Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings

Schaller F, Neudecker M, Saadatfar M, Delaney G, Schröder-Turk G, Schröter M (2015)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2015


Book Volume: 114

Pages Range: 158001

Journal Issue: 15

DOI: 10.1103/PhysRevLett.114.158001


In particulate soft matter systems the average number of contacts \textitZ 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 \textit{ϕ}\textsubscript{\textitg}}. We find that \textitZ is a monotonically increasing function of \textit{ϕ}\textsubscript{\textitg}} for all \textit{α}. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction \textit{ϕ}\textsubscript{\textitl}}\textsubscript{ }computed from a Voronoi tessellation. \textitZ can be expressed as an integral over all values of \textit{ϕ}\textsubscript{\textitl}}: Z(\textit{ϕ}\textsubscript{\textitg}},\textit{α},\textitX)=∫Z\textsubscript{\textitl}}(\textit{ϕ}\textsubscript{\textitl}},\textit{α},\textitX)\textitP(\textit{ϕ}\textsubscript{\textitl}}|\textit{ϕ}\textsubscript{\textitg}})\textit{dϕ}\textsubscript{\textitl}}. The local contact number function\textit{ Z}\textsubscript{\textitl}}(\textit{ϕ}\textsubscript{\textitl}},\textit{α},\textitX) describes the relevant physics in term of locally defined variables only, including possible higher order terms\textit{ X}. The conditional probability P(\textit{ϕ}\textsubscript{\textitl}}|\textit{ϕ}\textsubscript{\textitg}}) to find a specific value of \textit{ϕ}\textsubscript{\textitl}} given a global packing fraction \textit{ϕ}\textsubscript{\textitg}} is found to be independent of \textit{α} and \textitX. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.

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Schaller, F., Neudecker, M., Saadatfar, M., Delaney, G., Schröder-Turk, G., & Schröter, M. (2015). Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings. Physical Review Letters, 114(15), 158001. https://dx.doi.org/10.1103/PhysRevLett.114.158001


Schaller, Fabian, et al. "Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings." Physical Review Letters 114.15 (2015): 158001.

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