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The dynamic interaction between granular flowing masses and rigid obstacles is a complex phenomenon characterised by both large displacements and high strain rates. In case the flowing mass is modelled as a continuum, its numerical simulation requires both advanced computational tools and constitutive relationships capable of predicting the mechanical behaviour of the same material under both fluid and solid regimes. In this paper, the authors employed the open‐source ANURA3D code, based on the Material Point Method (MPM), and a multi‐regime constitutive model. A series of impacts characterised by different velocities, initial void ratios, front inclinations and impacting mass lengths have been simulated. The MPM numerical results are critically compared with those obtained by using a Discrete Element Method (DEM) numerical code. The model capability of simulating material regime transitions, from fluid to solid and vice versa, is shown to be crucial for reproducing the mechanical response of the flowing mass put in evidence by DEM data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Here we demonstrate the use of magnetic resonance imaging for monitoring a laser-polarized xenon ( 129 Xe) gas working as a fluidizing phase for a glass bead pack, inside a straight circular tube, simulating a granular gas-fluidized bed. The imaging method enabled encoding spatially resolved velocity and diffusion 2D-axial maps of the gas vertical upflow at variable flow regimes. From these maps one could identify gas flow transitions, hysteresis loops, regions of stagnation, and reversed flow, all of which associated, as well as complementary, to reported flow dynamics probing the particles inside the bed. In particular, we focused on the initial stage of bubbling where quantitative data on gas flow spatial maps and their potential correlation with the granular particles dynamics are scarce. [ABSTRACT FROM AUTHOR]

The behaviour of granular column collapses is associated with the dynamics of geohazards, such as debris flows, landslides and pyroclastic flows, yet their underlying physics is still not well understood. In this paper, we explore granular column collapses using the sphero-polyhedral discrete element method, where the system contains two types of particles with different frictional properties. We impose three different mixing ratios and multiple different particle frictional coefficients, which lead to different run-out distances and deposition heights. Based on our previous work and a simple mixture theory, we propose a new effective initial aspect ratio for the bi-frictional granular mixture, which helps unify the description of the relative run-out distances. We analyse the kinematics of bi-frictional granular column collapses and find that deviations from classical power-law scaling in both the dimensionless terminal time and the dimensionless time when the system reaches the maximum kinetic energy may result from differences in the initial solid fraction and initial structures. To clarify the influence of initial states, we further decrease the initial solid fraction of granular column collapses, and propose a trial function to quantitatively describe its influence. Due to the utilization of a simple mixture theory of contact occurrence probability, this study can be associated with the friction-dependent rheology of granular systems and friction-induced granular segregations, and further generalized to applications with multiple species of particles in various natural and engineering mixtures. [ABSTRACT FROM AUTHOR]

We discuss the multiscale modeling of a granular material trapped between continuum elastic domains. The amorphous granular region, usually termed "gouge," is under high confinement pressure, to represent the loading of faults at depth. We model the granularity of gouge using the discrete element method (DEM), while the elastic regions surrounding it are represented with two continuum domains modeled with the finite element method (FEM). We resort to a concurrent coupling of the discrete and continuum domains for a proper transmission of waves between the discrete and continuum domains. The confinement pressure results in the appearance of a new kind of ghost forces, which we address via two different overlapping coupling strategies. The first one is a generalization to granular materials of the bridging method, which was originally introduced to couple continuum domains to regular atomic lattices. This method imposes a strong formulation for the Lagrange constraints at the coupling interface. The second strategy considers a weak formulation. Different DEM samples sizes are tested in order to determine at which scale a convergence of the elastic properties is reached. This scale sets the minimal mesh element size in the DEM/FEM interface necessary to avoid undesirable effects due to an elastic properties mismatch. Then, the two DEM/FEM strategies are compared for a system initially at equilibrium. While the performance of both strategies is adequate, we show that the strong coupling is the most stable one as it generates the least spurious numerical noise. Finally, as a practical example for the strong coupling approach, we analyze the propagation of pressure and shear waves through the FEM/DEM interface and discuss dispersion as function of the incoming wave frequency. [ABSTRACT FROM AUTHOR]

We provide a numerical platform for the analysis of particle shape and topology effect on the macroscopic behavior of granular media. We work within a discrete element method (DEM) framework and apply a peridynamic model for deformable particles accounting for deformation and damage of individual particles. To accommodate arbitrary particle shapes including nonconvex ones as well as particle topology, an efficient method is developed to keep intraparticle peridynamic interaction within particle boundaries. Particle contact with the rigid boundary wall is computed analytically to improve accuracy. To speed up simulations with particles of different shapes and sizes the initial configuration is chosen using security disks containing different particle shapes that are placed in a jammed state using an optimization-based method. The effect of particle shape and topology on settling and compaction of the aggregate for deformable particles is analyzed. [ABSTRACT FROM AUTHOR]

Earthquake-induced liquefaction is always a concern when the soil near the surface of a site is composed of relatively loose saturated sand. One of liquefaction mitigation methods is to induce gas bubbles into the deposit to reduce the degree of saturation. A coupled pore-scale model is presented herein to investigate liquefaction resistance of desaturated granular materials. The multiphase fluid, which mimics the behavior of air and water, is modeled using the multiphase single component lattice Boltzmann method. The solid phase is modeled using the discrete element method. The coupled framework was utilized to study the behavior of a soil deposit with the different degrees of saturation of 100%, 92%, and 82% during an earthquake loading. Based on the results of the simulations performed, liquefaction occurred in the fully saturated granular deposit and was not observed anywhere at depth in the desaturated deposits. It has also been found that reducing the saturation level from 100% to 92% significantly affects behavior. In desaturated deposits, higher average coordination number, lower pore pressure buildup, and slower effective stress decay were observed compared to fully saturated deposits. However, it turned out that a further reduction in the degree of saturation from 92% to 82% does not have a significant impact on the calculated parameters. [ABSTRACT FROM AUTHOR]

