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A generalised D matrix for anisotropic elastic granular media
Author(s) -
Du Jiang,
Dusseault Maurice B.
Publication year - 1994
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.1610180204
Subject(s) - anisotropy , strain rate tensor , tensor (intrinsic definition) , viscous stress tensor , infinitesimal strain theory , cauchy stress tensor , matrix (chemical analysis) , stress (linguistics) , classical mechanics , cauchy elastic material , deformation (meteorology) , mechanics , poisson's ratio , materials science , mathematics , geometry , physics , poisson distribution , constitutive equation , finite element method , composite material , optics , thermodynamics , statistics , linguistics , philosophy
A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain.