Classical Discrete Element Method Research Articles

Discrete element simulations to predict the response of bio-cemented sands

Discrete element method (DEM)-based numerical models in the YADE environment are used to simulate the constitutive response of uncemented and bio-cemented sands to investigate the influence of boundary conditions, loading and testing conditions, and material types. Both the classical DEM model and the pore scale finite volume (PFV)-coupled DEM model are used to simulate the response of saturated uncemented and lightly cemented sands with a rigid wall boundary under both drained and undrained triaxial compression. A DEM model with flexible boundaries created using particle facet (PFacet) elements is used to simulate undrained triaxial compression of moderately cemented sands, including the influence of confining stress. The PFacet-based model is used to predict the transition from barreling failure to shear banding when the confining stress or the cementation degree increases. The classical DEM model with cohesive bonds of uniform strength is also used to successfully simulate the uniaxial compression response of a sand with an extremely high degree of cementation. Finally, this paper presents a particle-packing model consisting of multiple solid phases for cemented sands based on the understanding that not all particle types will have the same cohesive properties. This multiple solid-phase model is a refinement of the classical DEM model that represents the particle physics more realistically, especially for heterogeneous systems. A preliminary parametric study is carried out considering varying cohesive properties and volume fractions for the different solid phases.

Order reduction of fracture mechanics in porous microstructures: A multiscale computing framework

We present a multiscale framework to systematically reduce the order of fracture-mechanics computations in complex porous microstructures captured by a pore-scale image (e.g., X-ray μCT). The framework allows formulating approximations that are more accurate than classical discrete element methods (DEM) and faster than high-fidelity direct numerical simulation (DNS) techniques, such as phase-field models (PFM). We propose two such approximations called the pore-level multiscale method (PLMM) and the image-based discrete element method (iDEM), the latter a generalization of classical DEM wherein the solid geometry is not simplified. Unlike iDEM, PLMM is equipped with the ability to iteratively control errors away from, but not at, the cracks. We refer to the uncorrected approximation as M0, and that with ω corrections as Mω. Both methods are based on the hypotheses that (H1) cracks nucleate at geometric constrictions of the solid, and (H2) bending/torsion moments at such constrictions are negligible. iDEM additionally assumes that (H3) the geometric enlargements of the solid are rigid. Through a series of benchmarks, performed on complex geometries subject to hydraulic, tensile, shear, and compressive loading, we show that H1 is largely valid under non-compressive loading, and H2 degrades the most under shear loading when bending/torsion moments dominate. H3 has two consequences: (1) M0 predictions can be reproduced by iDEM at a fraction of the cost, (2) but to compute them, iDEM’s parameters (spring constants) must be calibrated to reference data, which may not be available. Moreover, the calibrated parameters are non-unique and depend on the reference data chosen. The foregoing benchmarks are validated against two well-known PFMs, in which inherent uncertainties and deficiencies are also identified, especially under compressive loading. These are attributed to the so-called energy splits used. Lastly, we derive and validate closed-form expressions for the tensile and shear strengths of the solid used by PLMM/iDEM and the length-scale parameter and fracture toughness in PFM. This work provides fundamental insights into how porous materials fail, and how accurate approximations based on such understanding can be constructed and refined in the future.

A discrete element framework for modeling the mechanical behaviour of snow Part II: model validation

A micro-scale modelling approach of snow based on the extension of the classical discrete element method has been presented in the first part of this study. This modelling approach is employed to predict the mechanical response of snow under compression dependent on strain rate, initial density and temperature. Results obtained under a variety of conditions are validated with experimental data for both micro- and macro-scale, in particular the broad range between ductile i.e. low deformation rates and brittle i.e. high deformation rates regimes are investigated. For this purpose snow is assumed to be composed of ice grains that are inter-connected by a network of bonds between neighbouring grains. This arrangement represents the micro-scale of which the interaction is described by inter-granular collision and bonding. Hence, the response on a macro-scale is largely determined by inter-granular collisions and deformation and failure of bonds during a loading cycle. Consequently, validation was first carried out on micro-scale deformations at different loading rates and temperatures. Hereafter, macro-scale simulations of confined and unconfined, deformation-controlled compression tests have been predicted and were successfully compared to experimental data reported in literature.

