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| Titel |
Generation of Random Particle Packings for Discrete Element Models |
| VerfasserIn |
S. Abe, D. Weatherley, T. Ayton |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250064922
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| Zusammenfassung |
| An important step in the setup process of Discrete Element Model (DEM) simulations is the
generation of a suitable particle packing. There are quite a number of properties such a
granular material specimen should ideally have, such as high coordination number, isotropy,
the ability to fill arbitrary bounding volumes and the absence of locked-in stresses. An
algorithm which is able to produce specimens fulfilling these requirements is the insertion
based sphere packing algorithm originally proposed by Place and Mora, 2001 [2] and
extended in this work.
The algorithm works in two stages. First a number of “seed” spheres are inserted into
the bounding volume. In the second stage the gaps between the “seed” spheres
are filled by inserting new spheres in a way so they have D+1 (i.e. 3 in 2D, 4 in
3D) touching contacts with either other spheres or the boundaries of the enclosing
volume.
Here we present an implementation of the algorithm and a systematic statistical analysis
of the generated sphere packings. The analysis of the particle radius distribution shows that
they follow a power-law with an exponent - D (i.e. -3 for a 3D packing and -2 for 2D).
Although the algorithm intrinsically guarantees coordination numbers of at least 4 in 3D and
3 in 2D, the coordination numbers realized in the generated packings can be significantly
higher, reaching beyond 50 if the range of particle radii is sufficiently large. Even for
relatively small ranges of particle sizes (e.g. Rmin = 0.5Rmax) the maximum coordination
number may exceed 10.
The degree of isotropy of the generated sphere packing is also analysed in both 2D and
3D, by measuring the distribution of orientations of vectors joining the centres of adjacent
particles. If the range of particle sizes is small, the packing algorithm yields moderate
anisotropy approaching that expected for a face-centred cubic packing of equal-sized
particles. However, once Rmin < 0.3Rmax a very high degree of isotropy is demonstrated in
both 2D and 3D.
The analysis demonstrates that this space-filling packing algorithm fulfills many of the
requirements required to produce granular material specimens for DEM simulations. These
include a high coordination number, isotropy and the absence of lock-in stresses. The
algorithm has been implemented as a module (called gengeo[1]) for the Python[3]
scripting language and provides the capacity to fill arbitrary bounding volumes or
combinations of bounding volumes. The main disadvantage of this space-filling packing
approach is the inability to specify a priori the particle size distribution of the final
specimen.
References
[1]Â Â Â The gengeo source code is available via the ESyS-Particle software repository,
https://launchpad.net/esys-particle.
[2]   Place, D., and P. Mora (2001), A random lattice solid model for simulation of
fault zone dynamics and fracture process, in Bifurcation and Localisation Theory
for Soils and Rocks 99, edited by D. A. Mühlhaus H-B. and E. Pasternak, AA
Balkema Rotterdam/Brookfield.
[3]Â Â Â The Python Language website is http://www.python.org. |
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