Simulation Of Granular Materials Research Articles

Mesoscale simulation of granular materials under weak shock compaction–pore size distribution effects

This research established a systematic method to generate various pore-size distributions (PSDs) and studied the effect of PSDs on the shock compaction response of granular materials using two-dimensional mesoscale simulations under identical porosity. Simulations utilized various PSDs for three particle shapes (circle, ellipse, and square). Contacting particle configurations using three PSDs, characterized by spatially uniform distributed pores to heterogeneous distributed pores, and non-contacting particle configurations under a single case of PSD were tested. The PSD of generated particle sets was characterized using coordination number, mean diameter, and bimodality coefficient as statistical metrics. Mesoscale simulations showed that regardless of the conditions of pore distributions, shock compaction of granular materials consistently demonstrates a precursor, shock compaction front, and end. However, the shock compaction velocity of contacting particles was dependent on the PSDs despite the constant initial porosity. The compaction velocity was faster in particle configurations with relatively uniform pore distributions than in heterogeneous pore distributions, which our study demonstrated can be attributed to particle rearrangement during compaction. Circular-shaped particles had high sensitivity in shock compaction response to the various PSDs. Furthermore, a contacting particle configuration tended to propagate the shock compaction wave relatively faster than particles that were in a non-contact configuration. This study established the relative importance of considering PSD as a metric over the coordination number in studies of the shock compaction response of granular materials. Further, insights are provided on the evolving shock substructure to characterize the shock compaction response of granular materials.

A Simplified Calibration Procedure for DEM Simulations of Granular Material Flow

The discrete element method (DEM) has emerged as an essential computational tool in geotechnical engineering for the simulation of granular materials, offering significant advantages over traditional continuum-based methods such as the finite element method (FEM) and the finite difference method (FDM). The DEM’s ability to model particle-level interactions, including contact forces, rotations, and particle breakage, allows for a more precise understanding of granular media behavior under various loading conditions. However, accurate DEM simulations require meticulous calibration of input parameters, such as particle density, stiffness, and friction, to effectively replicate real-world behavior. This study proposes a simplified calibration procedure, intended to be conducted prior to any granular material flow DEM modeling, based on three fundamental physical tests: bulk density, surface friction, and angle of repose. The ability of these tests, conducted on dry quartz sand, to accurately determine DEM micromechanical parameters, was validated through numerical simulation of cylinder tests with varying height-to-radius ratios. The results demonstrated that this calibration approach effectively reduced computational complexity while maintaining high accuracy, with validation errors of 0% to 12%. This research underscores the efficacy of simplified DEM calibration methods in enhancing the predictive reliability of simulations, particularly for sand modeling in geotechnical applications.

Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials

Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials

Multi-GPUs DEM algorithm and its application in the simulation of granular materials

The Discrete Element Method (DEM) is one of the most common numerical approach for modeling the physical and mechanical properties of granular materials. However, its computational efficiency can be a major bottleneck, which significantly hinders its application in engineering fields. To overcome this challenge, a multi-GPU framework with OpenMP has been developed. In this framework, the DEM particles in 3D space and their corresponding contact information are sorted in a given direction in the simulation, and each GPU device handles a subdomain of particles and relative contacts. Additionally, the contact information is densely arranged to minimize memory usage. To further enhance efficiency, sorting and packing algorithms for the contact information have been introduced. During calculating loop, the number of contacts on each device is monitored, and the spatial division of devices is adjusted to balance memory distribution. The efficacy of the multi-GPU algorithm is verified through a chute flow test. Using numerical results, the segregation process and mechanics of granular materials during sliding have been studied in detail. Furthermore, the simulations demonstrate that the developed multi-GPU algorithm greatly enhances computational efficiency and reduces memory usage per device.

