VGeST - Virtual Geoscience Simulation Tools

Ellipse Packing

This research was undertaken by Dr. Romain Guises during his PhD studies while at Imperial College under the supervision of Dr. J-P Latham and Prof. Antonio Munjiza, with assistance from AMCG’s Dr. Jiansheng Xiang.

The packing of particles is recognised to be a critically important process in many industrial fields, especially in powder technology, powder metallurgy, ceramics, pharmaceutical and the mineral industries. It also remains a focus of intense research in physical, chemical and environmental science.

By coupling the DEM with a finite element formulation (FEMDEM), the realism of particulate modelling has been greatly improved by taking into account the internal deformations of the particle that are a physical consequence of the stress generated by the interactions.

To study the influence of shape, the particle form was examined using ellipses with a range of aspect ratios for friction and frictionless cases. The emergent properties of the granular packs considered in the study were packing density, coordination number, and force distribution. The spatial distribution of the maximum differential stress can also be examined. A set of sedimentation experiments was carried out as summarised below.

Packs of 900 particles are shown where on the left the packs are frictionless and on the right, they are frictional (μ = 0.5). The aspect ratios of the ellipses vary from 1.0 (circle) top, 1.4 middle and 5.0 bottom. The colour scheme varies between blue for (unstressed) to red colour (highly stressed) and the scale is identical for each figure.

The influence of aspect ratio and friction on porosity, left and on coordination number, right, is rigorously examined in the graphs below. The increase in the packing density above that for random packed frictional circular particles for aspect ratios of ~1.6 supports 3D experimental results reported in the literature for ellipsoids.

The influence of friction on coordination number is dramatically shown by the distribution of the number of contacts per particle for a packing of ellipses of aspect ratio 2.5 for frictionless (left) and frictional systems (right). It is shown that the eccentricity of the particles not only significantly influences the final density of the pack but also the distribution of the stress and the contact forces. The presence of surface friction increases the amount of disorder within the granular system.

Stress heterogeneities and force chain patterns propagate through the particles more efficiently than for the frictionless systems. The results shown below also suggest that for the monodisperse systems investigated, the coordination number is one of the factors that control the distribution of the stress within a granular medium. The figure shows distributions of the average value of the differential stress over the area of the grain (depth normalised) for two granular packs of 900 grains. Identical stress distributions are observed for two packs with identical z but different particle shapes, suggesting a strong control of z on stress distributions. However, the difference in packing density of 5% is significant. FEMDEM provides a powerful simulation technology to probe curious granular phenomena. Further details may be found in Guises PhD Thesis (2008) and Guises et al. (2009).

References

Guises PhD Thesis

Guises, R., Xiang , J., Latham, J.-P., Munjiza, A. 2009. Granular packing: Numerical Simulation and Characterization of the Effect of Particle Shape, Granular Matter, , Vol 11, 281-292  doi:10.1007/s10035-009-0148-0.