Rotary drums are widely used in industry, however, determining granular dynamics within them is still a complex task, thus remaining a focal point of research over the years. In this context, experimental techniques require numerical support to obtain data that is not easily acquired experimentally. One well-established numerical technique for studying particulate systems is the Lagrangian approach embed with Discrete Element Method (DEM). Although, DEM has limitations related to the definition of input parameters. It is crucial that DEM input parameters be measured and/or calibrated to reliably represent the granular behavior. These parameters are related to particle properties such as density, Young's modulus, Poisson's ratio, among others, and particle interactions, such as coefficients of restitution, static friction, and rolling friction. This study explores the experimental determination of interaction parameters preceding the acquisition of DEM input parameters in a rotary drum. Statistical analysis highlights the importance of each parameter and their combined interactions with the static angle of repose. The granular materials used were: soybeans, glass beads, polyacetal, 6 mm steel, and 4 mm steel. The coefficient of restitution was determined via free-fall methodology using equipment that verifies particle trajectory, static friction coefficient through equilibrium between weight and resistance forces, rolling friction coefficient using a launching device on surfaces of different roughness, and static angle of repose in a rectangular box with sections where particles rested. After removing the partition, angles were measured at both top and bottom sections. Regression techniques using a neural network created in Python were employed for both measurements. Experimental investigations and numerical simulations using DEM indicated that the coefficient of restitution depends on the thickness and type of material of the flat surfaces, showing an asymptotic behavior with increasing surface thickness. The static friction coefficient increased on rougher surfaces and in particles with greater imperfections. Rolling friction coefficient also increased on rough surfaces. Analysis of the angle of repose revealed that granular properties influence the response, such as static and rolling friction coefficients, whereas the coefficient of restitution had no significant influence. Neural network correlation coefficients exceeded 0.95, indicating a strong association between the variables. Our findings revealed that mathematical models can be used in conjunction with static repose angle experiments to calibrate DEM parameters for more robust and complex simulations. This research also quantifies and provides insights into the interactions between DEM parameters in direct measurement experiments, promoting more efficient calibration for future research. [Display omitted] • Restitution coefficient varies with surface thickness and material. • Increased surface roughness and imperfections raise static friction coefficients. • Rougher surfaces and smaller particles lead to higher rolling friction coefficients. • Granular properties, diameter, and density affect the static angle of repose. • Artificial Neural Networks have been employed for DEM parameters determination. [ABSTRACT FROM AUTHOR]

Understanding motion-induced terrain deformation is essential for improving predictive models in geotechnical engineering, infrastructure development, and robotics. The existing analysis assumes a uniform and unchanged environment and lacks a description of the terrain deformation induced by motion, which is particularly significant when the grains are loosely packed. To address this gap, we performed numerical investigations to mathematically model the changes in the surrounding environment and their corresponding effects on resistance. Specifically, we examined the response of granular materials and the energy variation of the particles during motion. Increased energy in the direction of motion was categorized as influences above or below the medium surface. Aligned with the influencing factors, two variables were considered to quantify the impact on the drag force. Building upon the energy analysis and the framework of Resistive Force Theory, we proposed a drag force model for buried motion in loose granular terrain. Compared with the experimental data, the average predictive error decreased from 17.8% to less than 2.7%. Our study provides a feasible approach for incorporating the effects of terrain deformation into a drag force model, thereby enhancing the accuracy and contributing to the development of granular locomotion. • The impact of motion-induced terrain deformation on the surface layer is modeled. • Granular pile formation leads to increased depth of buried objects. • The flow of particles raises local packing density. • A drag force model integrated with environmental changes is established and verified. [ABSTRACT FROM AUTHOR]

In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb's friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Numerical simulation based on the discrete element method (DEM) is used to investigate the flow field generated when a cylindrical obstacle is placed in a supersonic granular stream. Robust validation of the simulation model is performed by comparing numerical results with experiments. Experiments are performed using a two-dimensional set-up generating rapid granular flow owing to gravity. DEM simulations demonstrate that a rapid gas-like stream of grains suddenly decelerates across the shock wave and finally collapses into a slow-moving heap at the cylinder. The volume fraction suddenly increases across the shock layer and remains constant thereafter. The flow physics of the shock wave and the granular heap is elucidated through fundamental fluid dynamic quantities such as the velocity, volume fraction, pressure and granular temperature. It is shown that the interaction of grains with a cylindrical obstacle results in the generation of pressure, which is responsible for sustaining static granular heaps on the cylinder. The total pressure is resolved into collisional and streaming components. A streaming pressure is generated owing to velocity fluctuations, and is found to be significant only in the shock wave region. The observations show that the rheological complexity offered by granular shock waves is a direct manifestation of the dissipative and frictional nature of granular collisions. The new insight into the granular heaps could be relevant to a variety of applications involving granular-fluid–solid interactions. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the mechanical properties of a binary mixture of similar prolate ellipsoids of various particle shapes and fines' contents using the discrete element method. The ratio of the major axis of a small ellipsoid to that of a large ellipsoid is 0.2. Because all particles have the same shape, the particle shape of the binary mixture is defined unambiguously. The effect of fines content is examined with samples of the same particle shape. The effect of particle shape is examined by comparing the samples of different particle shapes. Very dense samples are generated and sheared under drained and constant volume conditions. The macroscopic and microscopic behaviors of these samples are studied at both peak and critical states. The mechanical behavior can be grouped into two or three regions for our binary mixture depending on the fines content. Although the critical state line varies with fines content, a unified critical state line is identified using the intergranular void ratio, which is a function of fines content and a parameter. The parameter is a constant for the samples of the same particle shape. This constant is different for the samples of different particle shapes. The finding explains why some studies defined the parameter as a function of fines. The intergranular void ratio does not relate well to the peak friction angle. The microscopic behavior is examined through contact normal, particle orientation, and stress partition. Although some microscopic parameters can identify the region where the sample belongs, we do not find any dominant microscopic parameter that relates to the macroscopic behavior of a binary mixture of various fines contents. [ABSTRACT FROM AUTHOR]

