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Computer Simulation of Random Sphere Packing in an Arbitrarily Shaped Container

S.X. Li1, L. Zhao1, Y.W. Liu2
State Key Lab for Turbulence and Complex System Study, College of Engineering, Peking University, Beijing, China. E-mail: (S.X. Li)
Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

Computers, Materials & Continua 2008, 7(2), 109-118.


Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.


sphere packing, random packing, computer simulation, relaxation algorithm, containers.

Cite This Article

S. . Li, L. . Zhao and Y. . Liu, "Computer simulation of random sphere packing in an arbitrarily shaped container," Computers, Materials & Continua, vol. 7, no.2, pp. 109–118, 2008.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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