Dynamics of Drag and Force Distributions for Projectile Impact in a Granular Medium

Ciamarra, Massimo Pica; Lara, Antonio H.; Lee, Andrew T.; Goldman, Daniel I.; Vishik, Inna; Swinney, Harry L.

doi:10.1103/physrevlett.92.194301

Cited by 152 publications

(182 citation statements)

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“…Even though their energies are typically many orders of magnitude smaller than those of meteorite impacts, these small scale experiments on granular impacts may be relevant to planetary impact processes, as the progression of crater morphologies as a function of impact energy has been shown to mirror that seen in lunar craters [4]. In these impact experiments, physicists have also been interested in the penetration of the impacting sphere in the granular target [8,9,10,11,12,13,14]. Indeed, despite recent progress on the complex rheology of granular matter [15], the penetration dynamics of a solid sphere into a granular medium is still difficult to understand well as it involves both the complex drag resulting from frictional and collisional processes, and the final stop involving the complex "liquid/solid" transition exhibited by granular matter [16].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of grain ejection by sphere impact on a granular bed

2009

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The dynamics of grain ejection consecutive to a sphere impacting a granular material is investigated experimentally and the variations of the characteristics of grain ejection with the control parameters are quantitatively studied. The time evolution of the corona formed by the ejected grains is reported, mainly in terms of its diameter and height, and favourably compared with a simple ballistic model. A key characteristic of the granular corona is that the angle formed by its edge with the horizontal granular surface remains constant during the ejection process, which again can be reproduced by the ballistic model. The number and the kinetic energy of the ejected grains is evaluated and allows for the calculation of an effective restitution coefficient characterizing the complex collision process between the impacting sphere and the fine granular target. The effective restitution coefficient is found to be constant when varying the control parameters.

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Section: Introductionmentioning

confidence: 99%

Dynamics of grain ejection by sphere impact on a granular bed

2009

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“…As in ref. 8, for a 4.46-cm-diameter steel cylinder dropped sideways onto a bed of 0.46-0.64 cm diameter rods, the stopping time, t stop , seems constant for fast impacts; however, this is only the limiting behaviour as t stop increases for slower impacts. This trend for stopping time with impact speed may also be seen in the raw data of ref.…”

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Unified force law for granular impact cratering

2007

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Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events 1-5 and to probe the unusual nature of the granular state of matter [6][7][8][9][10] . Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed 6 ; linear in speed 7 ; constant, proportional to the initial impact speed 8 ; and proportional to depth 9,10 . This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed 11,12 . To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into noncohesive glass beads, we reproduce previous observations 6-10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.To measure dynamics, we use a line-scan digital CCD (chargecoupled device) camera to image a finely striped transparent rod attached vertically to the top of the projectile (see the Methods section). The instantaneous speed is the key quantity, deduced from the displacement of the striped pattern between successive frames. The temporal precision is 20 μs, set by the 50 kHz frame rate of the line-scan camera. The position resolution is 100 nm, set by the 3.8 μm per pixel magnification divided by the square root of the number of pixels. These combine to give a velocity resolution of 0.5 cm s −1 . Besides measurement fidelity, another advantage of our method is that it applies even to very deep impacts-as long as the striped rod does not submerge.Our complete dynamics data set is shown in Fig. 1, which shows position z, velocity v, and acceleration a, versus time t, for initial impact speeds, v 0 , ranging from 0 to −400 cm s −1 . Time is measured from initial impact; position is measured upwards from the granular surface, opposite to gravity. A striking feature is that, although the final position is approached smoothly, the velocity vanishes abruptly with a discontinuity in acceleration. Similar behaviour is evident in data from an embedded accelerometer (P. B. Umbanhowar, private communication, 2004; J. C. Amato, private communication, 2005). This is counter to the viscous approach to a stable equilibrium, where acceleration vanishes continuously, but it permits the stopping time, t stop , to be easily gauged from the velocity versus time data. Note that t stop actually decreases with increasing impact speed; surprisingly, deeper penetration requires less time. Evidently, granular matter is very different from ordinary ...

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“…The agreement between the model and the experiments is very good for low and intermediate Froude numbers, but differences arise when Fr * 80. A plausible explanation of such behavior is that some velocity-dependent term needs to be included in the drag force on the ball (see, e.g., [11,[13][14][15][16]), whose rela- tive weight would increase with Fr. From the fitting procedure leading to Fig.…”

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Role of Air in Granular Jet Formation

et al. 2007

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A steel ball impacting on a bed of very loose, fine sand results in a surprisingly vigorous jet which shoots up from the surface of the sand [D. Lohse et al., Phys. Rev. Lett. 93, 198003 (2004)]. When the ambient pressure p is reduced, the jet is found to be less vigorous [R. Royer et al., Nature Phys. 1, 164 (2005)]. In this Letter we show that p also affects the rate of penetration of the ball: Higher pressure increases the rate of penetration, which makes the cavity created by the ball close deeper into the sand bed, where the hydrostatic pressure is stronger, thereby producing a more energetic collapse and jetting. The origin of the deeper penetration under normal ambient pressure is found to lie in the extra sand fluidization caused by the air flow induced by the falling ball.

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Dynamics of Drag and Force Distributions for Projectile Impact in a Granular Medium

Cited by 152 publications

References 24 publications

Dynamics of grain ejection by sphere impact on a granular bed

Dynamics of grain ejection by sphere impact on a granular bed

Unified force law for granular impact cratering

Role of Air in Granular Jet Formation

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