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Collision detection of convex polyhedra on the NVIDIA GPU architecture for the discrete element method
Abstract
Convex polyhedra represent granular media well. This geometric representation may be critical in obtaining realistic simulations of many industrial processes using the discrete element method (DEM). However detecting collisions between the polyhedra and surfaces that make up the environment and the polyhedra themselves is computationally expensive. This paper demonstrates the significant computational benefits that the graphical processor unit (GPU) offers DEM. As we show, this requires careful consideration due to the architectural differences between CPU and GPU platforms. This paper describes the DEM algorithms and heuristics that are optimized for the parallel NVIDIA Kepler GPU architecture in detail. This includes a GPU optimized collision detection algorithm for convex polyhedra based on the separating plane (SP) method. In addition, we present heuristics optimized for the parallel NVIDIA Kepler GPU architecture. Our algorithms have minimalistic memory requirements, which enables us to store data in the limited but high bandwidth constant memory on the GPU. We systematically verify the DEM implementation, where after we demonstrate the computational scaling on two large-scale simulations. We are able achieve a new performance level in DEM by simulating 34 million polyhedra on a single NVIDIA K6000 GPU. We show that by using the GPU with algorithms tailored for the architecture, large scale industrial simulations are possible on a single graphics card.
... Common collision detection methods include installing optoelectronic, force-controlled, and joint torque sensors in specific parts of the robot [9][10][11][12] or detecting the relative position relationship between robot and human through vision systems, imaging systems, ranging systems, and envelope box methods [13][14][15] to ensure the safety of human-robot collaboration systems through pre-collision safety mechanisms. However, some of the systems are more complex in composition, have various types of sensors, have poor backward compatibility, have long fusion response time, and incur expensive system costs, thus making them not suitable for large-scale dissemination and use. ...
... where and denote the force and moment of the robot linkage − 1 on the linkage , respectively; and denote the force and moment of the robot linkage + 1 on the linkage , respectively; , and , denote the position vector from the coordinate origin to the center of mass attached on robot joints and + 1, respectively; denotes the inertia tensor of robot linkage with respect to the center of mass ; and × denotes the Coe-style force term. For the n-degree-of-freedom robot, when there is no load at its end, the extrapolated recursive formulas from Equations (15)-(17) can calculate = − and = − , which are then carried over to gravity compensation Formula (12) to (14) in the stationary state. The required gravity compensation values for the six-axis force/torque sensor at the base, namely and , can be solved for when the robot is in motion. ...
... , which are then carried over to gravity compensation Formula (12) to (14) in the stationary state. The required gravity compensation values for the six-axis force/torque sensor at the base, namely S f and S M, can be solved for when the robot is in motion. ...
After years of more rigid and conventional production processes, the traditional manufacturing industry has been moving toward flexible manufacturing and intelligent manufacturing in recent years. After more than half a century of development, robotics has penetrated into all aspects of human production and life, bringing significant changes to the development of human society. At the same time, the key technology of human–machine cooperative operation has become a research hotspot, and how to realize a human–machine integrated safety system has attracted attention. Human–machine integration means that humans and robots can work in the same natural space, coordinating closely and interacting naturally. To realize real human–robot integration under human–robot cooperative operation, the good judgment of intentional interaction and accidental collision and the detection of collision joints and collision points when accidental collision occurs are the key points. In this paper, we propose a method to identify the collision joints by detecting real-time current changes in each joint of the robot and solve the collision point location information of the collision joints through the principle of virtual displacement and the principle of force method using the force sensor data installed at the base of the robot as the known condition. The results show that the proposed method of identifying the collision joints using changes in joint current and then establishing a collision detection algorithm to solve the collision point location is correct and reliable.
... Recently, the graphics processor unit (GPU) has become an alternative computational platform for DEM, which enables the movement of tens of millions of particles and the movement of non-sphere particles to be performed within a realistic time. Combined CPU-GPU simulation has proven effective and efficient in simulating the structure of several top layers [20,32]. However, the cost of obtaining the whole burden structure of an operating furnace remains exceptionally high. ...
... The model was validated with experimental data [32] in terms of trajectory lines. The parameters used in the experiment and simulation are listed in Table 5. ...
The burden structure directly decides the distribution of gas flow inside a blast furnace (BF). Falling, stacking, and descending bulk materials are the three main processes for burden formation, among which the stacking process plays a decisive role. The Discrete Element Method (DEM) and theoretical modelling were combined to predict stacking behavior in this study. Falling and stacking behaviors were first simulated based on DEM. The repose angle during the stacking process and mass fraction distribution in the radial direction were analyzed. Then, the upper, centroid, and lower trajectory falling lines were determined, and a polynomial relation was found between the angle and the packing height. The influences of three parameters on the repose angle were investigated. Compared with the natural repose angle and chute inclination angle, the effects of the trajectory line depth appeared trivial. The polynomial relation between the repose angle and the packing height was specified to be a function of the natural angle of repose and the chute inclination angle. A three-trajectory falling model and quadratic expression were embedded in the theoretical model, yielding a self-adaption packing model. The model was proved reliable with a low relative error, below 15%.
... The BlazeDEM-GPU framework was developed in consortium with the University of Pretoria, South Africa and the Council for Scientific and Industrial Research (CSIR), South Africa. The project received significant financial, experimental and human capital support from IMT Lille Douai, France enabled upscaling to industrial-scale research using BlazeDEM-GPU [20,21,19,22]. Govender is the primary developer of BlazeDEM-GPU, and continually extending the software's capabilities to expand application domains [23,24,25]. ...
... Development contributions to BlazeDEM-GPU include the extension of the broad-phase grid-based spatial partitioning to the boundaryvolume hierarchy (BVH) by Lubbe et al. [26,27]. BlazeDEM-GPU, initially considered penetration distance to resolve particle-particle contact [20,21,28,19]. However, this resulted in instabilities in determining contact directions [19,2,3]. ...
Force chain networks are generally applied in granular materials to gain insight into inter-particle granular contact. For conservative spherical particle systems, i.e. frictionless and undamped, force chains are information complete due to symmetries resulting from isotropy and constant curvature of a sphere. In fact, for conservative spherical particle systems, given the geometry and material, the force chain network uniquely defines the contact state that includes elastic forces, penetration distance, overlap volume, contact areas and contact pressures in a particle system. This is, however, not the case for conservative non-spherical particle systems. The reason is that a force chain network is not sufficient to uniquely define the contact state in a conservative non-spherical particle system. Additional information is required to define the contact state of non-spherical granular systems. Traction chain networks are proposed to complement force chain networks for the improved quantification of the state of contact of a granular system.
... The BlazeDEM-GPU framework was developed in consortium with the University of Pretoria, South Africa and the Council for Scientific and Industrial Research (CSIR), South Africa. The project received significant financial, experimental and human capital support from IMT Lille Douai, France enabled upscaling to industrial-scale research using BlazeDEM-GPU [20,21,19,22]. Govender is the primary developer of BlazeDEM-GPU, and continually extending the software's capabilities to expand application domains [23,24,25]. ...
... Development contributions to BlazeDEM-GPU include the extension of the broad-phase grid-based spatial partitioning to the boundaryvolume hierarchy (BVH) by Lubbe et al. [26,27]. BlazeDEM-GPU, initially considered penetration distance to resolve particle-particle contact [20,21,28,19]. However, this resulted in instabilities in determining contact directions [19,2,3]. ...
Force chain networks are generally applied in granular materials to gain insight into inter-particle granular contact. For conservative spherical particle systems, i.e. frictionless and undamped, force chains are information complete due to symmetries resulting from isotropy and constant curvature of a sphere. In fact, for conservative spherical particle systems, given the geometry and material, the force chain network uniquely defines the contact state that includes elastic forces, penetration distance, overlap volume, contact areas and contact pressures in a particle system. This is, however, not the case for conservative non-spherical particle systems. The reason is that a force chain network is not sufficient to uniquely define the contact state in a conservative non-spherical particle system. Additional information is required to define the contact state of non-spherical granular systems. Traction chain networks are proposed to complement force chain networks for the improved quantification of the state of contact of a granular system.
https://arxiv.org/abs/2106.03771
... For example, Latham et al 24,25 used X-ray computed tomography (X-ray CT) to scan realistic particles and convert these particles to triangular tessellations for performing DEM simulations. Govender et al [26][27][28][29][30] developed Blaze-DEM for using triangular tessellations for simulating realistic particles, which can effectively deploy graphics processing unit (GPU) of a computer to accelerate simulations. The open-source DEM code YADE has built-in functions to use triangular tessellations for simulating realistic particles 31 . ...
