Keywords: contact stiffness, force network, shear strength, dense particulates, shape effects, powders and grains.

The strength characteristics and micromechanical behaviour of dense particulate systems are influenced by the ability of the particles to deform along the normal and tangential directions to the contact plane, i.e, the normal and tangential contact stiffnesses of the particles. However, in practice, the measurement of tangential contact stiffness between particles is often ignored in experimentally characterising particles. It is not entirely clear as to what extent ignoring the measurement of tangential stiffness or the variations in its measurement would affect the predictions on the assembly characteristics of particulate systems. In this study, we investigate the role of contact stiffness on the microscopic and macroscopic deformation characteristics of three-dimensional dense particulate assemblies made of non-spherical particles and subjected to quasi-static shearing. For comparison purposes, we also performed simulations using dense assemblies containing sphere particles, subjected to identical test conditions.

We simulated the shear deformation characteristics of particulate assemblies using three-dimensional DEM [1]. Three assemblies containing different shape of the particles were generated: sphere and two cases of ovoids, viz., oblate, and prolate assemblies [2]. The method models the interaction between contiguous particles as a dynamic process, and the time evolution of the particles is advanced using an explicit finite difference scheme. A simple force mechanism was employed between contacting particles. Linear normal and tangential contact springs were assigned with wide ranging values of the spring stiffness ratio k (ratio of tangential to normal spring stiffness), and slipping between particles would occur whenever the specified contact friction coefficient of 0.5 was attained.

The particle arrangements were initially random, isotropic and homogeneous. During the subsequent tri-axial compression test, the height of the assembly was slowly reduced at a constant rate along the 2-2 (vertical) direction, while maintaining a constant horizontal stress along the 1-1 direction and zero strain along 3-3 direction (mixed boundary condition). The vertical strain was advanced in small increments of . The average stress tensor  [1] in a granular assembly can be directly computed and the orientation of the contacts (fabric tensor) during mechanical loading is characterised as suggested by Satake [3].

The evolution of deviator stress ratio ( ), for sphere assemblies show that the variations in the spring stiffness ratio k has resulted in no significant changes on the plots. In contrast, the deviator stress ratio for the case of non-sphere assemblies depends on the variations in the spring stiffness ratio assigned at particle-scale.

The analysis showed that, the variation in the contact fraction (proportion of contacts) in sphere systems is clearly less sensitive to the stiffness ratio. For non-sphere system, and increase in the stiffness ratio tends to result a decrease in the proportion of contacts.

When the evolution of the stress ratio is compared to the evolution of the fabric tensor, we do not see a strong correlation between them during shearing. However, inspired by previous work [4,5], if only the 'strong' contacts that carry normal force greater than the average contact force are used in order to calculate the fabric anisotropy, we observed better correlation between the macroscopic stress ratio and the fabric anisotropy of the strong contacts during shearing. The characteristics of stress ratio can be attributed to the nature of the anisotropic orientation of the heavily loaded contacts: for sphere assemblies, an increase in the stiffness ratio of particles did not result in a significant change in the anisotropy of the heavily loaded contacts. For the non-sphere systems considered here, anisotropy of the heavily loaded contacts decreases for an increase in the value of stiffness ratio k.

In summary, the variations in the contact stiffness ratio of particles affect the micromechanical characteristics of non-sphere particulate systems more dominantly than the sphere particulate systems. Hence, attention must be paid to measure both the normal and tangential contact stiffnesses when characterising non-sphere fine particulates to estimate their assembly strength characteristics during shearing.

1

P.A. Cundall and O.D.L Strack, "Discrete numerical model for granular assemblies", Geotechnique, 29(1), 47-65, 1979.

2

H.G. Matuttis, S. Luding and H.J. Herrmann, "Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles", Powder Technology, 109, 278-292, 2000. doi:10.1016/S0032-5910(99)00243-0

3

M. Satake, "Fabric tensor in granular materials", In Deformation and Failure of Granular Materials, ed. by P.A. Vermeer and H.J. Luger (Balkema, Rotterdam, 1982), 63-68.

4

F. Radjai, H. Troadec and S. Roux, "Key features of granular plasticity". In Advances in granular materials: Fundamentals and applications, eds. S. J. Antony et al., Proceedings of Royal Society of Chemistry, London, 157-184, 2003.

5

C. Thornton and S.J. Antony, "Quasi-static deformation of particulate media", Philosophical Transactions of the Royal Society of London A, 356, 2763-2782, 1998. doi:10.1098/rsta.1998.0296

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