Lift and drag in intruders moving through hydrostatic granular media at high speeds

Finite size effects during the penetration of objects in a granular medium

In many industrial or geotechnical applications, objects move through a granular medium and an important issue is the prediction of the force that develops during the motion of the intruder. In this paper, we experimentally study the vertical penetration of intruders into granular media and analyze both the average force and the fluctuations during motion. We investigate configurations where the size of the intruder becomes close to a few grain sizes, a regime that has not been studied before. Finite size effects are observed, showing that both the mean force and the fluctuations significantly increase when decreasing the ratio of the intruder size to the particle size, and scaling laws are identified to characterize this effect. The role of a conical tip in front of the cylinder to facilitate the penetration is also studied, showing that it is more efficient when the aspect ratio between the intruder size and the grain size is low.

Biomimetic intruder tip design for horizontal penetration into a granular pile

In nature, woodpeckers peck trees with no reported brain injury. A highly functional system comprising a hyoid bone, smooth skull, straight pointed beak with varying lengths of upper and lower beak bones, and rhamphotheca is one of the adaptations that enable efficient pecking. Soil penetration is an energy-intensive procedure used in civil infrastructure applications and is often followed by pushing, impact driving, and digging. This study uses discrete element modeling to evaluate the effect of woodpecker beak mimetic intruder tip design with wedge offsets on lift and drag forces during horizontal penetration into granular piles. The findings show that the wedge offsets of the intruder have a negligible effect on drag forces. By contrast, lift forces can be manipulated by adjusting the top and bottom offsets of the intruder, which can be used to guide the intruder upward, downwards, or horizontally. Furthermore, as the width of the intruder increased, the lift and drag forces also increased.

Drag on a circular intruder traversing a shape-heterogeneous granular mixture

The main aim of our work is to explore the effect of particle shape heterogeneity on the dynamics of an intruder moving through a two-dimensional mixture of dumbbells and disks. In spite of similar physical conditions (the mass of the dumbbell is the same as that of the disk) and the same area fraction, we noticed a significant difference in the drag experienced by the intruder as the mixture concentration varies. The propagation of stress from the intruder to the granular grains manifests in the form of force chains, and interestingly these force chains can vary significantly depending on the shape of the grains. These differences, however, appear to be suppressed in the frictionless case where the force chains cannot extend very far from the initial point of contact. Apart from particle shape, the effect of the area fraction of the system and the size of the intruder have also been explored. As the area fraction increases, the drag force on the intruder increases owing to the increase in the contact forces. Finally, we present the velocity and stress fields at different dumbbell fractions and for various intruder diameters to show the effect of the moving intruder on its surrounding particles.

Dynamical behaviors of self-propulsion intruder buried in granular materials

Self-propulsion intruder motion in particles is common in the field of biomimetic and exploration instrument development. In this paper, numerical simulations and laboratory experiments are conducted for the spiral upward phenomenal motion of self-propulsion spherical intruder in granular media. Dynamic particle buoyancy and particle Saffman lift are proposed to establish a dynamic model of the intruder under horizontal simple harmonic excitations. The dependencies of the net particle lift force on the horizontal displacement and the local fluidization parameters of granular are discussed. The results show that horizontal displacement of the intruder and the coordination number of particles are jointly determined by the excitation amplitude and frequency, and the intruder starts to rise when they simultaneously reach the critical value. The dynamic particle buoyancy and particle Saffman lift have clarified the ascent mechanics. Meanwhile, the motion trajectory of intruder in space is inverted conical spiral, and the vibration causes the gap filling effect after the local particle fluidization is the mechanism of the intruder floating up motion.

Controlling subterranean forces enables a fast, steerable, burrowing soft robot

Robotic navigation on land, through air, and in water is well researched; numerous robots have successfully demonstrated motion in these environments. However, one frontier for robotic locomotion remains largely unexplored-below ground. Subterranean navigation is simply hard to do, in part because the interaction forces of underground motion are higher than in air or water by orders of magnitude and because we lack for these interactions a robust fundamental physics understanding. We present and test three hypotheses, derived from biological observation and the physics of granular intrusion, and use the results to inform the design of our burrowing robot. These results reveal that (i) tip extension reduces total drag by an amount equal to the skin drag of the body, (ii) granular aeration via tip-based airflow reduces drag with a nonlinear dependence on depth and flow angle, and (iii) variation of the angle of the tip-based flow has a nonmonotonic effect on lift in granular media. Informed by these results, we realize a steerable, root-like soft robot that controls subterranean lift and drag forces to burrow faster than previous approaches by over an order of magnitude and does so through real sand. We also demonstrate that the robot can modulate its pullout force by an order of magnitude and control its direction of motion in both the horizontal and vertical planes to navigate around subterranean obstacles. Our results advance the understanding and capabilities of robotic subterranean locomotion.

Hysteresis of the drag force of an intruder moving into a granular medium

We numerically investigate the force-displacement relation of a moving intruder initially at rest into a granular medium. Our model granular medium is composed of one layer of coplanar polydisperse spheres subjected to a gravity field. The interactions between the grains are modelled by Hertzian contacts to which a viscous damping is applied. Moving it horizontally and with alternating positive and negative velocity, we recover a hysteresis of the force-displacement curve. Considering that the flow is plastic as the yield strength has been reached, we describe the transient part of the flow around the intruder. We show that the drag stress increases as its distance to an ultimate drag stress [Formula: see text] with a typical deformation [Formula: see text]: the drag stress-strains curve appears to exponentially decay as it saturates to this ultimate drag stress. This protocol of deformation highlights that the deformation of the grains is negligible compared to the deformation of the packing, i.e. related to the irreversible displacements of grains allowing the intruder to pass through. Simultaneously, the lift force is constant on average during the displacement of the intruder. We then give the different scaling laws of the yield strength, this ultimate drag stress, the characteristic deformation of the packing and the lift stress. Finally, we recover the complete hysteresis cycle of the drag force around the intruder.

