Discrete Element Method Codes Research Articles

Physics engine based simulation of shear behavior of granular soils using hard and soft contact models

Physics engines have been widely used to simulate physical and mechanical processes in modern video games to create an immersive and realistic gaming experience. This study explores the feasibility of using an open-source physics engine, Chrono, as a discrete element method (DEM) platform to simulate shear behavior of granular soils. This study develops a series of pre-processing, servo-controlling, and post-processing functions to improve the Chrono platform, so that Chrono can generate soil specimens with designed packing densities, perform laboratory test simulations such as direct shear tests, and output stress-strain, fabric, and force chains. Traditional DEM codes use soft contact models (e.g., Hertzian contact model) to determine inter-particle contact forces, while most physics engines use a hard contact model (e.g., non-smooth contact dynamics) to determine inter-particle contact forces. The hard contact model enables physics engines to use large time steps in iterations without affecting the numerical stability and simulation accuracy, which remarkably accelerate simulation speeds compared with traditional DEM codes. Based on systematical comparisons between simulation results of two contact models and experimental results, this study demonstrates that the hard contact model can yield the shear behavior of granular soils observed in soft contact model simulations and laboratory tests.

Shared memory parallelization for high-fidelity large-scale 3D polyhedral particle simulations

Particle shape plays a vital role in granular material behavior, but simulations with realistic particle shapes are uncommon due to significant computational demands of complex particle geometry representation. In this work, BLOKS3D, a polyhedral Discrete Element Method (DEM) and impulse-based DEM (iDEM) codes are parallelized to enable large-scale simulations with realistic particle shapes on readily accessible multi-core machines. Data structures used in the original codes were redesigned and optimized, leading to 15% improved performance of the original serial codes. New parallel algorithms were developed resulting in 28 times performance improvement on a 48-core (quad-CPU) shared memory system over single core serial algorithm. The parallelized 3D polyhedral DEM and iDEM were applied to series of column collapse simulations. The codes successfully reproduced the runout distance in granular column collapse experiments. The particle force data from both parallelized DEM and iDEM matched data from the serial algorithm. The new parallel implementation of iDEM was then demonstrated with unprecedented 52 million 3D polyhedral particles simulations. This work will benefit future granular material studies with the newly introduced capacity to run large-scale simulations with realistic particle shapes on shared memory hardware platforms readily accessible to many engineers and researchers.

Validating N-body code chrono for granular DEM simulations in reduced-gravity environments

ABSTRACT The Discrete Element Method (DEM) is frequently used to model complex granular systems and to augment the knowledge that we obtain through theory, experimentation, and real-world observations. Numerical simulations are a particularly powerful tool for studying the regolith-covered surfaces of asteroids, comets, and small moons, where reduced-gravity environments produce ill-defined flow behaviours. In this work, we present a method for validating soft-sphere DEM codes for both terrestrial and small-body granular environments. The open-source code chrono is modified and evaluated first with a series of simple two-body-collision tests, and then, with a set of piling and tumbler tests. In the piling tests, we vary the coefficient of rolling friction to calibrate the simulations against experiments with 1 mm glass beads. Then, we use the friction coefficient to model the flow of 1 mm glass beads in a rotating drum, using a drum configuration from a previous experimental study. We measure the dynamic angle of repose, the flowing layer thickness, and the flowing layer velocity for tests with different particle sizes, contact force models, coefficients of rolling friction, cohesion levels, drum rotation speeds, and gravity levels. The tests show that the same flow patterns can be observed at the Earth and reduced-gravity levels if the drum rotation speed and the gravity level are set according to the dimensionless parameter known as the Froude number. chrono is successfully validated against known flow behaviours at different gravity and cohesion levels, and will be used to study small-body regolith dynamics in future works.

