Micromechanical Aspects of Isotropic Granular Assemblies With Linear Contact Interactions

[+] Author and Article Information
R. J. Bathurst

Civil Engineering Department, Royal Military College of Canada, Kingston, Ontario, Canada K7K 5L0

L. Rothenburg

Civil Engineering Department, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

J. Appl. Mech 55(1), 17-23 (Mar 01, 1988) (7 pages) doi:10.1115/1.3173626 History: Received January 02, 1987; Revised August 19, 1987; Online July 21, 2009


The paper presents a micromechanical analysis of plane granular assemblies of discs with a range of diameters, and interacting according to linear contact force-interparticle compliance relationships. Contacts are assumed to be fixed and indestructible. Macroscopically, the system is described in terms of a two-dimensional analogue of generalized Hooke’s law. Explicit expressions for elastic constants in terms of microstructure are derived for dense isotropic assemblies. It is shown that Poisson’s ratio for dense systems depends on the ratio of tangential to normal contact stiffnesses. The derived expression for Poisson’s ratio is verified by numerically simulating plane assemblies comprising 1000 particles. The effect of density on Poisson’s ratio is investigated using numerical simulations. The theory of dense plane systems is extended to dense three-dimensional systems comprising spheres. Finally, it is shown that Poisson’s result ν=1/4 is recovered for spherical particles with central interactions.

Copyright © 1988 by ASME
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