In order to accelerate simulations of assemblies of highly deformable grains, a novel numerical approach, called Soft Discrete Element Method (SDEM) is presented. It consists in extending the classical DEM by introducing the deformability of the grains in a simplified way. Simple kinematics are postulated in order to represent the ovalisation of the grains and their local deformations around interparticle contacts. Adequate equations of motion are derived, and a contact model is proposed in the framework of elastic frictionless grains. Comparisons are made with existing analytical and numerical solutions, and the ability of this method to simulate the compressibility and some micromechanical aspects of this class of materials is validated. Upon implementation in optimized DEM codes, the SDEM is expected to allow large scale simulations of samples of deformable particles. [ABSTRACT FROM AUTHOR]

Granular heat transfer is encountered in many industries, including food production, solar energy harvesting and nuclear engineering. The present study investigates influence of vibration characteristics on granular heat transfer in a vibrationally fluidized bed of particles using a thermal discrete element method. The bed is heated by transferring a constant heat flux from its bottom wall. Vibrations generally had two influences: first, particles reached a higher average temperature, and second, they attained more uniform temperature distribution. The particles average temperature generally increased by increasing vibration amplitude and frequency. However, the best temperature uniformity occurred in an optimal set of amplitudes and frequencies. Contrary to claims in previous studies, the effective thermal conductivity (ETC) of the vibrated bed was not the only determining parameter for quality of heat transfer. Other parameters such as flow patterns, convective and diffusive motions must be also analyzed to evaluate the heating process in vibrating beds. Evolution of temperature profile of particles after 10 min of heating within (a) a fixed bed, and beds vibrated with frequency of 20 Hz and with amplitudes of (b) 1 mm, (c) 3 mm, and (d) 6 mm. [Display omitted] • Vibration characteristics effects on heat transfer in granular beds were studied. • Vibrations enhance the average temperature and temperature uniformity of particles. • Particles average temperature increase by increasing amplitude and frequency. • Maximum temperature uniformity occurred in an optimal amplitude and frequency set. • Generation of heating cycles plays a significant role in granular heat transfer. [ABSTRACT FROM AUTHOR]

Vertical chutes and pipes are a common component of many industrial apparatus used in the transport and processing of powders and grains. Here, a typical arrangement is considered first in which a hopper at the top feeds the chute and a converging outlet at the bottom controls the mass flux. Discrete element method (DEM) simulations reveal that steady uniform flow is only observed for intermediate flow rates, with jamming and unsteady waves dominating slow flows and non-uniform wall detachment in fast flow. Focusing on the steady uniform regimes, a progressive idealisation is carried out by matching with equivalent DEM simulations in periodic cells. These investigations justify a one-dimensional continuum modelling of the problem and provide key test data. Novel exact solutions are derived here for vertical flow using a linear version of the ' $\mu(I),\varPhi(I)$ -rheology', for which the bulk friction $\mu$ and steady solid volume fraction $\varPhi$ depend on the inertial number I. Despite not capturing the full nonlinear complexities, the solutions match important aspects of the DEM flow fields and reveal simple scaling laws linking many quantities of interest. In particular, this study clearly demonstrates a linear relation between the chute width and the size of the shear zones at the walls. This finding contrasts with previous works on purely quasi-static flow, which instead predict a roughly constant shear zone width, a difference which implies that finite-size effects are minimal for the inertial flows studied here. [ABSTRACT FROM AUTHOR]

Understanding the effect of particle size on the shear strength of granular materials is important for geotechnical design and construction. However, previous studies show contradicting results on the relationship between particle size and shear strength. Additionally, the effect of particle breakage on this relationship has not been fully revealed. In this study, a series of biaxial tests have been simulated with the discrete element method to explore the particle-size effect of sand considering the role of particle breakage. The sand specimens have parallel particle-size distributions. The sequential breakage model has been used to simulate particle breakage, which is a combination of replacement and cluster methods. The main conclusions of this study are: (1) the relationship of peak shear strength and particle size depends on the crushability of particles and relative density of specimens; (2) the particle size and crushability have a very slight effect on the residual shear strength; and (3) at the microscale, the relationship between shear strength and particle size is positively related to the friction utilization ratio. [ABSTRACT FROM AUTHOR]

The cascade finishing used for surface finishing, cleaning, deburring, and stress relieving in industry has been increasing rapidly as a final manufacturing step in industry. The process was highly shown to be capable to improve the surface integrity and mechanical properties of workpieces. The effects of process parameters on velocity of granular media in cascade finishing have not yet been studied, which is an obstacle for process optimization. In this study, the behavior of the granular media in the vibrating flow field was simulated by discrete element method. The velocity of the granular media acting on the workpieces were obtained and analyzed. To verify the simulation results, the velocity was experimentally measured using laser displacement sensors. The effect of some parameters on the velocity was obtained through this study. [ABSTRACT FROM AUTHOR]

Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration for free surface flows. Concentration profiles predicted by incorporating this segregation velocity model into a continuum advection–diffusion–segregation transport model match DEM simulation results well for a wide range of particle size and density ratios. Most surprisingly, the DEM simulations and the segregation velocity model both show that the segregation direction for a range of size and density ratios depends on the local species concentration. This leads to a methodology to determine the combination of particle size ratio, density ratio and particle concentration for which a bidisperse mixture will not segregate. [ABSTRACT FROM AUTHOR]

