几何与物理相结合的三维域颗粒堆积算法

An Algorithm for Particle Packing in 3D Space by Considering Geometric and Physical Factors

在离散元仿真和离散元与有限元耦合问题的前期准备阶段,必须快速在一个指定区域产生互不交迭的、堆积密度尽可能高的颗粒集,以模拟真实的离散状物质.文中针对三维域颗粒集的生成,提出一种几何与物理相结合的颗粒堆积移动模型.首先采用构造法在容器底部产生第一层颗粒.对于后续颗粒的移动方向,其与容器边界接触按物理学弹性碰撞理论计算;与颗粒接触按纯几何方法计算,即以连续2次接触点的法线向量的叉积向量确定新的移动方向,且使新方向有向下的趋势.该模型保证颗粒连续3次接触的目标不同,其稳定态位置快速收敛于3个支撑目标之上,从而满足颗粒静止的物理条件;颗粒间的接触检测基于容器区域规则划分的网格单元,并充分利用颗粒移动模型的特点,根据颗粒的位置和移动方向,按网格层、网格行在网格单元中寻找即将接触的颗粒.实例结果表明,最终产生颗粒集的时间与颗粒数量成线性关系,且颗粒集密度高,耗时也比较短.

In the preparation stage of the discrete element method（DEM） simulation and the coupling of the FEM and the DEM,it is essential to generate a high-density granular assembly in a relatively short time with no overlapping in a specified region to simulate practical granular material.With a combination of geometry and physics,this paper puts forward a particle moving model for packing in 3D region.The model generates the first layer particles on the bottom of the container with the constructive method.Two different methods are adopted to calculate the moving direction of the subsequent particles according to their different contacting condition.If the particle collides with the container boundary,the direction is calculated according to the physical elastic collision theory.If the particle collides with another particle,the direction is calculated with a purely geometrical method,that is,the cross product of the particle＇s two consecutive contact normal vectors determines the particle＇s next direction,and the direction is made to have a downward trend.The model ensures that the particle contacts with different objects within three consecutive contacts,and that its final stable position converges quickly on three supporting target and satisfies the physical condition of the stationary particles.The contact detection between particles is based on the regularly partitioned grid cell in the packing area.According to the position and the moving direction of the particle,the algorithm makes full use of the characteristics of the particle moving model to search for the particles to collide in the grid cells of the grid rows at different grid levels.The experiment results show that the time to create the granular particles set is linear with the particle number and this process is completed in a comparatively short time with high-density particles set.