The importance of modelling ballast particle shape in the discrete element method

The discrete element method has been used to model railway ballast. Particles have been modelled using both spheres and clumps of spheres. A simple procedure has been developed to generate clumps which resemble real ballast particles much more so than spheres. The influence of clump shape on the heterogeneous stresses within an aggregate has been investigated, and it has been found that more angular clumps lead to a greater degree of homogeneity. A box test consisting of one cycle of sleeper load after compaction has been performed on an aggregate of spheres and also on an alternative aggregate of clumps. The interlocking provided by the clumps provides a much more realistic load- deformation response than the spheres and the clumps will be the basis for future work on ballast degradation under cyclic loading.     

A discrete element method-based approach to predict the breakage of coal

Pulverization is an essential pre-combustion technique employed for solid fuels, such as coal, to reduce particle sizes. Smaller particles ensure rapid and complete combustion, leading to low carbon emissions. Traditionally, the resulting particle size distributions from pulverizers have been determined by empirical or semi-empirical approaches that rely on extensive data gathered over several decades during operations or experiments, with limited predictive capabilities for new coals and processes. This work presents a Discrete Element Method (DEM)-based computational approach to model coal particle breakage with experimentally characterized coal physical properties. The effect of select operating parameters on the breakage behavior of coal particles is also examined.     

A modelling and verification approach for soybean seed particles using the discrete element method

To build a discrete element method (DEM) model of soybean seed particles, the shape and size of soybean seed particles were measured and analysed. The results showed that the shape of a soybean seed particle could be approximated to an ellipsoid and that the dispersity in size could be approximated by a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. On this basis, an approach for modelling soybean seed particles based on the multi-sphere (MS) method was proposed. The soybean seed particle was simplified to an ellipsoid with the averaged size of one hundred randomly selected soybean seeds. The model of a single soybean seed particle was built by filling spheres within the ellipsoid. For modelling soybean seed assembly, the primary dimension was generated according to the normal distribution, and the other secondary dimensions were calculated based on their relationships with the primary dimension. In this way, the model of soybean seed assembly with different sizes and distributions was built. In this paper, four varieties of soybean seed were used. By comparing the simulated results and experimental results both in piling tests and “self-flow screening” tests, when the number of filling spheres was five, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modelling method for soybean seed particles that we proposed were verified. Finally, an application case was employed to show how to use the soybean seed particle model and the discrete element method to analyse the discharging process of a silo.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Prediction of hopper discharge rate using combined discrete element method and artificial neural network

An Artificial Neural Network (ANN) was developed to predict the mass discharge rate from conical hoppers. By employing Discrete Element Method (DEM), numerically simulated flow rate data from different internal angles (20°–80°) hoppers were used to train the model. Multi-component particle systems (binary and ternary) were simulated and mass discharge rate was estimated by varying different parameters such as hopper internal angle, bulk density, mean diameter, coefficient of friction (particle-particle and particle-wall) and coefficient of restitution (particle-particle and particle-wall). The training of ANN was accomplished by feed forward back propagation algorithm. For validation of ANN model, the authors carried out 22 experimental tests on different mixtures (having different mean diameter) of spherical glass beads from different angle conical hoppers (60° and 80°). It was found that mass discharge rate predicted by the developed neural network model is in a good agreement with the experimental discharge rate. Percentage error predicted by ANN model was less than ±13%. Furthermore, the developed ANN model was also compared with existing correlations and showed a good agreement.     

A study of transverse ply cracking using a discrete element method

We study the transverse cracking of the 90° ply in [0/90]_S cross-ply laminates by means of a discrete element method. To model the 90° ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice model fibers, and springs with random breaking thresholds represent the disordered matrix material in between. The spring-lattice is coupled by interface springs to two rigid bars which represent the two 0° plies in the model, which could be sublaminate as well. Molecular dynamics simulation is used to follow the time evolution of the model system. It was found that under gradual loading of the specimen, after some distributed cracking, segmentation cracks occur in the 90° ply which then develop into a saturated state where the ply cannot support additional load. The stress distribution between two neighboring segmentation cracks was determined, furthermore, the dependence of the microstructure of damage on the ply thickness was also studied. To give a quantitative characterization of stiffness degradation, the Young modulus of the system is monitored as a function of the density of segmentation cracks. The results of the simulations are in satisfactory agreement with experimental findings and with the results of analytic calculations.     

DEM simulation of the packing structure and wall load in a 2-dimensional silo

The filling and discharge of a two-dimensional wedged-bottom silo holding circular objects was modelled using DEM technique to examine the influence of method of silo filling on distribution of orientations of unit vectors normal to contact points (contact normals) and normal contact forces. It was found that packing structure determined through method of generation of grain bedding significantly influenced distribution of contact normals. Nearly hexagonal network of contact normals was obtained for central filling of silo while sprinkle filling provided higher anisotropy of contact normals. The significance of frictional conditions and number of particles in system on distribution of contact normals was analysed. Increase in number of grains reduced disturbance from boundaries on behaviour of assembly. Distribution of loads on silo bottom obtained in simulation for different wall roughness was found in qualitative agreement with experimental data.     

Aggregate distribution influence on the indirect tensile test of asphalt mixtures using the discrete element method

The purpose of this study is to investigate the effect of horizontal aggregate distribution, i.e. aggregate distribution in horizontal cross sections, on the indirect tensile (IDT) test of asphalt mixtures. An index of aggregate homogeneity, used to evaluate the aggregate distribution in a two-dimensional (2D) cross section, was comprehensively described; the horizontal aggregate distribution was evaluated by the index. A microstructure-based discrete element model for predicting the IDT test results was established by a discrete element program called particle flow code in two dimensions (PFC2D). Based on this model and by loading horizontal cross sections of asphalt mixtures along different directions, the effects of horizontal aggregate distribution on the splitting strength and maximum horizontal stress with regard to an IDT test were numerically simulated by means of the discrete element method; the obtained results were verified by performing an actual IDT test. Results reveal that the splitting strengths and maximum horizontal stresses in the IDT test exhibit anisotropy. Furthermore, it is revealed that there is an insignificant correlation between the horizontal aggregate distributions and the average splitting strengths and average maximum horizontal stresses, as well as a significant correlation between the horizontal aggregate distributions and the variations in the splitting strengths and maximum horizontal stresses.     

Effect of vibration direction on the packing of sphero-cylinders

Particle packing is widely encountered when coping with granular materials, while mechanical vibration is usually used for packing densification. Vibration direction has been proven to be crucial for the ordered packing of spherical particles, but there are few reports for non-spherical ones in this regard. In this study, the effect of vibration direction on the macroscopic and microscopic packing parameters of sphero-cylinders are systematically examined using discrete element method (DEM). Due to the anisotropic shapes of sphero-cylinders, their packing characteristics are much richer and also more complex than those of spheres. It is found that vibration direction affects both the packing density and the packing structure of sphero-cylinders through tuning their orientation distributions and contact modes. Moreover, vibration direction plays a significant role in determining the optimal vibration intensities for dense packing. When the sphericity of Voronoi cell decreases and/or the density increases, the Nematic order parameter increases accordingly. Besides, no obvious relationship between the packing density and the average contact number is observed.     

Generation of porous particle structures using the void expansion method

The newly developed “void expansion method” allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller “void-particles”. Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles’ mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.     

A discrete element method for the simulation of CFRP cutting

Orthogonal machining of unidirectional carbon fiber-reinforced polymer (UD-CFRP) composites is simulated using discrete element method (DEM). The objective of this work is to present a simple numerical model that allows the study the machining of unidirectional composites during orthogonal cutting. To control the physicochemical phenomena that occur during cutting, it is necessary to identify the parameters of contact, very difficult to measure experimentally. The DEM numerical simulation is presented then as an alternative to the problem. This tool has helped to recreate the physical mechanisms identified experimentally and to understand the origin of the abrasive wear of carbide tools. The observation of the chip formation using a high speed video camera made possible to validate qualitatively the results of numerical simulation by discrete elements. This tool can also determine the cutting forces quite close to reality.     