Three-dimensional simulation of granular materials by discrete element method (DEM) by considering the fracture effect of particles

Coarse-grained materials, such as sand and gravel, exhibit a significant dependence on particle failure rate, which greatly influences their engineering behavior. This research focuses on the three-dimensional modeling of grain material behavior using the discrete element method (DEM) with PFC3D software and FISH programming language. The specific objective is to model the particle breakage phenomenon and its impact on resistance behavior and deformation. To accurately represent the non-spherical shape of the particles, an interconnected sphere approach was employed. The modeling of grain failure was achieved by establishing a failure criterion that considers two critical conditions: the heterogeneity of contact forces and stress within the particle. The proposed model and criteria were validated through comparison with triaxial experimental results obtained from the Purulia dam gravel. The results demonstrate that the developed model successfully captures the essential aspects of particle failure and its influence on the behavior of the granular environment. The simulations accurately represent the resistance behavior and deformation characteristics observed in the triaxial experiments. This validates the effectiveness of the proposed model in simulating the significant effects of particle failure on the behavior of coarse-grained materials. The findings of this study contribute to a deeper understanding of the complex behavior of coarse-grained materials, particularly in terms of their response to particle failure. The developed DEM model, incorporating the particle breakage phenomenon, provides a valuable tool for accurately predicting and analyzing the behavior of granular materials in various engineering applications.

Spatial–temporal multiscale discrete–continuum simulation of granular flow

Modeling and simulation of granular materials have received great attention in a wide range of scientific and engineering fields. With various discrete or continuum-based methods facing different aspects of the complexity of granular materials, their multi-scale coupling may lead to more effective and efficient methods. In this work, a novel spatial–temporal multiscale method is proposed with spatially overlapped continuum and discrete systems running alternately at different time steps to accelerate the simulation. The continuum system aims at predicting the potential position of each particle, and the discrete system is utilized to provide particle-level information and correct the prediction of the continuum system. The feasibility and accuracy of this method are demonstrated by comparing to typical traditional methods for silo discharge.

Imaginary Coating Algorithm Approaching Dense Accumulation of Granular Material in Simulations with Discrete Element Method

The difficulty of obtaining a densely packed granular material as an initial condition is a very common problem in numerical simulations of granular materials. In this article, an Imaginary Coating Algorithm (ICA) is introduced. To avoid unreasonable particle deformation when using a longer time step and a lower Young’s modulus, the radii used in calculating the action forces in a binary collision are slightly larger than the real values. In other words, an imaginary coat is added to each particle or element. To validate this algorithm, simulations were carried out by using ÅDEM, and a A Discrete Element Method (DEM) software program was developed. Compared with traditional Simulated Annealing Algorithms (SAA), this technique can approach the densely packed state with less CPU/GPU time and is easy to operate.

Simulation of granular materials with the discrete element method to investigate their suitability as crash‐absorber in ship collisions

AbstractIn recent years, the idea of increasing the crash‐worthiness of ships by filling their double hull structure with granules has been studied. To this end, different granular materials have been investigated in [1, 2] with the result, that expanded glass materials are best suited for this purpose. Based on this work, it is important to gain deeper insights into the breakage behavior of expanded glass particles performing numerical investigations. The corresponding simulation procedure as well as the computational results are presented in this contribution.

A Partitioned Scheme for Coupling of FEM and DEM Simulations of Granular Materials

AbstractIn this contribution, a simple uniaxial compaction of granular materials is considered in preparation for studying the collision behavior of double‐hull vessels filled with granular materials. The top compressing plate is deformable and modeled by the finite element method (FEM). The particles modeled using the discrete element method (DEM) are compressed by the top plate. To this end, a partitioned technique to couple the continuum approach (FEM) and particle discretization (DEM) is presented. Full agreement of the computed reaction force in DEM with the pressure applied on the top plate in FEM implies accuracy of the used coupling technique.

