limit velocity is given by the equilibrium between gravity driving and dissipation by the shocks. Moreover, the rough plane acts as a periodic potential trap whose width and depth decrease when the angle is increased: the static angle straight phi(s) corresponds to the angle for which the trap disappears; the dynamical angle straight phi(d) to that for which the limit velocity is sufficient to escape from the trap. Finally, a continuous description of the force globally acting on the grain is proposed, which preserves this hysteretic behavior.

Dynamics of spherical particles on a surface: collision-induced sliding and other effects

We present a model for the motion of hard spherical particles on a two-dimensional surface. The model includes both the interaction between the particles via collisions and the interaction of the particles with the substrate. We analyze in detail the effects of sliding and rolling friction, which are usually overlooked. It is found that the properties of this particulate system are influenced significantly by the substrate-particle interactions. In particular, sliding of the particles relative to the substrate after a collision leads to considerable energy loss for common experimental conditions. The presented results provide a basis that can be used to realistically model the dynamical properties of the system, and provide further insight into density fluctuations and related phenomena of clustering and structure formation.

Geometrical model for a particle on a rough inclined surface

A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good qualitative agreement with recent experiments on a ball moving on a rough inclined line.