... Many DEM codes can effectively deploy GPU of a computer to accelerate simulations, such as YADE, Blaze-DEM, and Rocky DEM. Govender et al 26,27 reported that the Blaze-DEM could simulate 32×10 6 triangular tessellation particles in 32 minutes using a computer having NVIDIA Quadro K6000 GPU (30720 physical threads) and an Intel i7 3.5 GHz Extreme Edition CPU with 32 GB of RAM under OpenSuse Linux 13.1. ...
Discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate realistic particles, which is computationally demanding when simulating many particles. This paper demonstrates the potential of using a physics engine technique to simulate realistic particles. The physics engines are originally developed for video games for simulating physical and mechanical processes that occur in the real world to produce realistic game experiences. The simulation accuracy and efficiency of physics engines have been significantly improved in the last two decades allowing them to be used as a scientific tool in many disciplines. This paper introduces modeling methodologies of physics engine including realistic particle representation and the contact model. Then, oedometer tests are simulated using realistic particles scanned by X‐ray computed tomography (X‐ray CT). The simulation results agree well with experimental results. This paper demonstrates that physics engines can output contact parameters for geotechnical analysis and force chains for visualization.
... Then during the narrow phase, we calculate the resulting force �⃗ F res i and torque �⃗ F res i using the previously calculated N i . In this paper, the collision detection algorithm provided in [51] is used. ...
The computer simulation of powder bed fusion (PBF) with an electron beam (EB) source at the mesoscale is relevant since the simulation output can be used to estimate solidified material properties and predict possible defects. A high-fidelity simulation with high resolution is computationally heavy, which is why 3D simulations of multilayered samples are rarely used in engineering tasks. We developed the simulation package for additive manufacturing (KiSSAM) that implements the known mathematical models in 3D on a GPU with high performance. KiSSAM includes an implementation of lattice Boltzmann method (LBM) optimized for a GPU; a dynamic mesh for the melt pool; an adaptive mesh for the heat solver; a GPU-powered ray tracer and Monte-Carlo scattering solver for beam absorption, and a high-performance DEM solver for powder particle deposition. All aspects of PBF are implemented with optimized algorithms, so the results of the simulation can be obtained in a few hours. In this paper, we demonstrate the applications of the software for PBF-EB simulation tasks.
... For example, Latham et al. [17,18] scanned realistic particles with three-dimensional X-ray computed tomography (3D Xray CT) and used triangular face tessellations to model these particle geometries in DEM simulations. Govender et al. [19][20][21][22] developed Blaze-DEM, a DEM code able to use triangular face tessellations to model realistic particles, to simulate the granular flow in a rotating drum. Recent commercial DEM codes, such as Itasca PFC 6.0 [23] and Rocky DEM [24], can also use triangular tessellations in the simulation of realistic particles. ...
The discrete element method (DEM) is the most widely applied numerical tool to simulate triaxial test, a common geotechnical test to measure the shear strength of soil. However, the typical DEM model uses sphere clusters to approximate soil particles, which is not sufficiently accurate to simulate realistic soil particles. This paper shows the potential of using a physics engine technique as a promising alternative to typical DEM method. Originally developed for simulating realistic physical and mechanical processes in video games and computer-animated films, physics engines have developed quickly and are being applied in scientific computing. Physics engines use triangular face tesselations to represent realistic objectives, which provides higher accuracy to model realistic soil particle geometries. In this paper, physics engine is applied to simulate true triaxial tests of Monterey No. 0 sand. The numerical results agree well with experimental results. This study provides DEM modelers with the physics engine technique as another promising option to simulate realistic soil particles in geotechnical tests.
... In this context, many researchers have shifted their research interest in mixing of granular matter from spheres to nonspherical particles. Currently, the numerical models applied to describe the shape of non-spherical particles include super-ellipsoid model [28], multi-sphere model [29] and polyhedral model [30][31][32][33][34][35][36][37]. The super-ellipsoid model using a mathematical formula to characterize particle shape shows its high accuracy. ...
Mixing of granular matter with irregular shapes is complicated and essential in many key industrial areas. In this case, the mixing process and flow behaviors of different shaped tetrahedra in a rotating drum with a filling level of 40.5% were numerically reproduced by using discrete element method (DEM). The effects of rotation speed and particle shape parameters (height ratio η and eccentricity ξ) on the mixing process, macroscopic charac-teristics (packing density, free surface profile, granular temperature), microscopic characteristics (coordination number, radial distribution function, contact force, total force), and transfer/dissipation of energy (total kinetic energy and power draw) were systematically investigated; meanwhile, corresponding mechanisms have been explored by analyzing the circulation time. The results show that the mixing rate increases with the sphericity when the flow regime is cascading; however, when the flow pattern is rolling or cataracting, the mixing rate decreases with the sphericity. The variations of macro-/microscopic flow properties and energy transfer/dissipation of tetrahedra change with the rotation speed and shape parameters. The mechanism affecting the flow behavior of different-shaped tetrahedra lies in the fact that the larger circulation time allows more slippages ranular system, which enhances the convective mixing of tetrahedra in one circulation, thus increasing the mixing rate.
... In this context, many researchers have shifted their research interest in mixing of granular matter from spheres to nonspherical particles. Currently, the numerical models applied to describe the shape of non-spherical particles include super-ellipsoid model [28], multi-sphere model [29] and polyhedral model [30][31][32][33][34][35][36][37]. The super-ellipsoid model using a mathematical formula to characterize particle shape shows its high accuracy. ...
Mixing of granular matter with irregular shapes is complicated and essential in many key industrial areas. In this case, the mixing process and flow behaviors of different shaped tetrahedra in a rotating drum with a filling level of 40.5% were numerically reproduced by using discrete element method (DEM). The effects of rotation speed and particle shape parameters (height ratio η and eccentricity ξ) on the mixing process, macroscopic characteristics (packing density, free surface profile, granular temperature), microscopic characteristics (coordination number, radial distribution function, contact force, total force), and transfer/dissipation of energy (total kinetic energy and power draw) were systematically investigated; meanwhile, corresponding mechanisms have been explored by analyzing the circulation time. The results show that the mixing rate increases with the sphericity when the flow regime is cascading; however, when the flow pattern is rolling or cataracting, the mixing rate decreases with the sphericity. The variations of macro-/microscopic flow properties and energy transfer/dissipation of tetrahedra change with the rotation speed and shape parameters. The mechanism affecting the flow behavior of different-shaped tetrahedra lies in the fact that the larger circulation time allows more slippages to occur in the granular system, which enhances the convective mixing of tetrahedra in one circulation, thus increasing the mixing rate.
... GPU's constant memory was utilized for time-saving memory access. Gravity packing of polydisperse and polyhedral materials was studied by numerous researchers [50,53,[71][72][73]77]. GPU-DEM architecture to study reverse faulting through layers of sand was studied in detail by Hazeghian and Soroush [78]. ...
Large deformation near surface excavations and openings has been frequently simulated in geotechnical problems. Mesh-based approaches for large-scale simulation have long been the preferred method due to their capacity to handle real-world domain sizes and processing advantage over particle-based methods. Particle-based methods, on the other hand, are better at mimicking local straining processes like fracturing. Moreover, field-scale numerical simulations based on discrete element based approaches have become possible thanks to the rapid development of graphical processing unit (GPU) cores for general purpose computing over the last decade. As graphics cards are now found in nearly all personal computer (PC)s, the vast majority of researchers may take advantage of their processing capability and create parallelism in their code while reducing computational time. However, most of the GPU cards are based on single precision which are not suitable for double precision computation required in solving geotechnical mechanisms. Hence, selection of a suitable graphic card is also vital in achieving the desired simulation. The goal of this study is to summarize existing research on the types of geotechnical issues addressed via application of general-purpose computing of graphical processing unit (GPGPU), as well as address the difficulties encountered in implementing various numerical algorithms on the GPU architecture. The survey suggested that GPU based discrete element method and combined finite discrete element method are the most popular techniques for solving geomechanical issues due to their intrinsic numerical structure that is suited for parallelization.
... This simplifies a lot contact search techniques, by special algorithms developed for convex bodies. This is quite popular in DEM implementations -particularly when handling interactions between spheres, ellipsoids (or superellipsoids) and convex polyhedra (see e.g.: [33][34][35][36]). When concavities are present, one can face scenarios with multiple pointwise contact pairs. ...
The mechanical behavior of multibody systems can be modeled with several numerical methods. One can mention the Multibody Dynamics (MBD), the Finite Element Method (FEM), the Discrete Element Method (DEM) among others, which have the common feature of solving for the dynamics of a system of rigid/flexible bodies. In this context, the mechanical contact interaction between bodies has to be considered in the model. First, one needs to adopt a strategy to seek for contact occurrence and, when it is detected, to evaluate and include contributions into the mathematical model. However, handling contacts in such models is not a straightforward task, as they can be numerous (depending on the number of bodies considered in the model) and complex, due to the particularities in the geometric shape that each body presents, influencing in contact detection and in its inclusion, as a contribution into the model.
