颗粒增强复合材料的几何模型数值模拟方法研究

为了在细观层次上模拟混凝土和土石混合体等颗粒增强复合材料，假设颗粒为凸多面体.首先研究由随机八面体随机变形得到任意凸多面体及其参数方程的方法，然后研究凸多面体内部与外部的判定条件、点到多面体的距离和两多面体之间距离的计算方法，从而得到了一个生成具有大量多面体随机分布区域的方法.为了提高模拟区域中多面体的含量，还给出了下降算法.实验表明:可以按二级配生成多面体含量达35%（体积比）的模拟区域，为从细观层次研究混凝土、土石混合体等颗粒增强复合材料，提供了创建几何模型的方法.

Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials

To simulate the meso-level structures of multiphase particle-reinforced composite materials, such as concrete and soil-rock mixture, the corresponding reinforcing particles were assumed as convex polyhedrons. Firstly, the method was developed for obtaining an arbitrary polyhedron as well as its parametric equation through transformation of a randomly chosen octahedron. Secondly, the conditions for determining whether a spatial point is in the interior or exterior of a given convex polyhedron were presented. Moreover, the procedure for calculating the distance between a spatial point and a convex polyhedron or the distance between 2 polyhedrons was established, based on which the algorithm to generate a region with abundant randomly distributed convex polyhedrons was proposed. In order to increase the content of the polyhedrons in the region to be simulated, the descent algorithm was presented. The numerical results show that, for the 2-graded distribution, the content of the generated polyhedrons in the simulated region reaches 35% (volume ratio), with higher content realizable through combination of this method and those previously published. The work provides an effective way to build realistic meso-level geometric models for particle-reinforced composite materials.