Network flow model of force transmission in unbonded and bonded granular media
Abstract
An established aspect of force transmission in quasistatic deformation of granular
media is the existence of a dual network of strongly versus weakly loaded particles.
Despite significant interest, the regulation of strong and weak forces through the
contact network remains poorly understood. We examine this aspect of force transmission
using data on microstructural fabric from: (I) three-dimensional discrete element
models of grain agglomerates of bonded subspheres constructed from in situ synchrotron
microtomography images of silica sand grains under unconfined compression and (II)
two-dimensional assemblies of unbonded photoelastic circular disks submitted to biaxial
compression under constant volume. We model force transmission as a network flow and
solve the maximum flow-minimum cost (MFMC) problem, the solution to which yields a
percolating subnetwork of contacts that transmits the "maximum flow" (i.e., the highest
units of force) at "least cost" (i.e., the dissipated energy from such transmission).
We find the MFMC describes a two-tier hierarchical architecture. At the local level,
it encapsulates intraconnections between particles in individual force chains and
in their conjoined 3-cycles, with the most common configuration having at least one
force chain contact experiencing frustrated rotation. At the global level, the MFMC
encapsulates interconnections between force chains. The MFMC can be used to predict
most of the force chain particles without need for any information on contact forces,
thereby suggesting the network flow framework may have potential broad utility in
the modeling of force transmission in unbonded and bonded granular media.
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https://hdl.handle.net/10161/10931Published Version (Please cite this version)
10.1103/PhysRevE.91.062204Publication Info
Tordesillas, Antoinette; Tobin, Steven T; Cil, Mehmet; Alshibli, Khalid; & Behringer,
Robert P (2015). Network flow model of force transmission in unbonded and bonded granular media. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 91(6). 10.1103/PhysRevE.91.062204. Retrieved from https://hdl.handle.net/10161/10931.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Robert P. Behringer
James B. Duke Professor of Physics
Dr. Behringer's research interests include granular materials: friction, earthquakes,
jamming; nonlinear dynamics; and fluids: Rayleigh-Benard convection, the flow of thin
liquid films, porous media flow, and quantum fluids. His studies focus particularly
on experiments (with some theory/simulation) that yield new insights into the dynamics
and complex behavior of these systems. His experiments involve a number of highly
novel approaches, including the use of photoelasticity for probing granular
This author no longer has a Scholars@Duke profile, so the information shown here reflects
their Duke status at the time this item was deposited.

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