Anisotropic elastic theory of preloaded granular mediaC. Gay1 and R. A. da Silveira2
1 Centre de recherche Paul Pascal-CNRS - Av. Schweitzer, 33600 Pessac, France
2 Lyman Laboratory of Physics, Harvard University - Cambridge, MA 02138, USA
received 5 January 2004; accepted in final form 27 July 2004
A macroscopic elastic description of stresses in static, preloaded granular media is derived systematically from the microscopic elasticity of individual inter-grain contacts. The assumed preloaded state and friction at contacts ensure that the network of inter-grain contacts is not altered by small perturbations. The texture of this network, set by the preparation of the system, is encoded in second- and fourth-order fabric tensors. A small perturbation generates both normal and tangential inter-grain forces, the latter causing grains to reorient. This reorientation response and the incremental stress are expressed in terms of the macroscopic strain.
45.70.Cc - Static sandpiles; granular compaction.
46.25.-y - Static elasticity.
62.20.Dc - Elasticity, elastic constants.
© EDP Sciences 2004