Granular Media Research Articles

Effect of skull morphology on fox snow diving

Certain fox species plunge-dive into snow to catch prey (e.g., rodents), a hunting mechanism called mousing. Red and arctic foxes can dive into snow at speeds ranging between 2 and 4 m/s. Such mousing behavior is facilitated by a slim, narrow facial structure. Here, we investigate how foxes dive into snow efficiently by studying the role of skull morphology on impact forces it experiences. In this study, we reproduce the mousing behavior in the lab using three-dimensional (3D) printed fox skulls dropped into fresh snow to quantify the dynamic force of impact. Impact force into snow is modeled using hydrodynamic added mass during the initial impact phase. This approach is based on two key facts: the added mass effect in granular media at high Reynolds numbers and the characteristics of snow as a granular medium. Our results show that the curvature of the snout plays a critical role in determining the impact force, with an inverse relationship. A sharper skull leads to a lower average impact force, which allows foxes to dive head-first into the snow with minimal tissue damage.

Multiscale modeling of coupled thermo-hydro-mechanical behavior in ice-bonded granular media subject to freeze-thaw cycles

We present a novel multiscale framework that integrates the single-point multiphase material point method (MPM) and the discrete element method (DEM) to model the complex freeze-thaw behavior of ice-bonded granular media. The proposed numerical framework is featured by (a) employing the continuum-based MPM to solve the macroscopic governing equations for granular systems involving thermo-hydro-mechanical (THM) coupling and phase transitions, and (b) using the grain-scale discontinuum-based DEM to capture the thermodynamically sensitive mechanical behaviors of ice-bonded granular media. The multiscale framework is constructed by attaching a DEM-based representative volume element (RVE) at each material point in MPM. This RVE serves as a live sample of each material point to track the state-dependent effective stress with respect to the local deformation and thermodynamic conditions like ice saturation, bridging the macroscopic phenomena and the underlying microstructural evolution. In particular, we implement a semi-implicit staggered integration scheme for the macroscale THM-coupled MPM to boost computational efficiency and enhance numerical stability. We also propose an innovative ice saturation-dependent bond contact to effectively reproduce the thermodynamically sensitive mechanical behaviors. The new multiscale framework is first benchmarked against analytical solutions for 1D non-isothermal consolidation problems. We then demonstrate its exceptional capability in simulating intricate freeze-thaw behavior of granular media through a boundary value problem involving cyclic freeze-thaw actions. Further cross-scale analyses reveal its potential in capturing key loading- and state-dependent THM responses with explainable microstructural mechanisms during complex freezing and thawing loading conditions.

Deformation and Frictional Failure of Granular Media in 3D Analog and Numerical Experiments

Frictional sliding along grain boundaries in brittle shear zones can result in the fragmentation of individual grains, which ultimately can impact slip dynamics. During deformation at small scales, stick–slip motion can occur between grains when existing force chains break due to grain rearrangement or failure, resulting in frictional sliding of granular material. The rearrangement of the grains leads to dilation of the granular package, reducing the shear stress and subsequently leading to slip. Here, we conduct physical experiments employing HydroOrbs, an elasto-plastic material, to investigate grain comminution in granular media under simple shear conditions. Our findings demonstrate that the degree of grain comminution is dependent on both the normal force and the size of the grains. Using the experimental setup, we benchmark Discrete Element Method (DEM) numerical models, which are capable of simulating the movement, rotation, and fracturing of elasto-plastic grains subjected to simple shear. The DEM models successfully replicate both grain comminution patterns and horizontal force fluctuations observed in our physical experiments. They show that increasing normal forces correlate with higher horizontal forces and more fractured grains. The ability of our DEM models to accurately reproduce experimental results opens up new avenues for investigating various parameter spaces that may not be accessible through traditional laboratory experiments, for example, in assessing how internal friction or cohesion affect deformation in granular systems.

