Penetration of projectiles into granular targets

Hierarchical Supramolecular Aggregation of Molecular Nanoparticles for Granular Materials with Ultra High-Speed Impact-Resistance

The high-speed impact-resistanct materials are of great significance while their development is hindered by the intrinsic tradeoff between mechanical strength and energy dissipation capability. Herein, the new chemical system of molecular granular material (MGM) is developed for the design of impact-resistant materials from the supramolecular complexation of sub-nm molecular clusters (MCs) and hyper-branched polyelectrolytes. Their hierarchical aggregation provides the origin of the decoupling of mechanical strengths and structural relaxation dynamics. The MCs' intrinsic fast dynamics afford excellent high-speed impact-resistance, up to 5600 s-1 impact in a typical split-Hopkinson pressure bar test while only tiny boundary cracks can be observed even under 7200 s-1 impact. The high loadings of MCs and their hierarchical aggregates provide high-density sacrificial bonding for the effective dissipation of the impact energy, enabling the protection of fragile devices from the direct impact of over 200 m s-1 bullet. Moreover, the MGMs can be conveniently processed into protective coatings or films with promising recyclability due to the supramolecular interaction feature. The research not only reveals the unique relaxation dynamics and mechanical properties of MGMs in comparison with polymers and colloids, but also develops new chemical systems for the fabrication of high-speed impact-resistant materials.

Impact craters formed by spinning granular projectiles

Craters formed by the impact of agglomerated materials are commonly observed in nature, such as asteroids colliding with planets and moons. In this paper, we investigate how the projectile spin and cohesion lead to different crater shapes. For that, we carried out discrete element method computations of spinning granular projectiles impacting onto cohesionless grains for different bonding stresses, initial spins, and initial heights. We found that, as the bonding stresses decrease and the initial spin increases, the projectile's grains spread farther from the collision point, and in consequence, the crater shape becomes flatter, with peaks around the rim and in the center of the crater. Our results shed light on the dispersion of the projectile's material and the different shapes of craters found on Earth and other planetary environments.

Scaling laws of plume-induced granular cratering

Extraterrestrial landing often requires firing a high-speed plume towards a planetary surface, and the resulting gas-granular interactions pose potential hazards to the lander. To investigate these jet-induced cratering dynamics, an experiment campaign covering a range of gas and granular properties relevant to the lunar and Martian environments was conducted in a large-scale vacuum chamber. Despite the variations in jet Mach number, mass flow rate, and composition of the granular phase investigated in this work, the observed time evolution of crater depth displays a consistent transition from an early-stage linear to a late-stage sublinear growth. To explain these scaling relations, a model that relates the kinetic energy gained by the particles per unit time to the power of the impinging jet is introduced. From this model, erosion rates and the critical depth at which the transition occurs can be extracted, and they are shown to depend on the gas impingement pressure, which was varied by changing ambient pressure, jet Mach number, mass flow rate, and nozzle height above the surface. These results highlight key mechanisms at work in the dynamics of plume-induced cratering and help to develop an understanding of optimal rocket engine firing times for future landings.

Roles of packing fraction, microscopic friction, and projectile spin in cratering by impact

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.

Unified penetration depth of low-velocity intruders into granular packings

Penetration of intruders into granular packings is well described by separately considering the dry or wet case of granular environments in previous experiments and simulations; however, the unified description of such penetration depth in these two granular media remains elusive due to lacking clear explanations about its origins. Based on three-dimensional discrete element method simulations, we introduce a power-law fitting form of the final penetration depth of a spherical intruder with low velocity vertically penetrating into dry and wet granular packings, excellently expressed on a master curve as a power-law function of a dimensionless impact number that is defined as the square root of the ratio between the inertial stress of the intruder and the linear combination of the mean gravitational stress and the cohesive stress exerted on each grain in the packings, as a remarkable extension of the inertial number in dry granular flows. This scaling robustly provides physical insights inherent in the unified description of the material properties of granular packings and the impactor penetration conditions on the final penetration depth in the impact tests, providing evidence of impact properties in different disciplines and applications in science and engineering.

