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We present an algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity. The algorithm is designed for use in discrete element analysis of granular and multibody systems exhibiting discontinuous behaviour. Contact detection usually consists of a spatial sorting phase and a contact resolution phase. The spatial sorting phase seeks to avoid an all‐to‐all body comparison by culling the number of objects which are potential contactors of a given object. The contact resolution phase resolves the details of the contact between two given objects. The algorithm presented here (called DFR) addresses the contact resolution phase and is applicable to convex geometries and to a restricted set of concave geometries. Examination of the algorithm establishes an upper bound linear computational complexity, of order O(N), with respect to the number of points (N) used to define the object boundary. The DFR algorithm is combined with a modified heapsort algorithm for spatial sorting of M bodies which has complexity O(M log M) and is applied to a baseline granular simulation problem to test its efficiency.

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.

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.

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.

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.

The purpose of this paper is to find a convenient contact detection algorithm in order to apply in distinct element simulation.

Taking the most computation effort, the performance of the contact detection algorithm highly affects the running time. The algorithms investigated in this study consist of Incremental Sort-and-Update (ISU) and Double-Ended Spatial Sorting (DESS). These algorithms are based on bounding boxes, which makes the algorithm independent of blocks shapes. ISU and DESS algorithms contain sorting and updating phases. To compare the algorithms, they were implemented in identical examples of rock engineering problems with varying parameters.

The results show that the ISU algorithm gives lower running time and shows better performance when blocks are unevenly distributed in both axes. The conventional ISU merges the sorting and updating phases in its naïve implementation. In this paper, a new computational technique is proposed based on parallelization in order to effectively improve the ISU algorithm and decrease the running time of numerical analysis in large-scale rock mass projects.

In this approach, the sorting and updating phases are separated by minor changes in the algorithm. This tends to a minimal overhead of running time and a little extra memory usage and then the parallelization of phases can be applied. On the other hand, the time consumed by the updating phase of ISU algorithm is about 30 percent of the total time, which makes the parallelization justifiable. Here, according to the results for the large-scale problems, this improved technique can increase the performance of the ISU algorithm up to 20 percent.

This paper aims to construct smooth poly-ellipsoid shapes from synchrotron microcomputed tomography (SMT) images on sand and to develop a new discrete element method (DEM) contact detection algorithm.

Voxelated images generated by SMT on Colorado Mason sand are processed to construct smooth poly-ellipsoidal particle approximations. For DEM contact detection, cuboidal shape approximations to the poly-ellipsoids are used to speed up contact detection.

The poly-ellipsoid particle shape approximation to Colorado Mason sand grains is better than a simpler ellipsoidal approximation. The new DEM contact algorithm leads to significant speedup and accuracy is maintained.

The paper limits particle shape approximation to smooth poly-ellipsoids.

Poly-ellipsoids provide asymmetry of particle shapes as compared to ellipsoids, thus allowing closer representation of real sand grain shapes that may be angular and unsymmetric. When incorporated in a DEM for computation, the poly-ellipsoids allow better representation of particle rolling, sliding and interlocking phenomena.

Method to construct poly-ellipsoid particle shapes from SMT data on real sands and computationally efficient DEM contact detection algorithm for poly-ellipsoids.

The efficiency of a discrete element implementation relies on several factors, including the particle representation, neighbor‐sorting algorithm, contact resolution, and force generation. The focus of this paper is on the four‐arc approximation for an ellipsoid – a geometrical representation useful in simulations of large numbers of smoothly shaped particles. A new contact resolution algorithm based on the four‐arc approximation is presented, which takes advantage of the properties of the geometry to provide favorable empirical convergence properties compared with the method proposed earlier. Special attention is given to the software implementation of the algorithm, and a discussion of the computational efficiency of the algorithm is provided.

Particles in granular matter can have very different and irregular shapes. The computational treatment of nonspherical objects is a major difficulty in the simulation of granular flows. In this paper, two basic strategies for contact resolution between objects described by level surfaces are presented and analyzed. They are based on the iterative solution of systems of nonlinear equations. The major difficulties are pinpointed and necessary steps toward a generic algorithm are proposed. A test case of colliding cardioids in two dimensions is used to demonstrate the algorithms and illustrate common pitfalls.

Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.

In this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.

Numerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.

The equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.

A new spatial reasoning algorithm that can be used in multi‐body contact detection is presented. The algorithm achieves the partitioning of N bodies of arbitrary shape and size into N lists in order O(N) operations, where each list consists of bodies spatially near to the target object. The algorithm has been tested for objects of arbitrary shape and size, in two and three dimensions. However, we believe that it can be extended to dimensions of four and higher. The algorithm (CGRID) is a binning algorithm that extends traditional binning algorithms so that the arbitrary sizes and shapes can be handled efficiently. The algorithm has applications in discrete element, finite element, molecular dynamics, meshless methods, and lattice‐Boltzmann codes and also in domains such as path planning, target acquisition and general clustering problems.

This paper presents a general procedure for solving 3D contact problems with implicit finite element codes. Emphasis is put on generality and robustness. Bodies in contact can be 3D solids or shells. Material and geometric nonlinearities can be dealt with (elasto‐plasticity, elasto‐visco‐plasticity, nonlinear elasticity, large displacements, strains and rotations). Different kinds of interaction are supported (tied, slip, friction). Advantage is taken of the solution history in order to improve the efficiency of the search algorithm. Numerical examples illustrate the general character of the proposed algorithm.

Contact interaction and contact detection (CD) remain key components of any discontinua simulations. The methods of discontinua include combined finite-discrete element method (FDEM), discrete element method, molecular dynamics, etc. In recent years, a number of CD algorithms have been developed, such as Munjiza–Rougier (MR), Munjiza–Rougier–Schiava (MR-S), Munjiza-No Binary Search (NBS), Balanced Binary Tree Schiava (BBTS), 3D Discontinuous Deformation Analysis and many others. This work aims to conduct a numerical comparison of certain algorithms often used in FDEM for bodies of the same size. These include MR, MR-S, NBS and BBTS algorithms.

Computational simulations were used in this work.

In discrete element simulations where particles are introduced randomly or in which the relative position between particles is constantly changing, the MR and MR-S algorithms present an advantage in terms of CD times.

This paper presents a detailed comparison between CD algorithms. The comparisons are performed for problem cases with different lattices and distributions of particles in discrete element simulations. The comparison includes algorithms that have not been evaluated between them. Also, two new algorithms are presented in the paper, MR-S and BBTS.