In this work, we propose an integrated framework for handling and managing the automatic contact detection between bodies within a whole complex multibody system. Both rigid and flexible bodies can be considered. Strategies such as MBD, FEM and DEM can be employed together with the proposed strategy. Pointwise contact interactions are modeled based on the geometric description of each body’s boundary, with the aid of the master–master contact formulation.
A hierarchy of bounding volumes for the collision detection is employed, ruling the creation of a contact–candidates pairs list, for which the Local Contact Problem (LCP) is solved — as a detailed determination for the contact pointwise location on local surface parameterizations, representing bodies’ boundaries. As the contact interface, we employ a particular hybrid law that can represent a classical linear contact stiffness, Hertzian contact and other possibilities, together with a barrier to avoid penetration between bodies.
We show applications of the technique involving general rigid polyhedra in contact with beam finite elements — as a FEM/DEM coupling, such as rolling rigid bodies, as a classical multibody dynamics application. The herein proposed strategy can be incorporated using distinct time-integration solvers, such as it is independent on MBD/FEM/DEM particularities.
... Nonetheless, widely-available (twodimensional) image analysis methods can capture averaged statistics relating to these properties, and the full, three-dimensional geometries of particles may be accurately captured using 3D scanning methodologies [17,18]. The accurate measurement of particle geometry is, however, only half of the battle, as the implementation of complex shapes in DEM simulations usually requires a rework of the contact detection algorithm, as well as other parts of the DEM model, relating to the mechanical forces and heat transfer between particles [19][20][21][22][23][24][25][26]. While this is not necessarily the case for 'clump' (multi-sphere/gluedsphere) methods [27], such methods are generally considered not to be suitable for modelling highly angular particles. ...
Calibration and validation represent crucial but often-overlooked ingredients in the successful application of discrete element method (DEM) simulations. Without rigorous calibration/validation protocols, the results of DEM simulations can be imprecise or even unphysical, yet all too often the methods used by practitioners are at best cursory, and at worst entirely absent. As the particle-handling industries show an increasing interest in DEM, it is vital that this issue be resolved lest a potentially powerful tool be written off by industry as unreliable. In this work, we provide a concise overview of contemporary methods used in the calibration and validation of DEM simulations of powder flows, providing practical insights into their strengths and weaknesses, and ideas for manners in which they may be improved and/or rendered more easily adoptable in the future.
... De nombreux travaux de recherche ont utilisé la MED avec des formes de particules complexes, telles que les particules de forme ovales 3D [211,315], les clusters rigides 1 [206,291], les polyèdres convexes [135], les super ellipsoïdes [432], et récemment des formes réalistes de granulats [206,416,210,226], voir la figure 2.1(b). En fonction de l'échelle choisie, chaque particule peut représenter un ensemble de granulats, un granulat, ou une partie de granulat [20]. ...
Cette thèse s'inscrit dans le cadre du conditionnement des déchets de faible activité et à vie longue d'ORANO, constitués majoritairement de graphite, de magnésium et de résidus d'uranium. Les déchets sont immobilisés dans un conteneur métallique par une matrice à base de ciment de laitier Alcali-Activé. L'eau dans les pores de ciment peut accélérer les réactions de corrosion des phases métalliques, telles que le magnésium, et l'uranium. L'expansion due à la formation de produits de corrosion peut entrainer des microfissures dans la matrice cimentaire. Le colis de déchets cimentés est caractérisé par une forte hétérogénéité matérielle à différentes échelles, et son comportement mécanique est impacté par l'existence d'éventuelles fissures à l'échelle microscopique. La méthode FE² a été introduite comme une méthode générale multi-échelle pour résoudre des problèmes de structures hétérogènes non linéaires. À l’échelle macroscopique, chaque point d'intégration du maillage éléments finis est associé à un volume élémentaire représentatif (VER). L'inconvénient majeur de cette méthode est le coût de calcul prohibitif, car il est requis, pour chaque étape de calcul, de résoudre un problème non linéaire dans un VER en chaque point d'intégration à l'échelle macroscopique. Une nouvelle méthode multi-échelle basée sur le machine-learning, appelée k-means FE², est développée ici pour résoudre des problèmes multi-échelle non linéaires généraux avec des variables internes et des comportements dépendant de l'histoire de chargement. Le problème à l’échelle macroscopique est réduit en construisant des clusters de points de Gauss dans une structure qui sont estimés être dans le même état mécanique. Un algorithme de machine-learning k-means clustering est utilisé pour sélectionner les points de Gauss en fonction de leur état de déformation. Ensuite, pour tous les points de Gauss d'un cluster, un seul problème microscopique non linéaire est résolu, et sa réponse est transférée à tous les points d'intégration du cluster en termes de propriétés mécaniques. La convergence de la méthode k-means FE² doit être vérifiée par rapport le nombre de clusters dans la structure macroscopique, et la solution de référence EF². La méthode k-means FE² est appliquée sur un problème de déchets cimentés en considérant des microstructures avec plusieurs fractions volumiques de graphite
... In order to describe non-spherical particles, different shape representation approaches have been proposed. With some approaches, non-spherical particles can be described by just one single particle, such as the ellipsoid approach [13][14][15], super-ellipsoid approach [6,[16][17][18] or polyhedron approach [19][20][21][22][23]. Non-spherical particles can also be described as a composite of some component particles with different numbers, such as the multi-sphere approach [24][25][26] or multi-super-ellipsoid approach [27,28]. ...
Fluidization of non-spherical particles is a common process in energy industries and chemical engineering. Understanding the fluidization of non-spherical particles is important to guide relevant processes. There already have been numerous studies which investigate the behaviors of different non-spherical particles during fluidization, but the investigations of the fluidization of polyhedral particles do not receive much attention. In this study, the investigation of the fluidization of polyhedral particles described by the polyhedron approach is conducted with a numerical CFD-DEM method. Experiments of the fluidization of three kinds of polyhedral particles are conducted under the same condition with corresponding simulations to validate the accuracy of our CFD-DEM model. The results indicate that our CFD-DEM model with the polyhedron approach can predict the behaviors of polyhedral particles with reasonable accuracy. Fluidization behaviors of different polyhedral particles are also investigated in this study. Compared to spherical particles, the motion of polyhedral particles is stronger, and mixing degree is higher under the same fluidization gas velocity.
... The algorithm is typically referred to as GJK-algorithm, constructed by the first letters of the authors' last names. Expansions [175,177,178,179,180] exist for more sophisticated problems. ...
Colloids are large molecules or small particles in solution with a typical size between 1 - 1000 nm. Colloids can be synthesized in various geometries and are typically stabilized with CTAB or oleic acid as surfactant. They have a distribution in size and self-assemble into crystalline structures. To understand the assembly process, we need to understand the role of a size distribution, a colloids shape, and interactions of surfactant molecules with each other and a solvent. Using computer simulations these three questions will be addressed in this thesis. The role of size is investigated with spheres in event-driven molecular dynamics simulations (EDMD). For a Gaussian distribution in radius, we confirm a slowing down of crystal formation. With EDMD accelerated by swaps, we see more complex crystals like Laves phases and Frank Kasper phases form. For a binary distribution we find that Laves phases may form due to nucleation and growth and spinodal decomposition. In order to investigate the impact of shape, event-chain Monte Carlo (ECMC) is adapted to polyhedral particles. We changed the update rules, and created obtuse-reflected-event-chain (OREC). By introducing velocities into ECMC Newtonian event-chain (NEC) was created. We were able to increase the performance by up to an order of magnitude. The algorithm to efficiently calculate the space between polyhedrons in directed motion is a modification of Snethen's XenoCollide. It is part of the successful adaption of event-chains to polyhedral particles. The impact of polymers on the surface of a colloid is investigated on the example of triangles with polysterol surfactants. The phase behavior observed by experimental collaborators can almost completely be explained by a triangles shape rounded due to the surfactant molecules. For short surfactant molecules, soft attractive forces are necessary to explain the crystal structure formed in experiment.
... The Blaze-DEM framework allows for efficient representation and computation for both spherical and polyhedral (convex and non-convex) shaped particles. The details of the contact algorithms used in the code can be found in (Govender et al., 2014;Govender et al., 2015). In addition to the outlined contact algorithms, for this study the screw geometry is represented as a stereolithography (STL) surface mesh, which is converted in situ to triangular prisms to enable polyhedral contact between particles and the screw geometry using the same volume contact method. ...