A Eulerian Monte Carlo method for the numerical solution of the multivariate population balance equation

Statistical descriptions of particulate phases and granular media based on the notion of a property distribution are particularly advantageous for dense, many-particle dispersions since they support the direct evaluation of Eulerian property statistics, permit a kinematically simple treatment of particle collisions and feature a model complexity that is independent of the number of physical particles. On the minus side, the property distribution is governed by a high-dimensional population balance equation (PBE) whose moment reduction is accompanied by a challenging closure problem and engenders intricate dynamical nonlinearities. Circumventing both the curse of dimensionality and the moment closure problem, we present a Eulerian Monte Carlo (EMC) solution method that harnesses a representation of the property distribution in terms of an ensemble of property samples and is based on a statistical enforcement of the spatially and temporally discretized PBE. After application of a kinetic finite volume scheme, the PBE is subjected to a fractional steps decomposition that separates spatial transport from transport in property space. Conceptually, spatial transport is emulated by assembling the ensemble in one spatial grid cell from samples drawn from the ensembles in neighbouring cells at the previous time point. In this regard, we propose a two-level sampling scheme that is sensitive to large-scale features of the marginal velocity distribution and effectively reduces the instantaneous sampling error. The property transport step, by contrast, is based on the method of characteristics and involves the propagation of individual samples as property characteristics in time. While the sampling error afflicting the property statistics needs to be controlled using a top-level time or ensemble averaging, the EMC method remains well-conditioned for an arbitrary number of samples, is easy to implement and involves a computational expense that scales only linearly with the number of particle properties. Based on two benchmark examples, we analyze the spatial and statistical convergence properties of the EMC method and demonstrate its capacity to capture multiple crossings of particle trajectories. A third example involves the two-way coupled transport of size-polydispersed inertial particles in an inhomogeneous flow field.

Terraced slope metasurface in granular media

SUMMARY In this work, the propagation and attenuation of vertically polarized surface waves when interacting with terraced slopes is studied experimentally and numerically. To validate the devised simulation, a laboratory-scale physical model is tested in order to examine the attenuation properties of this well-known artificial landform. The experiment involves formation of a terraced slope, in a laboratory setup, via use of an unconsolidated granular medium made of silica microbeads. This granular medium exhibits a gravity-induced power-law stiffness profile, resulting in a depth-dependent velocity profile. A piezoelectric actuator was used to excite vertically polarized surface acoustic modes localized near the surface of the medium. The three components of the particle velocity field of these modes were measured by means of a 3-D laser Doppler vibrometer. In accordance with the terraced slope, a simple inclined plane was further tested to investigate and highlight the differences in terms of wave propagation along these two different ground formations. The results of this research provide significant experimental evidence that the terraced slopes form mechanisms which attenuate low-frequency surface waves, thus acting as metasurfaces. This work suggests the use of laboratory-scale physical models to investigate the wave propagation in different landforms, which extend beyond typical horizontal ground morphologies, and which could be linked to atypical wave propagation properties, possibly even influencing propagation of seismic waves.

Embedded Printing of Hydrogels and Watery Suspensions of Cells in Patterned Granular Baths.

Bioprinting within support media has emerged as the superior alternative to conventional extrusion printing. Not only because it allows for more freedom over the shapes that can be printed but also because it allows for the printing of inks that would not retain shape fidelity in freeform deposition such as watery liquids. Apart from functioning as mechanical support during embedded printing, hydrogel microparticle support media can provide the unique advantage of offering distinct chemotactic cues to cells printed in the baths by varying the composition of the hydrogel microparticles. There is great potential in compartmentalized granular baths consisting of different hydrogel particle materials in the field of tissue engineering, as these allow for the local inclusion of properties or cues to guide tissue development. In this work, we present a method to create compartmentalized embedding baths by printing multiple granular hydrogel materials that are widely used in tissue engineering. After adapting the volume fraction (φp) of the particles in the bath, we print within them using both inks composed of hydrogel or of cells and other particles suspended in watery liquid. Our process consists of the following three steps: First, the hydrogel microparticles are packed at a φp that allows them to be extruded while being reversibly jammed, facilitating the localized deposition of the granular media to form a compartmentalized bath. Second, each granular media is deposited in succession to create a packed suspension compartment, and by adding liquid post deposition, φp is reduced to allow for embedded printing. Finally, we demonstrate the printing of multiple inks within the compartmentalized embedding bath and highlight the distinct differences between using inks composed of hydrogels or inks composed of particles suspended in watery liquid. This approach combines the advantages of embedded printing through the use of granular media with the added ability to pattern multiple bioactive granular materials to locally affect the behavior of cells printed within the bath. We expect that this workflow will allow researchers to create spatially compartmentalized, customized bioactive embedding baths that allow for the embedded printing of inks composed of hydrogels, cells, and other particles adapted to their need.