Investigating the upper limit for applying the coarse grain model in a discrete element method examining mixing processes in a rolling drum

Mixing is an essential manufacturing process in various industries. The processing procedure and final product quality depend on the homogeneity of mixing. Because it is difficult to evaluate mixing systems experimentally, the discrete element method is commonly employed. However, as the number of particles increases, this approach incurs huge computational costs. The coarse grain model offers a potential solution, but its applicability has not been widely demonstrated; this study aimed to elucidate the upper limit for applying the coarse grain model. To determine the appropriate simulation parameters, calibrations were performed by comparing the powder bed in experiments versus simulations. Various mixing processes were numerically evaluated, and the mixing characteristics were qualitatively consistent among all coarse-grained ratios. These mixing systems were also evaluated quantitatively based on Lacey’s mixing index, which indicated that the upper limit of the coarse-grained ratio was five times. It is therefore important to secure a sufficient number of particles in each cell and to use an appropriate number of cells. This study clarified the upper application limit and criteria for the coarse grain model and verified the maximum coarse-grained ratio (five times). This approach can be used to determine the coarse-grained ratio and reduce computational costs.     

Simulation of the packing of granular mixtures of non-convex particles and voids characterization

The simulation of granular materials has considerably developed in the last decades essentially with simple geometry particles. The purpose of this paper is to study granular systems of non-convex particles which are present in many industrial processes. Two shapes of large and two shapes of small non-convex particles resulting from the cutting of a hollow cylinder are modelled, and binary mixtures containing varying proportions of small and large particles are generated with a Monte Carlo simulation. Two different states of the granular systems are studied: suspensions and packings obtained after sedimentation. No contact force model is used and only steric repulsion is taken into account. The density, the pore size distribution and the tortuosity of the granular systems are studied. The results are compared to those obtained with granular systems of convex particles.     

Time reversibility of the discrete element method

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.     

Convergence and stability analysis of the deformable discrete element method

This work investigates numerical properties of the algorithm of the discrete element method (DEM) employing deformable circular disks presented in the authors' earlier publication. The new formulation called the deformable DEM (DDEM) enhances the standard DEM (SDEM) by introducing an additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. An accurate computation of the contact forces would require an iterative solution of the implicit relationship between the contact forces and particle displacements. In order to preserve efficiency of the DEM, the new formulation has been adapted to the explicit time integration. It has been shown that the explicit DDEM algorithm is conditionally stable and there are two restrictions on its stability. Except for the limitation of the time step as in the SDEM, the stability in the DDEM is governed by the convergence criterion of the iterative solution of the contact forces. The convergence and stability limits have been determined analytically and numerically for selected regular and irregular configurations. It has also been found out that the critical time step in DDEM remains unchanged with respect to the SDEM.     

The importance of parameter-dependent coefficient of restitution in discrete element method simulations

The coefficient of restitution (COR) is an important constant that represents the energy dissipation during contact between two objects. Simulation using the conventional discrete element method (DEM) involves a constant COR. This study presents a DEM simulation method that uses a parameter-dependent COR. The parameter-dependent COR was obtained from a collision incident between spherical particles and a plate surface using a drop-test apparatus. Glass and polypropylene beads of 3–6-mm diameter were used while acrylic and steel were used as the plate surfaces. The particle trajectories were captured by a high-speed camera and analyzed by an image analyzer. The COR was then correlated to a parameter-dependent COR function that depends on the material, impact velocity, and temperature. Free-fall DEM simulations using a constant COR and parameter-dependent COR were compared. The parameter-dependent COR approach obtained better agreement with experimental results than the constant-COR approach. The proposed concept could be applied for other material combinations with a wide range of operating conditions to obtain a database of parameter-dependent COR values for the simulation of solid handling applications.     