Sink versus tilt penetration into shaken dry granular matter: The role of the foundation

We study the behavior of cylindrical objects as they sink into a dry granular bed fluidized due to lateral oscillations. Somewhat unexpectedly, we have found that, within a large range of lateral shaking powers, cylinders with flat bottoms sink vertically, while those with a "foundation" consisting of a shallow ring attached to their bottom, tilt besides sinking. The latter scenario seems to dominate independently from the nature of the foundation when strong enough lateral vibrations are applied. We are able to explain the observed behavior by quasi-2D numerical simulations, which also demonstrate the influence of the intruder's aspect ratio. The vertical sink dynamics is explained with the help of a Newtonian equation of motion for the intruder. Our findings may shed light on the behavior of buildings and other manmade structures during earthquakes.

Impact in granular matter: Force at the base of a container made with one movable wall

In geotechnics as well as in planetary science, it is important to find a means by which to protect a base from impacts of micrometeoroids. In the moon, for example, covering a moon base with regolith, and housing such regolith by movable bounding walls, could work as a stress-leaking shield. Using a numerical model, by performing impacts on a granular material housed in a rectangular container made with one movable sidewall, it is found that such wall mobility serves as a good means for controlling the maximum force exerted at the container's base. We show that the force exerted at the container's base decreases as the movable wall decreases in mass, and it follows a Janssen-like trend. Moreover, by making use of a dynamically defined redirecting coefficient K(X), proposed by Windows-Yule et al. [Phys. Rev. E 100, 022902 (2019)2470-004510.1103/PhysRevE.100.022902], which depends on the container's width X, we propose a model for predicting the maxima measured at the container's base. The model depends on the projectile and granulate properties, and the container's geometry.

Rolling away from the Wall into Granular Matter

The sedimentation of solid objects into granular matter near boundaries is an almost virgin field of research. Here we describe in detail the penetration dynamics of a cylindrical object into a quasi-2D granular medium. By tracking the trajectory of the cylinder as it penetrates the granular bed, we characterize two distinct kinds of motion: its center of mass moves horizontally away from the lateral wall, and it rotates around its symmetry axis. While the repulsion is caused by the loading of force chains between the intruder and the wall, the rotation can be associated to the frictional forces between the grains and the intruder. Finally, we show the analogies between the sedimentation of twin intruders released far from any boundaries, and that of one intruder released near a vertical wall.

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.

Explosion cratering in 3D granular media

Sudden release of energy in an explosion creates craters in granular media. In comparison with well-studied impact cratering in granular media, our understanding of explosion cratering is still primitive. Here, we study low-energy lab-scale explosion cratering in 3D granular media using controlled pulses of pressurized air. We identify four regimes of explosion cratering at different burial depths, which are associated with distinct explosion dynamics and result in different crater morphologies. We propose a general relation between the dynamics of granular flows and the surface structures of the resulting craters. Moreover, we measure the diameter of explosion craters as a function of explosion pressure, duration and burial depth. We find that the size of the craters is non-monotonic with increasing burial depth, reaching a maximum at an intermediate burial depth. In addition, the crater diameter shows a weak dependence on explosion pressure and duration at small burial depths. We construct a simple model to explain this finding. Finally, we explore the scaling relations of the size of explosion craters. Despite the huge difference in energy scales, we find that the diameter of explosion craters in our experiments follows the same cube root energy scaling as explosion cratering at high energies. We also discuss the dependence of rescaled crater sizes on the inertial number of granular flows. These results shed light on the rich dynamics of 3D explosion cratering and provide new insights into the general physical principles governing granular cratering processes.

