Granular flow down an inclined plane: Bagnold scaling and rheology

Granular flow-solid wall interaction: investigation of the teapot effect

The evolution of granular flows generally involves solid boundaries, which add complexity to their dynamics and pose challenges to understand relevant natural and industrial phenomena. While an interesting "teapot effect" has been observed for liquid flowing over the solid surface of a teapot's spout, a similar phenomenon for discrete particles receives far less attention. In this work, we experimentally investigated the interactions between granular flows and a wedge-shaped solid edge (spout), showing that the trailing edge of the solid boundary plays a key role in causing velocity non-uniformity and splitting the flow into "dispersed" and "uniform" regions. Tuning the parameters (inclination angle, particle diameter, radii and surface roughness of the trailing edge) of the granular flow, a dimensionless number was summarized and successfully predicted the dispersion of the granular flows. Moreover, we also proved that introducing stronger cohesive forces between particles could harness the granular flows from heterogenous structures to grain clusters, which can be employed to switch between different flow regimes and regulate the dispersion behavior of particle flows. This study reveals the interaction of granular flow over complex solid boundaries, potentially offering new insights into particle-dominated flow dynamics.

Role of inertia in the starting and stopping mechanisms of granular flows

It is well known that a pile of grains starts and stops flowing at different angles of repose. It is also known that such starting and stopping angles exhibit thickness-dependent behavior, with deeper layers beginning to flow more readily and arresting at lower angles than shallower materials. These considerations have motivated various rheological assumptions in granular constitutive laws. This paper demonstrates that such observations can instead be partly attributed to inertial effects. In particular, we examine the roles of two control parameters characterizing conventional chute flow experiments: the rate of inclination of the chute, and the threshold surface velocity associated with identification of the flow. Both of these parameters control the system's momentum at different instances. We perform two-dimensional discrete element simulations and also develop a one-dimensional analytic model based on the standard μ(I) rheology. Results indeed indicate a difference between the starting and stopping angles as well as a thickness dependency, despite the absence of any hysteresis or material length scale in the underlying rheological model. Higher threshold velocities are shown to produce higher angles at which flow begins. In addition, the starting (stopping) angle increases (decreases) with the applied inclination rate. For thick enough granular layers, no matter how small the rate is, critical angles are shown to deviate from the quasistatic limit. Therefore, inertial effects should not a priori be neglected. To finalize our argument, we show the effect of the inclination rate and the threshold velocity in a laboratory setup, using small-scale experiments of an inclined chute.

Rheology of nonconvex granular flows based on particle rotational characteristics

Particle shape has a profound impact on the flow behaviors of granular materials, yet effectively incorporating the role of particle shape into granular rheology remains challenging. In this study, we employ three representative types of nonconvex particles generated through the multisphere approach and identify a consistent one-to-one relationship between the rescaled friction coefficient and the inertial number I across both inertial and quasistatic flow regimes. However, variations in particle shape cause notable deviations in rheological data compared to their spherical counterparts. Based on the observed dependence of rheological data on I for various nonconvex particles and their convergence at high I, we propose an inertial number I_{s} to effectively capture the impact of particle shape on flow states. The model parameters defining I_{s} are shown to be nearly independent of flow states and configurations, with physical interpretations related to particle rotational characteristics during shear. For practical application, we propose an empirical formula to capture the dependence of model parameters on particle geometrical shapes. The robustness of the proposed model is validated by predicting flow in an inclined flow configuration and applying it to additional nonconvex particles with more irregular and asymmetric features. This establishes a crucial foundation for extending the application of this generalized rheological model to other complex granular flows.

