Commercial Discrete Element Method Research Articles

ESTUDIO COMPARATIVO DEL FACTOR DE EMPAQUETAMIENTO MEDIANTE SOFTWARES DE ELEMENTOS DISCRETOS

This paper performs a study of the Packing Fraction (PF) in different commercial DEM (Discrete Element Method) software. For this purpose, the influence of different geometrical and particle characteristic parameters on the PF by filling a cylindrical container are analyzed. The simulation software used are DigiDEM, DigiPac and StarCCM+. Simulations are performed to compare the simulation time and verification of results; the influence of increasing the particle diameter in the same container, the influence of increasing the particle diameter and the container in proportion, the influence of increasing the h/d ratio in cylindrical particles "pellets" and the influence of decreasing the h/d ratio in cylindrical particles "disks".

Applications of DEM particle breakage models in mineral industrial

Modeling processes are carried out in the mineral industry as well as in many areas depending on the development of computer technologies and software. Discrete Element Method (DEM) is used in modeling studies to explain the interaction of particles with other particles and communication equipment. The DEM provides the capability to simulate the movement of the granular media in a series of computational processes of each individual particle that consists of the granular media. It is becoming increasingly widely used to predict energy consumption, wear, particle breakage and particle size distribution in crushing and grinding processes that can be described in terms of granular materials using DEM. The selection of particle breakage models used by commercial software for modeling DEM particle breakage is important. In this study, it is summarized the studies have been carried out to understand the performance of particle breakage methods, which are Bonded Particle Model (BPM), Fast Breakage Model (FBM) and Particle Replacement Model (PRM), in the modeling of comminution equipment. In addition, the relationship between particle and breakage energies and theory of applied forces are described in detail for three breakage models existing in commercial DEM simulators.

A modified particle contact model for matching the ratios of uniaxial compressive to tensile strength of brittle rocks

The Hertz-Mindlin with bonding (HMB) contact model in the commercial discrete element method (DEM) software EDEM is widely used to simulate and analyze the mechanical behavior of rocks. However, it cannot match the high ratios of uniaxial compressive strength (UCS) to tensile strength (TS) observed in brittle rocks like basalt. In this study, a modified HMB contact model was developed by adequately considering the contribution of moment to stress and the influence of normal stress on shear strength. At the same time, a DEM parameters inversion method was proposed to achieve rapid and accurate calibration of various microscopic parameters. The results indicate that the moment-contribution factor and maximum tensile strength in the modified HMB contact model are two key parameters affecting the UCS/TS ratio. Specifically, the moment-contribution factor mainly affects UCS, while also jointly influencing TS together with the maximum tensile strength. The modified HMB contact model successfully achieves the high UCS/TS ratio that aligns with the test value and exhibits significant pressure-dependence. This model proves to be appropriate for accurately simulating the mechanical behavior of brittle rocks.

DEM investigation on the mechanical behavior of mudstone in the hollow cylinder torsional shear test

The discrete element method (DEM) has been used to investigate the mechanical and failure behavior and the associated micro-cracking process of mudstone under the hollow cylinder torsional test by using a commercial DEM code PFC3D. Micro-parameters of the numerical model were first calibrated to the experimental results of the uniaxial compression tests and the uniaxial tensile tests. Based on the calibration results, numerical hollow cylindrical torsional shear tests were carried out under three typical stress conditions, i.e. triaxial compression, torsional compression and pure torsional shear. The numerical results show that the mechanical behavior of mudstone, in terms of rock strength, micro-crack initiation and propagation, and failure mode, can be significantly affected by principal stress rotation, which is in line with previous experimental results. The analysis of the micro-crack process confirms that the principal stress rotation plays an important role in the initiation and propagation of micro-cracks. It is shown that the microcracks induced by tensile stress occur in a preferential direction parallel to the major principal stress σ1, while the orientation distribution of the shear micro-cracks is related to the shear bands. Furthermore, the initial micro-crack stress is found to decrease after introducing the principal stress rotation, which provides a new interpretation of degradation of strength and permeability of mudstone under principal stress rotation. Three typical failure modes of specimens in different loading states are reproduced in this study, and the microscopic mechanism is also discussed. Based on this study, it is found that ignoring the principal stress rotation may overrate the stability and tightness of underground storage in bedded rock salt caverns.