This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows. [ABSTRACT FROM AUTHOR]

Vibratory finishing realizes the finishing of the workpiece surface by vibrationally-fluidized granular media. Due to the granular media's fluidized nature, vibratory finishing can be applied to surface finishing in restricted space, such as the cavity of integral casting casing. In this work, taking the typical elongated pipe-cavity inside the casings as the analysis object, based on the discrete element method (DEM), a series of simulations were carried out on the length and diameter of pipe-cavity, the load of media, vibration amplitude, and frequency. The frequency multiplication of the normal contact force between the granular media and the surface in restricted space was discovered. A method of processing contact force data based on the Fourier transform was proposed. And then, the normal contact force, its average, and coefficient of variation at different positions of the slender pipe-cavity were analyzed. It is found that the normal force fluctuates along the axial direction and is symmetric on the circumferential positions. Furthermore, the effects of various variables, including length, diameter, load, amplitude, and frequency on the normal force, have been obtained. The method and results can reference studying the dynamic behavior of granular media in restricted space. [ABSTRACT FROM AUTHOR]

The collapse of a granular column in a liquid is investigated using numerical simulations. From previous experimental studies, it has been established that the dynamics of the collapse is mostly influenced by the Stokes number $St$ , comparing grain inertia and viscous fluid dissipation, and the initial volume fraction of the granular column $\phi _i$. However, the full characterization of the collapse in the $(St,\phi _i)$ plane is still missing, restricting its modelling as a physical process for geophysical applications. Only numerical tools can allow the variation over the parameter space $(St,\phi _i)$ that is hardly reachable in experiments as well as a full description of the granular phase that plays a major role in dense granular flows. For this purpose, a dedicated numerical model is used including a discrete element method to resolve the granular phase. The specific objectives of the paper are then twofold: (i) the characterization of the dynamics of the collapse and its final deposit with respect to $(St,\phi _i)$ to complement available experimental data, and (ii) the description of the granular rheology according to these two dimensionless numbers including dilatancy effects. A simple predictive model stems from the obtained results, allowing one to explain the evolution of the final deposit with $(St,\phi _i)$. [ABSTRACT FROM AUTHOR]

Process industries often involve handling non-cohesive solid materials which vary in size and shape. A comprehensive understanding of such systems helps in effective handling of industrial operations. Here, we studied heterogeneous mixtures of dumbbells and discs flowing out of a two-dimensional silo using discrete element method simulations. We analysed discharge dynamics of the mixtures in two regimes, namely the free-flow regime ($W/d>=15$) and the interrupted flow regime ($W/d), where $W$ and $d$ are the orifice width and diameter of each of the circles of a dumbbell. One of the intriguing results is a decrease in the flow rate $Q$ of mixtures with an increase in the fraction of dumbbells $X_{db}$ in both of the regimes analysed. This can be attributed to the geometrical interlocking among the particles and a hindrance to the rotation of dumbbells. The time-averaged (coarse-grained) flow fields reveal an increase in the size of the stagnant zone beside the orifice with an increase in $X_{db}$. The stagnant zone hinders the particles flowing next to it, which is another reason for a decrease in $Q$ with an increase in $X_{db}$. In the interrupted flow regime, we investigated clogged states of the mixtures using arch morphology, the fraction of dumbbells and number of particles in an arch, and avalanche sizes. [ABSTRACT FROM AUTHOR]

During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the $\mu (I)$ -rheology (where $\mu$ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible $\mu (I)$ -rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353–588). These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum. [ABSTRACT FROM AUTHOR]

This article presents the results of level-set (LS) discrete element method (DEM) simulations with experimental comparisons of flexible boundary plane strain tests in granular media. The grain-scale micromechanics at the particle level is captured well with LS-DEM, while the overall macroscopic response of the specimen is in quite good agreement with the simulation results. Onset and evolution of localized zones of shear strain accompanied by a significant amount of grain rotation could be well apprehended in the simulations, while the bulging of the specimen could be noticed in the experimental findings as well as in the model predictions. Multiple zones of shear strain accumulation in conjugate arrays were also observed on subsequent biaxial shearing of the sand specimen. The computational results furnish a quantitative estimate of the evolution of force chains and grain fabric orientation. Initially, these force chains were isotropic which on further deformation oriented in the direction of loading, and the grains aligned themselves in their preferred fabric orientation and remained in that fashion till the end of biaxial loading. [ABSTRACT FROM AUTHOR]

Summary: An algorithm is presented for discrete element method simulations of energy‐conserving systems of frictionless, spherical particles in a reversed‐time frame. This algorithm is verified, within the limits of round‐off error, through implementation in the LAMMPS code. Mechanisms for energy dissipation such as interparticle friction, damping, rotational resistance, particle crushing, or bond breakage cannot be incorporated into this algorithm without causing time irreversibility. This theoretical development is applied to critical‐state soil mechanics as an exemplar. It is shown that the convergence of soil samples, which differ only in terms of their initial void ratio, to the same critical state requires the presence of shear forces and frictional dissipation within the soil system. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of a disk-shaped rotor rotating inside a granular medium using the discrete element method, and the torque, quantitatively characterizing the resultant of drag forces on the rotor from surrounding particles, is mainly explored. The existence of a dumbbell-shaped region induced by the rotating rotor may essentially give rise to the steady state independent of initial loading conditions, in which the pressure difference between the upper and lower surfaces of the disk disappears and the torque always tends to a stationary value. Furthermore, the rotation of the rotor induces an anisotropic structure with the formation of arches that screen the vertical pressure, leading to the occurrence of the low-pressure region above the rotor. Finally, a scaling law of the torque with the depth is proposed, in which the rotation speed of the rotor as an affecting factor is also taken into account. Unlabelled Image • The drag force experienced by a disk-shaped rotor is studied based on DEM. • The steady state is independent of the initial loading conditions. • The rotation of the rotor induces a dumbbell-shaped activated region. • The formation of arch structure screens the vertical pressure. • The scaling law of the torque with the depth and the rotation speed is proposed. [ABSTRACT FROM AUTHOR]

Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas–solids mixture. Previous efforts to resolve the solids' heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle–wall separation distance and asymptotically decays to zero for large particle–wall separation distances, seaming together the unbounded and near-wall regions. [ABSTRACT FROM AUTHOR]

We propose a new way to estimating interparticle contact forces in granular materials, based on the combination of experimental measurements and numerical techniques that take the contact laws respectively from Molecular Dynamics and Non-Smooth Contact Dynamics discrete element methods. Tests are performed in quasi-static conditions on a two-dimensional granular assembly; 80 MPixel pictures of the assembly are shot throughout each test. Image processing and Digital Image Correlation are used in order to get information on the geometry of the assembly (particles and contact points position) and the rigid-body motion of particles (displacements and rotation); based on this information, numerical methods can be applied to assess contact forces. 2D DEM simulations are also performed and the same information is extracted and used for contact force estimation, so that the numerical methods can be validated. The reproducibility of the original set of contact forces is shown to be dependent on the displacement history for the first method, based on contact elasticity, and on the degree of force indeterminacy for the Contact Dynamics-based one. The validation phase also includes a perturbation analysis to predict the influence of measurement error (bad contact detection) when applying the Contact Dynamics-based method, which shows the robustness of this method. After this validation phase, the methods are applied to experimental data. Measurement error on kinematic measurements turns out to be quite significant for the first approach, while it does not affect the second, for which the accuracy of the force estimation can be assumed to be mainly dependent on the degree of force indeterminacy of the system. [ABSTRACT FROM AUTHOR]

The paper examines the mechanics and physics of granular material responses at the macroscopic and microscopic levels during both monotonic and cyclic loadings. A numerical analysis referring to a long retaining wall is conducted using a two-dimensional discrete element model representing a granular system with a free top surface. On one of the lateral boundaries referring to the retaining wall, both active and passive loadings were applied monotonically as well as cyclically. First, the development of sheared zones and classic failure wedges resulting from active and passive monotonic displacements are discussed with respect to Rankine's and Roscoe's solution angles. Then, a series of loading cycles were performed using slow small-amplitude displacements at different stress states chosen before the occurrence of failure along the passive monotonic stress response curve. Particular interest is focused on the ultimate asymptotic cyclic response of the granular system, the occurrence of a high-mobility (convective) zone and a detailed macroscopic and microscopic analysis. Finally, major kinematical features that are displayed during cyclic loading from different starting stresses to eventually reach the same asymptotic state were elucidated through particle vortex-like flux formations, including contact rotations. The change in material stiffness was also investigated based on the evolution of strong and weak contact networks, together with the analysis of fabric anisotropy within the entire domain, including the high-mobility zone considered separately. [ABSTRACT FROM AUTHOR]

Erosion processes and the associated static/flowing transition in granular flows are still poorly understood despite their crucial role in natural hazards such as landslides and debris flows. Continuum models do not yet adequately reproduce the observed increase of runout distance of granular flows on erodible beds or the development of waves at the bed/flow interface. Discrete Element Methods, which simulate each grain's motion and their complex interactions, provide a unique tool to investigate these processes numerically. Among them, Convex Methods (CM), resulting from the convexification of Contact Dynamics methods, benefit from a robust theoretical framework, ensuring the convergence of the numerical solution at every time iteration. They are also intrinsically more stable than classical Molecular Dynamics methods. However, although already implemented in engineering fields, CMs have not yet been tested in the framework of flows on erodible beds. We present here a Convex Optimization Contact Dynamics (COCD) method and prove that it generates a numerical solution verifying Coulomb's law at each contact and iteration. After its calibration and validation with experiments and another widely used Contact Dynamics method, we show that our simulations accurately reproduce qualitative and even many quantitative characteristics of experimental granular flows on erodible beds, including the increase of runout distance with the thickness of the erodible bed, the change of the static/flowing interface and the presence of erosion waves behind the flow front. Beyond erosion processes, our article endorses CMs as potential accurate tools for exploring complex granular mechanisms. • The method COCD is based on an implicit scheme and large time step values are used. • The computational efficiency of COCD is derived from existing convex solvers. • Simulations of granular flows are compared to laboratory scale experiments. • COCD reproduces the complex interaction between the flow and the erodible layer. • Convex methods are relevant for the simulation of complex granular flow processes. [ABSTRACT FROM AUTHOR]

Producing of granular media with irregular shapes is one of the significant challenges in different fields related to granular particles. Representing inaccurate and simplified particles can result in wrong predictions. In this paper, a new statistical and optimization-based algorithm is presented by which 3D particles with complex shapes are generated on a random container. Stochastic conditional sampling along with an optimization method are combined such that particle with realistically and controllable shapes are generated. Depending on the initial shape of the container, a pack of spheres is generated. Then, an iterative optimization-based conditional sampling is proposed by which other complex shape descriptors are considered and can help to avoid artifacts and unrealistic shapes. The proposed method is applied to two examples wherein the particles reproduction and controllability of algorithm is demonstrated. The performance of the algorithm, in terms of shape reproduction, is also quantified using various utilized statistical measures. Unlabelled Image • An automatic algorithm for producing irregular particles is presented. • The proposed method is based on the input morphological statistics. • An optimization algorithm is developed to include the statistics. • The results are compared with the initial data. [ABSTRACT FROM AUTHOR]

