We use numerical simulation to investigate the effect an intruder's shape has on the drag and lift forces that it experiences while moving through a granular medium composed of polydisperse disks of mean diameter d. The intruder velocity,v, was varied from 0.1 \sqrt(dg) to 20 \sqrt(dg). For frictionless particles (μ= 0.0)there is a gradual increase in drag force with increasing v, whereas for frictional systems (μ= 0.1,0.5) a constant drag regime appears at low velocities. The drag force depends weakly on the shape of the object provided that the cross-section is same. The drag force depends linearly on the immersion depth, while there is very little variation in lift force with depth for certain shapes. The lift experienced by the object is a strong function of its shape at a given velocity. Shape has an effect on the distribution of contacts around the surface of the intruder which may result in a strong lift for certain shapes. We also show the force profiles around the intruder surface.
A simple model for intruder in vibrating granular bed is constructed by introducing a term that governs frequency dependent granular bed density. Varying the vibrating frequency will drive the buoyant force acting on the intruder by the granular bed. Swapped regions of rising and sinking intruder compared to other reported result have bee found.
Understanding the penetration dynamics of intruders in granular beds is relevant not only for fundamental physics, but also for geophysical processes and construction on sediments or granular soils in areas potentially affected by earthquakes. In this work, we use Lock-in accelerometry to study the penetration of intruders into quasi-2D granular matter fluidized by lateral shaking. We observed that there are two well-defined stages in the penetration dynamics as the intruder sinks into the granular material.
We consider the rearrangements of a vertical twodimensional granular packing induced by the withdrawal of an intruder. Here, we focus on the influence of the size of the intruder on the reorganization process. The long term evolution of the granular packing is investigated as well as the avalanche dynamics that characterize the short term rearrangements around the intruder. For small enough intruder, we observe the formation of arches that periodically destabilize and influence the reorganization dynamics of the two-dimensional packing through larger rearrangement events.
DEM simulations were used to study the sensitivity of a granular system to the change of the mechanical properties of the grains, applied to the penetration of a cylindrical intruder near a vertical wall. The simulations reproduce a real experimental setup, changing the friction, the Young modulus and the restitution coefficient of the particles.
The drag of an elliptic intruder in a two-dimensional granular environment is numerically studied. The movement parallel to the major axis of the intruder is found to be unstable. The drag law is given by the sum of the yield force and the dynamic term, the latter of which is approximately reproduced by a simple collision model. The flow field around the intruder for sufficiently larger drag force is well fitted by the streamlines obtained from the perfect fluid. The stress fields around the intruder are also investigated when the movement of the intruder is balanced with interactions with the…
When an object penetrates into granular matter near a boundary, it experiences a horizontal repulsion due to the intruder-grain-wall interaction. Here we show experimentally that a square cuboid intruder, released from rest with no initial velocity, neara vertical wall to its left, goes through three distinct kinds of motion: it first tilts clockwise, then 'slides' away from the wall,and finally tilts counterclockwise. This dynamic highly favors both repulsion and penetration of the cuboid intruder as compared to that observed from its release farther away from the wall
We study experimentally the dynamics of a dense intruder sinking under gravity inside a vibrated 2D granular packing. The surrounding flow patterns are characterized and the falling trajectories are interpreted in terms of an effectivive friction coefficient related to the intruder mean descent velocity (flow rules). At higher confining pressures i.e. close to jamming, a transition to intermittent dynamics is evidenced and displays anomalous "on-off" blockade statistics. A systematic analysis of the flow rules, obtained for different intruder sizes, either in the flowing regime or averaged ove…
We computationally determine the force on single spherical intruder particles in sheared granular flows as a function of particle size, particle density, shear rate, overburden pressure, and gravitational acceleration. The force scales similarly to, but deviates from, the buoyancy force predicted by Archimedes' principle. The deviation depends only on the intruder to bed particle size ratio, but not the density ratio or flow conditions. We propose a simple force model that successfully predicts whether intruders rise or sink, knowing only the size and density ratios, for a variety of flow conf…
A model is developed to explain rise time of a spherical intruder placed in a granular bed, which is considered as fluid. Phenomenon of rising intruder in a granular bed is well known as Brazil nut effect. Radius of the intruder is varied with $R_n = R_0 n, n = 1 .. 10$. An approximation for $t << τ$ is chosen in order to simplify the solution of second order differential equation of intruder vertical position to obtain the rise time T. A non-physical parameter $α$ and also transformation from $T$ to $T'$ are needed to be introduced in order to control the results to mimic reported experiment …
We investigate experimentally the dynamics of an intruder dragged by a constant force in an assembly of horizontally vibrated grains close to jamming. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value of the packing fraction which increases with the applied force, the intruder exhibits an intermittent creep motion with strong fluctuations reminiscent of a crackling noise signal. These fluctuations behave in a critical manner at the jamming transition unveilled in a previous study. The transition separates a regime where the in…
A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction $\sim 10-50%$ the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the Fluctuation-Dissipation relation and the presence of a net entropy flux - from the flu…
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, sugg…
Using simulations and a virtual-spring-based approach, we measure the segregation force, Fseg, over a range of size-bidisperse mixture concentrations, particle size ratios, and shear rates to develop a model for Fseg that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single intruder assumption applies and provides an accurate description of the pressure partitioning between species.
