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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 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.

This paper aims to present performance comparison between O(n²) and O(n) neighbor search algorithms, studies their effects for different particle shape complexity and computational granularity (CG) and investigates the influence on superlinear speedup of 3D discrete element method (DEM) for complex-shaped particles. In particular, it aims to answer the question: O(n²) or O(n) neighbor search algorithm, which performs better in parallel 3D DEM computational practice?

The O(n²) and O(n) neighbor search algorithms are carefully implemented in the code paraEllip3d, which is executed on the Department of Defense supercomputers across five orders of magnitude of simulation scale (2,500; 12,000; 150,000; 1 million and 10 million particles) to evaluate and compare the performance, using both strong and weak scaling measurements.

The more complex the particle shapes (from sphere to ellipsoid to poly-ellipsoid), the smaller the neighbor search fraction (NSF); and the lower is the CG, the smaller is the NSF. In both serial and parallel computing of complex-shaped 3D DEM, the O(n²) algorithm is inefficient at coarse CG; however, it executes faster than O(n) algorithm at fine CGs that are mostly used in computational practice to achieve the best performance. This means that O(n²) algorithm outperforms O(n) in parallel 3D DEM generally.

Taking for granted that O(n) outperforms O(n²) unconditionally, complex-shaped 3D DEM is a misconception commonly encountered in the computational engineering and science literature.

The paper clarifies that performance of O(n²) and O(n) neighbor search algorithms for complex-shaped 3D DEM is affected by particle shape complexity and CG. In particular, the O(n²) algorithm outperforms the O(n) algorithm in large-scale parallel 3D DEM simulations generally, even though this outperformance is counterintuitive.

The purpose of this paper is to extend complex-shaped discrete element method simulations from a few thousand particles to millions of particles by using parallel computing on department of defense (DoD) supercomputers and to study the mechanical response of particle assemblies composed of a large number of particles in engineering practice and laboratory tests.

Parallel algorithm is designed and implemented with advanced features such as link-block, border layer and migration layer, adaptive compute gridding technique and message passing interface (MPI) transmission of C++ objects and pointers, for high performance optimization; performance analyses are conducted across five orders of magnitude of simulation scale on multiple DoD supercomputers; and three full-scale simulations of sand pluviation, constrained collapse and particle shape effect are carried out to study mechanical response of particle assemblies.

The parallel algorithm and implementation exhibit high speedup and excellent scalability, communication time is a decreasing function of the number of compute nodes and optimal computational granularity for each simulation scale is given. Nearly 50 per cent of wall clock time is spent on rebound phenomenon at the top of particle assembly in dynamic simulation of sand gravitational pluviation. Numerous particles are necessary to capture the pattern and shape of particle assembly in collapse tests; preliminary comparison between sphere assembly and ellipsoid assembly indicates a significant influence of particle shape on kinematic, kinetic and static behavior of particle assemblies.

The high-performance parallel code enables the simulation of a wide range of dynamic and static laboratory and field tests in engineering applications that involve a large number of granular and geotechnical material grains, such as sand pluviation process, buried explosion in various soils, earth penetrator interaction with soil, influence of grain size, shape and gradation on packing density and shear strength and mechanical behavior under different gravity environments such as on the Moon and Mars.

The purpose of this paper is to present a new and efficient technique for discrete element modelling using non-convex polyhedral grain shapes.

The efficiency of the technique follows from the use of grains that are dilated versions of the basic polyhedral grain shapes. Dilation of an arbitrary polyhedral grain is accomplished by placing the center of a sphere of fixed radius at every point on the surface. The dilated vertices become sphere segments and the edges become cylinder segments. The sharpness of the vertices and edges can be adjusted by varying the dilation radius. Contacts between two dilated polyhedral grains can be grouped into three categories; vertex on surface, vertex on edge, and edge on edge, or in the grammar of the model, sphere on polygonal surface, sphere on cylinder, and cylinder on cylinder. Simple, closed-form solutions exist for each of these cases.

The speed of the proposed polyhedral discrete element model is compared to similar models using spherical and ellipsoidal grains. The polyhedral code is found to run about 40 percent as fast as an equivalent code using spherical grains and about 80 percent as fast as an equivalent code using ellipsoidal grains. Finally, several applications of the polyhedral model are illustrated.

Few examples of discrete element modeling studies in the literature use polyhedral grains. This dearth is because of the perceived complexity of the polyhedral coding challenges and the slow speed of the codes compared to codes for other grain shapes. This paper presents a much simpler approach to discrete element modeling using polyhedral grain shapes.