Relationship between vortex structures and shear localization in 3D granular specimens based on combined DEM and Helmholtz–Hodge decomposition

The paper presents three-dimensional simulation results of granular vortex structures in cohesionless initially dense sand during quasi-static plane strain compression. The sand behaviour was simulated using the discrete element method (DEM). Sand grains were modelled by spheres with contact moments to approximately capture the irregular grain shape. The Helmholtz–Hodge decomposition of the displacement vector field obtained with DEM was used. The variational discrete multiscale vector field decomposition allowed for separating a vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. A direct correlation between vortex structures and shear localization was studied. The simulation results showed that vortex structures were closely connected to spontaneous shear localization. They localized early in locations wherein a shear zone ultimately developed. They were affected by the specimen depth.     

Discrete element simulation of dynamic behaviour of partially saturated sand

The discrete element method (DEM) together with the finite element method (FEM) in LS-DYNA was employed to investigate the dynamic behaviour of sand under impact loading. In this approach, the partially saturated sand was modelled in DEM with capillary forces being taken into account through an implicit capillary contact model, while other solids were simulated using FEM. A slump test was first performed with dry sand to calibrate the contact parameters in DEM. Low velocity impact tests were then conducted to investigate the effect of water saturation on the shape and height of sand piles after impact, and to validate the simulations. It was found in the experiments that an increasing water saturation (in the range between 10 and 30 %) affected the height of sand pile for a given drop height due to an increasing cohesion between particles. The simulations captured the experimental ejecta patterns and sand pile height. Finally, a low confinement split Hopkinson pressure bar test from earlier literature was modelled; the DEM–FEM simulations could reproduce the trends of experimentally observed stress–strain curves of partially saturated sand under high strain rate loading, indicating that it was feasible to model dynamic behaviour of dry and wet sand with low saturation (<20 %) in LS-DYNA; however, a number of questions remain open about the effect of grain shape, grain crushing and viscosity.     

Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images

The objective of this study is to predict the dynamic modulus of asphalt mixture using both two-dimensional (2D) and three-dimensional (3D) Distinct Element Method (DEM) generated from the X-ray computed tomography (X-ray CT) images. The 3D internal microstructure of the asphalt mixtures (i.e., spatial distribution of aggregate, sand mastic and air voids) was obtained using the X-ray CT. The X-ray CT images provided exact locations of aggregate, sand mastic and air voids to develop 2D and 3D models. An experimental program was developed with a uniaxial compression test to measure the dynamic modulus of sand mastic and asphalt mixtures at different temperatures and loading frequencies. In the DEM simulation, the mastic dynamic modulus and aggregate elastic modulus were used as input parameters to predict the asphalt mixture dynamic modulus. Three replicates of a 3D DEM and six replicates of a 2D DEM were used in the simulation. The strain response of the asphalt concrete under a compressive load was monitored, and the dynamic modulus was computed. The moduli of the 3D DEM and 2D DEM were then compared with both the experimental measurements results. It was revealed that the 3D discrete element models successfully predicted the asphalt mixture dynamic modulus over a range of temperatures and loading frequencies. It was found that 2D discrete element models under predicted the asphalt mixture dynamic modulus.     

Investigations of quasi-static vortex structures in 2D sand specimen under passive earth pressure conditions based on DEM and Helmholtz–Hodge vector field decomposition

The paper presents some two-dimensional simulation results of granular vortex-structures in cohesionless initially dense sand during a quasi-static passive wall translation. The sand behaviour was simulated using the discrete element method (DEM). Sand grains were modelled by spheres with contact moments to approximately capture the irregular grain shape. In order to detect vortex-structures, the Helmholtz–Hodge decomposition of a vector field from DEM calculations was used. This approach enabled us to distinguish both incompressibility and vorticity in the granular displacement field. In addition the predominant periods of vortices during horizontal wall movement were determined. The vortices were strongly connected to shear localization. They localized in locations where shear zones ultimately developed. In addition, the vortex-structures were calculated during plane strain compression.     