When a cylindrical object penetrates granular matter near a vertical boundary, it experiences two effects: its center of mass moves horizontally away from the wall, and it rotates around its symmetry axis. Here we show experimentally that, if two identical intruders instead of one are released side-by-side near the wall, both effects are also detected. However, unexpected phenomena appear due to a cooperative dynamics between the intruders. The net horizontal distance traveled by the common center of mass of the twin intruders is much larger than that traveled by one intruder released at the s…
The drag of two cylindrical intruders in a two-dimensional granular environment is numerically studied by the discrete element method. We find the yield force, below which the intruders cannot move because of interactions with the surrounding particles. Above the yield force, on the other hand, the intruders can move at a constant speed. We investigate the relationship between the drag force and the steady speed of the intruders, where the speed becomes higher as the distance between the intruders decreases. We confirm that the origin of the yield is the Coulombic friction between the particle…
Projectile impact into a light granular material composed of expanded polypropylene (EPP) particles is investigated systematically with various impact velocities. Experimentally, the trajectory of an intruder moving inside the granular material is monitored with a recently developed non-invasive microwave radar system. Numerically, discrete element simulations together with coarse-graining techniques are employed to address both dynamics of the intruder and response of the granular bed. Our experimental and numerical results of the intruder dynamics agree with each other quantitatively and are…
We experimentally study quasi-2d dilute granular flow around intruders whose shape, size and relative impact speed are systematically varied. Direct measurement of the flow field reveals that three in-principle independent measurements of the non-uniformity of the flow field are in fact all linearly related: 1) granular temperature, 2) flow field divergence and 3) shear-strain rate. The shock front is defined as the local maxima in each of these measurements. The shape of the shock front is well described by an inverted catenary and is driven by the formation of a dynamic arch during steady fl…
We study experimentally and computationally the dynamics of granular flow during impacts, where intruders strike a collection of disks from above. In the regime where granular force dynamics are much more rapid than the intruder motion, we find that the particle flow near the intruder is proportional to the instantaneous intruder speed; it is essentially constant when normalized by that speed. The granular flow is nearly divergence-free and remains in balance with the intruder, despite the latter's rapid deceleration. Simulations indicate that this observation is insensitive to grain propertie…
We study the dynamic process occurring when a granular assembly is displaced by a solid impactor. The momentum transfer from the impactor to the target is shown to occur through sporadic, normal collisions of high force carrying grains at the intruder surface. We therefore describe the stopping force of the impact through a collisional based model. To verify the model in impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium using high-speed imaging of its trajectory. By varying the intruder shape and granular target, intruder-grain inter…
We compute the mean square displacement (MSD) of intruders immersed in a freely cooling granular gas made up of smooth inelastic hard spheres. In general, intruders and particles of the granular gas are assumed to have different mechanical properties, implying that non-equipartition of energy must be accounted for in the computation of the diffusion coefficient $D$. In the hydrodynamic regime, the time decay of the granular temperature $T$ of the cooling granular gas is known to be dictated by Haff's law; the corresponding decay of the intruder's collision frequency entails a time decrease of …
We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intru…
Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.