Stress based multi-contact model for discrete-element simulations

The aim of this study is to introduce a stress-based non-binary contact model missing in classical discrete element method (DEM). To tackle this issue, a classical force-displacement contact law is generalized by utilizing the trace of the particle stress tensor to make all contacts dependent on all other contacts of a particle and thus, to account for multiple contacts simultaneously acting on a single particle. Simulation results for uniaxial confined (oedometric) compression employing our new multi-contact model were compared with the classical discrete element formulation, an existing strain-based multi-contact model, and experimental data. The satisfactory agreement between these results supports the validity of our new contact model. Several test examples at higher load levels show that our generalized contact model is able to capture the stronger non-linearity at higher stresses. Due to its simplicity, the proposed multi-contact model can easily be integrated in any DEM implementation, remaining relatively fast when compared to more complex methods or even a discretization of particles, e.g. by FEM.

Effect of the clump size for bonded particle model on the uniaxial and tensile strength ratio of rock

The Discrete Element Method (DEM) has been increasingly used to study the behaviour of rock. Despite the advantage of classical DEM formulations in using simple interaction laws to model fracture initiation and propagation, they have limitations to properly simulate brittle rock behaviour. The code cannot predict the high values of unconfined compressive strength/tensile strength (UCS/TS) ratio associated with non-linear failure envelopes, as observed for hard rock, such as granite, unless significant modifications are made. This paper proposes and implements a clumped-particle model into a two-dimensional DEM code. The increase in the interaction between discrete elements, which locally increases the density of interparticle bonds, can improve the results to obtain the desired values of UCS/TS ratio. This approach seems able to significantly increase both the potential and the predictive capabilities of DEM for rock modelling purposes. The novelties introduced in this work are the presentation of a numerical procedure to determine the equivalent micro-mechanical properties of intact rocks and, aware of a gap in our knowledge, the characterisation of uncertainties that a clumped-particle model introduces in the numerical results. A series of numerical simulations, including uniaxial compression and direct tension tests, were carried out, by varying the relation between the clump and the minimum particle radius, using the Monte Carlo simulation technique. The results were compared with experimental data on Lac du Bonnet granite, from the bibliography, which allowed to determine the equivalent micro-mechanical properties. Results, from a simulation using a core sample of Lac du Bonnet granite, show that the variance in the values of the mechanical properties calculated decreases with the decrease in the particle radius, but the influence of the clump size on the behaviour requires the execution of a considerable amount of simulations to achieve results with an acceptable relative error of 5%. Nevertheless, the mechanical behaviour obtained from DEM simulations was in good agreement with the experimental data and the model captured both the tensile and the unconfined compression strength values.

XDEM multi-physics and multi-scale simulation technology: Review of DEM–CFD coupling, methodology and engineering applications

The extended discrete element method (XDEM) multi-physics and multi-scale simulation platform is being developed at the Institute of Computational Engineering, the University of Luxembourg. The platform is an advanced multi-physics simulation technology that combines flexibility and versatility to establish the next generation of multi-physics and multi-scale simulation tools. For this purpose, the simulation framework relies on coupling various predictive tools based on an Eulerian and Lagrangian approach. The Eulerian approach represents the wide field of continuum models; the Lagrangian approach is perfect for characterising discrete phases. Continuum models thus include classical simulation tools, such as computational fluid dynamics simulation and finite element analysis, while an extended configuration of the classical discrete element method addresses the discrete (e.g., particulate) phase. Apart from predicting the trajectories of individual particles, XDEM-suite extends the application of the XDEM to estimating the thermodynamic state of each particle using advanced and optimised algorithms. The thermodynamic state may include temperature and species distributions due to chemical reaction and external heat sources. Hence, coupling these extended features with either computational fluid dynamics simulation or finite element analysis opens a wide range of applications as diverse as pharmaceuticals, agriculture, food processing, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology.

An attempt to study conversion of biomass spheres in a stove using a DEM-CFD approach

