基于球形颗粒几何排列的离散元试样高效生成方法

Construction approach of DEM samples with high efficiency based on geometrical packing of spherical particles

在球体离散元数值模拟中,颗粒的初始排列状态是影响计算效率和计算结果的重要环节。本文采用前进面几何构造算法,提出了一种基于网格搜索的球形颗粒随机排列高效算法。通过求解空间三边方程,满足了粒径设置的任意大小的颗粒依次置入前进面的外侧,并与构成前进面的三个颗粒相互接触。为获得高体积分数的颗粒簇,该算法允许颗粒改变其粒径大小。采用颗粒网格化方法可以简化前进面的搜索,并由此提高排列效率。通过计算平均配位数、体积分数和二阶结构张量的特征值,对不同粒径比下得到的立方体试样进行了分析,得到试样配位数及体积分数均随着粒径比的增大而增大,且得到的试样为各向同性。此外,空间网格的大小和初始颗粒的生成点对随机排列的效率均会产生显著的影响。最后,对非规则铁路道砟进行了精细构造及压碎模拟,发现DEM模拟得到的应力-应变曲线与试验结果基本吻合,验证了该算法得到的颗粒试样在模拟道砟裂纹起裂、扩展等过程的有效性。

In the numerical simulation of spherical discrete element method(DEM),the computational efficiency and precision is affected by the initial construction of particles.Using the advancing front approach,a random packing algorithm with high efficiency based on the spatial gridding is proposed.New particles with random sizes are sequentially inserted into a predefined void space to make contact with at least other three existing neighboring particles by analytically solving the tri-lateration equations.In this proposed algorithm,the particles can be arranged with random sizes to obtain a low-porosity particle samples.To improve the efficiency of packing algorithm,a feasible measure of the spatial gridding is proposed to simplify the detection of the advancing fronts and to improve the computational efficiency.When the generated packing structures are filled with spherical particles,the physical properties,including the average coordination number,the solid fraction,the second-order fabric tensor,are analyzed with different radius ratios.With this packing algorithm,the sphere-filled samples are isotropic,and both of the coordination number and the solid fraction increase with the increase of radius ratio.Moreover,the grid size and the initial particle packing point can also significantly influence the generation efficiency.Finally,the railway ballast particle is constructed with this proposed algorithm to simulate the breakage process under compression with DEM.Basically,the stress-strain curve of DEM simulation matches well with the experimental results,and it verifies the effectiveness of the generation and evolution process of crack in ballast particle.