Local origin of global contact numbers in frictional ellipsoid packings.
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.
Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.|Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Goettingen, Germany.
Fabian M
FM
Schaller
Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Goettingen, Germany.
Max
M
Neudecker
Applied Maths, RSPhysSE, The Australian National University, Canberra, ACT 0200, Australia.
Mohammad
M
Saadatfar
CSIRO Mathematics, Informatics and Statistics, Clayton South, Victoria 3168, Australia.
Gary W
GW
Delaney
Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.|Murdoch University, School of Engineering and IT, Mathematics and Statistics, Murdoch, Western Australia 6150, Australia.
Gerd E
GE
Schröder-Turk
Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Goettingen, Germany.
Matthias
M
Schröter