Recent progress on the discrete element method simulations for powder transport systems: A review

Powder transport systems are ubiquitous in various industries, where they can encounter single powder flow, two-phase flow with solids carried by gas or liquid, and gas–solid–liquid three-phase flow. System geometry, operating conditions, and particle properties have significant impacts on the flow behavior, making it difficult to achieve good transportation of granular materials. Compared to experimental trials and theoretical studies, the numerical approach provides unparalleled advantages over the investigation and prediction of detailed flow behavior, of which the discrete element method (DEM) can precisely capture complex particle-scale information and attract a plethora of research interests. This is the first study to review recent progress in the DEM and coupled DEM with computational fluid dynamics for extensive powder transport systems, including single-particle, gas–solid/solid–liquid, and gas–solid–liquid flows. Some important aspects (i.e., powder electrification during pneumatic conveying, pipe bend erosion, non-spherical particle transport) that have not been well summarized previously are given special attention, as is the application in some new-rising fields (ocean mining, hydraulic fracturing, and gas/oil production). Studies involving important large-scale computation methods, such as the coarse grained DEM, graphical processing unit-based technique, and periodic boundary condition, are also introduced to provide insight for industrial application. This review study conducts a comprehensive survey of the DEM studies in powder transport systems.     

Numerical study on compression processes of cohesive bimodal particles and their packing structure

In this study, the compression characteristics of bimodal cohesive particles were investigated using a discrete element method (DEM) simulation. The compression and packing processes were simulated under different conditions of size ratios of 1–4 and fine particle mixing ratios of 0–0.5. The cohesive force was expressed using the surface energy proposed by the Johnson-Kendall-Roberts (JKR) cohesion model having a surface energy of 0–0.2 J/m². The calculated results demonstrated that even in the case of cohesive particles, an increase in the particle size ratio reduced the void fraction of the powder bed during the packing and compression processes. In addition, it was found that the cohesive force decreased the contact number, especially the coarse-coarse contacts, although it had little impact on the void fraction. Our DEM simulations suggested that it is necessary to evaluate the contact numbers even under similar void fractions, which will be essential in the case of different material mixtures, such as all-solid-state batteries.     

Study on the void reduction behaviour of porous asphalt pavement based on discrete element method

The objective of this study was to analyse the void reduction behaviour of porous asphalt mixture under load. A three-dimensional discrete element model of porous asphalt mixture based on aggregate gradation and void gradation was built in PFC3D software. The parameter of the model was obtained from creep test. The rutting test was simulated using this discrete element model. And a new method was developed to obtain and analyse the void structure in discrete element model. The simulation results were compared with one of the laboratory test. The comparative analysis indicates that, the discrete element method can be used to simulate the creep response and void reduction behaviour of porous asphalt mixture. Further research shows that porosity, effective porosity, number of connected components and section pores have a good correlation with strain of porous asphalt mixture. With the increase in strain, the proportion of section pores with diameter less than 2 mm increases. In the initial stage of loading, the void reduction is the main reason for rut increment of porous asphalt mixture. In the later stage, the void structure is almost incompressible; the lateral deformation of mixture becomes the domination factor.     

A calibration framework for discrete element model parameters using genetic algorithms

In this research, a universal framework for automated calibration of microscopic properties of modeled granular materials is proposed. The proposed framework aims at industrial scale applications, where optimization of the computational time step is important. It can be generally applied to all types of DEM simulation setups. It consists of three phases: data base generation, parameter optimization, and verification. In the first phase, DEM simulations are carried out on a multi-dimensional grid of sampled input parameter values to generate a database of macroscopic material responses. The database and experimental data are then used to interpolate the objective functions with respect to an arbitrary set of parameters. In the second phase, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the calibration multi-objective optimization problem. In the third phase, the DEM simulations using the results of the calibrated input parameters are carried out to calculate the macroscopic responses that are then compared with experimental measurements for verification and validation.The proposed calibration framework has been successfully demonstrated by a case study with two-objective optimization for the model accuracy and the simulation time. Based on the concept of Pareto dominance, the trade-off between these two conflicting objectives becomes apparent. Through verification and validation steps, the approach has proven to be successful for accurate calibration of material parameters with the optimal simulation time.