The mechanical behavior of granular materials is not yet well understood, although recent advances in field measurement and in numerical modelling triggered some considerable progress. Discrete modelling methods have an important role to play in this research field, since they are realistic both at the sample-scale and at the grain-scale. Conventional discrete methods commonly represent particles such as sand grains as discs or spheres, but a large number of researchers are now making efforts to introduce more complex shapes in order to account in a more realistic manner for some interlocking or rolling resistance phenomena.
An efficient method has been developped to generate random 2D granular samples, fulfilling some target conditions in terms of void ratio, size distribution, aspect ratio, orientation, sphericity, rugosity, etc. This method is based on the discrete Fourier transform and on a contrained Voronoi tessellation and gives very satisfactory results, which will make it possible in a short while to introduce in DEM softwares some perfectly controled discrete samples, and to submit them to various mechanical sollicitations. It will then be possible to perform a number of so-called "numerical experiments", in order to study the effect of different shape descriptors on the mechanical response of the granular material.
On-going work in dedicated to an extension of this method to the more general 3D case, and to the study of the flow of a granular medium with complex particle shapes through a hopper.
Figure 1. Examples of six random generations of grains with similar target properties in terms of aspect ratio, circularity, angularity and regularity.
Figure 2. Filling technique called ODEC (Overlapping Discrete Element Cluster), replacing a grain of complex shape by a collection of discs in order to introduce this shape in a discrete computation code.
Figure 5. Examples of 3D granular packings.
Figure 3. Exemple of packing obtained with these techniques.
Figure 4. Extension to the 3D case: comparison between real sand grains (a. Michigan Dune Sand ; b. Tecate River Sand) and virtual grains generated from experimental Fourier spectrums. Arrows point out some fortuitous similarities and emphasize the potential of the method.