The impact of single passive intruders into granular particles has been studied in detail. However, the impact force produced by multiple intruders separated at a distance from one another, and hence the effect of their presence in close proximity to one another, is largely unexplored. Here, we use numerical simulations and laboratory experiments to study the force response of two parallel rods intruding vertically into granular media while varying the gap spacing between them. We also explored the effect of variations in friction, intruder size, and particle size on the force response. The ne…
We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a 2D granular material comprised of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: a frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid …
When an intruder strikes a granular material from above, the grains exert a stopping force which decelerates and stops the intruder. Many previous studies have used a macroscopic force law, including a drag force which is quadratic in velocity, to characterize the decelerating force on the intruder. However, the microscopic origins of the force law terms are still a subject of debate. Here, drawing from previous experiments with photoelastic particles, we present a model which describes the velocity-squared force in terms of repeated collisions with clusters of grains. From our high speed phot…
The intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media. We propose a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder. From the analytic solution of the segregation velocity we can analyze the transition from the upward to downward intruder's movement.
We report a new lift force model for intruders in dense, granular shear flows. Our derivation is based on the thermal buoyancy model of Trujillo & Hermann[L. Trujillo and H. J. Herrmann, Physica A 330, 519 (2003).], but takes into account both granular temperature and pressure differences in the derivation of the net buoyancy force acting on the intruder. In a second step the model is extended to take into account also density differences between the intruder and the bed particles. The model predicts very well the rising and sinking of intruders, the lift force acting on intruders as determine…
We investigate the motion of groups of intruders in a two-dimensional granular system by using discrete numerical simulations. By imposing either a constant velocity or a thrusting force on larger disks (intruders) that move within smaller ones (grains), we obtained instantaneous positions and components of forces for each intruder and grain. We found that (i) intruders cooperate even when at relatively large distances from each other; (ii) the cooperative dynamics is the result of contact chains linking the intruders as well as compaction and expansion of the granular medium in front and behi…
We discuss the results of simulations of an intruder pulled through a two-dimensional granular system by a spring, using a model designed to lend insight into the experimental findings described by Kozlowski et al. [Phys. Rev. E, 100, 032905 (2019)]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions …
We investigate computationally the pullout of a spherical intruder initially buried at the bottom of a granular column. The intruder starts to move out of the granular bed once the pulling force reaches a critical value, leading to material failure. The failure point is found to depend on the diameter of the granular column, pointing out the importance of particle-wall interaction in determining the material response. Discrete element simulations show that prior to failure, the contact network is essentially static, with only minor rearrangements of the particles. However, the force network, w…
We investigate the effective friction encountered by an intruder moving through a sedimented medium which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction $μ_e$ on a spherical intruder is captured by the inertial number $I$ given by the ratio of the time scale over which the intruder moves and the inertial time scale of the granular medium set by the overburden pressure. Further, $μ_e$ is described by the function $μ_e(I) = μ_s + αI^β$, where $μ_s$ is the static friction, and $α$ and $β$ are material depen…
Applying mechanical perturbations in a granular assembly may rearrange the configuration of the particles. However, the spatial propagation of an event is not related to the size of the external perturbation alone. Thus, the characteristic length scale of an event is not well defined. In this study, we trigger rearrangements by driving two intruders through a vertical two-dimensional packing of disks. The amplitude of the rearrangements of the granular assembly appearing around the two evolving intruders is related to their separating distances. We show that there exists a characteristic dista…
We measure the quasi-static friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasi-static…
The drag acting on an intruder in a three-dimensional frictionless dry granular environment is numerically studied. It is found the followings: (i) There is no yield force for the motion of the intruder without the gravity. (ii) The drag is proportional to the cross section of the moving intruder. (iii) If the intruder is larger than surrounding grains, the drag is proportional to the moving speed $V$ of the intruder for dense systems, but it exhibits a crossover from quadratic to linear dependences of the moving speed when the volume fraction of the surrounding grains is much lower than the j…
