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On statistical description of stress and fabric in granular materials
Author(s) -
Mehrabadi M. M.,
NematNasser S.,
Oda M.
Publication year - 1982
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610060107
Subject(s) - microscale chemistry , granular material , plane (geometry) , stress (linguistics) , contact force , centroid , point (geometry) , mechanics , contact mechanics , mathematics , materials science , structural engineering , geometry , engineering , classical mechanics , physics , composite material , finite element method , linguistics , philosophy , mathematics education
The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.