DEM analysis of the effect of bond pattern on the load bearing capacity of barrel vaults under vertical loads

Bond patterns influence responses of masonry barrel vaults to mechanical loads. In this research, the discrete element method (DEM) was applied to investigate how bond patterns affect the static load bearing capacity of barrel vaults under vertical loads. The two most widely-used bond patterns (transverse and longitudinal) were studied. Using a commercial DEM software, 3DEC, vaults with different angles of embrace were prepared according to both patterns, and then loaded in three alternative ways until failure. The failure loads were recorded, and compared for the two alternative patterns of each overall geometry. Two competing effects were found: 1) in transversal vaults the arches work nearly independently of each other which decreases the load resistance in comparison to longitudinal vaults; 2) larger size of the voussoirs along the arch direction increases the load bearing.

DEM analysis of the effect of bond pattern on the load bearing capacity of barrel vaults under vertical loads

Bond patterns influence responses of masonry barrel vaults to mechanical loads. In this research, the discrete element method (DEM) was applied to investigate how bond patterns affect the static load bearing capacity of barrel vaults under vertical loads. The two most widely-used bond patterns (transverse and longitudinal) were studied. Using a commercial DEM software, 3DEC, vaults with different angles of embrace were prepared according to both patterns, and then loaded in three alternative ways until failure. The failure loads were recorded, and compared for the two alternative patterns of each overall geometry. Two competing effects were found: 1) in transversal vaults the arches work nearly independently of each other which decreases the load resistance in comparison to longitudinal vaults; 2) larger size of the voussoirs along the arch direction increases the load bearing.

Algorithm for generation of 3D polyhedrons for simulation of rock particles by DEM and its application to tunneling in boulder-soil matrix

The shape of rock particle can profoundly affect its mechanical behaviors due to the interlocking force associated with morphological features. In this study, a hybrid extension method encompassing both convexity control and overlap detection was developed to generate three-dimensional (3D) polyhedrons for simulating irregularly shaped rock particles by discrete-element-method (DEM). Based on a random initial tetrahedron, a polyhedron can be extended from a simple shape to a complex one by adding new tetrahedrons. To control polyhedron convexity, a two-step method derived from the definition of convexity was proposed in this study. Moreover, the enhanced Gilbert–Johnson–Keerthi (GJK) algorithm was applied for overlap detection during the extension process of polyhedron generation. With the proposed hybrid extension method (HEM), a numerical model for simulation of tunnelling in boulder-soil matrix was built in the commercial DEM software; then, extensive parametric studies were performed to explore the influence of several factors (boulder size, orientation, position, and morphology) on tunnelling. The simulation results demonstrate the efficiency and reliability of the proposed algorithm and revealed the ground movement patterns in case an undetected large boulder was accidently encountered by tunnelling at shallow depth.

Discrete Element Methods for Characterizing the Elastic Behavior of the Granular Particles

Abstract Focusing on characterizing the elastic behavior of the granular particles based on the discrete element method (DEM), this study utilized the Mustoe and Griffiths’ equations and a homogenization method to predict the performance of the continuous elastic medium precisely, including the elastic modulus, Poisson’s ratio, and the brittle fracture criterion. A commercial DEM software named Particle Flow Code in Two Dimensions (PFC2D) was used to conduct the numerical simulations because the macrobehavior predicted by the PFC2D highly depends on the sphere size and arrangements. The hexagonal parking arrangements were applied further herein for better theoretical calculations. With the combined analysis of the discontinuum theory and continuum theory, the DEM parameters were determined theoretically and were verified based on the virtual compression and tension tests. The factors (including sphere size, stiffness ratios, etc.) influencing the prediction accuracy were also analyzed further. The results showed that by the parameter determination methods proposed in this study, the behavior of the continuous elastic medium could be well characterized.

Calibration and Verification of Dynamic Particle Flow Parameters by the Back-Propagation Neural Network Based on the Genetic Algorithm: Recycled Polyurethane Powder.