Screw conveyors are widely used in several industries to transport various granular materials needed to manufacture products or components in a product chain. Degradation of the material and variable packing in the screw pitches are some of the significant operational concerns. This paper explores the effect that particle shape has on the material’s behaviour in screw conveyors. Specifically, faceted polyhedral particles are considered and computed on GPUs using the DEM code, Blaze-DEM. Particle shape significantly influences bulk discharge characteristics, in particular, for higher rotation speeds of the screw. Although spheres yield similar bulk discharge rates to symmetric and equiaxed polyhedra at lower rotational speeds, the packing structure and collision dynamics within the screw are shown to be significantly different between the particle shapes. In general polyhedra have a larger fraction of normal impacts between particles and increased abrasion with the screw and enclosing case. On the other hand, spheres have the highest fraction of energy dissipated as shear between particles.
... The DEM is a powerful numerical modeling technique used to simulate discontinuous rock mass movement and failure [3,4]. Souley and Homand [5] used the DEM for block systems to study the failure and characteristics of jointed rock slopes. ...
Slope failure induced by sublevel caving mining is a progressive process, resulting in the large deformation and displacement of rock masses in the slope. Numerical methods are widely used to investigate the above phenomenon. However, conventional numerical methods have difficulties when simulating the process of progressive slope failure. For example, the discrete element method (DEM) for block systems is computationally expensive and possibly fails for large-scale and complex slope models, while the finite difference method (FDM) has a mesh distortion problem when simulating progressive slope failure. To address the above problems, this paper presents a finite difference modeling method using the adaptive local remeshing technique (LREM) to investigate the progressive slope failure induced by sublevel caving mining. In the proposed LREM, (1) the zone of the distorted mesh is adaptively identified, and the landslide body is removed; (2) the updated mesh is regenerated by the local remeshing, and the physical field variables of the original computational model are transferred to the regenerated computational model. The novelty of the proposed method is that (1) compared with the DEM for block systems, the proposed LREM is capable of modeling the progressive slope failure in large-scale rock slopes; (2) the proposed method is able to address the problem of mesh distortion in conventional FDM modeling; and (3) compared with the errors induced by the frequent updating of the mesh of the entire model, the adaptive local remeshing technique effectively reduces calculation errors. To evaluate the effectiveness of the proposed LREM, it is first used to investigate the failure of a simplified slope induced by sublevel caving mining. Moreover, the proposed LREM is applied in a real case, i.e., to investigate the progressive slope failure induced by sublevel caving mining in Yanqianshan Iron Mine.
... Due to their simple geometry, the collision between cuboids and/or spheres is computationally easier [4][5][6][7], thus enhancing the speed and efficiency of the overall rendering process [2]. Collision detection algorithms are of utmost relevance in many heterogeneous applications spanning computer graphics for shape modelling and video games [8][9][10][11][12], robotics to prevent potential collisions in man-robot interactions [13][14][15][16][17], risk assessment associated to vessel collision [18] or machining of sculptured surfaces [19], and simulations of molecular or particle systems to estimate their thermodynamic properties [20,21]. ...
Collision between rigid three-dimensional objects is a very common modelling problem in a wide spectrum of scientific disciplines, including Computer Science and Physics. It spans from realistic animation of polyhedral shapes for computer vision to the description of thermodynamic and dynamic properties in simple and complex fluids. For instance, colloidal particles of especially exotic shapes are commonly modelled as hard-core objects, whose collision test is key to correctly determine their phase and aggregation behaviour. In this work, we propose the Oriented Cuboid Sphere Intersection (OCSI) algorithm to detect collisions between prolate or oblate cuboids and spheres. We investigate OCSI’s performance by bench-marking it against a number of algorithms commonly employed in computer graphics and colloidal science: Quick Rejection First (QRI), Quick Rejection Intertwined (QRF) and a vectorized version of the OBB-sphere collision detection algorithm that explicitly uses SIMD Streaming Extension (SSE) intrinsics, here referred to as SSE-intr. We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE-intr and OCSI maintain their speed independently of the objects’ geometry. While OCSI and SSE-intr, both based on SIMD parallelization, show excellent and very similar performance, the former provides a more accessible coding and user-friendly implementation as it exploits OpenMP directives for automatic vectorization.
... Collision detection technology is an effective way of processing interference information for various objects by their position and shape data (Guo et al., 2018). Furtherly, it can also analyze the magnitude and direction of the force generated when objects collide (Price et al., 2013;Zhang et al., 2015;Govender et al., 2015). While owing to the strong dependency on digital prototypes, a real-time reminding is extremely necessary if collision occurs no matter in an immersive or nonimmersive virtual environment, consequently, collision detection is a fundamental technology for virtual maintenance analysis. ...
Purpose
Virtual maintenance simulation is of great importance to help designers find and avoid design problems. During its simulation phase, besides the high precision requirement, collision detection must be suitable for all irregular objects in a virtual maintenance environment. Therefore, in this paper, a collision detection approach is proposed based on encapsulation for irregular objects in the virtual maintenance environment.
Design/methodology/approach
First, virtual maintenance simulation characteristics and several commonly used bounding boxes methods are analyzed, which motivates the application of encapsulation theory. Based on these, three different encapsulation methods are oriented to the needs of simulation, including encapsulation of rigid maintenance objects, flexible maintenance objects and maintenance personnel. In addition, to detecting collisions accurately, this paper divides the detection process into two stages. That is, in the first stage, a rough detection is carried out and then a tiny slice space is constructed to generate corresponding capsule groups, which will be redetected in the secondary stage. At last, several case studies are applied to illustrate the performance of the methodology.
Findings
The automatic construction algorithm for bounding boxes can be adapted to all forms of objects. The number of detection primitives are greatly reduced. It introduces the reachable space of the human body in maintainability as the collision search area.
Originality/value
The advantages of virtual maintenance simulation could also be advantageous in the industry with further studies. The paper believes this study is of particular interest to the readers of your journal.
... And recently, Zhao et al. [41] have addressed some deficiencies of using the rolling resistance model. Many researchers have worked on the DEM analysis based on sophisticated particle shapes, such as 3D oval particles [20,24], overlapping rigid clusters [19], convex polyhedral [8], superellipsoid [41], and level set [26]. As we know, the contact detection algorithm for spheres is easier than other types of particles. ...
Presented is a study on the geometrical characteristics of sand particles and the mechanical behavior of sand material under external loading. Based on computed tomography technique, a reconstruction method of granular particles was developed and used to build a database of 3D geometrical models for sand particles. The studied sand particles showed good regularities in morphological characteristics and thus were suitable to be used for the random generation of numerical samples. DEM tests using realistically shaped particles were proven to better simulate the mechanical behavior of the sample during elastoplastic loading stage, which was an issue for the simplified spherical particles. The generation, extension, and breakage of the force chains controlled the strain softening behavior of sands. Anisotropy analysis using the spherical harmonic series showed that the evolution of anisotropy directions and parameters corresponded well with the macroscopic mechanical behavior of the material. Pore volume computation based on Voronoi diagram was performed to illustrate the formation and evolution of localized shear zone. The mesoscopic analysis showed that particle shape significantly influences the mechanical behavior of sands and thus should be properly modeled in numerical simulations.
... Cundall and Hart [31][32][33], Itasca [34] developed the DEM. Over the past years a number of applications have been made using this method by various researchers [35][36][37][38][39][40][41][42][43]. Kulatilake [44] completed a software package named FRACNTWK, based on information given in many journal papers that he and his research group published from 1984 to now on the topic of fracture characterization and network modeling and they combined this with 3DEC in performing rock block stability analysis in both surface and underground excavations [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. ...
The stability of rock blocks is still a key problem in the rock excavation industry and therefore deserve further research and study. Due to the complicated nature of large-scale, three-dimensional developments in blocky rock masses, it is critical to conduct investigations into the stability of rock blocks and choose a reasonable excavation and rock-supporting scheme for design and construction purposes. This article introduces the basic analysis procedure of the General Block (GB) method and discuss the stability of rock blocks in an underground hydropower station at the Three Gorges Project. The application of the GB method mainly follows four basic steps: the discretization of the domain; removal of incomplete fractures; block identification and finally, the block stability analysis. Block identification is the most important of the four processes. A 3-D block model is set up and analyzed. The results from the analysis is used to evaluate the stability of the surrounding rock mass in the powerhouse during the process of excavation. The findings provide guidance on the excavation process and the support requirements for the underground power station. It is envisaged that model study will serve as a reference for the stability evaluation of rock blocks in some related fields.
... For geomaterials, and for rock materials in particular, a crucial requirement is that the packing is polydisperse, presents a relatively high density, and has an isotropic structure so as to avoid any bias related to its fabric when subjected to mechanical loading [7,4,16]. Numerical solutions has been recently proposed to perform large scale DEM simulations with non-spherical particles [12]. Nonetheless, spherical particle models prevail for simulating the mechanics of geological media due to the simplicity of their formulation as well as to their lesser computational demands compared to non-spherical particle models [37,15,13,24,47]. ...
