Discrete element method for 3D simulations of mechanical systems of non-spherical granular materials 非球形粒子を用いた粉粒体力学三次元シミュレーションのための離散要素法
Discrete element method for 3D simulations of mechanical systems of non-spherical granular materials
Granular materials are ubiquitous in nature and technology. Nevertheless, no macroscopic equation for granular materials is known. The discrete element method (DEM) has been widely used to simulate complex behavior of granular materials without constitutive laws. It has become increasingly clear that the dynamics of non-spherical granular materials is governed essentially by the deviations of the particle shape from ideal spheres. Up to now, among most of the simulations for round particles, a few DEM code modeled the particles with polyhedral shape while the contact force by the “penetration depth” which essentially is the same as for round particles. None of those methods so far can investigate “history effect” of granular materials (construction history dependent phenomena) for three dimensional cases, nor can they reproduced realistically high angles of repose on flat surface for practical friction parameters. The main objective of the study is to develop a DEM code for granular materials, using polyhedral particle shape, with a contact force model which takes into account the whole geometry of the “overlap polyhedron” between non-deformed polyhedral particles. The contact force point is defined as the center of mass of the overlap polyhedron and the normal force direction as the average of the area-weighted normals of the contact triangles formed by the centroid of the overlap polyhedron and the generated vertices (the intersection points of two polyhedra). The volume of the overlap polyhedron is used as a measure for the elastic force and its changes for the damping force in normal direction. The characteristic length is introduced in the contact force model, with which the continuum-mechanical sound velocity can be reproduced in DEM simulation of a spacefilling packing of cubic blocks. The two-dimensional Cundall-Strack model is generalized for three dimensions as the approximation for friction. A systematic approach for overlap computation is introduced and implemented to obtain the overlap polyhedron (its center of mass, volume and the normal of the contact area). Several methods and algorithms are presented with respect to the vertex and the face computation, the triangle intersection computation algorithms characterized by the point-direction form and the point-normal form representation of plane, the neighboring feature algorithm for vertex computation, to obtain the overlap geometry efficiently. To further improve the efficiency, a contact detection strategy which precedes overlap computation is also applied: The determination of possible contacting particle pairs via the neighborhood algorithm by sorting the axis-aligned bounding boxes (“sort and sweep”) in three dimensions; The refinement of the contact list via bounding spheres and extremal projections of vertices along the central line of the particle pairs. Simulation results for heaps constructed on flat surface show more realistic, high angles of repose than any penetration depth based simulations with either round or polyhedral particles. As verification, consistent results of angle of repose and of density patterns have been obtained from the DEM code and the experiments for quasi-two-dimensional heaps constructed by wedge sequences. The simulation results showed clear pressure dips for the heaps constructed by wedge-sequences and pressure maxima for the heaps constructed by layered sequences. This shows that the (construction) history effect on ground pressure distribution can be resolved with our DEM method. With the polyhedral DEM code, a larger phenomenology of granular materials is accessible than with round particles or with penetration depth based force models.