Determining a representative element volume for DEM simulations of samples with non-circular particles

Numerical studies on the number of particles or system size required to attain a representative element volume (REV) for discrete element method (DEM) simulations of granular materials have almost always considered samples with spherical or circular particles. This study considers how many particles are needed to attain a REV for 2D samples of 2-disc cluster particles where the particle aspect ratio (AR) was systematically varied. Dense and loose assemblies of particles were simulated. The minimum REV was assessed both by considering the repeatability of static packing characteristics and the shearing behaviour in biaxial compression tests, and by investigating the effect of sample size on the measured characteristics and observed shearing behaviour. The repeatability of the data considered generally improved with increasing sample size. The packing characteristics of the dense samples were more repeatable suggesting that the minimum REV reduces with increasing packing density. The minimum REV was observed to be sensitive to the characteristic measured. Although the overall responses of the samples during shear deformation were similar irrespective of the sample sizes, the smaller the sample size, the higher the fluctuations observed in the responses. Analysis of the coefficient of variation of the fluctuations around the critical state stress ratio can provide insight as to whether a REV is attained. The particle AR influences the effect of sample size on shearing characteristics and thus the minimum number of particles required to attain a REV; this can be explained by the influence of AR on the number of contacts within the samples.

DEM Analysis of Single-Particle Crushing Considering the Inhomogeneity of Material Properties

Crushing characteristics of single particles are the basis of granular material simulation with discrete element method (DEM). To improve the universality and precision of crushable DEM model, inhomogeneous stiffness and strength properties are introduced into the bonded particle method, with which the Weibull distribution and size effect of particle strength can be reproduced without deleting elementary balls. The issues of particle strength and carrying capacity under complex contact conditions are investigated in this work by symmetric loading tests, asymmetric loading tests, and ball–ball loading tests. Results of numerical experiments indicate that particle carrying capacity is significantly influenced by coordination numbers, the symmetry of contact points, as well as the relative size of its neighbors. Contact conditions also show impact on single-particle crushing categories and the origin position of inner particle cracks. The existing stress indexes and assumptions of particle crushing criterion are proved to be inappropriate for general loading cases. Both the inherent inhomogeneity and contact conditions of particles should be taken into consideration in the simulation of granular materials.

Analysis of One-Dimensional Compression under a Wide Range of Stress with Densely Arrayed BPM

In this paper, the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method (DEM) considering particle crushing. This model can solve the problem of pore calculation after the grains are crushed, and reduce the producing time of specimen. In this work, several one-dimensional compressing simulations are carried out to investigate the effect of particle crushing on mechanical properties of granular materials under a wide range of stress. The results show that the crushing process of granular materials can be divided into four different stages according to er-logσy curves. At the end of the second stage, there exists a yield point, after which the physical and mechanical properties of specimens will change significantly. Under extremely high stress, particle crushing will wipe some initial information of specimens, and specimens with different initial gradings and void ratios present some similar characteristics. Particle crushing has great influence on grading, lateral pressure coefficient and compressibility of granular materials, and introduce extra irreversible volume deformation, which is necessary to be considered in modelling of granular materials in wide stress range.

Multi-scale mechanics of sand based on FEM-DEM coupling method

Multiscale mechanics is one of the important mechanical behaviors of granular materials. To perform an efficient calculation of the multiscale mechanics of granular materials based on the coupling of FEM and DEM, a GPU-based solver named as Coupling Simulator (CoSim) is developed. Taking sand as the example of granular materials, triaxial tests are performed to verify the reliability of the multiscale simulation. Firstly, based on the laboratory tests, a parameter inversion method is introduced to obtain the contact parameters of the particles composing the RVE of the sand sample. Then the parameters and RVE sample are used for multi-scale simulation of the triaxial test. The numerical results show that the stress-strain relationship and deformation characteristics are corresponding well with that of the laboratory tests on the macro-scale. According the numerical tests, the meso-mechanical behaviors at different positions of the sample varies greatly, but the deformation and stress evolution of the sample on macro scale are all closely related. Unlike the shear bands where both of the volume expansion and dramatic adjustment of the meso-structure take place, a numerical invalidation of Gaussian points around the shear bands is induced by the volume expansion with no or very slight adjustment of the meso-structure takes place. Finally, the strength reduction method is induced to the multi-scale algorithm and is used for the stability analysis of a sand slope. The numerical results show that both of the factor of stability (FOS) and the obtained slide face are corresponding well with that of the limit equilibrium method. So, the developed GPU-based FEM-DEM coupling code can better be used for the multi-scale simulation of granular materials and geotechnical engineering.