Effects of particle elongation on dense granular flows down a rough inclined plane

Granular materials in nature are nearly always nonspherical, but particle shape effects in granular flow remain largely elusive. This study uses discrete element method simulations to investigate how elongated particle shapes affect the mobility of dense granular flows down a rough incline. For a range of systematically varied particle length-to-diameter aspect ratios (AR), we run simulations with various flow thicknesses h and slope angles θ to extract the well-known h_{stop}(θ) curves (below which the flow ceases) and the Fr-h/h_{stop} relations following Pouliquen's approach, where Fr=u/sqrt[gh] is the Froude number, u is the mean flow velocity, and g is the gravitational acceleration. The slope β of the Fr-h/h_{stop} relations shows an intriguing S-shaped dependence on AR, with two plateaus at small and large AR, respectively, transitioning with a sharp increase. We understand this S-shaped dependence by examining statistics of particle orientation, alignment, and hindered rotation. We find that the rotation ability of weakly elongated particles (AR≲1.3) remains similar to spheres, leading to the first plateau in the β-AR relation, whereas the effects of particle orientation saturate beyond AR≈2.0, explaining the second plateau. An empirical sigmoidal function is proposed to capture this nonlinear dependence. The findings are expected to enhance our understanding of how particle shape affects the flow of granular materials from both the flow- and particle-scale perspectives.

Soft matter physics of the ground beneath our feet

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology. Among these, soft matter physics has emerged as a fundamental nexus connecting and underpinning many research questions. This perspective article is a multi-voice effort to bring together different views and approaches, questions and insights, from researchers that work in this emerging area, the soft matter physics of the ground beneath our feet. In particular, we identify four major challenges concerned with the dynamics in and of the ground: (I) modeling from the grain scale, (II) near-criticality, (III) bridging scales, and (IV) life. For each challenge, we present a selection of topics by individual authors, providing specific context, recent advances, and open questions. Through this, we seek to provide an overview of the opportunities for the broad Soft Matter community to contribute to the fundamental understanding of the physics of the ground, strive towards a common language, and encourage new collaborations across the broad spectrum of scientists interested in the matter of the Earth's surface.

A soft departure from jamming: the compaction of deformable granular matter under high pressures

The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follow the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.

A single carbon nanotube-entangled high-performance buckypaper with tunable fracture mode

It is well known that the traditional buckypaper (BP) is composed of a certain number of short carbon nanotubes (CNTs) intertwined with each other and sliding always happens when the BP is under tensile and impact loading, which results in inferior mechanical properties compared to single CNTs. In this work, a highly-entangled single-wire BP (SWBP) structure is constructed by a modified self-avoiding random walk approach. The in-plane mechanical properties and impacting behaviors of the SWBPs with different entanglement degrees and interface frictions are systematically investigated via newly developed coarse-grained molecular dynamics (CGMD) simulation. A coarse-grained method can effectively reflect the inter-tube van der Waals (vdW) interactions and the mechanical behaviors of CNTs, including tension, bending and adhesion. In this work, from the tensile simulations of the SWBP, the results showed that the self-locking mechanism between entangled CNTs could significantly enhance the tensile resistance of the film. Besides, the mechanical properties of the SWBP are highly dependent on the entanglement degree and the interface friction between CNTs. Furthermore, two distinct fracture modes, ductile fracture and brittle fracture, are revealed, which can be efficiently controlled by changing the related friction between CNTs. From the impacting simulations, it is found that the impacting performance can be effectively tuned by adjusting the entanglement degree of the film. In addition, the kinetic energy of the projectile could be rapidly dissipated through the stretching and bending of CNTs in the SWBP. This work provides an in-depth understanding of the effect of interface friction and entanglement degree on the mechanical properties of the buckypaper and provides a reference for the preparation of strong CNT-based micromaterials.

High speed impact on granular media: breakdown of conventional inertial drag models

In this study, we extensively explore the impact process on granular media, particularly focusing on situations where the ratio of impact speed to acoustic speed is on the order of 0.01-1. This range significantly exceeds that considered in existing literature (0.0001-0.001). Our investigation involves a comprehensive comparison between our simulation data, obtained under high-speed conditions, and the established macroscopic drag models. In the high-speed regime, conventional drag force models prove inadequate, and the drag force cannot be separated into a depth-dependent static pressure and a depth-independent inertial drag, as suggested in previous literature. A detailed examination of the impact process in the high-speed limit is also presented, involving the spatio-temporal evolution of the force chain network, displacement field, and velocity field at the particle length scale. Unlike prior works demonstrating the exponential decay of pulses, we provide direct evidence of acoustic pulses propagating over long distances, reflecting from boundaries, and interfering with the original pulses. These acoustic pulses, in turn, induce large scale reorganization of the force chain network, and the granular medium continuously traverses different jammed states to support the impact load. Reorientation of the force chains leads to plastic dissipation and the eventual dissipation of the impact energy. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.

