Steady flow dynamics during granular impact

Force on a sphere suspended in flowing granulate

We investigate the force of flowing granular material on an obstacle. A sphere suspended in a discharging silo experiences both the weight of the overlaying layers and drag of the surrounding moving grains. In experiments with frictional hard glass beads, the force on the obstacle was practically flow-rate independent. In contrast, flow of nearly frictionless soft hydrogel spheres added drag to the gravitational force. The dependence of the total force on the obstacle diameter is qualitatively different for the two types of material: It grows quadratically with the obstacle diameter in the soft, low-friction material, while it grows much weaker, nearly linearly with the obstacle diameter, in the bed of glass spheres. In addition to the drag, the obstacle embedded in flowing low-friction soft particles experiences a total force from the top as if immersed in a hydrostatic pressure profile, but a much lower counterforce acting from below. In contrast, when embedded in frictional, hard particles, a strong pressure gradient forms near the upper obstacle surface.

Added-mass force in dry granular matter

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient C_{AM} which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient C_{AM} is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

Effect of two parallel intruders on total work during granular penetrations

The intrusion of single passive intruders into granular particles has been studied in detail. However, the intrusion 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 less explored. Here, we used 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 total work (W) of the two rods over the depth of intrusion was measured, and the instantaneous velocities of particles over the duration of intrusion were calculated by simulations. We found that the total work done by the intruders changes with distance between them. We observed a peak in W at a gap spacing of ∼3 particle diameters, which was up to 25% greater than W at large separation (>11 particle diameters), beyond which the total work plateaued. This peak was likely due to reduced particle flow between intruders as we found a larger number of strong forces-identified as force chains-in the particle domain at gaps surrounding the peak force. Although higher friction caused greater force generation during intrusion, the gap spacing between the intruders at which the peak total work was generated remained unchanged. Larger intruder sizes resulted in greater total work with the peak in W occurring at slightly larger intruder separations. Taken together, our results show that peak total work done by two parallel intruders remained within a narrow range, remaining robust to most other tested parameters.

Surprising simplicity in the modeling of dynamic granular intrusion

Granular intrusions, such as dynamic impact or wheel locomotion, are complex multiphase phenomena where the grains exhibit solid-like and fluid-like characteristics together with an ejected gas-like phase. Despite decades of modeling efforts, a unified description of the physics in such intrusions is as yet unknown. Here, we show that a continuum model based on the simple notions of frictional flow and tension-free separation describes complex granular intrusions near free surfaces. This model captures dynamics in a variety of experiments including wheel locomotion, plate intrusions, and running legged robots. The model reveals that one static and two dynamic effects primarily give rise to intrusion forces in such scenarios. We merge these effects into a further reduced-order technique (dynamic resistive force theory) for rapid modeling of granular locomotion of arbitrarily shaped intruders. The continuum-motivated strategy we propose for identifying physical mechanisms and corresponding reduced-order relations has potential use for a variety of other materials.

Power-Law Scaling of Early-Stage Forces during Granular Impact

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 stiffness of the grains, and the mass density of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggests that they may also apply to impacts into similar materials like foams and emulsions.

The role of initial speed in projectile impacts into light granular media

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 in congruent with existing phenomenological model on granular drag. Stepping further, we explore the ‘microscopic’ origin of granular drag through characterizing the response of granular bed, including density, velocity and kinetic stress fields at the mean-field level. In addition, we find that the dynamics of cavity collapse behind the intruder changes significantly when increasing the initial speed . Moreover, the kinetic pressure ahead of the intruder decays exponentially in the co-moving system of the intruder. Its scaling gives rise to a characteristic length scale, which is in the order of intruder size. This finding is in perfect agreement with the long-scale inertial dissipation type that we find in all cases.

Collision-based understanding of the force law in granular impact dynamics

We study the stopping force felt by an intruder impacting onto a granular medium. Variations in the shape of the intruder can influence the penetration depth by changing the inertial drag. We find this observed correlation can be explained by associating the velocity-dependent inertial drag to the energy dissipation that occurs through intermittent collisions of force-chain-like clusters, the mean behavior of which can be statistically described. In consequence, the stopping force can be captured through a proposed collisional model with good accuracy, and the observed impact dynamics data can be reproduced quantitatively.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a 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 and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.

