Analysis of a triangulation based approach for specimen generation for discrete element simulations

Discrete element methods are emerging as useful numerical analysis tools for engineers concerned with granular materials such as soil, food grains, or pharmaceutical powders. Obviously, the first step in a discrete element simulation is the generation of the geometry of the system of interest. The system geometry is defined by the boundary conditions as well as the shape characteristics (including size) and initial coordinates of the particles in the system. While a variety of specimen generation methods for particulate materials have been developed, there is no uniform agreement on the optimum specimen generation approach. This paper proposes a new triangulation based approach that can easily be implemented in two or three dimensions. The concept of this approach (in two dimensions) is to triangulate a system of points within the domain of interest, creating a mesh of triangles. Then the particles are inserted as the incircles of these triangles. Extension to three dimensions using a mesh of tetrahedra and inserting the inspheres is relatively trivial. The major advantages of this approach include the relative simplicity of the algorithm and the small computational cost associated with the preparation of an initial particle assembly. The sensitivity of the characteristics of the particulate material that is generated to the topology of the triangular mesh used is explored. The approach is compared with other currently used methods in both two and three dimensions. These comparisons indicate that while this approach can successfully generate relatively dense two-dimensional particle assemblies, the three- dimensional implementation is less effective at generating dense systems than other available approaches. The research presented in this paper made use of software developed by other researchers. For the two-dimensional study the program Triangle developed by Jonathan Shewchuk was used. The three-dimensional analysis used the Geompack++ program developed by Barry Joe as well as an implementation of the Jodrey and Tory (1985) algorithm by Monika Bargiel and Jacek Moscinski called NSCP3D.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

The importance of parameter-dependent coefficient of restitution in discrete element method simulations

The coefficient of restitution (COR) is an important constant that represents the energy dissipation during contact between two objects. Simulation using the conventional discrete element method (DEM) involves a constant COR. This study presents a DEM simulation method that uses a parameter-dependent COR. The parameter-dependent COR was obtained from a collision incident between spherical particles and a plate surface using a drop-test apparatus. Glass and polypropylene beads of 3–6-mm diameter were used while acrylic and steel were used as the plate surfaces. The particle trajectories were captured by a high-speed camera and analyzed by an image analyzer. The COR was then correlated to a parameter-dependent COR function that depends on the material, impact velocity, and temperature. Free-fall DEM simulations using a constant COR and parameter-dependent COR were compared. The parameter-dependent COR approach obtained better agreement with experimental results than the constant-COR approach. The proposed concept could be applied for other material combinations with a wide range of operating conditions to obtain a database of parameter-dependent COR values for the simulation of solid handling applications.     

Classical and non-classical kinematic fields of two-dimensional penetration tests on granular ground by discrete element method analyses

The penetration test is a widely used in-situ test in geotechnical engineering which mechanism is very important to geomechanics. This paper presents a numerical study on both classic and non-classic kinematic fields in penetration tests on granular ground. A two-dimensional Discrete Element Method (DEM) has been used to simulate penetration tests on a full-size granular ground that is under an amplified gravity and under a K ₀ lateral stress boundary. In addition to classical kinematic variables, i.e. displacement and velocity, a non-classical kinematic variable called the average pure rotation rate (APR), which represents particle sizes and particle rotations (M. J. Jiang et al. Kinematic models for non-coaxial granular materials: Part I: theories. Int J Numer Anal Methods Geomech 2005; 29(7): 643–661), is investigated in the penetration test. The DEM numerical results show that the penetration leads to significant changes in displacement, velocity and APR fields, making the soil near the penetrometer move in complex displacement and APR paths. In comparison to velocity field, APR field is very ‘localized’ in the area close to the penetrometer shoulder during penetration. Based on the normalized tip resistance, the penetration process can be described by three phases of penetration, in which the granular ground undergoes three types of failure mechanism, respectively.     

A discrete element method for the simulation of CFRP cutting

Orthogonal machining of unidirectional carbon fiber-reinforced polymer (UD-CFRP) composites is simulated using discrete element method (DEM). The objective of this work is to present a simple numerical model that allows the study the machining of unidirectional composites during orthogonal cutting. To control the physicochemical phenomena that occur during cutting, it is necessary to identify the parameters of contact, very difficult to measure experimentally. The DEM numerical simulation is presented then as an alternative to the problem. This tool has helped to recreate the physical mechanisms identified experimentally and to understand the origin of the abrasive wear of carbide tools. The observation of the chip formation using a high speed video camera made possible to validate qualitatively the results of numerical simulation by discrete elements. This tool can also determine the cutting forces quite close to reality.     