Study of shear behavior of granular materials by 3D DEM simulation of the triaxial test in the membrane boundary condition

This paper studies the shear behavior of granular materials by using a three-dimensional (3D) discrete element method (DEM) simulation of the triaxial test. The experimental triaxial tests were conducted on glass beads samples for verification. DEM simulations of the triaxial test were carried out in the membrane boundary condition consisting of 37,989 membrane particles. A new method that divides the irregular sample shape into two parts of cones and parts of three-dimensional simplexes is used to follow the volume change of irregular deformation of samples. The free rotatable upper platen is considered during the shearing process, which influences the shear behavior of samples especially in the residual stage and formations of a single shear band or X-shape shear band. The confining pressures have been demonstrated to influence the rotation angle and angular velocity of the upper platen. Moreover, the timing of replacing a rigid wall boundary condition with the membrane boundary condition is investigated, which affects the porosity of samples before shearing and the mechanical strength. The DEM model in the membrane boundary condition reflects well the evolution of irregular sample deformation and shear band in the shearing process. From the perspective of micro structures, the normal force decreases and the tangential stress increases during the shearing stage. This study greatly improves the accuracy of DEM simulations of the triaxial test in the membrane boundary condition.     

Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM

A quasi-static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three-dimensional DEM model. Grain roughness was modelled by means of symmetric clusters composed of rigid spheres imitating irregular particle shapes. The effect of grain roughness on shear strength, dilatancy, kinetic, elastic and dissipated energies was numerically analyzed. Some numerical results were compared with available experimental results.     

Micromechanical behaviour of Si-based particulate assemblies: A comparative study using DEM and atomistic simulations

In this paper, we investigate the micromechanical behaviour of Si-based particulate systems subjected to tri-axial compression loading. The investigations are based on three-dimensional discrete element modelling (DEM) and simulations. At first, we compare the variation of mean compressive stress for a silicon assembly subjected to tri-axial compression, predicted at two different scales: at the particulate scale, using the DEM simulation (mono-dispersed particulates) and at the atomistic scale using the molecular dynamics (MD) simulation results for silicon mono-crystal reported by Mylvaganam and Zhang (2003) [K. Mylvaganam, L. Zhang, Key Eng. Mater. 233–236 (2003) 615–620]. Both the simulation methods considered the silicon assembly subjected to an identical (tri-axial) loading condition. We observed a good qualitative agreement between the DEM and MD simulation results for the mean compressive stress when the assembly was subjected to small volumetric strain. However, at large volumetric strain, the mean stress of the silicon assembly predicted from MD simulation did not scale-up with the DEM results. This discrepancy could be due to that MD simulation is only valid for particle contacts, which are independent of one another and does not consider the inherent ‘discrete’ nature of particulates and the induced anisotropy prevailing at particulate scale. The micromechanical behaviour of particulate assemblies strongly depends on the inherent discrete nature of the particles, their single-particle properties and the induced anisotropy during mechanical loading. At the second stage, using DEM, we present the evolution of macroscopic compressive stress and several micromechanical features for four cases of the commonly used Si based poly-dispersed particulate assemblies (Si, SiC,Si₃N₄ and SiO₂) under tri-axial compression loading. We also present the evolution of several other phenomena occurring at particulate scale, such as the energy dissipation characteristics due to sliding contacts and the features of fabric structures developed during mechanical loading. The study shows that the single-particle properties of the Si based assemblies considered here significantly affect the micromechanical behaviour of the assemblies and DEM is a powerful tool to get insights on the internal behaviour of discrete particulates under mechanical loading.     

A Random Pairing Collision Model (RPCM) for Improving the DEM Simulation of Particle-Bed Collisions in Aeolian Sand Transport

The impact of sand particles with bed is the key process in aeolian sand transport. In this article, the discrete element method (DEM) is embedded to the large-eddy simulation (LES) method for simulating the wind-blown sand two-phase flow. A numerical model is developed to stochastically describe collisions between sand particles and bed within the DEM approach. Statistical features of major simulated motion parameters are undertaken and compared with measured data to verify the model. The probability distribution of the kinetic energy restitution coefficient is normal, and the probability density functions of the impact and lift-off angles are consistent with reported results. The probability density functions of three-dimensional impact and lift-off velocities are addressed in further detail.     

Study on a large-scale discrete element model for fine particles in a fluidized bed

The discrete element method (DEM) is widely used to comprehend complicated phenomena such as gas–solid flows. This is because the DEM enables us to investigate the characteristics of the granular flow at the particle level. The DEM is a Lagrangian approach where each individual particle is calculated based on Newton’s second law of motion. However, it is difficult to use the DEM to model industrial powder processes, where over a billion particles are dealt with, because the calculation cost becomes too expensive when the number of particles is huge. To solve this issue, we have developed a coarse grain model to simulate the non-cohesive particle behavior in large-scale powder systems. The coarse grain particle represents a group of original particles. Accordingly, the coarse grain model makes it possible to perform the simulations by using a smaller number of calculated particles than are physically present. As might be expected, handling of fine particles involving cohesive force is often required in industry. In the present study, we evolved the coarse grain model to simulate these fine particles. Numerical simulations were performed to show the adequacy of this model in a fluidized bed, which is a typical gas–solid flow situation. The results obtained from our model and for the original particle systems were compared in terms of the transient change of the bed height and pressure drop. The new model can simulate the original particle behavior accurately.     