The particles velocity vectors; (a) creation, (b) fully-developed pattern, (c) movement, and (d) destruction of a convection roll. • Influence of vibration amplitude and frequency on mixing in fluidized beds. • As the vibration strength increased, the convection rolls became fully developed. • The generation and movement of convection rolls played a fundamental role in mixing. • Mixing of particles was generally improved by increasing the vibration amplitude. • An optimal frequency was found in each amplitude, by which the best mixing occurred. The uniform mixing is necessary in many processes such as those used in pharmaceutical, chemical and petrochemical industries. The present work studies the influence of vibration characteristics on mixing of binary mixtures of spheres produced in a vibrationally fluidized bed by using discrete element method. Solid-like flow pattern was observed in low frequencies and amplitudes, while as the vibration got stronger, particles behaved fluid-like, and convection rolls were generated. The generation and movement of convection rolls played a fundamental role in mixing within vibrated beds. It was realized that mixing was generally improved by increasing the vibration amplitude. In contrast, an optimal frequency was found in each amplitude, by which the best mixing occurred. The particles average velocity always increased by amplitude at a fixed frequency, while the mixing was not necessarily improved. It was found that the results were in qualitative agreement with some previous experimental and numerical studies. [ABSTRACT FROM AUTHOR]

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology that does not suffer from such defects is proposed. In the framework of compressible $I$ -dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations. [ABSTRACT FROM AUTHOR]

Summary: Particle morphology plays a key role in affecting physical and mechanical behaviors of granular media. While various mathematical approaches and shape descriptors have been proposed to describe the morphological properties of granular particles, it remains a challenge to effectively incorporate them for efficient discrete modeling of granular materials. This study presents a new poly‐superellipsoid‐based approach for three‐dimensional discrete element method (DEM) modeling of non‐spherical convex particles. A uniform mathematical description of 3D poly‐superellipsoidal surface is employed to represent a realistic granular particle, which is shown to be versatile and effective in reproducing a wide range of shape features (including elongation, flatness, angularity, and asymmetry) for real particles in nature. A novel optimization approach based on hybrid Levenberg‐Marquardt (LM) and Gilbert‐Johnson‐Keerthi (GJK) algorithms is further developed for efficient and robust contact detection in DEM simulation of poly‐superellipsoidal assemblies. Simulations of granular packing and triaxial compression tests show that the proposed approach is generally robust and efficient for both dynamic and quasistatic modeling of granular media. [ABSTRACT FROM AUTHOR]

Structural characteristics are considered to be the dominant factors in determining the effective properties of granular media, particularly in the scope of transport phenomena. Enhancing heat management requires an improved fundamental understanding of thermal transport in granular media. In this study, the effects of packing structure on heat transfer in granular media are evaluated at macro- and grain-scales. At the grain-scale, a gas-solid coupling heat transfer model is adapted into a discrete-element-method to simulate this transport phenomenon. The numerical framework is validated by experimental data obtained using a plane source technique, and the Smoluchowski effect of the gas phase is found to be captured by this extension. By considering packings of spherical SiO 2 grains with an interstitial helium phase, vibration induced ordering in granular media is studied, using the simulation method developed here, to investigate how disorder-to-order transitions of packing structure enhance effective thermal conductivity. Grain-scale thermal transport is shown to be influenced by the local neighbourhood configuration of individual grains. The formation of an ordered packing structure enhances both global and local thermal transport. This study provides a structure-based approach to explain transport phenomena, which can be applied in properties modification for granular media. • A framework combining finite and discrete element simulations is proposed to study heat conduction in granular media. • Finite element analysis is used to improve the conventional analytical heat transfer model with an empirical correlation. • The modified heat transfer model is incorporated into the discrete element simulation. • Effects of structural transitions on effective thermal conductivity are evaluated by grain-scale structure index. [ABSTRACT FROM AUTHOR]

Abstract The paper aims to clarify the stress tensor definition and its symmetry property that applies to granular media, and conducts 3D Discrete Element Method (DEM) inspection of the stress tensor definitions provided in the literature. Various stress tensor formulas under static and dynamic conditions are summarized, compared and numerically inspected through different types of simulation, such as gravitational deposition, isotropic/oedometer compression and high-strain-rate (HSR) oedometer impact. The stress tensor symmetry is particularly discussed from the perspective of applying classical continuum mechanics to granular media. It is proved analytically and numerically that the stress tensor should be calculated by Bagi's formula, not Weber's formula or Drescher's formula, for a particle assembly or representative volume element (RVE) in static equilibrium. We propose to modify the De Saxcé and Nicot formulas by incorporating the boundary-radius-gap term such that they are consistent with Bagi's formula, which is particularly well-suited for studying granular phenomena that transition between static, quasi-static and dynamic conditions. It is shown from the perspective of stress tensor calculation that the number of particles in the RVE does not need to be large. Symmetry of averaged stress tensor can be accurately satisfied in static equilibrium of the granular DEM RVE, however it cannot in quasi-static or dynamic states due to imbalance of angular momentum of the granular DEM RVE (in comparison to the balance of angular momentum which is always satisfied in classical continuum mechanics). When the stress tensor definition is extended to "discontinuous" state with regard to discrete granular DEM RVEs, the calculated values need to be treated with caution. [ABSTRACT FROM AUTHOR]

In the complex granular flow, the shear and flow of particles lead to increase in temperature that can enchain behavioral modifications. However, their thermo-mechanical and electrical behavior is of great interest for applications such as rail transport, grinding, and granular material reproduction systems. To study these behaviors, a numerical experiment is carried out on a rotating drum model. This device makes it possible to generate continuous and controlled free surface flows. Relying on the NSCD approach, the location of the hottest zone and the evolution of the temperature are correlated with the evolution of the velocity field. [ABSTRACT FROM AUTHOR]