Active intruder motion in a two-dimensional granular medium

We studied an active intruder traversing a two-dimensional granular medium. First, we conducted experiments to analyze the motion of the active intruder within a bed of soft particles distributed throughout a horizontal container. Our observations revealed that the intruder preferentially moved along regions characterized by higher disorder. As a consequence of its motion, and as the intruder repeatedly traversed specific regions, the structure in the vicinity of the path, but also in more distant regions, gradually became more ordered. Additionally, the motion of the intruder tended to be localized in closed paths, with this effect becoming more pronounced at higher particle concentrations. Secondly, we analyzed the behavior of the active intruder within a slightly tilted container and under vibration and shearing conditions, which served to fluidize the granular bed. Our findings indicated that the trajectory of the intruder tended to intersect regions of the granular medium with lower structural order. The overall order and fluidization degrees were found to be the primary influences on the intruder’s penetration length. We used the sixth-bond-orientational order parameter to characterize the local structural aspects of the medium and the mean squared displacement to describe the dynamics of both the intruder and the medium. We conducted an experimental analysis of the ordering of the medium and motion of the intruder using network contact forces in a similar system based on soft gelatin particles. The results of this experimental analysis are consistent with the general results, showing that media with an ordered configuration exhibit more resistance than disordered media.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems. The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media, such as permeability, and fluid components, like viscosity. The primary aim is to deduce either constant pressure head or pressure profiles, given the known velocity field at a steady-state flow through a conduit containing obstacles, including walls, spheres, and grains. The lattice Boltzmann method (LBM) combined with automatic differentiation (AD) (AD-LBM) is employed, with the help of the GPU-capable Taichi programming language. A lightweight tape is used to generate gradients for the entire LBM simulation, enabling end-to-end backpropagation. Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media, leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity. The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency, making it a powerful tool for solving inverse fluid flow problems in various applications.

Evolution of anisotropic capillarity in unsaturated granular media within the pendular regime

While the shear behavior of granular soils is directly related to the microstructure of contacts which often leads to the coaxiality between Cauchy stress and Satake fabric tensors, it is generally accepted by the geomechanics and geotechnical engineering community that the capillary effects are isotropic. At low saturation levels, however, the pore fluid tends to form interparticle menisci that can also manifest an anisotropic structure, which may result in the development of anisotropic capillarity in wetted granular media. To study the interplay between the solid grain contacts and the liquid bridges at the micro-scales, this study adopts a coupled discrete element method that utilizes a linear contact model combined with a capillary model, and explores their effects by conducting a series of numerical experiments. The distributions of contact and capillary force orientations during the experiment are further investigated to better understand how their alignments affect the global response of the granular assembly subjected to a deviatoric loading. The results indicate that the global shear stress response is not only affected by the contact fabric but also by the network of liquid bridges, and we also observe that the particles may lose contact while the pendular menisci may not be destroyed during the elastic unloading.