Development of numerical scheme for phase field crystal deformation simulation

The phase field crystal (PFC) method is anticipated as a new multiscale method, because this method can reproduce physical phenomena depending on atomic structures in metallic materials on the diffusion time scale. Although the PFC method has been applied to some phenomena, there are few studies related to evaluations of mechanical behaviors of materials by appropriate PFC simulation. In a previous work using the PFC method, tensile deformation simulations have been performed under conditions where the volume increases during plastic deformation. In this study, we developed a new numerical technique for PFC deformation simulation that can maintain a constant volume during plastic deformation. To confirm that the PFC model with the proposed technique can reproduce appropriate elastic and plastic deformations, we performed a series of deformation simulations in one and two-dimensions. In one- and two-dimensional single-crystal simulations, linear elastic responses were confirmed in a wide strain rate range. In bicrystal simulations, we could observe typical plastic deformations due to the generation, annihilation and movement of dislocations, and the interaction between the grain boundary and dislocations. Moreover, the deformation behaviors of a nanopolycrystalline structure at high temperature were simulated and the intergranular deformations caused by grain rotation and grain boundary migration were reproduced.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

Stacking fault energies and slip in nanocrystalline metals

The search for deformation mechanisms in nanocrystalline metals has profited from the use of molecular dynamics calculations. These simulations have revealed two possible mechanisms; grain boundary accommodation, and intragranular slip involving dislocation emission and absorption at grain boundaries. But the precise nature of the slip mechanism is the subject of considerable debate, and the limitations of the simulation technique need to be taken into consideration. Here we show, using molecular dynamics simulations, that the nature of slip in nanocrystalline metals cannot be described in terms of the absolute value of the stacking fault energy-a correct interpretation requires the generalized stacking fault energy curve, involving both stable and unstable stacking fault energies. The molecular dynamics technique does not at present allow for the determination of rate-limiting processes, so the use of our calculations in the interpretation of experiments has to be undertaken with care.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

Modelling sheet-flow sediment transport in wave-bottom boundary layers using discrete-element modelling

Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.     

Strength of non-spherical particles with anisotropic geometries under triaxial and shearing loading configurations

This paper presents a study on the macroscopic shear strength characteristics of granular assemblies with three- dimensional complex-shaped particles. Different assemblies are considered, with both isotropic and anisotropic particle geometries. The study is conducted using the discrete element method (DEM), with so-called sphero-polyhedral particles, and simulations of mechanical true triaxial tests for a range of Lode angles and confining pressures. The observed mathematical failure envelopes are investigated in the Haigh–Westergaard stress space, as well as on the deviatoric-mean pressure plane. It is verified that the DEM with non-spherical particles produces results that are qualitatively similar to experimental data and previous numerical results obtained with spherical elements. The simulations reproduce quite well the shear strength of assemblies of granular media, such as higher strength during compression than during extension. In contrast, by introducing anisotropy at the particle level, the shear strength parameters are greatly affected, and an isotropic failure criterion is no longer valid. It is observed that the strength of the anisotropic assembly depends on the direction of loading, as observed for real soils. Finally simulations on a virtual shearing test show how the velocity profile within the shear band is also affected by the grain’s shape.     

Development of a reduced-order model for large-scale Eulerian–Lagrangian simulations

Multiphase flows with solid particles are commonly encountered in various industries. The CFD–DEM method is extensively used to simulate their dynamical behavior. However, the application of the CFD–DEM method to simulate industrial-scale powder processes unavoidably leads to huge computational costs. With the aim of overcoming this issue, we propose a nonintrusive reduced-order model for Eulerian–Lagrangian simulations (ROM-EL) to efficiently reproduce gas–solid flow in fluidized beds. In the model, a Lanczos based proper orthogonal decomposition (LPOD) is newly employed to efficiently generate a set of POD bases. After the numerical snapshots are projected onto the reduced space spanned by the POD bases, a series of multidimensional functions of POD coefficients are constructed using a surrogate interpolation method. To demonstrate the effectiveness of this model, validation studies are performed based on the simulations of a fluidized bed. The macroscopic properties, such as the particle distribution, bed height, pressure drop, and distribution of bubble size, are shown to agree well in the CFD–DEM model and ROM-EL. Further, our proposed ROM-EL reduces the computational cost by several orders of magnitude compared with the CFD–DEM simulation. Accordingly, the ROM-EL could significantly contribute to the progress of modeling and simulation for industrial granular flows.     