This study presents an experimental, computational, and analytical comparison of a submerged, double‐helix Archimedes screw generating propulsive force against a bed of glass beads. Three screws of different pitch lengths were studied. Each screw was tested at six speeds in approximately 10 trials for a total of 180 experimental trials. These experiments were then replicated in EDEM, a discrete element method (DEM) software program. DEM simulation results for thrust forces in the 30–120 rpm regime had a 5%–20% inflation of forces compared to experimental results. These simulations were then compared with resistive force theory (RFT) plate approximation of the screw geometries. We analyze a superposition‐based partition approach to the full‐length screws as well as force generation in shortened, one‐ and two‐blade screws. We find that the force generation is dependent on the flow patterns and cannot be reduced to partitioned approximations as with simple intruders. © 2018 American Institute of Chemical Engineers AIChE J, 65: 894–903, 2019 [ABSTRACT FROM AUTHOR]

In recent years, the multi-particle finite element method (MPFEM) has demonstrated its suitability for the micromechanical modelling of granular systems made up of highly deformable particles. This method combines the advantages of the finite element method to compute particles' deformations and of the discrete element method to simulate particles' interactions. Being computationally expensive, its main drawback is the limitation of the number of particles which can be included in a simulation. However, using a multi-scale approach, it is possible to deduce mesoscopic material properties from the simulation of a relatively small number of particles within an elementary volume, through appropriate averaging techniques. Such simulations are significantly influenced by the boundary conditions (BCs) applied. Periodic BCs are commonly admitted to be the most accurate. However, they are technically rather difficult to implement in the MPFEM because of the multiple contacts which need to be handled in the model. As a result, simplified BCs involving for example, rigid walls, remain used. This study analyses the effect of different types of BCs on the simulated mechanical response of a numerical granular sample, under quasi-static loading. Two different techniques for implementing full or simplified periodic BCs, introduced by Schmidt et al. [1] and Loidolt et al. [2] , respectively, were compared with simpler, non-periodic BCs. In the comparison, the same initial microstructure was used; it consisted of an assembly of 50 spherical particles with a periodic topology. The results suggest that considering the additional computational cost induced by the implementation of multi-point constraints, the advantage brought by periodic BCs is relatively limited. The study also highlights the differences between BC types and provides interpretations relative to the particularities of the numerical method used. [ABSTRACT FROM AUTHOR]

Blocky rock and stone structures (such as jointed rocks mass, masonry structures and railway ballast) are often submitted to dynamic effects. Their mechanical behaviour can be simulated with the discrete element method (DEM) using polyhedral elements. DEM models differ in how they compute the contact forces. Several studies have compared different contact constitutive laws, but little information is available in the literature on which contact treatment method (i.e. number of contacts between two elements, contact detection, contact orientation, area and overlap computation) to choose. The inclined slope, the perpendicular impact and the rocking block problems were simulated and applied as benchmark tests in the present study to compare three most popular polyhedral DEM contact treatment models for rigid elements, namely the Eliáš (available in Yade), the Gilbert-Johnson-Keerthi (GJK, widely implemented, here tested with PFC3D) and the Sub-Contact model (available in 3DEC), to see which ones could be precisely calibrated to analytic and experimental solutions. Sensitivity studies were also carried out on the effect of subdivision density of element surfaces and on the admissible timestep length. Experiences showed that while there are serious doubts about the applicability of the Eliáš volumetric model as it is sensitive to both variations in geometry and the results vary randomly with the timestep length, the GJK model is suitable to simulate granular materials because of its computational efficiency and robustness, and the Sub-Contact method is the proper choice to model structures where the contact surfaces are relatively large, as it operates multiple contacts between two elements and gives information about the force distribution on the surface of the elements. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract The rheological properties and dynamic behaviors of granular media under oblique impact are very sensitive to the variation of packing fraction. In this work, granular beds with different packing fraction have been obtained by changing the mixture ratio and diameter ratio of two components. Then, the influence of packing fraction on the dynamic characteristics of the two-dimensional granular beds subjected to oblique impact has been investigated using the discrete element method. Simulation results exhibit that there exists a critical packing fraction for the reversal of the penetration depth-packing fraction dependence. The linear relationship of horizontal penetration depth and impact velocity is still remained, but vertical penetration depth and impact velocity is held at the expense of correlation coefficient. However, if the packing fraction exceeds the critical domain of packing fraction, the resistance force cannot be decomposed into two independent functions proportional to the square of velocity and depth any more for impact angles larger than the critical angle, vice versa. Meanwhile, the dependence of stopping time on the impact velocity exhibits a criticality characteristic when packing fraction is in the critical range, that is, for an impact angle lower than critical angle, the stopping time generally increases linearly with impact velocity, while it decreases in an exponential manner for a larger impact angle. Based on the simulation results, the scaling relations between penetration depth, stopping time and packing fraction, impact angle have been proposed. Meanwhile, a phenomenological model describing the resistance force has been established considering the packing fraction Graphical abstract Unlabelled Image Highlights • A model describing the resistance force is presented considering the packing fraction. • The scaling laws between penetration depth, stopping time and packing fraction, impact angle have been proposed. • There is a critical packing fraction ϕ c for the reversal of the penetration depth-packing fraction dependence. [ABSTRACT FROM AUTHOR]