A combined finite‐discrete element method for simulating pharmaceutical powder tableting

The pharmaceutical powder and tableting process is simulated using a combined finite‐discrete element method and contact dynamics for irregular‐shaped particles. The particle‐scale formulation and two‐stage contact detection algorithm which has been developed for the proposed method enhances the overall calculation efficiency for particle interaction characteristics. The irregular particle shapes and random sizes are represented as a pseudo‐particle assembly having a scaled up geometry but based on the variations of real powder particles. Our simulations show that particle size, shapes and material properties have a significant influence on the behaviour of compaction and deformation. Copyright © 2005 John Wiley & Sons, Ltd.     

Granular temperature with discrete element method simulation in a bubbling fluidized bed

The Discrete Element Method (DEM) plays an important role in understanding and modeling the kinetic characteristics in granular systems. A soft-sphere method with a linear spring–dashpot model was used in the simulation of a bubbling fluidized bed. The time-averaged granular temperature and vertical particle velocity at different heights were numerically studied and compared to experimental measurements of Müller. The influence of a velocity-dependent coefficient of restitution and three drag models were also investigated in this work. Good agreement was found between the DEM simulation and Müller’s experiment, especially using the DiFelice drag model. The variable coefficient of restitution, with a sufficiently high yielding relative velocity, gives a granular temperature that is a little lower compared to that of a constant coefficient of restitution, while it predicts a more intense velocity fluctuation, with a lower yielding relative velocity. By comparing the granular temperature in the vertical direction and in the transverse direction, a strong anisotropy is found in the bed.     

A modelling and verification approach for soybean seed particles using the discrete element method

To build a discrete element method (DEM) model of soybean seed particles, the shape and size of soybean seed particles were measured and analysed. The results showed that the shape of a soybean seed particle could be approximated to an ellipsoid and that the dispersity in size could be approximated by a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. On this basis, an approach for modelling soybean seed particles based on the multi-sphere (MS) method was proposed. The soybean seed particle was simplified to an ellipsoid with the averaged size of one hundred randomly selected soybean seeds. The model of a single soybean seed particle was built by filling spheres within the ellipsoid. For modelling soybean seed assembly, the primary dimension was generated according to the normal distribution, and the other secondary dimensions were calculated based on their relationships with the primary dimension. In this way, the model of soybean seed assembly with different sizes and distributions was built. In this paper, four varieties of soybean seed were used. By comparing the simulated results and experimental results both in piling tests and “self-flow screening” tests, when the number of filling spheres was five, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modelling method for soybean seed particles that we proposed were verified. Finally, an application case was employed to show how to use the soybean seed particle model and the discrete element method to analyse the discharging process of a silo.     

Mixing assessment of non-cohesive particles in a paddle mixer through experiments and discrete element method (DEM)

In this study the mixing kinetics and flow patterns of non-cohesive, monodisperse, spherical particles in a horizontal paddle blender were investigated using experiments, statistical analysis and discrete element method (DEM). EDEM 2.7 commercial software was used as the DEM solver. The experiment and simulation results were found to be in a good agreement. The calibrated DEM model was then utilized to examine the effects of the impeller rotational speed, vessel fill level and particle loading arrangement on the overall mixing quality quantified by the relative standard deviation (RSD) mixing index. The simulation results revealed as the impeller rotational speed was increased from 10?RPM to 40?RPM, generally a better degree of mixing was reached for all particle loading arrangements and vessel fill levels. As the impeller rotational speed was increased further from 40?RPM to 70?RPM the mixing quality was affected, for a vessel fill level of 60% and irrespective of the particle loading arrangement. Increasing the vessel fill level from 40% to 60% enhanced the mixing performance when impeller rotational speed of 40?RPM and 70?RPM were used. However, the mixing quality was independent of vessel fill level for almost all simulation cases when 10?RPM was applied, regardless of the particle loading arrangement. Furthermore, it was concluded that the particle loading arrangement did not have a considerable effect on the mixing index. ANOVA showed that impeller rotational speed had the strongest influence on the mixing quality, followed by the quadratic effect of impeller rotational speed, and lastly the vessel fill level. The granular temperature data indicated that increasing the impeller rotational speed from 10?RPM to 70?RPM resulted in higher granular temperature values. By evaluating the diffusivity coefficient and Peclet number, it was concluded that the dominant mixing mechanism in the current mixing system was diffusion.     

