Summary
This paper presents a new sphere packing algorithm for generating granular structures in either two or three dimensions. Such a structure is often modeled by a parallelepiped containing spherical balls in three dimensions or by a rectangle filled with disks in two dimensions. The grains (spherical balls or disks) are separated by interfaces with specific thicknesses, called grain boundaries, and their size correspond to a size distribution experimentally obtained. The geometrical modeling of such a structure, which consists in determining the repartition of the set of disjoint grains according to the above specifications, can then be considered as the classic sphere packing problem. The proposed method is a constructive algorithm based on an advancing-front approach, which is well known in a different context, namely mesh generation. Since the use of the advancing-front approach leads to empty areas near front collisions, a point relocation algorithm, using weighted Delaunay triangulation, is then introduced to balance the local density on the whole structure. Moreover, we propose a method to transform spherical balls (disks) into polyhedral (polygonal) cells similar to the real grain shape. Numerical 2D and 3D examples are provided to illustrate the capability and the efficiency of our approach. The algorithms and techniques presented here can find applications to generate aggregates in all fields concerned by the granular structures such as metallurgy, ceramics, soil science, cements, biomechanics, etc.
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Benabbou, A., Borouchaki, H., Laug, P., Lu, J.: International Journal for Numerical Methods in Engineering (to appear, 2008)
Lu, K., Lu, J.: Materials Science and Engineering A 375, 38–45 (2004)
Kumar, K.S., Van Swygenhoven, H., Suresh, S.: Acta Materialia 51(19), 5743–5774 (2003)
Jodrey, W.S., Tory, E.M.: Phys Rev A 32, 4 (1985)
Lubachevsky, B.D., Stillinger, F.H.: Journal of Statistical Physics 60(5-6), 561–583 (1990)
Lin, X., Ng, T.: Geotechnique 47(2), 319–329 (1997)
Jiang, M.J., Konrad, J.M., Leroueil, S.: Computers and Geotechnics 30(7), 579–597 (2003)
Stillinger, F.H., Dimarzio, E.A., Kornegay, R.L.: J. Chem. Phys 40, 1564 (1964)
Visscher, W.M., Bolsterli, M.: Nature 239 (October 1972)
Bagi, K.: Mechanics of Materials 16(1-2), 101–110 (1993)
Han, K., Feng, Y.T., Owen, D.R.J.: Powder Technology 155, 33–41 (2005)
Bennett, C.H.: J Appl Phys 43, 6 (1972)
Feng, Y.T., Han, K., Owen, D.R.J.: International Journal for Numerical Methods in Engineering 56(5), 699–713 (2002)
Löhner, R., Onate, E.: International Journal for Numerical Methods in Engineering 61, 1977–1991 (2004)
Bagi, K.: Granular Matter 7, 31–43 (2005)
Stoyan, D.: Models of random systems of non-intersecting spheres. In: Prague Stochastics, JCMF 1998, pp. 543–547 (1998)
Häggström, O., Meester, R.: Random Struct. Algor. 9, 295–315 (1996)
Evans, J.W.: Rev Mod Phys 65, 1281–1304 (1993)
Cui, L., O’Sullivan, C.: Granular Matter 5(3), 135–145 (2003)
George, J.A.: Computer implementation of the finite element method, PhD thesis, Stanford university (1971)
Lo, S.H.: International Journal for Numerical Methods in Engineering 21, 1403–1426 (1985)
Delaunay, B.: Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 793–800 (1934)
George, P.L., Borouchaki, H.: Delaunay Triangulation and Meshing, Hermes, Paris (1998)
Yamakawa, S., Shimada, K.: International Journal for Numerical Methods in Engineering 57(13), 1923–1942 (2003)
Tao, N.R., Wang, Z.B., Tong, W.P., Sui, M.L., Lu, J., Lu, K.: Acta Materialia 50(18), 4603–4616 (2002)
Benabbou, A., Borouchaki, H., Laug, P., Lu, J.: Rapport de recherche Inria (6414) (2008), http://hal.inria.fr/inria-00203375/fr/
Laug, P., Borouchaki, H., Benabbou, A., Lu, J.: C. R. Mecanique 336, 506–511 (2008)
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Benabbou, A., Borouchaki, H., Laug, P., Lu, J. (2008). Sphere Packing and Applications to Granular Structure Modeling. In: Garimella, R.V. (eds) Proceedings of the 17th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87921-3_1
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DOI: https://doi.org/10.1007/978-3-540-87921-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87920-6
Online ISBN: 978-3-540-87921-3
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