Down-hill creep of a granular material under expansion/contraction cycles

We investigate the down-hill creep of an inclined layer of granular material caused by quasi-static oscillatory variations of the size of the particles. The size variation is taken to be maximum at the surface and decreasing with depth, as it may be argued to occur in the case of a granular soil affected by atmospheric conditions. The material is modeled as an athermal two dimensional polydisperse system of soft disks under the action of gravity. The slope angle is below the angle of repose and therefore the system reaches an equilibrium configuration under static external conditions. However, under a protocol in which particles slowly change size in a quasistatic oscillatory way, the system is observed to creep down in a synchronized way with the oscillation. We measure the creep advance per cycle as a function of the slope angle and the degree of change in particle size. We also find that the creep rate is maximum at the surface and smoothly decreases with depth, as it is observed to occur in the field.

Dipole screening in pure shear strain protocols of amorphous solids

When amorphous solids are subjected to simple or pure strain, they exhibit elastic increase in stress, punctuated by plastic events that become denser (in strain) upon increasing the system size. It is customary to assume in theoretical models that the stress released in each plastic event is redistributed according to the linear Eshelby kernel, causing avalanches of additional stress release. Here we demonstrate that, contrary to the uniform affine strain resulting from simple or pure strain, each plastic event is associated with a nonuniform strain that gives rise to a displacement field that contains quadrupolar and dipolar charges that typically screen the linear elastic phenomenology and introduce anomalous length scales and influence the form of the stress redistribution. An important question that opens up is how to take this into account in elastoplastic models of shear induced phenomena like shear banding.

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent -β. The static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension d_{f}. In three dimensions, d_{f}≈2.0 for 2.5≤β≤3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0≲d_{f}≲1.34 for 2.1≤β≤2.9. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long-wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.

Complex Memory Formation in Frictional Granular Media

Using numerical simulations it is shown that a jammed, random pack of soft frictional grains can store an arbitrary waveform that is applied as a small time-dependent shear while the system is slowly compressed. When the system is decompressed at a later time, an approximation of the input waveform is recalled in time-reversed order as shear stresses on the system boundaries. This effect depends on friction between the grains, and is independent of some aspects of the friction model. This type of memory could potentially be observable in other types of random media that form internal contacts when compressed.

Ultraslow Settling Kinetics of Frictional Cohesive Powders

Using discrete element method simulations, we show that the settling of frictional cohesive grains under ramped-pressure compression exhibits strong history dependence and slow dynamics that are not present for grains that lack either cohesion or friction. Systems prepared by beginning with a dilute state and then ramping the pressure to a small positive value P_{final} over a time τ_{ramp} settle at packing fractions given by an inverse-logarithmic rate law, ϕ_{settled}(τ_{ramp})=ϕ_{settled}(∞)+A/[1+Bln(1+τ_{ramp}/τ_{slow})]. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that τ_{slow} is set by the slow dynamics of structural void stabilization rather than the faster dynamics of bulk densification. We formulate a kinetic free-void-volume theory that predicts this ϕ_{settled}(τ_{ramp}), with ϕ_{settled}(∞)=ϕ_{ALP} and A=ϕ_{settled}(0)-ϕ_{ALP}, where ϕ_{ALP}≡.135 is the "adhesive loose packing" fraction found by Liu et al. [Equation of state for random sphere packings with arbitrary adhesion and friction, Soft Matter 13, 421 (2017)SMOABF1744-683X10.1039/C6SM02216B].