The discrete element method (DEM) is a powerful tool for simulating complex mechanical behaviors which discretizes the targeted medium with particles. The properties of particle assemblies used in DEM simulations directly impact the behavior of the simulated medium. It is thus of critical importance to generate particle assemblies so as to (1) avoid any bias induced by their fabric and (2) conform with the structural discontinuities of the medium under consideration. The main objective of this work is to propose an algorithm, inspired by the space-filling Apollony fractal, to generate sphere packings in geological objects as a first step toward their mechanical modeling with the DEM. In particular, we assess the relevance of the generated packings for simulating the behavior of a rocklike material, and we discuss the ability of the proposed approach to discretize geological models. The algorithm ensures the tangential conformity of spheres with the model boundaries internal and external, and enables to adapt the particle size distribution in the vicinity of structures of interest such as fractures or faults.
... Discrete element method (DEM) is a numerical modeling method based on discontinuity, which can simulate the movement and failure of discontinuity rock mass (Govender et al. 2015). However, the requirements of the computer are high and the calculation speed is slow, so it is difficult to be used in complex modeling. ...
In this study, the stability of jointed rock slope was evaluated using the finite element method (FEM) with the random-joints generation 2D model. The in-house model to simulate joints randomly generated in the rock was developed based on the Monte Carlo method and a normal probability distribution that can be obtained in the field investigation. The model was employed into COMSOL Multiphysics through a subroutine program written by MATLAB. As for the mechanical parameters of joints, the S-type weakening curve equation was used so that each joint has individual mechanical parameters. Compared to a conventional model to simulate the joints, the developed model can simulate the physical characteristics of the jointed rock slope, which reflects the control function of joints in the stability of the rock slope closed to the field. To validate the model, the failure case of jointed rock slope in the field was compared to one predicted by this random joint model. The results were in good agreement with deformation characteristics of the slope observed in the field.
... Collision detection between polyhedral particles is the most time consuming part of a DEM simulation. In Blaze-DEM [66,67,68] contact is split over three phases each with increasing computational cost. Contact between particles is rst detected using an ecient strategy during the broad phase identifying potential contact pairs which are resolved during a computationally more demanding narrow phase to establish whether two particles are actually in contact and if so to compute the resulting force direction and magnitude can be computed. ...
Granular material (GM) is the second most manipulated substance in the world and is present in most industries either as raw materials or finished products. Often the temperature of the granular material needs to be manipulated for example in the case of heating iron ore to induce a phase change or to be kept within a certain temperature range in the case of pharmaceutical powders and food products. Thus a detailed understanding of how heat is transferred in granular materials is essential. The most feasible numerical approach to study heat transfer in granular materials is using the discrete element method (DEM), where each particle is explicitly modeled. In terms of conductive heat transfer particle shape can be expected to have a significant effect on the heating of granular materials, due to the nature of the grain to grain contacts and packing topology which control the heat flow paths and the rate that heat is conducted along these. This paper considers the effect of particle shape on heat conduction in thermally simple or low Biot number granular materials using a polyhedral particle representation. The volume based contact model for granular heat conduction is firstly verified against the analytical solution for solid heat conduction as well as experiment with cubic particles. The resulting model is then used to study the effect of particle shape on the effective thermal conductivity (ETC) and heat distribution within packed stationary beds. It was found that for irregularly shaped (polyhedral) particles the ETC does not have a linear relationship with the packing density as found in previous studies with spherical and ellipsoidal shaped particles. Rather that there is an exponential dependence on the micro-structural quantities of contact area and isotropy, with non-homogeneity in the packing density resulting in complex conduction paths and dead zones affecting conduction thru the bed.
... Discrete element method (DEM) is one of the important tools to study the influence of the particle's shape on the marco-mechanical behaviors of granular materials. In DEM, to simulate the geometrical shape of the particle, oval particle in 3D [37,38], clusters of bounded circles/ spheres [39], overlapping rigid clusters [40], convex polygon-shaped particles [41,42], and convex polyhedral [43] are predominantly used. Whereas, the precision of the particle's model may vary greatly for different methods. ...
... GPUs are increasingly being used to implement compute nodes due to their vast processing power as a consequence of sheer speed and their reduced instruction set computing (RISC) architectures and low power consumption [45][46][47]. GPUs are specialized at certain operations requiring massive amounts of data at blazing speeds, at relatively low cost. Many GPUs carry multiple cores and are naturally suited to the kinds of calculations that are common in advanced physics and engineering. ...
Computational modelling in material science involves mathematical abstractions of force fields between particles with the aim to postulate, develop and understand materials by simulation. The aggregated pairwise interactions of the material’s particles lead to a deduction of its macroscopic behaviours. For practically meaningful macroscopic scales, a large amount of data are generated, leading to vast execution times. Simulation times of hours, days or weeks for moderately sized problems are not uncommon. The reduction of simulation times, improvedresultaccuracyandtheassociatedsoftwareandhardwareengineeringchallengesarethemain motivations for many of the ongoing researches in the computational sciences. This contribution is concerned mainly with simulations that can be done on a “standalone” computer based on Message Passing Interfaces (MPI), parallel code running on hardware platforms with wide specifications, such as single/multi-processor, multi-core machines with minimal reconfiguration for upward scaling of computational power. The widely available, documented and standardized MPI library provides this functionality through the MPI_Comm_size (), MPI_Comm_rank () and MPI_Reduce () functions. A survey of the literature shows that relatively little is written with respect to the efficient extraction of the inherent computational power in a cluster. In this work, wediscuss the main avenues available to tap into this extra power without compromising computational accuracy. We also present methods to overcome the high inertia encountered in single-node-based computational molecular dynamics.Webeginbysurveyingthecurrentstateoftheartanddiscusswhatittakestoachieveparallelism, efficiency andenhancedcomputationalaccuracythroughprogramthreadsandmessagepassinginterfaces. Several code illustrations are given. The pros and cons of writing raw code as opposed to using heuristic, third-party code are also discussed. The growing trend towards graphical processor units and virtual computing clouds for high-performance computing is also discussed. Finally, we present the comparative results of vacancy formation energy calculations using our own parallelized standalone code called Verlet–Stormer velocity (VSV) operating on 30,000 copper atoms. The code is based on the Sutton–Chen implementation of the Finnis–Sinclair pairwise embedded atom potential. A link to the code is also given.
Numerical modelling offers the opportunity to better understand, predict, and optimise the behaviours of industrial systems, and thus provides a powerful means of improving efficiency, productivity and sustainability. However, the accurate modelling of industrial-scale particulate and particle–fluid systems is, due to the complex nature of such systems, highly challenging. This challenge arises primarily from three factors: the lack of a universally accepted continuum model for particulate media; the computational expense of discrete particle simulations; and the difficulty of imaging industrial-scale systems to obtain validation data. In recent years, however, advances in software, hardware, theoretical understanding, and imaging technology have all combined to the point where, in many cases, these challenges are now surmountable—though some distance remains to be travelled. In this review paper, we provide an overview of the most promising solutions to the issues highlighted above, discussing also the major strengths and limitations of each.
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Interactions between irregular particles and structures always exist in the natural environment and industrial production process. For the desired simulation into the dynamic behaviors of arbitrarily shaped particles in complex structures, a general polygon mesh discrete element method (DEM) is developed based on the general energy-conserving contact theory. Within this method, a complete normal contact model for a contact pair with a complex contact region is proposed when the elastic strain energy density is utilized to specify a contact energy function. Since the shape of both complex particles and structures are uniformly constructed by polygon meshes, a unified contact detection implementation performed in this method is introduced in detail. This proposed method is characterized by the universal and uniform models of shape construction, contact detection, and contact force calculation for both particle-particle contact pairs and particle-structure contact pairs. To qualitatively demonstrate the conservation and robustness of the method, a set of validations or simulations considering the differently shaped particles, such as convex particles, concave particles, and particles with surface asperities, are applied. It is concluded from these validations or simulations that the general polygon mesh DEM and the corresponding proposed models are valid tools for research into the behavior of granular materials in complex structures.
Discontinuous deformation analysis (DDA), as a kind of deformable distinct element method (DDEM), features rigorous formulations but bears the Achilles’ heel of low efficiency. In this study, the explicit discontinuous deformation analysis (EDDA) is adapted for efficient large-scale computation. This EDDA/DDEM takes linear elastic polyhedral blocks as basic elements. The cell-mapping neighbor search and high-fidelity direct search are utilized to identify potential contacts. Explicit contact forces decouple the global equation into independent block-wise ones. Moreover, the data structures are carefully designed to reduce memory usage and enhance cache locality. GPU acceleration is exploited, endowing EDDA/DDEM the efficiency that is comparable with the state-of-art parallel distinct element method using rigid elements. In this study, the batch computation on a cloud GPU frees the user’s computer after launching the large-scale computation. The performance of EDDA/DDEM is explored using several large-scale tests of masonry walls and densely packed blocks. A test with over a million blocks is run for 100 thousand steps and only takes 2.5 days, proving the capability of the newly developed EDDA/DDEM to handle engineering analysis.