Numerical modelling of contact adhesion in a random assembly of elastic–plastic particles

The prediction of tensile strength properties of powder compacts remains an important industrial issue. In particular, one of the main problems of the powder compaction process is the failure of compacts. Indeed, some powder compacts exhibit cracks which appear during compaction. Such defects occur due to localised tensile or shear stresses, for example close to geometrical singularities. They are also related to the ability of a powder to create enough adhesion at contacts between particles to withstand tensile stresses. Therefore, cracks are a consequence of phenomena occurring at the particle scale and below, down to the molecular scale. To help understanding this mechanism, a particle-scale, numerical method called the multi-particle finite-element method was developed using the finite-element software suite Abaqus (Abaqus 6.14 Documentation, 2016). Such a method allowed to explicitly model the microstructure of a granular media idealised as an assembly of elastic–plastic spheres. The particles were meshed such that their deformations were fully taken into account, using a continuum-mechanics-based material model. The interactions between particles were managed using finite-element contact formulations. A multi-scale, adhesive contact model was developed based on the literature and implemented into the multi-particle finite-element code. The contact model was based on a surface energy formulation weighted by the roughness model developed by Pullen and Williamson (1972). It introduced a novel aspect, the development of adhesion under the effect of external mechanical loads, which is consistent with the cold compaction process. This model was then applied to predict the mesoscopic properties of a packing of spheres, i.e. its response to mechanical stresses of any type, in particular strongly deviatoric stress paths. Such a method intends to be a help toward the development of an efficient continuum model for the modelling of the powder compaction process.

Experimental Study of Flow and Heat Transfer in Granular Media

AbstractIn this paper, granular flow is studied using particle image velocimetry (PIV) in two different geometries, that is, rectangular box and cylindrical bladed mixer. Effects of parameters like blade rake angle, bed height, moisture content, and the number of blades were studied. The shear rate and velocity magnitude of granular bed were calculated using PIV. The presence of moisture in the granular bed added additional cohesive forces and reduced shear rate between different layers of particles. Shear rate and shear forces were maximal at the tip of the blade. Temperature variations in the granular bed were measured experimentally and results were compared for static and mixing beds.

Anisotropic Elastic Strain-Gradient Continuum from the Macro-Scale to the Granular Micro-Scale

A multi-scale framework is constructed for the computation of the stiffness tensors of an elastic strain-gradient continuum endowed with an anisotropic microstructure of arbitrarily-shaped particles. The influence of microstructural features on the macroscopic stiffness tensors is demonstrated by comparing the fourth-order, fifth-order and sixth-order stiffness tensors obtained from macro-scale symmetry considerations to the stiffness tensors deduced from homogenizing the elastic response of the granular microstructure. Special attention is paid to systematically relating the particle properties to the probability density function describing their directional distribution, which allows to explicitly connect the level of anisotropy of the particle assembly to local variations in particle stiffness and morphology. The applicability of the multi-scale framework is exemplified by computing the stiffness tensors for various anisotropic granular media composed of equal-sized spheres. The number of independent coefficients of the homogenized stiffness tensors appears to be determined by the number of independent microstructural parameters, which is equal to, or less than, the number of independent stiffness coefficients following from macro-scale symmetry considerations. Since the modelling framework has a general character, it can be applied to different higher-order granular continua and arbitrary types of material anisotropy.

A new multiscale Cosserat model for size effect simulation in granular media

The Cosserat continuum, which contains a length scale factor l reported to link with the material’s grain size, is seemingly reasonable to describe the size effect of granular media. However, the physical meaning of l is still unclear, and its potential in describing the size effect is seldom studied. In this work, the performance of the conventional Cosserat model in capturing the size effect of granular media is firstly assessed. A new multiscale Cosserat constitutive model with an additional higher-order internal length scale vector Dq is then proposed based on the conventional Cosserat theory. The advantage of the proposed multiscale Cosserat model in size effect simulation for granular media is discussed through numerical simulations of centrifuge slope experiments and triaxial compression tests. The analysis results denote that the multiscale Cosserat continua are more sensitive to size effect than the conventional Cosserat continua, and the length scale vector Dq is like a symmetry-breaking factor that can trigger asymmetric deformation in structures; the influences of length scale factor l and Dq are seemingly opposite on stress concentration. This subtly improved constitutive model has the potential to simulate the size effect of a wider variety of materials.

Blast wave pressure measurement and analysis in air and granular media inside a shock tube using a fiber Bragg grating sensor.