The discrete element method (DEM) is commonly used to study various powders in motion during transportation, screening, mixing, etc.; this requires several microscopic parameters to characterize the complex mechanical behavior of the particles. Herein, a new discrete element parameter calibration method is proposed to calibrate the ultrafine agglomerated powder (recycled polyurethane powder). Optimal Latin hypercube sampling and virtual simulation experiments were conducted using the commercial DEM software; the microscopic variables included the static friction coefficient between the particles, collision recovery coefficient, Johnson–Kendall–Roberts surface energy, static friction coefficient between the particles and wall, and collision recovery coefficient. A predictive model based on genetic-algorithm-optimized feedforward neural network (back propagation) was developed to calibrate the microscopic DEM simulation parameters. The cycle search algorithm and mean-shift cluster analysis were used to confirm the input parameters’ range by comparing the mean value of the dynamic angle of repose measured via the batch accumulation test. These parameters were verified by the baffle lifting method and the rotating drum method. This calibration method, once successfully developed, will be suitable for use in a variety of fine viscous powder dynamic flow conditions.

Comparison of breakage models in DEM in simulating impact on particle beds

The discrete element method (DEM) has proven to be a powerful tool to simulate processes involving particulate material. When simulating materials handling operations that lead to mechanical degradation as well as several types of crushers and mills, description of particle breakage inside the DEM environment becomes indispensable, since flow of solids, energy transfer and size reduction are deeply intertwined. However, breakage modeling in DEM is still in an earlier stage of development and comparatively limited work has been carried out demonstrating the validity and limitations of the various models pursued in the literature and already available in commercial DEM packages. The work analyzed particle breakage using three models available in commercial DEM simulation platforms: the bonded-particle model (BPM), the particle replacement model (PRM) and the fast-breakage model (FBM). These were initially calibrated on the basis of the distribution of breakage probabilities of individual 6.3–4.75 mm copper ore particles and, whenever possible, progeny size distributions. Breakage of particles in beds by impact by a falling steel ball is an interesting case for testing breakage models, besides an important microprocess in some comminution operations, since particles interact with each other and with the grinding medium. As such, the potential of the three models to describe size reduction was demonstrated through comparison of unconfined particle bed breakage experiments and simulations. The models demonstrated different abilities to describe the various aspects of breakage. The work then identified opportunities for improvement in each of the models.

Modeling the 2D behavior of dry‐stone retaining walls by a fully discrete element method

SummaryThe dry‐stone retaining walls (DSRW) have been tipped as a promising solution for sustainable development. However, before recently, their behavior is relatively obscure. In this study, discrete element method (DEM) approach was applied to simulate the plane strain failure of these walls. A commercial DEM package (PFC2D™) was used throughout this study. The authors used a fully discrete approach; thus, both the wall and the backfill were modeled as discrete elements. The methodology for obtaining the micromechanical parameters was discussed in detail; this includes the three mechanical sub‐systems of DSRWs: wall, backfill and interface. The models were loaded progressively until failure, and then the results were compared with the full‐scale experimental results where the walls were loaded, respectively, with hydrostatic load and backfill. Despite its complexity and its intensive calculation time, DEM model can then be used to validate a more simplified approach. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical Studies of Cutting Water Saturated Sand by Discrete Element Method

The discrete element method (DEM) has been recognized as an effective tool to simulate soil–tool interactions. In this study, a saturated sand cutting model is developed using a commercial DEM software, Particle Flow Code in Two Dimension (PFC 2D). In the model, soil are defined as particles with the basic PFC 2D model, full coupling with a deformable fluid. The mechanical interactions between particles and also between particles and the walls are modeled by sprints, dash-pots and friction sliders. The properties of the material and interactions (Poisson’s ratio, shear modulus and density, coefficients of restitution, rolling and static friction) relate to the particle properties and not to the bulk properties. Such quantitative and qualitative models are essential for improving the design, selection and use of water saturated sand cutting implements, in different field sand under different conditions. This paper describes a numerical experimental investigation of the failure characteristics of two-dimensional water saturated sand cutting. Comprehensive simulated tests were carried out on sandy loam using a box apparatus and two model plane blades of rake angles 30º, 60º and two angles of friction 32º,42º, respectively. Besides, there are two extreme densities of the sand, compacted and loose. These factors should provide a basis for the reliable prediction of the failure type.