Onset and dynamics of avalanches in a rotating cylinder: From experimental data to a geometric model

Particle image velocimetry has been applied to measure particle velocities on the free surface of a bed of particles within a rotating cylinder during avalanching. The particle velocities were used to examine the validity of existing avalanche models and to propose an alternative model. The movement of particles depends on their location on the surface of the bed: Particles located near the center of the bed travel the farthest, while the distance traveled decreases at an increasing rate for particles located farther from the center. The start of an avalanche can be determined to a single initiation point that can be located on the bottom half of the bed; the avalanche quickly propagates through the entire free surface with 90% of the surface in motion within 257 ms (approximately 20% of the total duration of an avalanche). The experimental insight is used to formulate a geometric model, in which three equal-sized sections flow down the bed surface during an avalanch. The predictions of the model are validated by experimental mixing measurements.

Discharge of elongated grains in silos under rotational shear

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate Q by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate Q on orifice diameter D, the spheres and rods show two distinct trends. For rods, in the small-aperture limit Q seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)2470-004510.1103/PhysRevE.103.062905]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall.

Large-scale frictionless jamming with power-law particle size distributions

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly 4 000 000 particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying power laws, we analyze the role of particle size distributions on the structure of jammed packings. The densest packings are obtained for size distributions that balance the relative abundance of large-large and small-small particle contacts. Although the proportion of rattler particles and mean coordination number strongly depend on the size distribution, the mean coordination of nonrattler particles attains the frictionless isostatic value of six in all cases. The size distribution of nonrattler particles that participate in the load-bearing network exhibits no dependence on the width of the total particle size distribution beyond a critical particle size for low-magnitude exponent power laws. This signifies that only particles with sizes greater than the critical particle size contribute to the mechanical stability. However, for high-magnitude exponent power laws, all particle sizes participate in the mechanical stability of the packing.

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.

Janssen effect in columns of fire ants

We study fire-ant columns, an active version of passive granular columns, and find that, despite the inherent activity of the ants and their natural tendency to rearrange, the ants develop force-chain structures that help support the weight of the column. Hence, the apparent mass at the bottom of the column saturates with added mass in a Janssen-like fashion, reminiscent of what is seen in passive-grain columns in wide containers. Activity-induced rearrangements within the column, however, lead to changes in the force-chain structure that slightly reduce the supportive nature of the force-chains over time and to fluctuations in the pressure at the bottom of the column that scale like the law of large numbers. We capture the experimental results in simulations that include not only friction with the walls, but also a fluctuating force that introduces activity and that effectively affects the force-chain structure of the ant collective.

Size segregation of disk particle in two-dimensional chute

Size segregation will lead to stratification of a particle system. At present, people have not fully understood the segregation mechanism. In this work, we have studied the size segregation behavior of two-component disk particles in chute flows. The effects of particle size ratio η, particle density ρ, static friction coefficient μ and chute angle α on size segregation are discussed. We use the discrete element method to simulate and calculate the force of disk large particles during segregation. Results show that the 'squeeze expulsion' mechanism plays a key role in the size segregation of a disk particle flow. We establish a physical model of 'squeeze expulsion' of disk particles and obtain the conditions for the formation of 'squeeze expulsion' mechanism.

Collective Drifts in Vibrated Granular Packings: The Interplay of Friction and Structure

We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stick slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.

Sheared granular matter and the empirical relations of seismicity

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Fatigue in assemblies of indefatigable carbon nanotubes

Despite being one of the most consequential processes in the utilization of structural materials, fatigue at the nano- and mesoscale has been marginally explored or understood even for the most promising nanocarbon forms—nanotubes and graphene. By combining atomistic models with kinetic Monte Carlo simulations, we show that a pristine carbon nanotube under ambient working conditions is essentially indefatigable—accumulating no structural memory of prior load; over time, it probabilistically breaks, abruptly. In contrast, by using coarse-grained modeling, we demonstrate that any practical assemblies of nanotubes, e.g., bundles and fibers, display a clear gradual strength degradation in cyclic tensile loading due to recurrence and ratchet-up of slip at the tube-tube interfaces, not occurring under static load even of equal amplitude.

Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology

Despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow, which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at finite rates, are compared with data.

A Novel Computational Approach Coupled with Machine Learning to Predict the Extent of Agglomeration in Particulate Processes

Solid particle agglomeration is a prevalent phenomenon in various processes across the chemical, food, and pharmaceutical industries. In pharmaceutical manufacturing, agglomeration is both desired in unit operations like wet granulation and undesired in unit operations such as agitated filter drying of highly potent active pharmaceutical ingredients (API). Agglomeration needs to be controlled for optimal physical properties of the API powder. Even after decades of work in the field, there is still very limited understanding of how to quantify, predict, and control the extent of agglomeration, owing to the complex interaction between the solvent and the solid particles and stochasticity imparted by mixing. Furthermore, a large size of industrial scale particulate process systems makes it computationally intractable. To overcome these challenges, we present a novel theory and computational methodology to predict the agglomeration extent by coupling the experimental measurements of agglomeration risk zone or "sticky zone" with discrete element method. The proposed model shows good agreement with experiments. Further, a machine learning model was built to predict agglomeration extent as a function of input variables, such as material properties and processing conditions, in order to build a digital twin of the unit operation. While the focus of the present study is the agglomeration of particles during industrial drying processes, the proposed methodology can be readily applied to numerous other particulate processes where agglomeration is either desired or undesired.

Lift force acting on an intruder in dense, granular shear flows

We report a lift force model for intruders in dense, granular shear flows. Our derivation is based on the thermal buoyancy model of Trujillo and Hermann [Physica A 330, 519 (2003)10.1016/S0378-4371(03)00621-6], but it 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 determined by discrete element model simulations, and the neutral-buoyancy limit of intruders in shear flows. Phenomenologically, we observe a cooling upon the introduction of an intruder into the system. This cooling effect increases with intruder size and explains the sinking of large intruders. On the other hand, the introduction of small to midsized intruders, i.e., up to four times the bed particle size, leads to a reduction in the granular pressure compared to the hydrostatic pressure, which in turn causes the rising of small to midsized intruders.

Sand creep motion in slow spin-up experiment: An analog of regolith migration on asteroids

We studied the creep motion of granular materials in a gradient potential field that is created using a slow spin-up experiment device. Natural sand confined in the acrylic box is spun up by a controlled turntable and the surface flows are captured using video-based measurements. Various spin-up accelerations were considered to understand the responses of creep motion on different accelerating paths. Convergent behaviors in the morphological change of sand surface were observed in the final steady state. To quantify the quasistatic spin-up process, we examined the net flux and the surface slope as a function of the spin rate and offset from the rotation axis. The creep motion of sand demonstrated behaviors similar to the regolith migration in numeric simulations. We have noticed the sand surface approaches criticality as the spin-up proceeding, consistent with the observation that top-shaped asteroids near limiting spin rate take on critical shapes. Comparisons to large-scale numeric simulations and analytical solutions reveal underlying similarities between the experiments and the million-year evolution of asteroid regolith under Yarkovsky-O'Keefe-Radzievskii-Paddack acceleration, which raises the possibility of studying asteroid surface processes in laboratory analog experiments.

Strain localization in planar shear of granular media: the role of porosity and boundary conditions

Shear strain localization into shear bands is associated with velocity weakening instabilities and earthquakes. Here, we simulate steady-state plane-shear flow of numerical granular material (gouge), confined between parallel surfaces. Both constant shear stress and constant strain-rate boundary conditions are tested, and the two types of boundary conditions are found to yield distinct velocity profiles and friction laws. The inertial number, I, exerts the largest control on the layers' behavior, but additional dependencies of friction on normal stress and thickness of the layer are observed under constant stress boundary condition. We find that shear-band localization, which is present in the quasistatic regime ([Formula: see text]) in rate-controlled shear, is absent under stress-controlled loading. In the latter case, flow ceases when macroscopic friction coefficient approaches the quasistatic friction value. The inertial regime that occurs at higher inertial numbers ([Formula: see text]) is associated with distributed shear, and friction and porosity that increase with shear rate (rate-strengthening regime). The finding that shear under constant stress boundary condition produces the inertial, distributed shear but never quasistatic, localized deformation is rationalized based on low fluctuations of shear forces in granular contacts for stress-controlled loading. By examining porosity within and outside a shear band, we also provide a mechanical reason why the transition between quasistatic and inertial shear coincides with the transition between localized and distributed strain.