An approach to calculating large strain accumulation for discrete element simulations of granular media

SummaryFor research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro‐level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid‐to‐particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH‐based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements.

Efficient flexible boundary algorithms for DEM simulations of biaxial and triaxial tests

The accurate modeling of boundary conditions is important in simulations of the discrete element method (DEM) and can affect the numerical results significantly. In conventional triaxial compression (CTC) tests, the specimens are wrapped by flexible membranes allowing to deform freely. To accurately model the boundary conditions of CTC, new flexible boundary algorithms for 2D and 3D DEM simulations are proposed. The new algorithms are computationally efficient and easy to implement. Moreover, both horizontal and vertical component of confining pressure are considered in the 2D and 3D algorithms, which can ensure that the directions of confining pressure are always perpendicular to the specimen surfaces. Furthermore, the boundaries are continuous and closed in the new algorithms, which can prevent the escape of particles from the specimens. The effectiveness of the proposed algorithms is validated by biaxial and triaxial simulations of granular materials. The results show that the algorithms allow the boundaries to deform non-uniformly on the premise of maintaining high control accuracy of confining pressure. Meanwhile, the influences of different lateral boundary conditions on the numerical results are discussed. It is indicated that the flexible boundary is more appropriate for the models with large strain or significant localization than rigid boundary.

Fast, flexible particle simulations — An introduction to MercuryDPM

We introduce the open-source package MercuryDPM, which we have been developing over the last few years. MercuryDPM is a code for discrete particle simulations. It simulates the motion of particles by applying forces and torques that stem either from external body forces, (gravity, magnetic fields, etc.) or particle interactions. The code has been developed extensively for granular applications, and in this case these are typically (elastic, plastic, viscous, frictional) contact forces or (adhesive) short-range forces. However, it could be adapted to include long-range (molecular, self-gravity) interactions as well.MercuryDPM is an object-oriented algorithm with an easy-to-use user interface and a flexible core, allowing developers to quickly add new features. It is parallelised using MPI and released under the BSD 3-clause licence. Its open-source developers’ community has developed many features, including moving and curved walls; state-of-the-art granular contact models; specialised classes for common geometries; non-spherical particles; general interfaces; restarting; visualisation; a large self-test suite; extensive documentation; and numerous tutorials and demos. In addition, MercuryDPM has three major components that were originally invented and developed by its team: an advanced contact detection method, which allows for the first time large simulations with wide size distributions; curved (non-triangulated) walls; and multicomponent, spatial and temporal coarse-graining, a novel way to extract continuum fields from discrete particle systems. We illustrate these tools and a selection of other MercuryDPM features via various applications, including size-driven segregation down inclined planes, rotating drums, and dosing silos. Program summaryProgram Title: MercuryDPMProgram Files doi: http://dx.doi.org/10.17632/n7jmdrdc52.1Licensing provisions: BSD 3-ClauseProgramming language: C++, FortranSupplementary material: http://mercurydpm.orgNature of problem: Simulation of granular materials, i.e. conglomerations of discrete, macroscopic particles. The interaction between individual grains is characterised by a loss of energy, making the behaviour of granular materials distinct from atomistic materials, i.e. solids, liquids and gases.Solution method: MercuryDPM (Thornton et al., 2013, 2019; Weinhart et al., 2016, 2017, 2019) is an implementation of the Discrete Particle Method (DPM), also known as the Discrete Element Method (DEM) (Cundall and Strack, 1979). It simulates the motion of individual particles by applying forces and torques that stem either from external forces (gravity, magnetic fields, etc.) or from particle-pair and particle–wall interactions (typically elastic, plastic, dissipative, frictional, and adhesive contact forces). DPM simulations have been successfully used to understand the many unique granular phenomena – sudden phase transitions, jamming, force localisation, etc. – that cannot be explained without considering the granular microstructure.Unusual features: MercuryDPM was designed ab initio with the aim of allowing the simulation of realistic geometries and materials found in industrial and geotechnical applications. It thus contains several bespoke features invented by the MercuryDPM team: (i) a neighbourhood detection algorithm (Krijgsman et al., 2014) that can efficiently simulate highly polydisperse packings, which are common in industry; (ii) curved walls (Weinhart et al., 2016) making it possible to model real industrial geometries exactly, without triangulation errors; and (iii) MercuryCG (Weinhart et al., 2012, 2013, 2016; Tunuguntla et al., 2016), a state-of-the-art analysis tool that extracts local continuum fields, providing accurate analytical/rheological information often not available from experiments or pilot plants. It further contains a large range of contact models to simulate complex interactions such as elasto-plastic deformation (Luding, 2008), sintering (Fuchs et al., 2017), melting (Weinhart et al., 2019), breaking, wet and dry cohesion (Roy et al., 2016, 2017), and liquid migration (Roy et al., 2018), all of which have important industrial applications.