Since the mixed granular flows containing multiple non-spherical DEM models in complex structures are still challenging for DEM applications, a unified method for creating level set functions of arbitrarily shaped particles constructed by different non-spherical DEM models was developed, and a particle–structure contact algorithm was proposed. At the initial moment, particles of arbitrary shapes constructed by spheres, superquadric equations, spherical harmonic functions, and polyhedral models were discretized using spatial level set functions, and complex structures were discretized into a series of triangular elements. Hence, the contact problem between arbitrarily shaped particles and complex structures was solved using the proposed contact algorithm between level set functions and triangular elements. Meanwhile, particle–particle contact points in mixed granular systems containing multiple non-spherical DEM models were calculated using the level set method . To examine the conservation, accuracy, and robustness of the proposed model, four sets of tests were performed and compared with the theoretical and experimental results, including a plane impacted by a single particle, the elastic collision between two particles, the accumulation of multiple particles, and the mixed granular flow in complex structures. The corresponding numerical results are in good agreement with the theoretical and experimental results, verifying that the present DEM model can accurately predict the motion characteristics of different non-spherical DEM models and can be widely applied to mixed granular flows involving multiple DEM models in complex structures.
A number of industrial applications require the control of granular material temperature across individual grains. Particle level simulations using the DEM is thus critical for optimization. However due to computational cost, particle shape in DEM is often omitted. In this paper advances in GPU computing via the Blaze-DEM code is used to study the effect of particle shape on heat transfer in a rotating drum. Shape irregularity was found to have the greatest effect with non-symmetric shapes having a better heat conduction of at-least 30%. A linear trend of system temperature as function of both RPM and fill level was found. In all cases temperature increased sub-linearly over time. All shapes where found to be sensitive to particle size increases larger than 1.5x. Finally significant diffusion of particles in the axial direction demonstrated the importance of considering the full domain rather than a slice to limit computational cost.
An under-resolved coupling strategy for the discrete element method (DEM) and the weakly compressible (WC) generalised finite difference method (GFD) is proposed. A novel filtering technique is proposed that allows for the recovery of a continuum porosity field in an arbitrary domain from DEM information. This allows fine spherical DEM particles to be treated in an under-resolved fashion using well-established drag relations for dynamic porous media to determine the fluid forces acting on them. To handle the momentum balance between phases, an inter-phase momentum transfer scheme is proposed as well. Verification and validation of the coupling strategy is performed. This includes comparisons to a fully-resolved WCGFD scheme when the associated computational cost allows for it. This strategy's benefits are seen when simulating a fluidised bed with an evolving fluid domain. It is shown that both under-resolved and fully-resolved dynamic information can seamlessly be treated with this scheme.
The Discrete Element Method (DEM) has been successfully used to further understand GM behaviour where experimental means are not possible or limited. However, the vast majority of DEM publications use simplified spheres with rolling friction to account for particle shape, with a few using clumped spheres and super quadratics to better capture grain geometric detail. In this study, we compare the shear strength of packed polyhedral assemblies to spheres with rolling resistance to account for shape. Spheres were found to have the highest shear resistance as the limited rolling friction model could not capture the geometric of rotation grains which caused reordering and dilation. This geometric arrangement causes polyhedra to align faces in the shear direction, reducing the resistance to motion. Conversely, geometric interlocking can cause jamming resulting in a dramatic increase in shear resistance. Particle aspect ratio (elongation and fatness) was found to significantly lower shear resistance, while more uniform aspect ratio’s increased shear resistance with shape non-convexity showing extremes of massive slip or jamming. Thus, while spheres with rolling friction may yield bulk shear strength similar to some polyhedra with a mild aspect ratio, the grain scale effect that leads to compaction and jamming from rotation and interlocking is missed. These results shed light on the complex impact that individual grain shape has on bulk behaviour and its importance.
The ice resistance on a ship hull affects the safety of the hull structure and the ship maneuvering performance in ice-covered regions. In this paper, the discrete element method (DEM) is adopted to simulate the interaction between level ice and ship hull. The level ice is modeled with 3D bonded spherical elements considering the buoyancy and drag force of the water. The parallel bonding approach and the de-bonding criterion are adopted to model the freezing and breakage of level ice. The ship hull is constructed with rigid triangle elements. To improve computational efficiency, the GPU-based parallel computational algorithm was developed for the DEM simulations. During the interaction between the ship hull and level ice, the ice cover is broken into small blocks when the inter-particle stress approaches the bonding strength. The global ice resistance on the hull is calculated through the contacts between ice elements and hull elements during the navigation process. The influences of the ice thickness and navigation speed on the dynamic ice force are analyzed considering the breakage mechanism of ice cover. The Lindqvist and Riska formulas for the determination of ice resistance on ship hull are employed to validate the DEM simulation. The comparison of results of DEM, Lindqvist, and Riska formula show that the DEM result is between those the Lindqvist formula and Riska formula. Therefore the proposed DEM is an effective approach to determine the ice resistance on the ship hull. This work can be aided in the hull structure design and the navigation operation in ice-covered fields.
Discrete element method (DEM) is an effective approach to investigate non-spherical granular systems that are widely encountered in nature, industry, and our daily life. To describe the complex shapes of non-spherical particles, different particle shape representation approaches have been developed. In this paper, comparative study of modeling tablets using multi-sphere approach, multi-super-ellipsoid approach, and polyhedron approach is done to investigate the effect of different approaches. The accuracy of these approaches is testified by experiments and corresponding simulations of the packing, heap forming, and the flow in a rotating drum with two kinds of biconvex tablets firstly. Then the simulations of the flow of two kinds of biconvex tablets in a horizontal rotating drum are carried out by DEM. The simulation results are compared to discuss the effect of different approaches, which include the repose angle, the tablet orientation, the axial movement and the axial mixing, the contact number, the percentage of the tablets reaching the free surface of the granular bed, and the computational efficiency. The results show that the simulations using multi-super-ellipsoid approach and polyhedron approach have some differences with those using multi-sphere approach.
The discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate soil particles, which is not efficient in simulating realistic particles. This paper demonstrates the potential of using a physics engine technique to address limitations of the DEM method. Physics engines are originally developed for video games for simulating physical and mechanical processes that occur in the real world to create an immersive and realistic gaming experience. Physics engines use triangular face tesselations to represent objectives, which provides higher accuracy for modeling realistic particle geometries. This paper has three objectives. First, this paper introduces the physics engine technique to the geotechnical community. Second, this paper develops a series of pre-processing, servo-controlling, and post-processing functions embedded into physics engine to generate soil specimens with designed packing densities, perform direct shear tests, and output simulation results including stress–strain relations, fabrics, and force chains. Third, this paper develops a miniature direct shear test that can be scanned by X-ray computed tomography (X-ray CT) for evaluating the simulation accuracy of the physics engine. The numerical results agree well with experimental results. This study provides DEM modelers with physics engine as one more option for simulating realistic particles.
The majority of publications in DEM use simplified particle shapes, in this study we use polyhedral shapes to determine the effect of particle shape on shear strength via a direct-shear test. Grain aspect ratio was found to be the primary determinant of shear strength with elongated polyhedra having a lower shear resistance. Grain irregularity also had a significant effect, shapes with isotropic contacts angles had the highest shear strength. The variability of granular material behavior due to shape was demonstrated by non-convex shapes re-orientating to jam in certain cases. Shapes with multi-stable packed orientations were found to offer the highest resistance to reordering under localized vibration.
In this work, the discharge of numerous polygonal particles in a hopper was investigated numerically and experimentally. To this end, a polygonal/polyhedral DEM model is proposed and implemented to simulate hopper operation in 2D and 3D. The results of a conservation test show that the proposed algorithm conserves energy better than the CP algorithm owing to its straightforward contact calculation. The model then is adopted to simulate the discharge of rod-shaped particles in hopper. Lab-scale experiments were also conducted for DEM model validation. To evaluate the influence of particle shape, outlet opening, and discharge slope angle, rod-shaped particles with triangular, square, pentagonal, and hexagonal cross-sections were used in the experiments and simulation. The results show that the discharge rate of non-spherical particles was significantly affected by the shape of particles, and inter-particle packing property was found to have stronger influence than rolling-related properties, such as roundness or moment of inertia. Conditional clogging phenomena of particles were observed, and the tendency of particle clogging was enhanced by high initial loading, narrow outlet opening, and low slope angle of the hopper outlet. The criteria conditions of particle clogging from experiments were satisfactorily reproduced in the simulation. Although the discharge rate increased with increasing initial loading, the discharge rate saturated at over M = 30 kg owing to the so called Janssen’s effect. The discharge corresponding to the change in particle shape and initial loading was in good agreement between the simulation and experimental results. The comparison of 2D/3D simulation shows that the experiments and simulations successfully minimized the 3D effect.
