复杂凸多面体随机紧密堆积组构性能的数值研究:形状参数的影响

Numerical study on fabric properties of random dense packing structures of complex convex polyhedrons:Effects of shape parameters

颗粒材料的宏观物理力学性能依赖于颗粒堆积体系的细观组构性能,研究颗粒堆积体系的组构性能有重要意义。然而,当前对颗粒堆积体系组构性能的研究集中于球、椭球和正则多面体等规则几何体,还未有对复杂凸多面体颗粒堆积体系组构性能的系统研究。本文基于旋转椭球面黄金螺旋网格构造了一组复杂凸多面体颗粒模型(Poly_(κ-n)_(gs)),然后基于松弛算法获得了Poly_(κ-n)_(gs)多面体的随机紧密堆积结构,最后研究了几何形状参数对Poly_(κ-n)_(gs)多面体随机紧密堆积体系组构性能的影响。结果表明,长径比κ和顶点数量ngs均对堆积体系的组构性能有影响,κ是主要影响因素。Poly_(κ-n)_(gs)多面体随机紧密堆积结构中颗粒的位置分布均匀,长径比κ越接近1,顶点数量ngs越大时,堆积结构表现出更强的位置长程有序性;颗粒方向分布不均匀,长径比κ越远离1,不均匀程度越高;最高堆积分数随长径比κ的增大先增大后减小,在κ=1时达到峰值;配位数分布服从高斯分布,平均配位数随形状参数的变化和堆积分数不同;面-面接触数量随长径比κ的增大先增大后减小,和堆积分数变化规律一致。本研究为复杂凸多面体颗粒的随机紧密堆积提供了数值模拟方案,得出的结论对含有凸多面体颗粒材料的设计和性能优化具有参考意义。

The macroscopic physical and mechanical properties of granular materials depend on the mesoscopic grain fabric properties of packingstructures of particles.It is of great significance to study the grain fabric properties of packingstructures of particles.However,current researches are mostly focused on regular geometric objects such as spheres,ellipsoids and regular polyhedrons,and there is no systematic study on the grain fabric properties of packingstructures of complex convex polyhedrons.In this paper,a set of complex convex polyhedron particle models(Poly_(κ-n)_(gs))were firstly generated based on spheroidal golden spiral lattice,the relaxation algorithm was then developed to obtain the random dense packingstructures,and finally the effects of shape parameters on the fabric properties of the random dense packingstructures of Poly_(κ-n)_(gs) were discussed.The results show the aspect ratioκand the number of vertices ngs both affect the fabric properties,whileκis the main factor.The location distribution of particles in the random dense packingstructures is homogeneous while the orientation distribution is not.The closer the aspect ratioκis to 1,and the larger the number of vertices ngs is,the stronger the spatial long-range order is in the packing.The farther the aspect ratioκis away from 1,the higher the heterogeneity of the orientation distribution is.The maximum packing density of Poly_(κ-n)_(gs) particles first increases and then decreases with the increase of the aspect ratioκ,and the peak is reached whenκ=1.The probability distribution of coordination number obeys Gaussian distribution and the variation of average coordination number with shape parameters is not consistent with the packing fraction.The number ratio of face to face(f-f)contact first increases and then decreases with the increase of aspect ratioκ,which is consistent with the variation of packing density.This research establishes a numerical framework for the simulation of dense packing of complex convex polyhedrons,and the conclusions provide references for the design and performance optimization of granular materials with convex polyhedrons.