In this work, we have demonstrated the use of a fiber Bragg grating (FBG) sensor to measure the pressure profile of blast waves generated inside a vertical shock tube (VST). An FBG pressure sensor probe has been designed and developed that can be incorporated into the wall of the VST. The VST facility is used to generate blast waves with decay times of the order of a few milliseconds to simulate explosive events. Pressure measurement experiments have been carried out at different incident blast wave peak pressures inside the VST. The FBG pressure sensor measurements are validated against a standard piezoelectric pressure transducer at an acquisition rate of 1MHz. The pressure signals of both sensors are found to match well with similar rise times and decay profiles. The validated FBG pressure sensor is then incorporated into a sand column mounted in the test section of the VST to measure the pressure profile of blast wave-induced stress waves in granular media. The FBG and piezoelectric pressure sensor data are compared using fast Fourier transform analysis and continuous wavelet transform. The feasibility of FBG sensors for blast pressure measurement under harsh conditions imposed inside shock tube environments is established.

Efficient discrete element modeling of heat generation and transfer in granular flows: Validation and application

This work presents an efficient Discrete Element Method (DEM) framework for the simulation of the thermal behavior of granular media. The main focus is on long-lasting granular flows, involving heat transfer and generation due to mechanical energy dissipation. The proposed approach uses efficient strategies to reduce the computational cost of the analyses and, therefore, to enable its application to problems of practical relevance. For instance, the contact area is adjusted to compensate for the artificial material softening that is typically considered in DEM to increase the time step size. After extended validation, the methodology is applied to the simulation of different setups of an experimental rotating drum. The numerical simulations presented good agreement with the experimental results and allowed a detailed analysis of the mechanisms and patterns of heat generation, which could not be extrapolated from the experimental campaign.

Predicting the precipitated calcium carbonate and unconfined compressive strength of bio-mediated sands through robust hybrid optimization algorithms

Biological soil stabilization through Microbial-Induced Calcite Precipitation (MICP) demonstrates the potential to be an eco-friendly and sustainable approach to enhance the strength properties of cohesionless granular soils. In this study, based on a comprehensive set of experimental data compiled from literature, the amounts of Precipitated Calcium Carbonate (PCC) and Unconfined Compressive Strength (UCS) of MICP-treated sands are estimated through hybridizing Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) models with metaheuristic algorithms. During the data extraction procedure, a total of 70 and 115 datasets are used to predict the PCC and UCS, respectively. Accordingly, five key features of urea concentration (Mu), calcium chloride (Mcc), optical density of bacterial suspension (OD600), pH and total volume of injection per volume of sample (Vt), are first selected as the inputs of the hybrid models to estimate the amount of calcium carbonate precipitation within the porous structure of MICP-treated granular medium. The experimental data on the PCC along with the basic characteristics of the host sand including mean grain size (D50), uniformity coefficient (Cu) and void ratio (e), are then adopted as the inputs of the numerical models in the second phase whilst the UCS of bio-mediated sands is set as the output. The performance and accuracy of implemented models are rigorously assessed through analyzing various statistical indices and performance criteria. According to the numerical analysis, the ANN-PSO and ANFIS-PSO hybrid models show the best performance in predicting PCC and UCS of bio-mediated sands, respectively. Using the well-established Gene Expression Programming (GEP) algorithm, practical correlations are developed to predict the PCC and UCS values of MICP-mediated soils based on the characteristics of biological binding agents as well as the host material. The Machine Learning (ML)-based models presented in this study provide engineers with a fruitful framework for the rough and preliminary estimation of the amount of calcite precipitation as well as the UCS of bio-mediated sands in the field prior to stabilization and performing complementary tests.

Enhancing undulation of soft robots in granular media: A numerical and experimental study on the effect of anisotropic scales

Generating efficient locomotion in granular media is important, although it is difficult for robots. Inspired by the fact that sand vipers usually have saw-like scales, in this study, we design a soft undulation robot with tangential anisotropic friction to enhance the undulation performance of soft robots in granular media. A mathematical model was derived and numerical simulations were conducted accordingly to investigate the effectiveness of tangential friction anisotropy for undulation gait generation in granular media. In particular, we introduce a pseudo-rigid-body dynamics model consisting of links and joints while simulating the pneumatic actuation method to more closely approximate the response of soft robots. Moreover, a soft snake-like robot was fabricated, and its forward and reverse undulations were compared in two sets of controlled experiments. The consistency between the experimental results and the numerical simulations confirms that tangential anisotropic friction induces a propulsive effect in undulation, thereby increasing the robot’s locomotion speed. This discovery provides new insights into the design of undulation robots in granular environments.

