A Micromechanical Description of Granular Material Behavior

1981/06/01 by J. Christoffersen, M. M. Mehrabadi, Morteza M. Mehrabadi +2 · 865 citations
Engineering · Mathematics · #Centroid #Classical mechanics #Composite material #Dilatant #Geometry #Geotechnical Engineering and Soil Mechanics #Granular flow and fluidized beds #Granular material #Kinematics #Materials science #Mathematics #Mechanics #Physics #Plasticity #Representation (politics) #Rock Mechanics and Modeling #Statistical physics #Thermodynamics #Virtual work #Work (physics)

paper · doi:10.1115/1.3157619

published in Journal of Applied Mechanics 48(2), 339-344 (ASM International)

openalex publication_date 1981/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

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