The highly complex dynamics of granular systems are notoriously difficult to predict using theoretical or empirical models. As such, the development and application of numerical models represents a significant focus of the field. This chapter provides an introduction to the main numerical methods used to model the dynamics of granular systems, including an overview of their underlying operation, and a discussion of their strengths and limitations. The focus of the chapter lies on the three methods most widely used in the study of granular segregation: the discrete element method, cellular automata, and Monte Carlo simulations.
A comprehensive study on the meso-mechanical behaviors of sand with its 2D geometrical models was presented in this study. Based on the 2D geometrical models’ database of sand particles, quantitative analysis on the geometrical characteristics of the studied sand particles was performed A new clump generation algorithm based on fewer multiple overlapping circles was provided to accurately model the shape of sand particles, and was used to build the discrete element method (DEM) numerical model of the sand sample for DEM biaxial tests. The macro- and meso-mechanical behaviors of the studied sand samples were systematically analyzed. Deformation was mainly localized in a X-shaped shear zone, in which the particles experienced large displacements and rotations. Development of stress-induced anisotropy in particle and void orientations, as well as the mesoscopic fabric, was significant during the shearing process. Continuous collapse, generation, reduction, and extension of force chains occurred during the shearing process, especially after the peak stress was reached. This led to the fluctuations in the evolution of deviatoric stress and volumetric strain at macroscale, as well as the fabric anisotropy at mesoscale.
An integral bridge is constructed without joints between the superstructure and substructure. This reduces the maintenance costs over the life of the bridge. However, since there are no joints present, the bridge can be viewed as a single structural element. This means that when the deck moves as a result of a temperature variation and the abutment moves relative to the backfill soil which it retains. In this study, the Discrete Element Method was used to model the soil behind an integral bridge abutment exposed to such thermal loading. Different particle shapes were modelled to study the effect of particle shape on the inter-particle shear forces in the backfill soil. It was found that the magnitude of these shear forces was linearly related to the sphericity of the particles modelled. Particles with lower sphericities (less smooth) experienced larger shear forces between them. It was also found that the shear forces between the particles decreased as the soil was cyclically loaded. Particles with higher sphericities experienced larger reductions of inter-particle shear forces as the number of cycles increased. The results suggest that, in order to limit the shear stresses within the soil, particles with higher
sphericities should be used as backfill behind integral bridge abutments.
Understanding the dynamical behavior of Granular Media (GM) is extremely important to many industrial processes. Thus simulating the dynamics of GM is critical in the design and optimization of such processes. However, the dynamics of GM is complex in nature and cannot be described by a closed form solution for more than a few particles. A popular and successful approach in simulating the underlying dynamics of GM is by using the Discrete Element Method (DEM). Computational viable simulations are typically restricted to a few particles with realistic complex interactions or a larger number of particles with simplified interactions. This paper introduces a novel DEM based particle simulation code (BLAZE-DEM) that is capable of simulating millions of particles on a desktop computer utilizing a NVIDIA Kepler Graphical Processor Unit (GPU) via the CUDA programming model. The GPU framework of BLAZE-DEM is limited to applications that require large numbers of particles with simplified interactions such as hopper flow which exhibits task level parallelism that can be exploited on the GPU. BLAZE-DEM also performs real-time visualization with interactive capabilities. In this paper we discuss our GPU framework and validate our code by comparison between experimental and numerical hopper flow.
Granular materials, such as sand and grains, are ubiquitous. Simulating the 3D dynamic motion of such materials represents a challenging problem in graphics because of their unique physical properties. In this paper we present a simple and effective method for granular material simulation. By incorporating techniques from physical models, our approach describes granular phenomena more faithfully than previous methods. Granular material is represented by a large collection of non-spherical particles which may be in persistent contact. The particles represent discrete elements of the simulated material. One major advantage of using discrete elements is that the topology of particle interaction can evolve freely. As a result, highly dynamic phenomena, such as splashing and avalanches, can be conveniently generated by this meshless approach without sacrificing physical accuracy. We generalize this discrete model to rigid bodies by distributing particles over their surfaces. In this way, two-way coupling between granular materials and rigid bodies is achieved.
The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.
Draglines are an expensive and essential part of open-cut coal mining. Small improvements in performance can produce substantial productivity increases and cost savings. The design of the bucket and the way in which it fills with overburden are very important to overall dragline performance. Here we use a discrete element model to simulate the filling process. It allows us to differentiate between the flow patterns for two competing bucket designs, evaluate the effect of rigging and variations in material properties, calculate fill times, estimate wear and its distribution, and determine regions of high compaction.
The geometry of convex polyhedra is described by a set of half spaces. This geometry representation is used in the discrete element method to model polyhedral particles. An algorithm for contact detection and the calculation of the interaction forces for these particles is presented. Finally the presented model is exemplified by simulating the particle flow through a hopper.
We present an algorithm for contact detection between polygonal (2-D) or polyhedral (3-D) convex particles in the Discrete Element Method (DEM). Noting that the space occupied by a polygon or polyhedron can be defined using a set of linear inequalities, we show that the task of contact detection can be cast as a standard problem in the field of convex optimization, for which there exist established solution procedures. The contact detection algorithm consists of two stages; first to establish intersection and then to calculate the contact point. We can establish intersection between a pair of particles by solving a linear program and, if there is an intersection, use the analytic center of the linear inequalities as the contact point. Once the contact point is obtained, the contact normal can be calculated from the gradient vector of an inner “potential particle” whose corners are rounded (c.f. [13]). The necessary mathematics is presented. Six examples are included to assess the performance of the algorithm in terms of speed and accuracy.
Granular flows are extremely important for the pharmaceutical and chemical industry, as well as for other scientific areas. Thus, the understanding of the impact of particle size and related effects on the mean, as well as on the fluctuating flow field, in granular flows is critical for design and optimization of powder processing operations.We use a specialized simulation tool written in C and CUDA (Compute Unified Device Architecture), a massive parallelization technique which runs on the Graphics Processing Unit (GPU). We focus on both, a new implementation approach using CUDA/GPU, as well as on the flow fields and mixing properties obtained in the million-particlerange.We show that using CUDA and GPUs, we are able to simulate granular flows involving several millions of particles significantly faster than using currently available software. Our simulation results are intended as a basis for enhanced DEM simulations, where fluid spraying, wetting and fluid spreading inside the powder bed is considered.
The flow of polyhedral granular particles in a small 3D slice hopper is studied experimentally and computationally by applying the discrete element method (DEM). A high speed camera was used to obtain the experimental results. The experimental packing structure, flow behaviour, arching and discharging in the hopper are analysed and compared with the DEM results for three hopper half angles. Reasonable agreement is shown on the static packing, flow behaviour and hopper discharge rates. The critical orifice length at which flow ceases to be smooth is investigated and arching of the material around the orifice is demonstrated experimentally and computationally. Spherical particles of nearly identical volume and density to the average of the polyhedral particles are also tested and compared to the polyhedra. The DEM is shown to be reasonably adept at modelling the interactions between polyhedral particles in a system in which there are very many possible particle geometrical interactions. Further work should consider the cohesion between the particles and the particle and the wall. Simulations of a greater number of particles in different hopper geometries should also be explored.
Purpose
Develop a new three‐dimensional discrete element code (BLOKS3D) for efficient simulation of polyhedral particles of any size. The paper describes efficient algorithms for the most important ingredients of a discrete element code.
Design/methodology/approach
New algorithms are presented for contact resolution and detection (including neighbor search and contact detection sections), contact point and force detection, and contact damping. In contact resolution and detection, a new neighbor search algorithm called TLS is described. Each contact is modeled with multiple contact points. A non‐linear force‐displacement relationship is suggested for contact force calculation and a dual‐criterion is employed for contact damping. The performance of the algorithm is compared to those currently available in the literature.
Findings
The algorithms are proven to significantly improve the analysis speed. A series of examples are presented to demonstrate and evaluate the performance of the proposed algorithms and the overall discrete element method (DEM) code.
Originality/value
Long computational times required to simulate large numbers of particles have been a major hindering factor in extensive application of DEM in many engineering applications. This paper describes an effort to enhance the available algorithms and further the engineering application of DEM.