A novel experimental setup for an oblique impact onto an inclined granular layer

We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and the inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be independently varied. The projectile-injection unit accelerates a plastic ball (6 mm in diameter) up to v_i ≃ 100 m s^-1 impact velocity. The barrel of the injection unit is made with a three-dimensional printer. The impact dynamics is captured by using high-speed cameras to directly measure the impact velocity and incident angle. The rebound dynamics of the projectile (restitution coefficient and rebound angle) is also measured. The final crater shapes are measured using a line-laser profiler mounted on the electric stages. By scanning the surface using this system, a three-dimensional crater shape (height map) can be constructed. From the measured result, we can define and measure the characteristic quantities of the crater. The analyzed result on the restitution dynamics is presented as an example of systematic experiments using the developed system.

Ray Systems and Craters Generated by the Impact of Nonspherical Projectiles

The impact of a spherical projectile on an evened-out granular bed generates a uniform ejecta of material and a crater with a raised circular rim. Recently, Sabuwala et al. [Phys. Rev. Lett. 120, 264501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.264501] found that the uniform blanket of ejecta changes to a set of radial streaks when a spherical body impacts on an undulated granular surface, being a plausible explanation to the enigmatic ray systems on planetary bodies. Here, we show that ray systems can also be generated by the impact of nonspherical projectiles on a flat granular surface. This is a reasonable explanation considering that meteorites are rarely spherical. Moreover, by impacting bodies of different geometries, we show that the crater size follows the same power-law scaling with the impact energy found for spherical projectiles, and the crater rim becomes circular as the impact energy is increased regardless of the projectile shape, which helps to understand why most impact craters in nature are rounded.

DEM simulation of the local ordering of tetrahedral granular matter

The formation and growth of local order clusters in a tetrahedral granular assembly driven by 3D mechanical vibration were captured in DEM (discrete element method) dynamic simulation using a multi-sphere model. Two important kinds of clusters, dimer and wagon wheel structures, were observed based on which the growth behavior and mechanism of each local cluster with different orientations/structures were investigated. The results show that during vibration, dimer clusters are formed first and then most of them grow into linear trimers and tetramers. Wagon wheel clusters are also frequently observed that grow into hexamers and, further, octamer and nonamer local clusters. Coordination number (CN) evolution indicates that the decrease of local mean CN can be regarded as the signal for the formation of local clusters in the tetrahedral particle packing system. Nematic order metric analysis shows that although the two basic structures (dimer and wagon wheel structures) grow into complex local clusters during packing densification, these local clusters are randomly distributed in the tetrahedral particle packing system. Stress analysis indicates that the dimer-based local clusters are mostly formed in the compaction state of the tetrahedral particle packing system during the vibrated packing densification process. In comparison, the wagon wheel-based local clusters need much stronger interaction forces from tetrahedral particles during vibrated packing densification.

Impact-Induced Energy Transfer and Dissipation in Granular Clusters under Microgravity Conditions

The impact-induced energy transfer and dissipation in granular targets without any confining walls are studied by microgravity experiments. A solid projectile impacts into a granular target at low impact speed (0.045≤v_{p}≤1.6  m s^{-1}) in a laboratory drop tower. Granular clusters consisting of soft or hard particles are used as targets. Porous dust agglomerates and glass beads are used for soft and hard particles, respectively. The expansion of the granular target cluster is recorded by a high-speed camera. Using the experimental data, we find that (i) a simple energy scaling can explain the energy transfer in both soft-particle and hard-particle granular targets, (ii) the kinetic impact energy is isotropically transferred to the target from the impact point, and (iii) the transferred kinetic energy is 2%-7% of the projectile's initial kinetic energy. The dissipative-diffusion model of energy transfer can quantitatively explain these behaviors.

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.