A new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations

In discrete element method (DEM) simulations of real scale, the spherical particles are commonly employed for increasing the computation speed, and the complex boundary models are represented by triangle meshes with controllable accuracy. A new contact detection algorithm has been developed to resolve the contacts between the spheres and the triangle mesh boundaries. The application of the barycentric coordinates makes this algorithm more efficient to identify contacts in the intersection test. As a particle probably collides with several triangles at the same time, the multiple contacts would be reported as face contacts, edge contacts, or vertex contacts. Moreover, the particle embedding in a triangle can be also contact with the edges or vertices of the next triangles. These contacts should be considered as invalid for updating contact forces in the DEM. To exclude invalid records from the multiple contacts, the algorithm gives attention to the mesh structure nearby contacts and analyzes all possible collision situations. Numerical experiments have been conducted to verify this algorithm by using the algorithm in the DEM simulation framework. The numerical results suggest that the algorithm can resolve all contacts precisely and stably when the spherical particles collide on the complex boundary circumstances. Copyright © 2013 John Wiley & Sons, Ltd.     

Discrete element modeling and experimental investigation of hot pressing of intermetallic NiAl powder

This paper presents the numerical and experimental analysis of hot pressing of NiAl powder with an emphasis on the best possible representation of its main stages: initial powder compaction and pressure-assisted sintering. The numerical study has been performed within the discrete element framework. In the paper, an original viscoelastic model of hot pressing has been used. In order to ensure that the applied values of material parameters in numerical simulations are appropriate, the reference literature has been reviewed. It produced the relations and equations to estimate the values of all required sintering material parameters of the considered viscoelastic model. Numerical simulations have employed the geometrical model of the initial dense specimen generated by a special algorithm which uses the real grain distribution of powder. The numerical model has been calibrated and validated through simulations of the real process of hot pressing of intermetallic NiAl material. The kinetics of compaction, sintering and cooling stage indicated by the evolution of density, shrinkage and densification rate have been studied. The comparison of numerical and experimental results has shown a good performance of the developed numerical model.     

A two-layer mesh method for discrete element simulation of gas-particle systems with arbitrarily polyhedral mesh

Inter-phase momentum coupling for particle flows is usually achieved by means of direct numerical simulation (DNS) or point source method (PSM). DNS requires the mesh size of the continuous phase to be much smaller than the size of the smallest particle in the system, whereas PSM requires the mesh size of the continuous phase to be much larger than the particle size. However, for applications where mesh sizes are similar to the size of particles in the system, neither DNS nor PSM is suitable. In order to overcome the dependence of mesh on particle sizes associated with DNS or PSM, a two-layer mesh method (TMM) is proposed. TMM involves the use of a coarse mesh to track the movement of particle clouds and a fine mesh for the continuous phase, with mesh interpolation for information exchange between the coarse and fine mesh Numerical tests of different interpolation methods show that a conservative interpolation scheme of the second order yields the most accurate results. Numerical simulations of a fluidized bed show that there is a good agreement between predictions using TMM with a second-order interpolation scheme and the experimental results, as well as predictions obtained with PSM. Copyright © 2015 John Wiley & Sons, Ltd.     

A discrete splitting finite element method for numerical simulations of incompressible Navier–Stokes flows

The presence of the pressure and the convection terms in incompressible Navier–Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill‐conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non‐linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd.     

A study of transverse ply cracking using a discrete element method

We study the transverse cracking of the 90° ply in [0/90]_S cross-ply laminates by means of a discrete element method. To model the 90° ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice model fibers, and springs with random breaking thresholds represent the disordered matrix material in between. The spring-lattice is coupled by interface springs to two rigid bars which represent the two 0° plies in the model, which could be sublaminate as well. Molecular dynamics simulation is used to follow the time evolution of the model system. It was found that under gradual loading of the specimen, after some distributed cracking, segmentation cracks occur in the 90° ply which then develop into a saturated state where the ply cannot support additional load. The stress distribution between two neighboring segmentation cracks was determined, furthermore, the dependence of the microstructure of damage on the ply thickness was also studied. To give a quantitative characterization of stiffness degradation, the Young modulus of the system is monitored as a function of the density of segmentation cracks. The results of the simulations are in satisfactory agreement with experimental findings and with the results of analytic calculations.     

A discrete element method-based approach to predict the breakage of coal

Pulverization is an essential pre-combustion technique employed for solid fuels, such as coal, to reduce particle sizes. Smaller particles ensure rapid and complete combustion, leading to low carbon emissions. Traditionally, the resulting particle size distributions from pulverizers have been determined by empirical or semi-empirical approaches that rely on extensive data gathered over several decades during operations or experiments, with limited predictive capabilities for new coals and processes. This work presents a Discrete Element Method (DEM)-based computational approach to model coal particle breakage with experimentally characterized coal physical properties. The effect of select operating parameters on the breakage behavior of coal particles is also examined.     