A cohesive fracture model for discrete element method based on polyhedral blocks

Failure processes are common in geomaterials under external loads. In this study, a cohesive fracture model (CFM) and its implementation in a graphical processing unit (GPU)-based discrete element method (DEM) solver is presented within the context of simulating the failure of rock and other geomaterials. The CFM and its GPU implementation advances the simulation of the processes of meso-fracture initiation, propagation, and interaction. The CFM discretizes a domain into a series of pre-defined rigid polyhedral blocks. These blocks are bonded along the contact faces by a cohesive criterion with normal and shear strengths. This poses a computational challenge as few DEM codes can simulate polyhedrons, and amongst those the limited number of particles and required computational run-time make it intractable to do simulations of more than a few thousand polyhedral elements. This makes it computationally infeasible to combine CFM with such DEM models for practical applications. However, the GPU based code Blaze-DEM does allow for simulations of tens of millions of polyhedrons within practical runtimes. In this study we implement the CFM in Blaze-DEM and show the efficiency and usefulness of the model using GPU compute. Two typical examples, including a block sliding along a slope and the fracture process of an arch structure, are used to verify the provided CFM. This is followed by the simulation of Brazilian tests and uniaxial tests of limestone using the CFM that are validated against laboratory experiments. These tests demonstrate that the provided CFM can simulate not only the fracture process well, but also mechanical behaviors at the meso and macro scale of the geomaterials. Furthermore, based on the failure mechanisms of the Brazilian test and uniaxial test, an inversion method is proposed to obtain the mechanical parameters in CFM.

Formulation and implementation of coupled forced heat convection and heat conduction in DEM

This paper presents the development, implementation and verification of a coupled convective–conductive heat flow and transport model in the discrete element method (DEM). Thermal conduction is already available in DEM codes such as the particle flow code (PFC). However, current DEM codes rarely account for convective heat transport. There are many important phenomena in different applications that involve convective heat transport due to flow of fluid through permeable solid material, where the fluid and the permeable solids have different initial temperatures. Heat transfer from convection is dependent on the fluid flow velocity through existing and new instantaneously forming flow paths in solid and is typically much faster than conduction. The complete formulation of the heat convection model, its implementation and coupling with fluid flow and heat conduction in PFC2D, and its validation are described in detail. While DEM has been widely used for studying fundamental mechanisms in geomaterials, little effort has been devoted toward extending DEM for studying coupling between conductive heat flow and convective heat transport problems. The developments presented in this paper will enable application of DEM to study coupled hydro-thermo-mechanical processes in geomaterials such as in geothermal systems, hydrocarbon production, environmental engineering and nuclear waste storage.

Models, algorithms and validation for opensource DEM and CFD-DEM

We present a multi–purpose CFD–DEM framework to simulate coupled fluid–granular systems. The motion of the particles is resolved by means of the Discrete Element Method (DEM), and the Computational Fluid Dynamics (CFD) method is used to calculate the interstitial fluid flow. We first give a short overview over the DEM and CFD–DEM codes and implementations, followed by elaborating on the numerical schemes and implementation of the CFD–DEM coupling approach, which comprises two fundamentally different approaches, the unresolved CFD–DEM and the resolved CFD–DEM using an Immersed Boundary (IB) method. Both the DEM and the CFD–DEM approach are successfully tested against analytics as well as experimental data.

Experimental validation of 2D DEM code by digital image analysis in tumbling mills

The discrete element method (DEM) is widely used as an optimization tool in the design of tumbling mills. Nevertheless, the experimental validation of DEM codes is an important step to guarantee that the system is well described and that the predictions are close to the real operating conditions. The power draw is the principal parameter used to validate DEM codes, but using this as the only reference can be inappropriate. The power draw can be fitted by simply changing the model constants until the predicted values are close to the experimental data, when the charge profile looks similar to the real operation and there is no experimental velocity profile with which to compare. This paper presents an experimental validation of a 2D DEM code by digital image analysis of the velocity profiles of the balls, the toe and shoulder angles and the predicted power draw. The experimental values were compared with the simulated data using different charge lifters and charge levels. The DEM simulation clearly shows that the velocity charge changes with a modification of the lifter profile. An accurate map of velocities at each location in the mill was obtained by digital image analysis and compared with DEM calculations. The simulated and experimental values are very close, leading to the conclusion that such DEM predictions represent an accurate description of the process in a tumbling mill.