Chrono::GPU: An Open-Source Simulation Package for Granular Dynamics Using the Discrete Element Method

We report on an open-source, publicly available C++ software module called Chrono::GPU, which uses the Discrete Element Method (DEM) to simulate large granular systems on Graphics Processing Unit (GPU) cards. The solver supports the integration of granular material with geometries defined by triangle meshes, as well as co-simulation with the multi-physics simulation engine Chrono. Chrono::GPU adopts a smooth contact formulation and implements various common contact force models, such as the Hertzian model for normal force and the Mindlin friction force model, which takes into account the history of tangential displacement, rolling frictional torques, and cohesion. We report on the code structure and highlight its use of mixed data types for reducing the memory footprint and increasing simulation speed. We discuss several validation tests (wave propagation, rotating drum, direct shear test, crater test) that compare the simulation results against experimental data or results reported in the literature. In another benchmark test, we demonstrate linear scaling with a problem size up to the GPU memory capacity; specifically, for systems with 130 million DEM elements. The simulation infrastructure is demonstrated in conjunction with simulations of the NASA Curiosity rover, which is currently active on Mars.

Structural analysis of disordered dimer packings

Jammed disordered packings of non-spherical particles show significant variation in the packing density as a function of particle shape for a given packing protocol. Rotationally symmetric elongated shapes such as ellipsoids, spherocylinders, and dimers, e.g., pack significantly denser than spheres over a narrow range of aspect ratios, exhibiting a characteristic peak at aspect ratios of α_max ≈ 1.4-1.5. However, the structural features that underlie this non-monotonic behaviour in the packing density are unknown. Here, we study disordered packings of frictionless dimers in three dimensions generated by a gravitational pouring protocol in LAMMPS. Focusing on the characteristics of contacts as well as orientational and translational order metrics, we identify a number of structural features that accompany the formation of maximally dense packings as the dimer aspect ratio α is varied from the spherical limit. Our results highlight that dimer packings undergo significant structural changes as α increases up to α_max manifest in the reorganisation of the contact configurations between neighbouring dimers, increasing nematic order, and decreasing local translational order. Remarkably, for α > α_max our metrics remain largely unchanged, indicating that the peak in the packing density is related to the interplay of structural rearrangements for α < α_max and subsequent excluded volume effects with unchanged structure for α > α_max.

A conveyor belt experimental setup to study the internal dynamics of granular avalanches

ABSTRACT

This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convective-bulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields' interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche's leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt's results showed the potential for further theoretical developments in rheology and segregation-coupled models.

An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments

The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less flowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity.

The angle of repose—i.e., the angle θr between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts θr as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle–particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as θr obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology.

Emergence of structure in columns of grains and elastic loops

It is possible to build free-standing, load-bearing structures using only rocks and loops of elastic material. We investigate how these structures emerge, and find that the necessary maximum loop spacing (the critical spacing) is a function of the frictional properties of the grains and the elasticity of the confining material. We derive a model to understand both of these relationships, which depends on a simplification of the behavior of the grains at the edge of a structure. We find that higher friction leads to larger stable grain-grain and grain-loop contact angles resulting in a simple function for the frictional critical spacing, which depends linearly on friction to first order. On the other hand, a higher bending rigidity enables the loops to better contain the hydrostatic pressure of the grains, which we understand using a hydroelastic scale. These findings will illuminate the stabilization of dirt by plant roots, and potentially enable the construction of simple adhesion-less structures using only granular material and fiber.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.