The importance of modelling ballast particle shape in the discrete element method

The discrete element method has been used to model railway ballast. Particles have been modelled using both spheres and clumps of spheres. A simple procedure has been developed to generate clumps which resemble real ballast particles much more so than spheres. The influence of clump shape on the heterogeneous stresses within an aggregate has been investigated, and it has been found that more angular clumps lead to a greater degree of homogeneity. A box test consisting of one cycle of sleeper load after compaction has been performed on an aggregate of spheres and also on an alternative aggregate of clumps. The interlocking provided by the clumps provides a much more realistic load- deformation response than the spheres and the clumps will be the basis for future work on ballast degradation under cyclic loading.     

A system for powder transport based on piezoelectrically excited ultrasonic progressive waves

The transport and dosage of granular materials are an important part of Process Engineering. Thereby, the food, chemical, pharmaceutical and coating industries set high demands on the transport and dosage performances of the used plants. In this context, Ultrasound Process Technology in the past years has developed itself into an attractive alternative compared to presently used classical technologies.

This paper describes the application of ultrasonic progressive waves in a powder-feeding device. The use of a specific pipe material with appropriate damping characteristics allows to generate a progressive wave using a single piezoelectric actuator. Small objects can be carried along the surface of a pipe by the elliptic motion at the surface, which is the result of a flexural progressive wave. The operational principle is the same as in travelling wave ultrasonic motors.

It was experimentally confirmed that the device can be used for feeding and supplying small amounts of powder. The powder-fed performance, however, strongly depends on environmental conditions, so that a control of the system is required. Construction and characteristics of a trial device are shown.     

A coupled meshfree/finite element method for automotive crashworthiness simulations

Mesh distortion induced numerical instability is a major roadblock in automotive crashworthiness finite element simulations. Remedies such as wrapping elements with null shells and deletion of distorted meshes have been adopted but none of them seems robust enough to survive various scenarios. Meshfree methods have been developed over the past almost twenty years in view of their capabilities in dealing with large material deformation and separation, but have remained in academic research due to their unaffordable high computational cost in solving large-scale industrial applications. This paper presents a coupled meshfree/finite-element method which allows engineers to model the severe deformation area with the meshfree method while keeping the remaining area modeled by the finite element methods. The method is implemented into LS-DYNA version 971 and its later versions so that it is available for automotive crashworthiness simulations. In the paper, one linear patch test and three crash examples are presented to demonstrate the accuracy of the meshfree formulation, its effectiveness in resolving mesh distortion difficulty, and the efficiency of the coupled meshfree/finite element solver in handling large-scale models.     

Microscopic investigation of the packing features of soft-rigid particle mixtures using the discrete element method

Soft-rigid mixtures (SRMs) have become popular materials in civil engineering applications for environmental protection because of their outstanding engineering properties. In soft-rigid granular systems, packing features strongly affect shear behavior and directly reflect internal stability. However, the packing features of SRMs have not been previously reported. The aim of this study is to explore the effect of material susceptibility on packing features from a microscopic perspective. First, fifty-three numerical assemblies were established to thoroughly investigate the effects of the size ratio and soft content on several microscopic quantities, e.g., the particle structure, stress network, and local void. Then, the effects of the confining stress and stiffness ratio were analyzed from another eighteen assemblies by six chosen indexes. The results provide microscopic insights into the void structures and stress transmission of SRMs in a packing state.     

Analytical study of the accuracy of discrete element simulations

The numerical errors was used to verify the correctness of key results. The truncation errors, which are larger than the round‐off errors by orders of magnitude, have a superlinear relationship with both the simulation time‐step and the interparticle collision speed. This remains the case regardless of the simulation details including the chosen contact model, particle size distribution, particle density or stiffness. Hence, the total errors can usually be reduced by choosing a smaller time‐step. Increasing the polydispersity in a simulation by including smaller particles necessitates choosing a smaller time‐step to maintain simulation stability and reduces the truncation errors in most cases. The truncation errors are increased by the dissipation of energy by frictional sliding or by the inclusion of damping in the system. The number of contacts affects the accuracy, and one can deduce that because 2D simulations contain fewer interparticle contacts than the equivalent 3D simulations, they therefore have lower accrued simulation errors. Copyright © 2016 John Wiley & Sons, Ltd.