The effect of grain shape and fracture on the interaction of high velocity granular slugs with rigid stationary targets is analysed for targets in normal and inclined orientations. The granular slugs comprise spherical, rod-shaped or cubic grains and are constructed by connecting together spherical sub-particles with either rigid or beam connectors. The case when grain fracture is suppressed (rigid connectors between sub-particles) is first analysed. With increasing grain aspect ratio, the grains tend to slide rather than roll on the target surface and this increases frictional interactions with the target surface. However, these enhanced frictional forces do not affect the momentum transmitted into normally oriented targets due to the symmetry of the problem. By contrast, the break in the symmetry for inclined targets results in the transmitted momentum increasing with grain aspect ratio. Fracture of the grains (as modelled by the fracture of the beam connectors between sub-particles) is shown to affect the momentum transmitted into the inclined targets. This is a consequence of fracture resulting in a change in grain shape. In this case the simulations show that the transmitted momentum is a function of the initial grain shape, the fracture properties of the grains and the impact velocity. In fact, grain fracture results in an enhanced transmitted momentum for initially cubic grains but fracture of grains with a high initial aspect ratio results in a reduction in transmitted momentum as these grains fragment into more spherically shaped grains. [ABSTRACT FROM AUTHOR]

A new conditional modeling along with a level-set method that can produce high quality and large packs of irregular particles is proposed. First, an initial pack of particles is generated statistically using the particles provided through an X-ray image. Then, the mismatch locations, wherein an error map identifies the particles manifest unrealistic shapes, are detected. Next, a level-set algorithm is applied to refine the defected particles using the statistical distributions extracted from the actual particles. The generated packs are statistically and physically (i.e. flow modeling) compared with the original particles and they all represent an excellent agreement. [ABSTRACT FROM AUTHOR]

A general contact modeling method of elastoplastic contact between particles is proposed to study the vibration and energy dissipation characteristics of the particle system. The basic form of constitutive equation concerning normal plasticity contact between particles is established and a dimensionless constitutive relation can be obtained based on the finite element method accordingly. A loading-unloading multipath model of elastoplastic contact between particles is presented. A theoretical formula of normal plastic energy dissipation is deduced. Based on the discrete element method， numerical simulations on the characteristics of vibration and energy dissipation for the particle system under harmonic excitation are carried out. The results show that the linear system exhibits the characteristics of nonlinear vibration caused by particles. Granular media appears to be a complicated nonlinear state of motion similar to the chaos near the resonance region. Although the way of energy dissipation on particle damping effect remains unchanged， normal plastic contact alters the dynamic contact behavior between particles and has great influence on the dynamic characteristics of the vibrating particle system. [ABSTRACT FROM AUTHOR]

In this work, an active set type method is considered in order to solve a mathematical problem that describes the frictionless dynamic contact of a multi-body rigid system, the so-called nonsmooth contact dynamics (NSCD) problem. Our aim, here, is to present the local treatment of contact conditions by an active set type method dedicated to NSCD and to carry out a comparison with the various well-known methods based on the bipotential theory and the augmented Lagrangian theory. After presenting the mechanical formulation of the NSCD and the resolution of the global problem concerning the equations of motion, we focus on the local level devoted to the resolution of the contact law. Then we detail the numerical treatment of the contact conditions within the framework of the primal-dual active set strategy. Finally, numerical experiments are presented to establish the efficiency of the proposed method by considering the comparison with the other numerical methods. [ABSTRACT FROM AUTHOR]

Based on the configuration of hexagonal packing of identical particles, the radial and the circumferential heterogeneous degrees for granular materials are defined. The relationship between original heterogeneous degrees and strain distribution are concerned. The consistency of strain distribution and heterogeneity is verified. Both configurations and force chains in specimens are analyzed to explore different deformation modes. In the loading process, the first peak stress is defined; the linear relationship between average heterogeneous degrees and first peak stress is clarified. According to the tensor theory, some quadratic invariants of the couple stress tensor are investigated to study the scope of the couple stress effect. Analyses of the volume average of the invariants are carried out to determine the effective range of the couple stress, namely the characterization size of the couple stress. [ABSTRACT FROM AUTHOR]

We performed a numerical analysis for simulating granular media structures containing non-spherical elements and the liquid trickle flow characteristics of such structures. Fully-Lagrangian numerical simulation methods can track all motion information for solid or liquid elements at each point in time. We introduced suitable compressibility to moving particle semi-implicit (MPS) and performed individual packing behavior calculations for non-spherical elements, based on discrete element method (DEM) with expanded functions. Rigid bodies-DEM is a method using a DEM contact force model that is expanded to handle the motion of freely shaped solids. It expresses complex shapes to enable low calculation costs and intuitive mounting. We used the boundary for the granular media configured with non-spherical elements to implement a trickle flow simulation based on weakly compressible-MPS. Even for elements of equal volume, different shapes changed the liquid passage velocity and hold-up amount. The mean downflow velocity of the liquid phase was not always dependent on the void fraction. For the plane of projection, we obtained a good correlation with the mean downflow velocity in each packed structure, and successfully performed arrangements according to the new liquid-passage shape coefficient. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2257-2271, 2017 [ABSTRACT FROM AUTHOR]

The numerical errors was used to verify the correctness of key results. The truncation errors, which are larger than the round-off errors by orders of magnitude, have a superlinear relationship with both the simulation time-step and the interparticle collision speed. This remains the case regardless of the simulation details including the chosen contact model, particle size distribution, particle density or stiffness. Hence, the total errors can usually be reduced by choosing a smaller time-step. Increasing the polydispersity in a simulation by including smaller particles necessitates choosing a smaller time-step to maintain simulation stability and reduces the truncation errors in most cases. The truncation errors are increased by the dissipation of energy by frictional sliding or by the inclusion of damping in the system. The number of contacts affects the accuracy, and one can deduce that because 2D simulations contain fewer interparticle contacts than the equivalent 3D simulations, they therefore have lower accrued simulation errors. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]