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 functions of the drag speed, with V=10.3-309 cm/s, and intruder depths, with D=3.75-37.5 cm. The drag forces on an intruder monotonically increase with V and D, and are larger for the circle. However, the lift force does not depend monotonically on V and D, and this relationship is affected by the shape of the intruder. The vertical force was negative for the half-circle, but for a small range of V and D, we measure positive lift. We find no sign change for the lift on the circle, which is always positive. The explanation for the nonmonotonic dependence is related to the decrease in contacts on the intruder as V increases. This is qualitatively similar to supersonic flow detachment from an obstacle. The detachment picture is supported by simulation measurements of the velocity field around the intruder and force profiles measured on its surface.
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…
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…
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…
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 l…
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\…
Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be reproduced by a simple analysis of a collision model between the intruder and particle flows. The crossover from Epstein's law to Stokes' law is also found for the low-speed regime as the time evolution of the drag force caused by beam particles. We also show the existence of turbulent-like behavior of the particle flows behind the intruder with the aid of the …
We report on experimentally measured drag force experienced by a solid cylinder penetrating a granular bed of glass beads including, specifically, a highly polydisperse sample with grain sizes in the range 1-100 μm. We consider both cases of lateral and axial intrusion in which the long axis of the cylinder is held horizontally and vertically, respectively. We explore different regimes of behavior for the drag force as a function of the penetration depth. In lateral intrusion, where the motion is effectively quasi-two-dimensional, we establish quantitative comparisons with existing theoretical…
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…
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 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 study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $ξ= F_\perp/F_\parallel$ is…
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 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…
This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisio…
Predicting the force exerted on an object as it penetrates a granular medium is of interest in engineering, locomotive, and geotechnical applications. Current models of granular drag, however, vary widely in applicability and parameterization, and the physical origin of the granular resistive force itself is a subject of debate. Here we perform constant speed penetration experiments, combined with calibrated, large-scale molecular dynamics simulations, at velocities up to 2 m/s to test the effect of impact velocity on the depth dependent `hydrostatic' drag force. We discover that the evolution…
We show how a weak force, $f$, enables intruder motion through dense granular materials subject to external mechanical excitations, in the present case stepwise shearing. A force acts on a Teflon disc in a two dimensional system of photoelastic discs. This force is much smaller than the smallest force needed to move the disc without any external excitation. In a cycle, material + intruder are sheared quasi-statically from $γ= 0$ to $γ_{max}$, and then backwards to $γ= 0$. During various cycle phases, fragile and jammed states form. Net intruder motion, $δ$, occurs during fragile periods genera…
The drag force exerted on an object intruding into granular media can depend on the object's velocity as well as the depth penetrated. We report on intrusion experiments at constant speed over four orders in magnitude together with systematic molecular dynamics simulations well beyond the quasi-static regime. We find that velocity dependence crosses over to depth dependence at a characteristic time after initial impact. This crossover time scale, which depends on penetration speed, depth, gravity and intruder geometry, challenges current models that assume additive contributions to the drag.
Compared to agile legged animals, wheeled and tracked vehicles often suffer large performance loss on granular surfaces like sand and gravel. Understanding the mechanics of legged locomotion on granular media can aid the development of legged robots with improved mobility on granular surfaces; however, no general force model yet exists for granular media to predict ground reaction forces during complex limb intrusions. Inspired by a recent study of sand-swimming, we develop a resistive force model in the vertical plane for legged locomotion on granular media. We divide an intruder of complex m…
Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This multi-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this behavior by modeling the media at the grain scale, but there is often interest in the macro-scale characterizations of such systems. We examine the efficacy of a m…
Characterizing forces on deformable objects intruding into sand and soil requires understanding the solid and fluid-like responses of such substrates and their effect on the state of the object. The most detailed studies of intrusion in dry granular media have revealed that interactions of fixed-shape objects during free impact (e.g. cannonballs) and forced slow penetration can be described by hydrostatic and hydrodynamic-like forces. Here we investigate a new class of granular interactions: rapid intrusions by objects that change shape (self-deform) through passive and active means. Systemati…
