A Micromechanical Description of Granular Material Behavior

[+] Author and Article Information
J. Christoffersen

Department of Solid Mechanics, The Technical University of Denmark, DK-2800, Lyngby, Denmark

M. M. Mehrabadi, S. Nemat-Nasser

Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Ill. 60201

J. Appl. Mech 48(2), 339-344 (Jun 01, 1981) (6 pages) doi:10.1115/1.3157619 History: Received March 01, 1980; Revised August 01, 1980; Online July 21, 2009


Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.

Copyright © 1981 by ASME
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