The objective of this study is conversion analysis of biomass fuel in a bubbling fluidized bed with a DEM-CFD coupling model. This approach is based on classical Discrete Element Method (DEM) in which the conversion of solid fuel is also involved. In addition, the dynamics and conversion of solid particles are coupled to the gas phase via heat, mass, momentum and species transfer with employing OpenFOAM as Computational Fluid Dynamics (CFD) tool. This leads to encompass the interaction between solid and gas phases. That is, the chemical and physical processes of solid conversion pointing to heat-up, drying, pyrolysis, combustion and gasification caused by interaction with the reactive gas phase are considered with implementing homogeneous and heterogeneous reactions in both solid and gas phases. The test case is considered as a 3D cylindrical chamber including a packed bed of beechwood spherical particles with size of 6 mm. Two gas inlets as primary and secondary are involved with ambient pressure and temperature at the bottom and top of the bed where the superficial gas velocity of primary inlet is high enough to fluidize particles. The aim of fluidization is better mixing of the particles with the gas phase to increase the heat and mass transfer rate. The required energy for solid conversion comes from high wall temperature defined as 700°C. The predicted results are the consumption and formation of wood, char, tar and volatile matters of the bed during conversion process. At the end, it is shown the temperature distribution of solid-gas phases including the flame at 300s.

Effects of grain morphology on critical state: a computational analysis

We introduce a new DEM scheme (LS-DEM) that takes advantage of level sets to enable the inclusion of real grain shapes into a classical discrete element method. Then, LS-DEM is validated and calibrated with respect to real experimental results. Finally, we exploit part of LS-DEM potentiality by using it to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope $$\lambda $$ , CSL intercept $$\varGamma $$ , and CS friction angle $$\varPhi _{\mathrm{CS}}$$ on the grain’s morphology, i.e., sphericity, roundness, and regularity. This study is carried out in three steps. First, LS-DEM is used to capture and simulate the shape of five different two-dimensional cross sections of real grains, which have been previously classified according to the aforementioned morphological features. Second, the same LS-DEM simulations are carried out for idealized/simplified grains, which are morphologically equivalent to their real counterparts. Third, the results of real and idealized grains are compared, so the effect of “imperfections” on real particles is isolated. Finally, trends for the CS parameters (CSP) dependency on sphericity, roundness, and regularity are obtained as well as analyzed. The main observations and remarks connecting particle’s morphology, particle’s idealization, and CSP are summarized in a table that is attempted to help in keeping a general picture of the analysis, results, and corresponding implications.

A Discrete/Continuous Numerical Approach to Multi-physics

A variety of technical applications are not only the physics of a single domain, but include several physical phenomena, and therefore are referred to as multi-physics. As long as the phenomena being taken into account is either continuous or discrete i.e. Euler or Lagrangian a homogeneous solution concept can be employed. However, numerous challenges in engineering include continuous and discrete phase simultaneously, and therefore cannot be solved only by continuous or discrete approaches. Problems include both a continuous and a discrete phase are important in applications of the pharmaceutical Industry e.g. drug production, agriculture and food processing industry, mining, construction and Agricultural machinery, metal production, power generation and systems biology.The Extended Discrete Element Method (XDEM) is a novel technique, which provides a significant advance for the coupled discrete and continuous numerical simulation concepts. It expands the dynamics of particles as described by the classical discrete element method (DEM) by a thermodynamic state or stress/strain coupled as fluid flow or structures for each particle in a continuum phase. XDEM additionally estimates properties such as the interior temperature and/or species distribution. These predictive capabilities are extended to fluid flow through an interaction by heat, mass and momentum transfer important for process engineering.

Validation of a model for physical interactions between pulp, charge and mill structure in tumbling mills

Modelling the pulp fluid and its simultaneous interactions with both the charge and the mill structure is an interesting challenge. The interactions have previously been modelled for dry grinding with a combination of discrete element method (DEM), smoothed particle hydrodynamics (SPH) and the finite element method (FEM), where the DEM particles or SPH particles represent the grinding balls and FEM is used to model the mill structure. In this work, the previous model is extended to include fluids with SPH. Wet milling with water and a magnetite pulp, for graded and mono-size charges are numerically modelled and validated. The internal working of the charge and the physical interaction between the charge and the mill structure is studied. The combined SPH–DEM–FEM model presented here can predict the classical DEM results, but can also predict responses from the mill structure, as well as the pulp liquid flow and pressure. Validation is conducted by comparing numerical results with experimental measurements from grinding in an instrumented small-scale batch ball mill equipped with an accurate torque metre. The simulated charge movement is also compared with high speed video of the charge movement for a number of cases. Numerical results are in good agreement with experimental measurements.

