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Full version, AVI, 24294K |
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Dynamic Triangulations for Efficient
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This research project involves using dynamic weighted Delaunay triangulations to support efficient large scale distinct element simulations of granular materials in 3D.
The Distinct Element Method (DEM) is used to perform computer simulations of highly discontinuous phenomena. DEM considers every particle in the system independently: each follows its own trajectory and interacts with the environment and other particles. One of the problems with DEM is the high computational cost associated with the localization of the interactions between the particles.
If the particles are discs (2D) or spheres (3D), an efficient collision detection method based on dynamic triangulations can be used, that reduces the number of potential collisions to O(n).
For more details, see "further reading", below.
Examples
VRML files are a good way to see the result of small 3D simulations. You can get a plug-in (Cortona for Windows or Cosmo, for SGI, Windows and Mac) to display VRML in your web browser or a stand-alone viewer (VRML for Linux).
Larger cases need more elaborate - but less interactive - tools. Most movies are in QuickTime or in AVI format for now. Both format should display fine on any platform. When both formats are available, the QuickTime version is usually better in quality but much larger in size, this is due to the tools I used to create them, but mostly to my limited knowledge about digital movies.
As of October 2001, there is about 205MB of pictures, movies and VRML files on this page!
Bold lines or links are those that I consider more interesting and are good for a first overview.
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Some files showing the triangulation used to detect contacts:
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Some simulations deal with packings of spheres of various sizes, in particular improving their density by tapping. Here are videos showing this on an example with 383 grains of 3 different sizes:
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These simulation show the influence of the tapping frequency on the packing process. Final views of 5575 similar grains after 10 seconds of vibrations followed by 2 seconds without vibrations. |
 
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Pouring grains in a cylinder:
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Hourglass flow:
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When some edges of the triangulation are mandatory, it becomes possible to construct clusters of grains of arbitrary shape. Here are some basic examples:
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Didier could show the forces among the grains in his 2D simulations. I tried to do the same in 3D, but it is harder to actually see something... The forces are represented as solid rods, blue for internal grain-grain forces and red for external grain-wall forces. The diameter of those rods grows with the magnitude of the force. The grains themselves are almost transparent. |
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Again in the goal of extending Didier's 2D simulations, here is a first attempt at reproducing the impact of a rock falling down on a granular bed.
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Here is a detailed view of the rearrangement of medium and small spheres that takes place when they leave space for a larger one. Bottom view of an experiment involving 1762 spheres: |
 
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Further reading
- Download my PhD Thesis in PDF, standard version, 12967K, or with low resolution images, 4365K.
- See my list of publications.
- I have a poster summarizing this whole project. You can see the 1999 version (PDF, 2305K) or the 2000 version (PDF, 2302K). They are really A0 documents, but Acrobat Reader does a fairly good job of displaying them. I have been more or less successful at getting A4 paper version of those, depending on the printer used.
- Didier Müller's bibliography.
- Our industrial partner Granulair Technologies offers consulting services, based on advanced numerical simulation, and provides solutions to improve manufacturing and product design for industrial processes employing granular or particulate technologies.
- At least two other researcher are involved in DEM for granular media here at EPFL: Mark Sawley (page at CSIRO, Australia) and Maher Moakher.
- Places to go to learn more about these topics, especially because of their large collections of links:
- David Eppstein's Geometry in Action has a page on Delaunay triangulations.
- The Powder Page.
- The Discrete Element Method at the Colorado School of Mines, the Particle Technologies Center at the New Jersey Institute of Technology, and many more sites about DEM around the world.
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©2002 ROSO-EPFL, 1015 Lausanne, Jean-Albert Ferrez update: 27 October 2002 |