Evidence of reverse and intermediate size segregation in dry granular flows down a rough incline

In a dry granular flow, size segregation had been shown to behave differently for a mixture containing a few large particles with a size ratio above 5 [N. Thomas, Phys. Rev. E 62, 961 (2000)1063-651X10.1103/PhysRevE.62.961]. For moderately large size ratios, large particles migrate to an intermediate depth in the bed: this is called "intermediate segregation." For the largest size ratios, large particles migrate down to the bottom of the flow: this is called "reverse segregation," in contrast with surface segregation. As the reversal and intermediate depth values depend on the fraction of particles, this numerical study mainly uses one single large tracer. Small fractions of large beads are also computed showing the link between single tracer behavior and collective segregation process. For each device (half-filled rotating tumbler and rough plane), two (2D) and three (3D) dimensional cases are distinguished. In the tumbler, the trajectories of a large tracer show that it reaches a constant depth during the flowing phase. For large size ratios, this depth is intermediate. A progressive sinking of the depth is obtained when the size ratio is increased. The largest size ratios correspond to tracers being at the bottom of the flowing layer. All 3D simulation results are in quantitative agreement with the experimental surface, intermediate, and reverse-segregation results. In the flow down a rough incline, a large tracer reaches an equilibrium depth during flow. For large size ratios, the depth is inside the bed, at an intermediate position, and for the largest size ratios, this depth is reverse, located near the bottom. Results are slightly different for a thin or a thick flow. For 3D thick flows, the reversal between surface and bottom positions occurs within a short range of size ratios: no tracer stabilizes near half-height and two reachable intermediate depth layers exist, below the surface and above the bottom reverse layer. For 3D thin flows, all intermediate depths are reachable by a tracer, depending on the size ratio. The numerical study of larger fractions of tracers (5% or 10%) shows the three segregation patterns (surface, intermediate, reverse) corresponding to the three types of equilibrium depth. The reversal is smoother than for a single tracer, and happens around the size ratio 4.5, in good agreement with experiments.

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.

Vertical dynamics of a horizontally oscillating active object in a two-dimensional granular medium

We use a discrete-element method simulation and analytical considerations to study the dynamics of a self-energized object, modeled as a disk, oscillating horizontally within a two-dimensional bed of denser and smaller particles. We find that, for given material parameters, the immersed object (IO) may rise, sink, or not change depth, depending on the oscillation amplitude and frequency, as well as on the initial depth. With time, the IO settles at a specific depth that depends on the oscillation parameters. We construct a phase diagram of this behavior in the oscillation frequency and velocity amplitude variable space. We explain the observed rich behavior by two competing effects: climbing on particles, which fill voids opening under the disk, and sinking due to bed fluidization. We present a cavity model that allows us to derive analytically general results, which agree very well with the observations and explain quantitatively the phase diagram. Our specific analytical results are the following. (i) Derivation of a critical frequency, f_{c}, above which the IO cannot float up against gravity. We show that this frequency depends only on the gravitational acceleration and the IO size. (ii) Derivation of a minimal amplitude, A_{min}, below which the IO cannot rise even if the frequency is below f_{c}. We show that this amplitude also depends only on the gravitational acceleration and the IO size. (iii) Derivation of a critical value, g_{c}, of the IO's acceleration amplitude, below which the IO cannot sink. We show that the value of g_{c} depends on the characteristics of both the IO and the granular bed, as well as on the initial IO's depth.

Numerical investigation of the cylinder movement in granular matter

We investigate numerically the mechanisms governing horizontal dragging of a rigid cylinder buried inside granular matter, with particular emphasis on enumerating drag and lift forces that resist cylinder movement. The recently proposed particle finite element method is employed, which combines the robustness of classical continuum mechanics formulations in terms of representing complex aspects of the material constitutive behavior, with the effectiveness of discrete element methods in simulating ultralarge deformation problems. The investigation focuses on the effect of embedment depth, cylinder roughness, granular matter macromechanical properties, and of the magnitude of the cylinder's horizontal displacement on the amplitude of the resisting forces, which are discussed in light of published experimental data. Interpretation of the results provides insight on how the material flow around the cylinder affects the developing resistance, and a mechanism is proposed to describe the development of a steady-state drag force at large horizontal movements of the cylinder.

Drag force on a spherical intruder in a granular bed at low Froude number

The drag force on an object, or "intruder," in a granular material arises from interparticle friction, as well as the cyclic creation and buckling of force chains within the material. In contrast to fluids, for which drag forces are well understood, there is no straightforward relationship between speed and mean drag force in granular materials. We investigate spherical intruder particles of varying radii moving at low speeds through granular beds. The system can be parametrized using the dimensionless Froude number Fr=2v/√[gR], for intruders of radius R moving at a speed v. For frictional systems, we find the drag force obeys a linear relationship with Fr for low Froude numbers above Fr>1. For Fr<1 we observe a deviation from this linear trend. This transition can be explained by considering the characteristic inertial and gravitational granular time scales of the system. We show that a suitably normalized measure of dissipated power obeys a linear relationship with the imposed intruder velocity, independent of the intruder dimensions. This is found to hold even for particles with no friction, identifying a relationship between the imposed motion of the intruder and the resistance of the granular material to purely geometric rearrangements.