A GENERALIZED D-MATRIX FOR ANISOTROPIC ELASTIC GRANULAR MEDIA

A matrix relating stress and elastic strain tensors for anisotropic pa rticulate materials has been derived. The magnitude of the matrix depe nds on the state of the material anisotropy. Anisotropy in granular ma terials depends on strain because normal and tangential particle conta ct forces, as well as the spatial distribution of the contacts, vary w ith stress and strain. However, the rotation tensor and the strain ten sor cannot be independent; they must satisfy certain constraints to me et the requirement for macroscopic stress tensor symmetry. These condi tions and constraints lead to the derivation of the matrix presented i n this article. The principal directions of the stress tensor and stra in tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction depende nt; these two aspects are also discussed in this paper. Whereas this m atrix can be used in static numerical analyses for elastic problems, w e note that this relationship can also be used as a basis upon which t o derive a fully incremental stress-strain relationship for anisotropi c granular materials in the plastic state, where the anisotropy is evo lving with strain.