Determining parameters of a discrete element model for soil–tool interaction

The discrete element method (DEM) has been recognized as an effective tool to simulate soil–tool interactions. However, most existing discrete element models were for cohesionless soils, and in those models there were limited discussions on selections and calibrations of model parameters. In this study, a soil–tool interaction model was developed using a commercial DEM software, Particle Flow Code in Three Dimensions (PFC 3D). In the model, soil particles were defined with the basic PFC 3D model particles, which consisted of balls with cohesive bonds between balls. The model parameters, bond normal and shear strengths, were determined based on intrinsic stresses of soil. The most sensitive model parameter, ball normal stiffness, was calibrated for two contrast soils: coarse and fine soils. The calibrations were performed through comparing the draught forces of a simple soil engaging tool simulated with the PFC 3D soil–tool interaction model and those estimated with the Universal Earthmoving Equation. The calibrated ball normal stiffness is 6 × 10 3 N m −1 for coarse soil and 2 × 10 4 N m −1 for fine soil.

Benchmark tests for verifying discrete element modelling codes at particle impact level

Over the past 30 years, the Discrete Element Method (DEM) has rapidly gained popularity as a tool for modelling the behaviour of granular assemblies and is being used extensively in both scientific and industrial applications. However, it is far from clear from reviewing the literature whether the large number of DEM codes have been verified and checked against fundamental benchmark problems. DEM simulates the dynamics of each particle in an assembly by calculating the acceleration resulting from all the contact forces and body forces. It is clearly necessary that such a model be validated or verified by comparing with experimental results, analytical solutions or other numerical results (e.g. Finite Element Analysis (FEA) results) at particle impact level. There appears to be no standard benchmark tests against which DEM codes can be verified. It is thus essential and useful to establish a set of standard benchmark tests to confirm that these DEM codes are modelling the particle dynamics as intended. This paper proposes a set of benchmark tests to verify DEM codes at particle impact level for spherical particles. The analytical solutions derived from elasticity theory for elastic normal collision of two spheres or a sphere with a rigid plane are first reviewed. These analytical solutions apply only to the elastic regime for normal impact. Secondly, the analytical solutions of frictional oblique impact between two spheres or a sphere with a rigid plane are scrutinized and derived. These analytical solutions originate from the dynamics principles and should be satisfied for any DEM contact force model with prescribed friction and restitution coefficients. A set of eight benchmark tests are designed and performed using commercial DEM codes. Test 1 and Test 2 consider the elastic normal impact of two spheres or a sphere with a rigid plane, whereas the other tests (Test 3–Test 8) investigate the energy dissipation due to the collision. These benchmark tests also involve different types of material. The DEM results were compared with the analytical solutions, experimental or FEA results found in the literature. All benchmark tests showed good to excellent match, providing a quantitative verification for the codes used in this study. These benchmark tests not only verify DEM codes but also enhance the understanding of fundamental impact phenomena for modelling a large number of particles.

Discrete element parameter calibration and the modelling of dragline bucket filling

The Discrete Element Method (DEM) is useful for modelling granular flow. The accuracy of DEM modelling is dependent upon the model parameter values used. Determining these values remains one of the main challenges. In this study a method for determining the parameters of cohesionless granular material is presented. The particle size and density were directly measured and modelled. The particle shapes were modelled using two to four spheres clumped together. The remaining unknown parameter values were determined using confined compression tests and angle of repose tests. This was done by conducting laboratory experiments followed by equivalent numerical experiments and iteratively changing the parameters until the laboratory results were replicated. The modelling results of the confined compression tests were mainly influenced by the particle stiffness. The modelling results of the angle of repose tests were dependent on both the particle stiffness and the particle friction coefficient. From these observations, the confined compression test could be used to determine the particle stiffness and with the stiffness known, the angle of repose test could be used to determine the particle friction coefficient. Usually DEM codes do not solve the equations of motion for so-called walls (non-granular structural elements). However, in this study a dynamic model of a dragline bucket is developed and implemented in a commercial DEM code which allows the dynamics of the walls to be modelled. The DEM modelling of large systems of particles is still a challenge and procedures to simplify and speed up the modelling of dragline bucket filling are presented. Using the calibrated parameters, numerical results of bucket filling are compared to experimental results. The model accurately predicted the orientation of the bucket. The model also accurately predicted the drag force over the first third of the drag, but predicted drag forces too high for the subsequent part of the drag.