Dynamic imaging of force chains in 3D granular media

Granular media constitute the most abundant form of solid matter on Earth and beyond. When external forces are applied to a granular medium, the forces are transmitted through it via chains of contacts among grains-force chains. Understanding the spatial structure and temporal evolution of force chains constitutes a fundamental goal of granular mechanics. Here, we introduce an experimental technique, interference optical projection tomography, to study force chains in three-dimensional (3D) granular packs under triaxial shear loads and illustrate the technique with random assemblies of spheres and icosahedra. We find that, in response to an increasing vertical load, the pack of spheres forms intensifying vertical force chains, while the pack of icosahedra forms more interconnected force-chain networks. This provides microscopic insights into why particles with more angularity are more resistant to shear failure-the interconnected force-chain network is stronger (that is, more resilient to topological collapse) than the isolated force chains in round particles. The longer force chains with less branching in the pack of round particles are more likely to buckle, which leads to the macroscopic failure of the pack. This work paves the way for understanding the grain-scale underpinning of localized failure of 3D granular media, such as shear localization in landslides and stick-slip frictional motion in tectonic and induced earthquakes.

Phosphate and illite colloid pose a synergistic risk of enhanced uranium transport in groundwater: A challenge for phosphate immobilization remediation of uranium contaminated environmental water

The phosphorus-containing reagents have been proposed to remediate the uranium contaminated sites due to the formation of insoluble uranyl phosphate mineralization products. However, the colloids, including both pseudo and intrinsic uranium colloids, could disturb the environmental fate of uranium due to its nonnegligible mobility. In this work, the transport pattern and micro-mechanism of uranium coupled to phosphate and illite colloid (IC) were investigated by combining column experiments and micro-spectroscopic evidences. Results showed that uranium transport was facilitated in granular media by forming the intrinsic uranyl phosphate colloid (such as Na-autunite) when the pH > 3.5 and CNa+ < 10 mM. Meanwhile, the mobility of uranium depended greatly on the typical water chemistry parameters governing the aggregation and deposit of intrinsic uranium colloids. However, the attachment of phosphate on illite granule increased the repulsive force and enhanced the dispersion stability of IC in the IC-U(VI)-phosphate ternary system. The non-preequilibrium transport and retention profiles, HRTEM-mapping, as well as TRLFS spectra revealed that the IC enhanced uranium mobility by forming the ternary IC-uranyl phosphate hybrid, and acted as the coagulation preventing agent for uranyl phosphate particles. This observed facilitation of uranium transport resulted from the formation of intrinsic uranyl phosphate colloids and IC-uranyl phosphate hybrids should be taken into consideration when evaluating the potential risk of uranium migration and optimizing the in-situ mineralization remediation strategy for uranium contaminated environmental water.

Dual-layer FePt-C granular media for multi-level heat-assisted magnetic recording

Multi-level magnetic recording is a new concept for increasing the data storage capacity of hard disk drives. However, its implementation has been limited by a lack of suitable media capable of storing information at multiple levels. Herein, we overcome this problem by developing dual FePt-C nanogranular films separated by a Ru-C breaking layer with a cubic crystal structure. The FePt grains in the bottom and top layers of the developed media exhibited different effective magnetocrystalline anisotropies and Curie temperatures. The former is realized by different degrees of ordering in the L10-FePt grains, whereas the latter was attributed to the diffusion of Ru, thereby enabling separate magnetic recording on each layer under different magnetic fields and temperatures. Furthermore, magnetic measurements and heat-assisted magnetic recording simulations showed that these media enabled 3-level recording and could potentially be extended to 4-level recording, as the ↑↓ and ↓↑ states exhibited non-zero magnetization.