In this work, the discrete element method (DEM) is used to assess powder flow from hoppers and the results are compared to widely-used hopper design charts. These design charts delineate mass-flow and funnel-flow behavior based on the hopper wall angle and a given set of material properties. The modeled system consists of hoppers with various wall angles and frictional, non-cohesive, spherical particles. The performance is assessed by measuring the particle residence times, particle velocities, and the extent of segregation during discharge. A Mass Flow Index (MFI) based on the velocity profile data is used to quantitatively characterize the nature of the flow pattern as mass-flow, funnel-flow, or some intermediate. The DEM predictions are generally in very good agreement with the Jenike design charts. The level of agreement shown here indicates that DEM cannot only reproduce the current estimates of hopper performance, but also provide additional insight into the flow–such as the internal granular structure–that may be difficult to obtain otherwise.
The Discrete Element Method (DEM) is becoming widely used to simulate particle flows. It is a versatile and powerful tool. Its main limitation, the CPU time required, is becoming less critical with the development of computer technology. Most DEM simulations consider spherical particles in three dimension (3D) or circles in 2D. Several researchers are developing models of non-circular particles in 2D, but there are few applications of DEM to non-spherical particles in 3D granular flow. This paper proposes a technique of sphere intersection for particle description that is applied here in 2D and 3D. It then describes a known technique of sphero-cylinders in 3D and applies it to small-scale simulations of discharge of frictionless particles, modelling contact normal forces, from a hopper. Aspect ratio for these particles is shown to have a negligible effect on discharge rate. Simulations in 2D showed that the disc-shaped particles discharged 40% faster than the circular particles. Program code tests are described to check the complex model of rotational dynamics for non-spherical particles in 3D.
An attempt is made to show that fundamental particles are manifestations of the geometry of space-time. This is done by demonstrating the existence of a purely geometrical model, which we have calledspherical rotation, that satisfies Dirac's equation. The model is developed and illustrated both mathematically and mechanically. It indicates that the mass of a particle is entirely due to the spinning of the space-time continuum. Using the model, we can show the distinction between spin-up and spin-down states and also between particle and antiparticle states. It satisfies Einstein's criteria for a model that has both wave and particle properties, and it does so without introducing a singularity into the continuum
As physical laws govern the motion of objects around us, a physically-based simulation plays an important role in computer graphics. For instance, the motion of a fluid, which is difficult to generate by hand, can be produced by solving the governing equations. Acceleration of a simulation is one of the most important research themes because the speed and stability of a simulation are essential for real-time applications.
A numerical tool known as the discrete element method (DEM) is used to study the motion of the ball charge in ball mills. In particular, the motion of individual balls in the ball charge is simulated. An interesting aspect of this simulation is that it yields the frequency distribution of ball collisions as a function of collision energy. The results of numerical simulations are compared with experiments: The angular positions of the toe and shoulder, the trajectory of two balls, and the power draft — all of these predictions are reasonably close to experimental measurements. An interesting sidelight of this study is that the collision frequency can be combined with the breakage property of particles to carry out direct simulation of particle fragmentation in ball mills. The rudiments of such a simulation are illustrated.
The distinct element method is a numerical model capable of describing the mechanical behavior of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis.
Adequacy of approximation of ellipsoidal particles composed of a set of sub-spheres for numerical Discrete Element Method
(DEM) simulations is examined. The algorithm of adaptive hierarchical multi-sphere (MS) model is suggested for composing elliptical
particles. Numerical simulation of the piling problem is used as a test problem for evaluating the adequacy of MS model approximation
in comparison to the model of smooth ellipses for multiparticle system. The accuracy of MS approximation with the increasing
number of sub-spheres is examined in detail by comparison of macroscopic and microscopic parameters of granular dynamics.
It was determined that the data on macroscopic parameters yielded by the MS model tend to converge to those of the smooth
ellipsoid with the increasing number of the constituent sub-spheres, and the MS model approximates the smooth perfect ellipsoid
with a reasonable number of sub-spheres within the limits of the appropriate tolerance. It can be concluded that a multi-sphere
model remains a realistic and relatively simple particle model applicable to DEM simulations of the behaviour of the real
smooth and rough elliptically shaped particles.
Collision detection (CD) between two objects is a complex task which demands spatial decomposition or bounding volume hierarchy in order to classify the features of the objects for a successful intersection test. Moreover, when the objects are complex and have concavities, holes, etc., the complexity of the decomposition increases and it is necessary to find a method which detects all special cases and degenerations.In this paper, we present a method for CD between complex polyhedra. We use a polyhedron representation based on simplicial coverings. With such as representation it is possible to model complex objects by using simpler objects (simplices), without any previous decomposition into convex pieces. The spatial decomposition so-called tetra-tree is utilized in order to classify the simplices of the covering, as well as a bounding volume hierarchy based on tetrahedra and spheres which allows us to drastically reduce the number of intersection tests between the features of both polyhedra. A time study has been performed to obtain a real time CD between two complex objects.
While the discrete element method (DEM) is attracting increasing interest for the simulation of industrial granular flow, much of the previous DEM modelling has considered two-dimensional (2D) flows and used circular particles. The inclusion of particle shape into DEM models is very important and allows many flow features, particularly in hoppers, to be more accurately reproduced than was possible when using only circular particles. Elongated particles are shown here to produce flow rates up to 30% lower than for circular particles and give flow patterns that are quite different. The yielding of the particle microstructure resembles more the tearing of a continuum solid, with large-scale quasi-stable voids being formed and large groups of particles moving together. The flow becomes increasingly concentrated in a relatively narrow funnel above the hopper opening. This encourages the hope that DEM may be able to predict important problems such as bridging and rat-holing. Increasing the blockiness or angularity of the particles is also shown to increase resistance to flow and reduces the flow rates by up to 28%, but without having perceptible effect on the nature of the flow. We also describe our methodology for constructing and modelling geometrically complex industrial applications in three dimensions and present a series of industrially important three-dimensional (3D) case studies. The charge motion in a 5 m diameter ball mill and in a Hicom nutating mill, discharge from single- and four-port cylindrical hoppers, and particle size separation by a vibrating screen are demonstrated. For each case, plausible particle size distributions (PSDs) have been used. The results obtained indicate that DEM modelling is now sufficiently advanced that it can make useful contributions to process optimisation and equipment design. Finally the parallelisation of such a DEM code is described and benchmark performance results for a large-scale 2D hopper flow are presented.
The distinct element method has advanced to a stage where the complex mechanical interactions of a discontinuous system can be modelled in three dimensions. An important component is the formulation of a robust and rapid technique to detect and categorize contacts between three-dimensional particles. The technique, described in Part I of this paper, can detect the contact between blocks of any arbitrary shape (convex or concave) and represent the geometrical and physical characteristics prescribed for the contact (e.g. three-dimensional rock joint behaviour). The method utilizes an efficient data structure which permits the rapid calculation on a personal computer of systems involving several hundred particles.
Granular mixing is a vital operation in food, chemical, and pharmaceutical industries. Although the tumbling blender is by far the most common device used to mix grains, surprisingly little is known about mixing or segregation in these devices. In this paper, we report the first fully three-dimensional (3D) particle dynamics simulations of granular dynamics in two standard industrial tumbling blender geometries: the double-cone and the V-blender. Simulations for both monodisperse and bidisperse (segregating) grain sizes are performed and compared with experiment. Mixing and transport patterns are studied, and we find in both tumblers that the dominant mixing mechanism, azimuthal convection, contends against the dominant bottleneck, axial dispersion. The dynamics of blending, on the other hand, differs dramatically between the two tumblers: flow in the double-cone is nearly continuous and steady, while flow in the V-blender is intermittent and consists of two very distinct processes.
GPU based particle simulation framework with fluid coupling ability
- G Neubauer
- C A Radeke
G. Neubauer, C.A. Radeke, GPU based particle simulation framework with fluid coupling ability (March 2014). <http://on-demand.gputechconf.com/
gtc/2014/poster/pdf/P4143>.
A GPU based polyhedral particle dem transport code
- N Govender
- D Wilke
- S Kok
- R Els
N. Govender, D. Wilke, S. Kok, R. Els, A GPU based polyhedral particle dem transport code (March 2014). <http://on-demand.gputechconf.com/gtc/
2014/poster/pdf/P4126>.
Development of a convex polyhedral discrete element simulation framework for NVIDIA kepler based GPUS
- Govender
Formulation of a three-dimensional distinct element model -part i: a scheme to detect and represent contacts in a system composed of many polyhedral blocks
P. Cundall, Formulation of a three-dimensional distinct element model -part i: a scheme to detect and represent contacts in a system composed of
many polyhedral blocks, Int. J. Rock Mech. 25 (1988) 107-116.