Granular response to impact: Topology of the force networks

The impact of an intruder on granular matter leads to the formation of mesoscopic force networks, which were seen particularly clearly in the recent experiments carried out with photoelastic particles [Clark et al., Phys. Rev. Lett. 114, 144502 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.144502]. 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 are dominant features in the networks that can be used to describe the intruder's dynamics. Here, we use topological tools, in particular persistent homology, to describe these features. Persistent homology allows quantification of both structure and time evolution of the resulting force networks. We find that there is a clear correlation of the intruder's dynamics and some of the topological measures implemented. This finding allows us to discuss which properties of the force networks are most important when attempting to describe the intruder's dynamics. In particular, we find that the presence of loops in the force network, quantified by persistent homology, is strongly correlated to the deceleration of the intruder. In some cases, particularly for the impact on soft particles, the measures derived from the persistence analysis describe the deceleration of the intruder even better than the total photoelastic activity. We are also able to define an upper bound on the relevant time scale over which the force networks evolve.

Force and Mass Dynamics in Non-Newtonian Suspensions

Above a certain solid fraction, dense granular suspensions in water exhibit non-Newtonian behavior, including impact-activated solidification. Although it has been suggested that solidification depends on boundary interactions, quantitative experiments on the boundary forces have not been reported. Using high-speed video, tracer particles, and photoelastic boundaries, we determine the impactor kinematics and the magnitude and timings of impactor-driven events in the body and at the boundaries of cornstarch suspensions. We observe mass shocks in the suspension during impact. The shock front dynamics are strongly correlated to those of the intruder. However, the total momentum associated with this shock never approaches the initial impactor momentum. We also observe a faster second front associated with the propagation of pressure to the boundaries of the suspension. The two fronts depend differently on the initial impactor speed v_{0} and the suspension packing fraction. The speed of the pressure wave is at least an order of magnitude smaller than (linear) ultrasound speeds obtained for much higher frequencies, pointing to complex amplitude and frequency response of cornstarch suspensions to compressive strains.

Asteroid surface impact sampling: dependence of the cavity morphology and collected mass on projectile shape

In-situ exploration and remote thermal infrared observation revealed that a large fraction of Solar System small bodies should be covered with granular regolith. The complex and varied geology of the regolith layer may preserve the historical records of the surface modification and topographic evolution experienced by asteroids, especially cratering processes, in which the projectile shape plays a crucial role. Regarding the impact sampling scheme, the projectile-shape dependence of both the cavity morphology and the collected mass remains to be explored. This paper studies the process of the low-speed impact sampling on granular regolith using projectiles of different shapes. The results demonstrate that the projectile shape significantly influences the excavation stage, forming cavities with different morphologies, i.e., cone-shaped, bowl-shaped and U-shaped. We further indicate that the different velocity distributions of the ejecta curtains due to the various projectile shapes result in various amounts of collected mass in sampler canister, regarding which the 60° conical projectile exhibits preferable performance for impact sampling scheme. The results presented in this article are expected to reveal the dependence of the excavation process on projectile shape under micro gravity and provide further information on the optimal designs of impact sampling devices for future sample-return space missions.

Universality in quasi-two-dimensional granular shock fronts above an intruder

We experimentally study quasi-two-dimensional 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 nonuniformity 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 flow. We find universality in the functional form of the shock front within the range of experimental values probed. Changing the intruder size, concavity, and impact speed only results in a scaling and shifting of the shock front. We independently measure the horizontal lift force on the intruder and find that it can be understood as a result of the interplay between the shock profile and the intruder shape.

Grain-scale modeling and splash parametrization for aeolian sand transport

The collision of a spherical grain with a granular bed is commonly parametrized by the splash function, which provides the velocity of the rebounding grain and the velocity distribution and number of ejected grains. Starting from elementary geometric considerations and physical principles, like momentum conservation and energy dissipation in inelastic pair collisions, we derive a rebound parametrization for the collision of a spherical grain with a granular bed. Combined with a recently proposed energy-splitting model [Ho et al., Phys. Rev. E 85, 052301 (2012)PLEEE81539-375510.1103/PhysRevE.85.052301] that predicts how the impact energy is distributed among the bed grains, this yields a coarse-grained but complete characterization of the splash as a function of the impact velocity and the impactor-bed grain-size ratio. The predicted mean values of the rebound angle, total and vertical restitution, ejection speed, and number of ejected grains are in excellent agreement with experimental literature data and with our own discrete-element computer simulations. We extract a set of analytical asymptotic relations for shallow impact geometries, which can readily be used in coarse-grained analytical modeling or computer simulations of geophysical particle-laden flows.