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Local origin of global contact numbers in frictional ellipsoid packings

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Schaller,  Fabian M.
Group Statistical mechanics of granular media, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Neudecker,  Max
Group Statistical mechanics of granular media, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Schröter,  Matthias
Group Statistical mechanics of granular media, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Schaller, F. M., Neudecker, M., Saadatfar, M., Delaney, G., Schröder-Turk, G. E., & Schröter, M. (2015). Local origin of global contact numbers in frictional ellipsoid packings. Physical Review Letters, 114(15): 158001. doi:10.1103/PhysRevLett.114.158001.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-5F1F-4
Abstract
In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl. The local contact number function Zl(ϕl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.