Abstract
Numerical simulation results show that the upper bound order of random packing densities of basic 3D objects is cube (0.78) > ellipsoid (0.74) > cylinder (0.72) > spherocylinder (0.69) > tetrahedron (0.68) > cone (0.67) > sphere (0.64), while the upper bound order of ordered packing densities of basic 3D objects is cube (1.0) > cylinder and spherocylinder (0.9069) > cone (0.7854) > tetrahedron (0.7820) > ellipsoid (0.7707) > sphere (0.7405); these two orders are significantly different. The random packing densities of ellipsoid, cylinder, spherocylinder, tetrahedron and cone are closely related to their shapes. The optimal aspect ratios of these objects which give the highest packing densities are ellipsoid (axes ratio = 0.8:1:1.25), cylinder (height/diameter = 0.9), spherocylinder (height of cylinder part/diameter = 0.35), tetrahedron (regular tetrahedron) and cone (height/bottom diameter = 0.8).
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We acknowledge Professor Pu Chen (Peking University) for his earnest help and support to this work. We thank Professor S. Torquato (Princeton University, U.S.), Dr. A. Kyrylyuk (Utrecht University, Holland), Dr. Xiaodong Jia (University of Leeds, U.K.) and Dr. Haiping Zhu (University of New South Wales, Australia) for their valuable discussion and help. This work was supported by the National Natural Science Foundation of China (Grant No. 10772005) and National Basic Research Program of China (Grant No. 2007CB714603).
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Li, S., Zhao, J., Lu, P. et al. Maximum packing densities of basic 3D objects. Chin. Sci. Bull. 55, 114–119 (2010). https://doi.org/10.1007/s11434-009-0650-0
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DOI: https://doi.org/10.1007/s11434-009-0650-0