Large-scale discrete element simulations, as well as a whole range of related problems, involve contact of a large number of separate bodies. In this context an e cient and robust contact detection algorithm is necessary. There has been a number of contact detection algorithms with total detection time (CPU time needed to detect all couples close to each other) proportional to N ln(N ) (where N is the total number of separate bodies) reported in recent years.In this work a contact detection algorithm with total detection time proportional to N is reported. The algorithm is termed NBS, which stands for no binary search. In other words, the proposed algorithm involves no binary search at any stage. In addition the performance of the algorithm in terms of total detection time is not in uenced by packing density, while memory requirements are insigniÿcant. The only limitation of the algorithm is its applicability to the systems comprising bodies of similar size. ? 1998 John Wiley & Sons, Ltd.

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In this paper, the Combined Finite-Discrete Element Method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both nonhomogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the corotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed. 2 seriously degrade the accuracy of the results. To overcome this problem, several approaches have been proposed, for example: smoothed finite element methods [18], nodal integration approaches [19] and composite elements [20,21]. The composite element is a good choice for FDEM especially in the cases that re-meshing is needed for the simulation of dynamic fracture propagation problems.The basic feature of a composite element is its "assemblage" which is composed of several subelements. These sub-elements are relatively independent but work together to improve accuracy of strain calculations. Camacho and Ortiz [20] described a novel triangular element in which a sixnoded triangle is constructed from four three-noded triangles with linear displacement fields in each sub-triangle and a continuous linear strain field over the assemblage. Guo et al. [21] presented a detailed analysis of several composite triangular elements based on Camacho and Ortiz's work. They also proposed an alternative composite triangle in which the volumetric strain is assumed to be constant over the whole triangle.

The problems posed by the need to consider angular shapes in order to achieve more realistic micro-mechanical models of rock particulates are introduced. A relatively simple and fast particle deposition algorithm for packing simulations is developed. The details of the algorithmic procedures for deposition of tetrahedron-shaped particles of different size and aspect ratio are outlined. Numerical results including predictions of porosity for spheres, tetrahedra, different particle size distributions, binary mixtures and tetrahedron shapes are presented. For the loose packing of spheres extrapolated to zero wall effect, the porosity obtained was 0·414. Mono-sized tetrahedron packs with wall effects for a 3·288 cm edged equilateral tetrahedron packing in a 30 × 30 × 30 cm box produced an average porosity of 0·627 with a value of 0·584 when extrapolated to zero wall effect. Binary mixtures of tetrahedra show the characteristic minimum in porosity for a size mixture. The minimum is less well defined than for spheres. Continuous size distributions of tetrahedra based on a truncated Schuhmann distribution from 0·28 to 2·8 cm edge length in a 10 × 10 × 10 cm box do not indicate that distributions with a lower uniformity will necessarily produce a minimum in porosity. For tetrahedra of constant volume the porosity increases with decreasing sphericity in tetrahedra with different aspect ratios.

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