SONG Lai-zhong, LI Yao-hui. Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials[J]. Applied Mathematics and Mechanics, 2015, 36(2): 220-232. doi: 10.3879/j.issn.1000-0887.2015.02.011
 Citation: SONG Lai-zhong, LI Yao-hui. Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials[J]. Applied Mathematics and Mechanics, 2015, 36(2): 220-232.

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

##### doi: 10.3879/j.issn.1000-0887.2015.02.011
Funds:  The National Natural Science Foundation of China（General Program)(11171181)
• Rev Recd Date: 2014-11-10
• Publish Date: 2015-02-15
• 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.
•  [1] 李友云, 何长洲, 崔俊芝, 龙述尧. 大量椭球颗粒随机分布三维区域的模拟及其四面体网格快速生成算法[J]. 计算力学学报, 2008,25(3): 319-325.(LI You-yun, HE Chang-zhou, CUI Jun-zhi, LONG Shu-yao. Numerical simulation on three-dimensional domains with large numbers of rains randomly distributed and fast algorithm to generate tetrahedron meshes[J]. Chinese Journal of Computational Mechanics,2008,25(3): 319-325.(in Chinese)) [2] YU Yan, CUI Jun-zhi, HAN Fei. An effective computer generation method for the composites with random distribution of large numbers of heterogeneous grains[J]. Composites Science Technology,2008,68(12): 2543-2550. [3] Zohdi T I. Computational optimization of the vortex manufacturing of advanced materials[J]. Computer Methods in Applied Mechanics and Engineering,2001,190(46/47): 6231-6256. [4] 刘光廷, 高政国. 三维凸型混凝土骨料随机投放算法[J]. 清华大学学报(自然科学版), 2003,43(8):1120-1123.(LIU Guang-ting, GAO Zheng-guo. Random 3-D aggregate structure for concrete[J]. J Tsinghua Univ(Sci & Technol),2003,43(8):1120-1123.(in Chinese)) [5] 孙立国, 杜成斌, 戴春霞. 大体积混凝土随机骨料数值模拟[J]. 河海大学学报(自然科学版), 2005,33(3):291-295.(SUN Li-guo, DU Cheng-bin, DAI Chun-xia. Numerical simulation of random aggregate model for mass concrete[J]. Journal of Hohai University(Natural Sciences),2005,33(3): 291-295.(in Chinese)） [6] 杜成斌, 孙立国. 任意形状混凝土骨料的数值模拟及其应用[J]. 水利学报, 2006,37(6): 662-667, 673.(DU Cheng-bin, SUN Li-guo. Numerical simulation of concrete aggregates with arbitrary shapes and its application[J]. Journal of Hydraulic Engineering,2006,37(6): 662-667, 673.(in Chinese)) [7] 方秦, 张锦华, 还毅, 张亚栋. 全级配混凝土三维细观模型的建模方法研究[J]. 工程力学, 2013,30(1): 14-20, 30.(FANG Qin, ZHANG Jin-hua, HUAN Yi, ZHANG Ya-dong. The investigation into three-dimension mesoscale modeling of fully-graded concrete[J]. Engineering Mechanics,2013,30(1): 14-20, 30.(in Chinese)) [8] 徐伟芳, 黄西成, 郝志明, 汪洋. “数值混凝土”建模研究[J]. 固体力学学报, 2013,33(专辑): 253-261.(XU Wei-fang, HUANG Xi-cheng, HAO Zhi-ming, WANG Yang. The study of the numerical concrete model[J]. Chinese Journal of Solid Mechanics,2013,33(S): 253-261.(in Chinese)) [9] SONG Lai-zhong, SONG Bi-wei. Approximations to a quadratic programming with quadratic constraints and their applications[J]. Journal of Information & Computational Science,2012,9(11): 3045-3054. [10] 宋来忠, 彭刚, 姜袁. 混凝土三维随机参数化骨料模型[J]. 水利学报, 2012,42(1):91-98.(SONG Lai-zhong, PENG Gang, JIANG Yuan. A three-dimensional model for concrete with random parameterized irregular aggregate[J]. Journal of Hydraulic Engineering,2012,42(1): 91-98.(in Chinese)) [11] Bazant Z P. Crack band theory for fracture of concrete[J]. Material and Structures,1983,93(16): 155-177. [12] 马怀发, 芈书贞, 陈厚群. 一种混凝土随机凸多边形骨料模型生成方法[J]. 中国水利水电科学研究院学报, 2006,4(3): 196-201.(MA Huai-fa, MI Shu-zhen, CHEN Hou-qun. A generating approach of random convex polygon aggregate model[J]. Journal of China Institute of Water Resources and Hydropower Research,2006,4(3): 196-201.(in Chinese)) [13] 赵晶晶, 章青, 黄丹, 沈峰. 低密度和高密度水化硅酸钙的纳米压痕数值模拟[J]. 应用数学和力学, 2013,34(11):1150-1156.(ZHAO Jing-jing, ZHANG Qing, HUANG Dan, SHEN Feng. Numerical simulation of nanoindentation for the LD and HD calcium silicate hydrates[J]. Applied Mathematics and Mechanics,2013,34(11): 1150-1156.(in Chinese)) [14] 赵金凤, 严颖, 季顺迎. 基于离散元模型的土石混合体直剪试验分析[J]. 固体力学学报, 2014,35(2): 124-134.(ZHAO Jin-feng, YAN Yin, JI Shun-ying. Analysis of direct shear test of soil-rock mixture[J]. Chinese Journal of Solid Mechanics,2014,35(2): 124-134.(in Chinese)) [15] YAN Ying, JI Shun-ying. Discrete element modeling of direct shear test for a granular material[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,34: 978-990. [16] 唐世斌, 唐春安, 梁正召, 张亚芳. 热传导与热应力的细观特性及热开裂过程研究[J]. 土木工程学报, 2012,45(2): 12-19.(TANG Shi-bin, TANG Chun-an, LIANG Zheng-zhao, ZHANG Ya-fang. Study of thermal conduction and thermal stress of concrete at mesoscopic level and its thermal cracking processes[J]. China Civil Engineering Journal,2012,45(2): 12-19.(in Chinese)）

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沈阳化工大学材料科学与工程学院 沈阳 110142