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

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

Coupled discrete element and finite volume solution of two classical soil mechanics problems

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier–Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle–fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.

Implementation of the Jäger contact model for discrete element simulations

AbstractIn three‐dimensional discrete element method (DEM) simulations, the particle motions within a granular assembly can produce bewildering sequences of movements at the contacts between particle pairs. With frictional contacts, the relationship between contact movement and force is non‐linear and path‐dependent, requiring an efficient means of computing the forces and storing their histories. By cleverly applying the principles of Cattaneo, Mindlin, and Deresiewicz, J”urgen Jäger developed an efficient approach for computing the full three‐dimensional force between identical elastic spheres that have undergone difficult movement sequences (J. Jäger, New Solutions in Contact Mechanics. WIT Press: Southampton, U.K.). This paper presents a complete Jäger algorithm that can be incorporated into DEM codes and also describes three special provisions for DEM simulations: (1) a method for handling particle pairs that undergo complex tumbling and twirling motions in three‐dimensions; (2) a compact data structure for storing the loading history of the many contacts in a large assembly; and (3) an approximation of the Jäger algorithm that reduces memory demand. The algorithm addresses contact translations between elastic spheres having identical properties, but it does not resolve the tractions produced by twisting or rolling motions. A performance test demonstrates that the algorithm can be applied in a DEM code with modest increases in computation time but with more substantial increases in required storage. Copyright © 2011 John Wiley & Sons, Ltd.

Discrete element parameter calibration and the modelling of dragline bucket filling

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

Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations

Discrete element method (DEM) models to simulate laboratory element tests play an important role in advancing our understanding of the mechanics of granular material response, including bonded or cemented, particulate materials. Comparisons of the macro-scale response observed in a real physical test and a “virtual” DEM-simulated test can calibrate or validate DEM models. The detailed, particle scale information provided in the DEM simulation can then be used to develop our understanding of the material behaviour. It is important to accurately model the physical test boundary conditions in these DEM simulations. This paper specifically considers triaxial tests as these tests are commonly used in soil mechanics. In a triaxial test, the test specimen of granular material is enclosed within a flexible latex membrane that allows the material to deform freely during testing, while maintaining a specified stress condition. Triaxial tests can only be realistically simulated in 3D DEM codes, however analogue, 2D, biaxial DEM simulations are also often considered as it is easier to visualize particle interactions in two dimensions. This paper describes algorithms to simulate the lateral boundary conditions imposed by the latex membrane used in physical triaxial tests in both 2D and 3D DEM simulations. The importance of carefully considering the lateral boundary conditions in DEM simulations is illustrated by considering a 2D biaxial test on a specimen of frictional unbonded disks and a 3D triaxial test on a bonded (cemented) specimen of spheres. The comparisons indicate that the lateral boundary conditions have a more significant influence on the local, particle-scale response in comparison with the overall macro-scale observations.

Prediction/Verification of Particle Motion in One Dimension with the Discrete-Element Method

Although the availability of discrete-element method (DEM) codes has improved, the need still exists to solve simple verification problems to obtain an understanding of these codes. Different DEM codes may have subtle differences in the manner in which the method is implemented, and the significance of these differences may be problem dependent. This paper investigates a series of simple, one and two-particle contact problems. These problems, which employ various types of damping, are shown to be equivalent to classical one-dimensional vibration problems. The solutions are discussed in the context of the DEM, and results from the DEM are shown to compare very well with the classical solutions. It is demonstrated that results from a well-known commercial two-dimensional code (PFC2D) and the open source three-dimensional code (YADE) yield identical solutions to these problems provided the problem solution process is manipulated properly. A discussion of the differences in how gravity and damping are implemented may be of interest to users of PFC2D.