XDEM employed to predict reduction of tungsten oxide in a dry hydrogen atmosphere

The extended discrete element method (XDEM) is a novel concept to model tungsten oxide reduction. The concept extends the classical discrete element method (DEM) with additional properties such as the thermodynamic state. Moreover, the concept treats a solid phase, represented by particles, and a fluid phase as two distinguished phases that are coupled through heat, mass and momentum transfer.In this study, reduction of WO3 to metallic tungsten in a dry hydrogen atmosphere is modelled by a direct oxygen removal from the solid oxide mechanism for which temperature and reaction progress are described by the discrete particle method (DPM). An outstanding feature of the herein proposed numerical concept is that powder particles are treated as individual entities which are described by its thermodynamic state, e.g. temperature and species distribution within the particle. Therefore, it allows a detailed and accurate characterisation of the reaction progress.XDEM predictions have been compared to isothermal literature experimentation with a high degree of accuracy. Therefore, the current approach provides a new and deep insight into the process, because particle temperatures, concentration of species and interaction of particles with the environment are inaccessible in a furnace during experiments.

An inexact interior point method for the large-scale simulation of granular material

Non-smooth contact dynamics provides an increasingly popular simulation framework for granular material. In contrast to classical discrete element methods, this approach is stable for arbitrary time steps and produces visually acceptable results in very short computing time. Yet when it comes to the prediction of draft forces, non-smooth contact dynamics is typically not accurate enough. We therefore propose to combine the method class with an interior point algorithm for higher accuracy. Our specific algorithm is based on the so-called Jordan algebras and exploits the relation to symmetric cones in order to tackle the conical constraints that are intrinsic to frictional contact problems. In every interior point iteration a linear system has to be solved. We analyze how the interior point method behaves when it is combined with Krylov subspace solvers and incomplete factorizations. We show that efficient preconditioners and efficient linear solvers are essential for the method to be applicable to large-scale problems. Using CG as a linear solver and incomplete LU factorizations, we substantially improve the accuracy in comparison to the projected Gauß–Jacobi solver.

A 3D discrete element modelling approach for rockfall analysis with drapery systems

This paper presents a novel approach for the simulation of rockfalls behind drapery systems which can be used to accurately assess the residual rockfall hazard involved with such systems. A discrete element model of drapery systems installed on rock slopes is presented where all the relevant interactions are taken into account. The approach is based on the classical discrete element method, where the block is represented by a rigid assembly of spheres. The slope is represented by triangular elements and the drapery is represented by spherical particles which interact remotely. The model is calibrated and validated by comparing the numerical predictions with experimental results. It is shown that the model can accurately predict block trajectories and block velocities for rockfall analysis with and without drapery.

Enhanced Thermal Process Engineering by the Extended Discrete Element Method (XDEM)

A vast number of engineering applications include a continuous and discrete phase simultaneously, and therefore, cannot be solved accurately by continu- ous or discrete approaches only. Problems that involve both a continuous and a discrete phase are important in applications as diverse as pharmaceutical industry e.g. drug production, agriculture food and process- ing industry, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology. A novel technique referred to as Extended Discrete Element Method (XDEM) is devel- oped, that offers a significant advancement for coupled discrete and continuous numerical simulation concepts. The Extended Discrete Element Method extends the dynamics of granular materials or particles as described through the classical discrete element method (DEM) to additional properties such as the thermodynamic state or stress/strain for each particle coupled to a continuum phase such as fluid flow or solid structures. Contrary to a continuum mechanics concept, XDEM aims at resolving the particulate phase through the various processes attached to particles. While DEM predicts the spacial-temporal position and orientation for each particle, XDEM additionally estimates properties such as the internal temperature and/or species distribution. These predictive capabilities are further extended by an interaction to fluid flow by heat, mass and momentum transfer and impact of particles on structures.

A contact dynamics approach to the Granular Element Method

We present a contact dynamics (CD) approach to the Granular Element Method (GEM) Andrade et al. (2012) [1], abbreviated here as CD–GEM. By combining particle shape flexibility through Non-Uniform Rational Basis Splines, properties of implicit time-integration discretization (e.g., larger time steps) and non-penetrating constraints, as well as a reduction to a static formulation in the limit of an infinite time step, CD–GEM targets system properties and deformation regimes in which the classical discrete element method either performs poorly or simply fails; namely, in granular systems comprising of rigid or highly stiff angular particles and subjected to quasi-static or intense dynamic flow conditions. The integration of CD and GEM is made possible while significantly simplifying implementation and maintaining comparable performance with existing CD approaches.