Ray Systems in Granular Cratering

In classical experiments of granular cratering, a ball dropped on an evened-out bed of grains ends up within a crater surrounded by a uniform blanket of ejecta. In this Letter, we show that the uniform blanket of ejecta changes to a ray system, or set of radial streaks of ejecta, where the surface of the granular bed includes undulations, a factor that has not been addressed to date. By carrying out numerous experiments and computational simulations thereof, we ascertain that the number of rays in a ray system ∝D/λ, where D is the diameter of the ball and λ is the wavelength of the undulations. Further, we show that the ejecta in a ray system originates in a narrow annulus of diameter D with the center at the site of impact. Our findings may help shed light on the enigmatic ray systems that ring many impact craters on the Moon and other planetary bodies.

Craters produced by explosions in a granular medium

We report on an experimental investigation of craters generated by explosions at the surface of a model granular bed. Following the initial blast, a pressure wave propagates through the bed, producing high-speed ejecta of grains and ultimately a crater. We analyzed the crater morphology in the context of large-scale explosions and other cratering processes. The process was analyzed in the context of large-scale explosions, and the crater morphology was compared with those resulting from other cratering processes in the same energy range. From this comparison, we deduce that craters formed through different mechanisms can exhibit fine surface features depending on their origin, at least at the laboratory scale. Moreover, unlike laboratory-scale craters produced by the impact of dense spheres, the diameter and depth do not follow a 1/4-power-law scaling with energy, rather the exponent observed herein is approximately 0.30, as has also been found in large-scale events. Regarding the ejecta curtain of grains, its expansion obeys the same time dependence followed by shock waves produced by underground explosions. Finally, from experiments in a two-dimensional system, the early cavity growth is analyzed and compared to a recent study on explosions at the surface of water.

Crater formation during raindrop impact on sand

After a raindrop impacts on a granular bed, a crater is formed as both drop and target deform. After an initial, transient, phase in which the maximum crater depth is reached, the crater broadens outwards until a final steady shape is attained. By varying the impact velocity of the drop and the packing density of the bed, we find that avalanches of grains are important in the second phase and hence affect the final crater shape. In a previous paper, we introduced an estimate of the impact energy going solely into sand deformation and here we show that both the transient and final crater diameter collapse with this quantity for various packing densities. The aspect ratio of the transient crater is however altered by changes in the packing fraction.

Collisional model of energy dissipation in three-dimensional granular impact

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 by using high-speed imaging of its trajectory. By varying the intruder shape and granular target, intruder-grain interactions are inferred from the consequent path. As a result, we connect the drag to the effect of intruder shape and grain density based on a proposed collisional model.

Unifying Impacts in Granular Matter from Quicksand to Cornstarch

A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact hardening in shear-thickening suspensions like cornstarch.

Scaling of liquid-drop impact craters in wet granular media

Combining high-speed photography with laser profilometry, we study the dynamics and the morphology of liquid-drop impact cratering in wet granular media-a ubiquitous phenomenon relevant to many important geological, agricultural, and industrial processes. By systematically investigating important variables such as impact energy, the size of impinging drops, and the degree of liquid saturation in granular beds, we uncover a scaling law for the size of impact craters. We show that this scaling can be explained by considering the balance between the inertia of impinging drops and the strength of impacted surface. Such a theoretical understanding confirms that the unique energy partition originally proposed for liquid-drop impact cratering in dry granular media also applies for impact cratering in wet granular media. Moreover, we demonstrate that compressive stresses, instead of shear stresses, control the process of granular impact cratering. Our study enriches the picture of generic granular impact cratering and sheds light on the familiar phenomena of raindrop impacts in granular media.

Raindrop impact on sand: a dynamic explanation of crater morphologies

As a droplet impacts upon a granular substrate, both the intruder and the target undergo deformation, during which the liquid may penetrate into the substrate. These three aspects together distinguish it from other impact phenomena in the literature. We perform high-speed, double-laser profilometry measurements and disentangle the dynamics into three aspects: the deformation of the substrate during the impact, the maximum spreading diameter of the droplet, and the penetration of the liquid into the substrate. By systematically varying the impact speed and the packing fraction of the substrate, (i) the substrate deformation indicates a critical packing fraction ϕ* ≈ 0.585; (ii) the maximum droplet spreading diameter is found to scale with a Weber number corrected by the substrate deformation; and (iii) a model of the liquid penetration is established and is used to explain the observed crater morphology transition.

