Impact of a Projectile on a Granular Medium Described by a Collision Model (original) (raw)
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Physical Review E, 2003
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking techniques. We identify all particles in the system and link their positions to form trajectories over long times. Thus, we identify particle collisions to measure the effective coefficient of restitution and find a broad distribution of values for the same impact angles. We find that the energy inelasticity can take on values greater than one, which implies that the rotational degrees play an important role in energy transfer. We also measure the distance and the time between collision events in order to directly determine the distribution of path lengths and the free times. These distributions are shown to deviate from expected theoretical forms for elastic spheres, demonstrating the inherent clustering in this system. We describe the data with a two-parameter fitting function and use it to calculated the mean free path and collision time. We find that the ratio of these values is consistent with the average velocity. The velocity distribution are observed to be strongly non-Gaussian and do not demonstrate any apparent universal behavior. We report the scaling of the second moment, which corresponds to the granular temperature, and higher order moments as a function of distance from the driving wall. Additionally, we measure long time correlation functions in both space and in the velocities to probe diffusion in a dissipative gas.
Granular dynamics during impact
Physical review letters, 2014
We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. We vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of the linear depth-dependent term in the stopping force. We propose a simple model to account for the strain dependence of this term, owing to increased pressure in the pile. Interestingly, we find that the presence of the fluid does not affect the impact dynamics, suggesting that dynamic friction is not a factor. Using a laser sheet scanning technique to visualize internal grain motion, we measure the trajectory of each grain throughout an impact. Microscopically, our results indicate that weaker initial force chains result in more irreversible, plastic rearrangements, suggesting static friction between grains does play a substantial role in the energy dissipation.
Penetrating a granular medium by successive impacts
Physical Review E, 2022
We consider the penetration dynamics of a vertical cylinder into a dry granular medium subjected to successive impacts. The depth of the impactor below the free surface z_N first evolves linearly with the impact number N and then follows a power-law evolution z_N ∝ N^1/3. The depth reached by the cylinder after a given number of impacts is observed to increase with the impact energy, but to decrease with its diameter and the density of the granular medium. We develop a model that accounts for the quasistatic and inertial granular forces applying on the cylinder to rationalize our observations. This approach reveals the existence of two intrusion regimes for large and small impact numbers, allowing all data to be rescaled on a master curve. Then, we extend the study to the effect of sidewalls on the dynamics of the impactor. We show that lateral confinement changes the dependence of the impactor depth on the impact number z_N(N). This effect is accounted for by considering the increase of the granular drag with the lateral confinement.
Particle Scale Dynamics in Granular Impact
We perform an experimental study of granular impact, where intruders strike 2D beds of photoelastic disks from above. High-speed video captures the intruder dynamics and the local granular force response, allowing investigation of grain-scale mechanisms in this process. We observe rich acoustic behavior at the leading edge of the intruder, strongly fluctuating in space and time, and we show that this acoustic activity controls the intruder deceleration, including large force fluctuations at short time scales. The average intruder dynamics match previous studies using empirical force laws, suggesting a new microscopic picture, where acoustic energy is carried away and dissipated.
Microstructure evolution during impact on granular matter
Physical Review E, 2012
We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.
Sphere penetration by impact in a granular medium: A collisional process
Europhysics Letters, 2009
The penetration by a gravity-driven impact of a solid sphere into a granular medium is studied by two-dimensional simulations. The scaling laws observed experimentally for both the final penetration depth and the stopping time with the relevant physical parameters are here recovered numerically without the consideration of any microscopic solid friction but with dissipative collisions only. Dissipative collisional processes are thus found as essential in catching the penetration dynamics in granular matter whereas microscopic frictional processes can only be considered as secondary effects.
Drag-force regimes in granular impact
Physical Review E, 2014
We study the penetration dynamics of a projectile incident normally on a substrate comprising of smaller granular particles in three-dimensions using the discrete element method. Scaling of the penetration depth is consistent with experimental observations for small velocity impacts. Our studies are consistent with the observation that the normal or drag force experienced by the penetrating grain obeys the generalized Poncelet law, which has been extensively invoked in understanding the drag force in the recent experimental data. We find that the normal force experienced by the projectile consists of position and kinetic-energy-dependent pieces. Three different penetration regimes are identified in our studies for low-impact velocities. The first two regimes are observed immediately after the impact and in the early penetration stage, respectively, during which the drag force is seen to depend on the kinetic energy. The depth dependence of the drag force becomes significant in the third regime when the projectile is moving slowly and is partially immersed in the substrate. These regimes relate to the different configurations of the bed: the initial loose surface packed state, fluidized bed below the region of impact, and the state after the crater formation commences.
Model for collisions in granular gases
Physical Review E, 1996
We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision ͑smooth, reflecting or sticky͒ is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.