Impact of an intruder on granular matter leads to formation of mesoscopic force networks seen particularly clearly in the recent experiments carried out with photoelastic particles, e.g., Clark et al., Phys. Rev. Lett., 114 144502 (2015). These force networks are characterized by complex structure and evolve on fast time scales. While it is known that total photoelastic activity in the granular system is correlated with the acceleration of the intruder, it is not known how the structure of the force network evolves during impact, and if there is a dominant features in the networks that can be …
We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call "fluidisation" this first transition. A second transition is observed within the intermit…
Making use of the system of pulling a spherical intruder in static three-dimensional granular media, we numerically study the scaling law for the drag force $F_{\rm drag}$ acting on the moving intruder under the influence of the gravity. Suppose if the intruder of diameter $D$ immersed in a granular medium consisting of grains of average diameter $d$ is located at a depth $h$ and moves with a speed $V$, we find that $F_{\rm drag}$ can be scaled as $(D+d)^{ϕ_μ} h^{α_μ}$ with two exponents $ϕ_μ$ and $α_μ$, which depend on the friction coefficient $μ$ and satisfy an approximate sum rule $ϕ_μ+α_μ\…
We show how the Gillespie algorithm, originally developed to describe coupled chemical reactions, can be used to perform numerical simulations of a granular intruder particle colliding with thermalized bath particles. The algorithm generates a sequence of collision ``events'' separated by variable time intervals. As input, it requires the position-dependent flux of bath particles at each point on the surface of the intruder particle. We validate the method by applying it to a one-dimensional system for which the exact solution of the homogeneous Boltzmann equation is known and investigate the …
Recently, a new nonlocal granular rheology was successfully used to predict steady granular flows, including grain-size-dependent shear features, in a wide variety of flow configurations, including all variations of the split-bottom cell. A related problem in granular flow is that of mechanically-induced creep, in which shear deformation in one region of a granular medium fluidizes its entirety, including regions far from the sheared zone, effectively erasing the yield condition everywhere. This enables creep deformation when a force is applied in the nominally quiescent region through an intr…
We study the dynamics of an intruder moving through a fluidized granular medium in three dimensions ($d=3$). The intruder and grains have both translational and rotational degrees of freedom. The energy-dissipation mechanism is solid friction between all pairs of particles. We keep the granular system fluidized even at rather high densities by randomly perturbing the linear and angular velocities of the grains. We apply a constant external force of magnitude $F$ to the intruder, and obtain its steady state velocity $V_s$ in the center-of-mass frame of the grains. The $F$-$V_s$ relation is of g…
Recently, experiments showed that forces on intruders dragged horizontally through dense, hydrostatic granular packings mainly depend on the local surface orientation and can be seen as the sum of the forces exerted on small surface elements. In order to understand such forces more deeply, we perform 2D soft-sphere molecular dynamics simulation, on similar set up, of an intruder dragged through a 50-50 bi-disperse granular packing, with diameters 0.30 and 0.34 cm. We measure, for both circular and half-circle shapes, the forces parallel (drag) and perpendicular (lift) to the drag direction as …
We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions base…
We study the quasi-static penetration of a flexible beam in a two-dimensional dense granular medium lying on an horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading/unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single non dimensional parameter: L/Lc, the ratio of the length of the flexible beam L to Lc, a bending …
We study the compaction and mobility properties of a dense granular material under weak random vibration. By putting in direct contact millimetric glass beads with piezoelectric transducers we manage to inject energy to the system in a disordered manner with accelerations much smaller than gravity, resulting in a slow compaction dynamics and no convection. We characterize the mobility inside the medium by pulling through it an intruder grain at constant velocity. We present an extensive study of the relation between drag force and velocity for different vibration conditions and sizes of the in…
The rheological properties of granular matter within a two-dimensional flow around a moving disk is investigated experimentally. Using a combination of photoelastic and standard tessellation techniques, the strain and stress tensors are estimated at the grain scale in the time-averaged flow field around a large disk pulled at constant velocity in an assembly of smaller disks. On the one hand, one observes inhomogeneous shear rate and strongly localized shear stress and pressure fields. On the other hand, a significant dilation rate, which has the same magnitude as the shear strain rate, is rep…
We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces, and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, amplitude, and the packing density of grains. We de…
We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the mass density of the grains, and the elastic modulus of the grains according to power-law scaling forms that a…
