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As particulate systems evolve, sliding, rolling and collision contacts all produce forces that discrete element method (DEM) methods aim to predict. Verification of friction rarely takes high priority in validation studies even though friction plays a very important role in applications and in mathematical models for numerical simulation. The purpose of this paper is to address sliding friction in finite element method (FEM)/DEM and rolling friction in DEM.

Analytical solutions for “block sliding” were used to verify the authors' tangential contact force implementation of 2D FEM/DEM. Inspired by the kinetic art work Liquid Reflections by Liliane Lijn, which consists of free balls responding within a rotating shallow dish, DEM was used to simulate rolling, sliding and state‐of‐rest of spherical particles relative to horizontal and inclined, concave and flat spinning platforms. Various material properties, initial and boundary conditions are set which produce different trajectory regimes.

Simulation output is found to be in excellent agreement when compared with experimental results and analytical solutions.

The more widespread use of analytically solvable benchmark tests for DEM and FEM/DEM codes is recommended.

Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are non‐trivial. Many molecular dynamics and non‐deformable discrete element applications employ an explicit integration for resolving orientation, often involving products of matrices, which have well‐known drawbacks. The purpose of this paper is to investigate commonly used algorithms for resolving rotational motion and describe the application of quaternion‐based approaches to discrete element method simulations.

Existing algorithms are compared against a quaternion‐based reparameterization of both the central difference algorithm and the approach of Munjiza et al. for finite/discrete element modeling (FEM/DEM) applications for the case of torque‐free precession.

The resultant algorithms provide not only guaranteed orthonormality of the resulting rotation but also allow assumptions of small‐angle rotation to be relaxed and the use of a more accurate Taylor expansion instead.

The approaches described in this paper balance ease of implementation within existing explicit codes with computational efficiency and accuracy appropriate to the order of error in many discrete element method simulations.

A critical step toward an efficient contact detection algorithm is to localize the contact search to the immediate neighborhood of each particle. In particular, cell‐based algorithms are simple and require O(N) computations but become inefficient when the particles are not roughly the same diameter. The purpose of this paper is to describe a hierarchical search method with the simplicity and efficiency of the neighbor search algorithm but which is insensitive to size gradation.

In this method, particles are allocated to cells based on their location and size within a nested hierarchical cell space. Contact searches are limited to neighboring particles of equal size within their own hierarchy and occasionally with particles of larger size when no contacts are found within their own hierarchy.

The method is shown to be effective for the most severe case of highly segregated particle distributions in which a large particle is surrounded by particles of much smaller size.

This paper is of value in concentrating on particular issues in implementing the hierarchical contact detection algorithm in a parallel computing environment using message‐passing interface.

The purpose of this paper is to show how particle scale simulation of industrial particle flows using DEM (discrete element method) offers the opportunity for better understanding of the flow dynamics leading to improvements in equipment design and operation.

The paper explores the breadth of industrial applications that are now possible with a series of case studies.

The paper finds that the inclusion of cohesion, coupling to other physics such fluids, and its use in bubbly and reacting flows are becoming increasingly viable. Challenges remain in developing models that balance the depth of the physics with the computational expense that is affordable and in the development of measurement and characterization processes to provide this expanding array of input data required. Steadily increasing computer power has seen model sizes grow from thousands of particles to many millions over the last decade, which steadily increases the range of applications that can be modelled and the complexity of the physics that can be well represented.

The paper shows how better understanding of the flow dynamics leading to improvements in equipment design and operation can potentially lead to large increases in equipment and process efficiency, throughput and/or product quality. Industrial applications can be characterised as large, involving complex particulate behaviour in typically complex geometries. The critical importance of particle shape on the behaviour of granular systems is demonstrated. Shape needs to be adequately represented in order to obtain quantitative predictive accuracy for these systems.

The purpose of this paper is to present a 2D combined finite‐discrete element method (FEM‐DEM) to model the multi‐fracture of beam structures and an application of the method to an ice‐structure interaction problem.

In the method, elastic beams and their fracture are modelled according to FEM by using nonlinear Timoshenko beam elements and cohesive crack model. Additionally, the beam elements are used to tie the discrete elements together. The contact forces between the colliding beams are calculated by using the DEM.

Three numerical examples are given to verify the method. Further, the method is applied to model the failure process of a floating ice beam against an inclined structure. Based on the comparison of the experiments and the simulation, a good agreement between the results is observed.

In the context of combined FEM‐DEM, the two novel features presented in this paper are: the use of Timoshenko finite element beams with damping to calculate internal forces and to combine the discrete elements; and the bending failure by the cohesive crack approach while simultaneously keeping track of the position of the neutral axis of the beam.

The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned.

The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established.

Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined.

This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed.

The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.

The purpose of this paper is to present a simple non‐symmetric shape, the poly‐ellipsoid, to describe particles in discrete element simulations that incur a computational cost similar to ellipsoidal particles.

Particle shapes are derived from joining octants of eight ellipsoids, each having different aspect ratios, across their respective principal planes to produce a compound surface that is continuous in both surface coordinate and normal direction. Because each octant of the poly‐ellipsoid is described as an ellipsoid, the mathematical representation of the particle shape can be in the form of either an implicit function or as parametric equations.

The particle surface is defined by six parameters (vs the 24 parameters required to define the eight component ellipsoids) owing to dependencies among parameters that must be imposed to create continuous intersections. Despite the complexity of the particle shapes, the particle mass, centroid and moment of inertia tensor can all be computed in closed form.

The particle can be implemented in any contact algorithm designed for ellipsoids with minor modifications to determine in which pair of octants the potential contact occurs.

The poly‐ellipsoid particle is a computational device to represent non‐spherical particles in DEM models.

The purpose of this paper is to present large‐scale parallel direct numerical simulations of granular flow, using a novel, portable software program for discrete element method (DEM) simulations.

Since particle methods provide a unifying framework for both discrete and continuous systems, the program is based on the parallel particle mesh (PPM) library, which has already been demonstrated to provide transparent parallelization and state‐of‐the‐art parallel efficiency using particle methods for continuous systems.

By adapting PPM to discrete systems, results are reported from three‐dimensional simulations of a sand avalanche down an inclined plane.

The paper demonstrates the parallel performance and scalability of the new simulation program using up to 122 million particles on 192 processors, employing adaptive domain decomposition and load balancing techniques.

The purpose of this paper is to present a new method for the detection and resolution of the contact point between two ellipsoids. Numerical simulations of ellipsoidal particles in a rotary cylinder are also presented.

An algebraic condition is developed for the internal contact between two ellipsoids and an efficient contact detection algorithm for overlapping ellipsoids is implemented.

This method was found to have the advantages of effectiveness and speed in the detection and resolution of the contact point.

The dynamics of granular materials are of great importance in many industries dealing with powders and grains, such as pharmaceutical, chemical, and food industries. The main difficulty of such simulations is the excessive CPU time required for a large number of particles. In the discrete element method, contact detection between grains is the most expensive step in solving a nonlinear system for determination of the contact point, the normal vector and the overlap distance between ellipsoids. The numerical behavior and the optimization of the new algorithm presented in this paper are important also.