Penetration depth scaling for impact into wet granular packings

We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but with smaller penetrations. Neither viscous drag nor density effects can explain the enhancement to the stopping force. The penetration depth exhibits a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices.

Granular impact cratering by liquid drops: Understanding raindrop imprints through an analogy to asteroid strikes

When a granular material is impacted by a sphere, its surface deforms like a liquid yet it preserves a circular crater like a solid. Although the mechanism of granular impact cratering by solid spheres is well explored, our knowledge on granular impact cratering by liquid drops is still very limited. Here, by combining high-speed photography with high-precision laser profilometry, we investigate liquid-drop impact dynamics on granular surface and monitor the morphology of resulting impact craters. Surprisingly, we find that despite the enormous energy and length difference, granular impact cratering by liquid drops follows the same energy scaling and reproduces the same crater morphology as that of asteroid impact craters. Inspired by this similarity, we integrate the physical insight from planetary sciences, the liquid marble model from fluid mechanics, and the concept of jamming transition from granular physics into a simple theoretical framework that quantitatively describes all of the main features of liquid-drop imprints in granular media. Our study sheds light on the mechanisms governing raindrop impacts on granular surfaces and reveals a remarkable analogy between familiar phenomena of raining and catastrophic asteroid strikes.

Forces encountered by a sphere during impact into sand

We describe direct measurements of the acceleration of an object impacting on a loosely packed granular bed under various pressures, using an instrumented sphere. The sphere acts as a noninvasive probe that measures and continuously transmits the acceleration as it penetrates into the sand, using a radio signal. The time-resolved acceleration of the sphere reveals the detailed dynamics during the impact that cannot be resolved from the position information alone. Because of the unobstructed penetration, we see a downward acceleration of the sphere at the moment the air cavity collapses. The compressibility of the sand bed is observed through the oscillatory behavior of the acceleration curve for various ambient pressures; it shows the influence of interstitial air on the compaction of the sand as a function of time.

Penetration of granular projectiles into a water target

The penetration of low-speed projectiles into a water target has been studied in the last several years to understand the physics behind the formation and collapse of cavities. In such studies, the projectiles employed were solid bodies or liquid drops. Here we report similar impact experiments using granular projectiles, with the aim to investigate how the morphology of the cavities is determined by the balance between the dynamic pressure exerted by the fluid and the cohesive strength of the impactors. From the results we present and discuss in this manuscript, we speculate on the dynamics of meteorite disintegration in the atmosphere of our planet.

Depth-dependent resistance of granular media to vertical penetration

We measure the quasistatic 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 quasistatic friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.

Flow-mediated coupling on projectiles falling within a superlight granular medium

Interesting collective motion emerges when several heavy intruder disks fall in a loose packed, quasi-two-dimensional granular bed of extremely light grains [F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Nat. Commun. 1, 123 (2010)]. In particular, when two disks impact side by side, they initially repel and then they attract each other until they finally stop. Here we perform experiments and discrete-element soft-particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. We find that (1) the drag force on the disks fluctuate with a characteristic length linked to force chains that build up and break; (2) the repulsive force is present when the separation of the intruder disks is less than 6 times the size of the grains of the granular bed, which is the size of an aperture that allows a continuous discharge flow from a container; (3) the attractive force has a range of action between 5 and 6 times the size of the intruder disks; and (4) attraction exists only when intruders move faster than 1 m/s. These results suggest that repulsion originates from jamming of grains between intruders, and it supports the idea that attraction could be due to a "granular pressure" drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect. However, our results do not rule out other mechanisms of interaction, like fluctuation-induced forces.