A fictitious domain approach for the simulation of dense suspensions

Low Reynolds number concentrated suspensions do exhibit an intricate physics which can be partly unraveled by the use of numerical simulation. To this end, a Lagrange multiplier-free fictitious domain approach is described in this work. Unlike some methods recently proposed, the present approach is fully Eulerian and therefore does not need any transfer between the Eulerian background grid and some Lagrangian nodes attached to particles. Lubrication forces between particles play an important role in the suspension rheology and have been properly accounted for in the model. A robust and effective lubrication scheme is outlined which consists in transposing the classical approach used in Stokesian Dynamics to our present direct numerical simulation. This lubrication model has also been adapted to account for solid boundaries such as walls. Contact forces between particles are modeled using a classical Discrete Element Method (DEM), a widely used method in granular matter physics. Comprehensive validations are presented on various one-particle, two-particle or three-particle configurations in a linear shear flow as well as some O(103) and O(104) particle simulations.

Application of XDEM as a novel approach to predict drying of a packed bed

A majority of solid fuels especially biomass contains moisture, which may amount up to the mass of the dry particles. Thus it is important to determine the details of drying when considering biomass as a fuel. Therefore, the objective of this work is to apply the Extended Discrete Element Method (XDEM) as a numerical simulation framework to prediction of drying within a packed bed reactor. The novel numerical concept resolves the particulate phase by the classical Discrete Element Method (DEM), however, extends it by the thermodynamic state e.g. temperature distribution and evaporation of water content of each particle in conjunction with heat and mass transfer to the surrounding gas phase. The latter is described by a continuous approach namely a set of differential conservation equations as employed in Computational Fluid Dynamics (CFD) for porous media. Comparison with measurement was carried out and good agreement was achieved.

Tilting process with humidity: DEM modeling and comparison with experiments

Granular matter is present everywhere in our practical lives and mostly used in natural environment (i.e. classical atmospheric conditions). This fact implies that the humidity rate which controls the water content can be involved in their behaviors. Especially adhesion forces between grains are linked to this humidity rate. Here we study a well known experiment defined as a laboratory test for avalanches. We continuously tilt a box filled with grains up to the appearance of precursors and full avalanches. These avalanches are directly proportional to the forces acting at the contact level between grains. We use a numerical approach based on the classical discrete element methods ‘spring-Dashpot’ with soft model. Firstly, we check the ability of our code to handle tilting experiments, then, an extra adhesion term linked to the humidity rate is added. Full comparison between ‘dry’ case and humid case is done.

A DEM model for soft and hard rocks: Role of grain interlocking on strength

The Discrete Element Method (DEM) is increasingly used to simulate the behavior of rock. Despite their intrinsic capability to model fracture initiation and propagation starting from simple interaction laws, classical DEM formulations using spherical discrete elements suffer from an intrinsic limitation to properly simulate brittle rock behavior characterized by high values of UCS/TS ratio associated with non-linear failure envelopes, as observed for hard rock like granite. The present paper shows that the increase of the interaction range between the spherical discrete elements, which increases locally the density of interaction forces (or interparticle bonds), can overcome this limitation. It is argued that this solution represents a way to implicitly take into account the degree of interlocking associated to the microstructural complexity of rock. It is thus shown that increasing the degree of interlocking between the discrete elements which represent the rock medium, in addition to enhancing the UCS/TS ratio, results in a non-linear failure envelop characteristic of low porous rocks. This approach improves significantly the potential and predictive capabilities of the DEM for rock modeling purpose. A special emphasis is put on the model ability to capture the fundamental characteristics of brittle rocks in terms of fracture initiation and propagation. The model can reproduce an essential component of brittle rock failure, that is, cohesion weakening and frictional strengthening as a function of rock damage or plastic strain. Based on model predictions, it is finally discussed that frictional strengthening may be at the origin of the brittle ductile transition occurring at high confining pressures.

Coupling Continuous and Discontinuous Descriptions to Model First Body Deformation in Third Body Flows

The present paper proposes an extension of the classical discrete element method used to study third body flows. Based on the concept of the tribological triplet proposed by Godet and Berthier, the aim of this work is to enrich description, by accounting for the deformation of the first body and investigating its influence on third-body rheology. To achieve this, a novel hybrid approach that combines continuous and discontinuous descriptions is used. To illustrate the advantage of such modeling, comparisons with the classical approach, which considers the first body as rigid, are performed in terms of macroscopic friction coefficient and velocity and stress profiles.