Translational-rotational coupling during the scattering of a frictional sphere from a flat surface

At a macroscopic level, concepts such as "top spin," "back spin," and "rolling" are commonly used to describe the collision of balls and surfaces. Each term refers to an aspect of the coupling of rotational motion during the collision of a spherical particle with a planar surface. In this paper, we explore the mechanisms of energy transfer involving the collision of a rotating sphere and a surface using a model of frictional interactions developed for a granular material. We present explicit analytical treatments for the scattering and derive expressions for two important limiting classes: energy conserving collisions and collisions subject to rapid transverse dissipation.

Efficacy of simple continuum models for diverse granular intrusions

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 macro-scale continuum approach in modeling and understanding the physics of various macroscopic phenomena in a variety of granular intrusion cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to experimental data in four quasi-2D intrusion cases: (1) depth-dependent force response in horizontal submerged-intruder motion; (2) separation-dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development during vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces while providing key meso- and macro-scopic insights. The modeling results are then compared to experimental data. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as a conceptual understanding of various granular intrusion phenomena.

Structured fabrics with tunable mechanical properties

Structured fabrics, such as woven sheets or chain mail armours, derive their properties both from the constitutive materials and their geometry^1,2. Their design can target desirable characteristics, such as high impact resistance, thermal regulation, or electrical conductivity^3-5. Once realized, however, the fabrics' properties are usually fixed. Here we demonstrate structured fabrics with tunable bending modulus, consisting of three-dimensional particles arranged into layered chain mails. The chain mails conform to complex shapes², but when pressure is exerted at their boundaries, the particles interlock and the chain mails jam. We show that, with small external pressure (about 93 kilopascals), the sheets become more than 25 times stiffer than in their relaxed configuration. This dramatic increase in bending resistance arises because the interlocking particles have high tensile resistance, unlike what is found for loose granular media. We use discrete-element simulations to relate the chain mail's micro-structure to macroscale properties and to interpret experimental measurements. We find that chain mails, consisting of different non-convex granular particles, undergo a jamming phase transition that is described by a characteristic power-law function akin to the behaviour of conventional convex media. Our work provides routes towards lightweight, tunable and adaptive fabrics, with potential applications in wearable exoskeletons, haptic architectures and reconfigurable medical supports.

Intrusion into Granular Media Beyond the Quasistatic Regime

The drag force exerted on an object intruding into granular media is typically assumed to arise from additive velocity and depth dependent contributions. We test this with intrusion experiments and molecular dynamics simulations at constant speed over four orders of magnitude, well beyond the quasistatic regime. For a vertical cylindrical rod we find velocity dependence only right after impact, followed by a crossover to a common, purely depth-dependent behavior for all intrusion speeds. The crossover is set by the timescale for material, forced to well up at impact, to subsequently settle under gravity. These results challenge current models of granular drag.

Experimental assessment of the effective friction at the base of granular chute flows on a smooth incline

We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from θ=13.4^{∘} to 83.6° and various gate openings of the chute. We find that the effective basal friction coefficient μ_{B}, obtained from the ratio of the longitudinal force to the normal one, exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle holdup H (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tanθ. The deviation from tanθ can be interpreted as a contribution from the sidewall to the overall friction. At larger angles, the basal friction μ_{B} saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as Fr=U[over ¯]/(gHcosθ)^{1/2}, where U[over ¯] is the mean flow velocity. Second, the mean velocity scales with the particle holdup H with a power exponent close to 1/4, contrasting with the Bagnold scaling (U[over ¯]∼H^{3/2}).

Self-diffusion scalings in dense granular flows

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid volume fractions that are important in those terrestrial gravitational shearing flows that are dominated by collisional interactions. Diffusion over this range of solid fraction has not been well characterized in previous studies. We first compare the measured values with an empirical scaling based on shear rate previously proposed in the literature, and highlight the presence of anisotropy and the solid fraction dependence. We then compare the numerical measurements with those predicted by the kinetic theory for shearing flows of inelastic spheres and offer an explanation for why the measured and predicted values differ.