Preliminary Hydrodynamic Modeling of Fluidized Beds of Single Component and Binary Particle System in Compartmented Gasifier

In the present study, three-dimensional simulation using computational fluid dynamics (CFD, FLUENT 6.3.26) and experiments were conducted on a transparent cold-flow gas-solid bubbling compartmented fluidized bed gasifier (CFBG) model with identical diameter as the pilot-scaled CFBG. Using Eulerian-Eulerian granular model with closure laws according to the kinetic theory of granular flow that based on modified drag model simulations were conducted to model the hydrodynamics of CFBG in terms of gas-solid flow pattern, bed expansion ratio, bed pressure drop and bubble diameter. The model was resolved by semi-implicit method for pressure-linked equation (SIMPLE) algorithm in CFD. Different inerts like river sand, quartz sand, and alumina were used to examine the hydrodynamics behaviors both in single component and binary system where biomass, palm shell, was mixed with river sand. The modeling predictions compared reasonably well with experimental bed expansion ratio measurements and qualitative gas-solid flow patterns. Pressure drops predicted by the simulations were in relatively close agreement with experimental measurements. Furthermore, the simulated bubble diameters showed similarities with the Darton et al., bubble size equation.     

Validation of microparameters in discrete element modeling of sea ice failure process

A GPU-based discrete element method (DEM) with bonded particles is investigated to simulate the mechanical properties of sea ice in uniaxial compressive and three-point bending tests. Both the uniaxial compressive strength and flexural strength of sea ice are related to the microparameters in DEM simulation including particle size, sample size, bonding strength, and interparticle friction coefficient. These parameters are analyzed to build the relationship between the material macrostrengths of sea ice and the microparameters of the numerical model in DEM simulations. Based on this relationship, the reasonable microparameters can be calculated by given macrostrengths in the applications of simulating the failure processes of sea ice. In this simulation, both uniaxial compressive strength and flexural strength of ice increase with the increasing ratio of sample size and particle size. The interparticle friction coefficient is directly related to the compressive strength but has little effect on the flexural strength. In addition, numerical simulations are compared with experimental data to show the performance of the proposed model, and a satisfactory agreement is achieved. Therefore, this microparameter validation approach based on macrostrengths can be applied to simulate the complicated failure process of sea ice interacting with offshore platform structures.     

SPH and FEM Investigation of Hydrodynamic Impact Problems

Simulation of hydrodynamic impact problems and its effect on surrounding structures, can be considered as a fluid structure coupling problem. The application is mainly used in automotive and aerospace engineering and also in civil engineering. Classical FEM and Finite Volume methods were the main formulations used by engineers to solve these problems. For the last decades, new formulations have been developed for fluid structure coupling applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic) and DEM (Discrete Element Method). Up to these days very little has been done to compare different methods and assess which one would be more suitable. In this paper the mathematical and numerical implementation of the FEM and SPH formulations for hydrodynamic problem are described. From different simulations, it has been observed that for the SPH method to provide similar results as FEM Lagrangian formulations, the SPH meshing, or SPH particle spacing needs to be finer than FEM mesh. To validate the statement, we perform a simulation of a hydrodynamic impact on an elasto-plastic plate structure. For this simple, the particle spacing of SPH method needs to be at least two times finer than FEM mesh. A contact algorithm is performed at the fluid structure interface for both SPH and FEM formulations. In the paper the efficiency and usefulness of two methods, often used in numerical simulations, are compared.     

Comparative study of two phase-field models for grain growth

There exist different phase-field models for the simulation of grain growth in polycrystalline structures. In this paper, the model formulation, application and simulation results are compared for two of these approaches. First, we derive relations between the parameters in both models that represent the same set of grain boundary energies and mobilities. Then, simulation results obtained with both models, using equivalent model parameters, are compared for grain structures in 2D and 3D. The evolution of the individual grains, grain boundaries and triple junction angles is followed in detail. Moreover, the simulation results obtained with both approaches are compared using analytical theories and previous simulation results as benchmarks. We find that both models give essentially the same results, except for differences in the structure near small shrinking grains which are most often locally and temporary for large grain structures.