The Double Hierarchy Method. A parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM

Abstract

In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027-1032) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.

Pulse fracture simulation in shale rock reservoirs: DEM and FEM–DEM approaches

“…The discrete element method (DEM) is an alternative and efficient numerical technique to reproduce multifracture situations in a solid. The simulation of the cracking response of concrete and geomaterials have been extensively treated in the last years using the DEM [5,8,9,13,14,17,18,20,23,24,26,27], or a combination of DEM and FEM procedures [11,18,19,24,25,28].…”

Influence of DE-cluster refinement on numerical analysis of rockfall experiments

“…The general coupling of the two participating methods (DEM, FEM) was discussed in detail in recent publications such as [5][6][7]15,21]. In particular, [5][6][7] describe the possibility to apply the aforementioned coupling to analyse rockfall events modelling the interaction of the rock with the ground.…”

“…For the present work three variants are of particular interest (described in [21]), where d e is used to express the smallest distance to the line element in contact. The geometric contact conditions are stated in Table 1.…”

Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

“…The coefficient µ represents the friction coefficient (usually that of Coulomb). In this work, the contact between DE particles was computed with the classical Hertz-Mindlin contact model [10], while that between DE particles and planar boundaries was considered with the Double Hierarchy Method (H 2 ) [38].…”