A class of particulate problems suited to FDEM requiring accurate simulation of shape effects in packed granular structures

In many granular material simulation applications, DEM capability is focused on the dynamic solid particulate flow properties and on systems in which millions of particles are involved. The time of relevance is many seconds or even minutes of real time. Simplifying assumptions are made to achieve run completion in practical timescales. There are certain applications, typically involving manufactured particles, where a representative pack is of the order of a thousand particles. More accurate capturing of the influence of complex shape is then often possible. Higher accuracies are necessary to model the topology of the void space, for example, for further CFD simulation and optimisation of fluid flow properties. Alternatively, the accuracy may be critical for structural performance and the force or stress transmission through the contact points is to be controlled to avoid material damage and poor function. This paper briefly summarises methods for simulation of shape effects on packing structures in the granular community and narrows the scope to problems where shape effects are of overriding concern. Two applications of mono-sized, mono-shaped packing problems are highlighted: catalyst support pellets in gas reforming and concrete armour units in breakwater structures. The clear advantages of FDEM for complex-shaped particle interactions in packed systems with relatively few particles are discussed. A class of particulate problems, ‘FDEM-suited’ problems, ones that are ideal to be solved by FDEM rather than by DEM, is proposed for science and engineering use.

Linear‐frictional contact model for 3D discrete element simulations of granular systems

SummaryThe linear‐frictional contact model is the most commonly used contact mechanism for discrete element (DEM) simulations of granular materials. Linear springs with a frictional slider are used for modeling interactions in directions normal and tangential to the contact surface. Although the model is simple in two dimensions, its implementation in 3D faces certain subtle challenges, and the particle interactions that occur within a single time step require careful modeling with a robust algorithm. The paper details a three‐dimensional algorithm that accounts for the changing direction of the tangential force within a time step, the transition from elastic to slip behavior within a time step, possible contact sliding during only part of a time step, and twirling and rotation of the tangential force during a time step. Without three of these adjustments, errors are introduced in the incremental stiffness of an assembly. Without the fourth adjustment, the resulting stress tensor is not only incorrect but it is also no longer a tensor. The algorithm also computes the work increments during a time step, both elastic and dissipative.

A Random Angular Bend Algorithm for Two- Dimensional Discrete Modeling of Granular Materials.

Generation of particles with irregular shape and the overlap detection are crucial for numerical simulation of granular materials. This paper presents a systematic approach to develop a two-dimensional random particle model for numerical simulation of granular materials. Firstly, a random angular bend (RAB) algorithm is proposed and coded in Python to simulate the geometric model of individual particle with irregular shape. Three representative parameters are used to quantitatively control the shape feature of generated polygons in terms of three major aspects, respectively. Then, the generated geometrical models are implemented into particle flow code PFC2D to construct the clump library. The clumps are created via the mid-surface method. Besides, an overlap detection algorithm is developed to address the difficulties associated with spatial allocation of irregularly shaped particles. Finally, two application examples are adopted to validate the feasibility of the proposed algorithm in the numerical modeling of realistic granular materials. The study provides a solid foundation for the generation and simulation of the granular materials based on angular bend theory.

Three‐dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials

SummaryThe paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three‐dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi‐static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).