A Solution for the Stress Distribution in a Granular Medium

We propose an example of an incremental elastic problem for a granular material. The mechanical behavior of this material is sensitive to the confining pressure that typically is applied before any loading. Experiments, numerical simulations, and theoretical models show that the effective elastic moduli of a granular medium are function of the confining pressure in non-linear way. Therefore, if we consider a reference state where the pressure is not constant the material behaves differently in each point and, for example, the stress associated to a subsequently loading should be obtained as solution of a non-homogeneous material. We focus our attention on this kind of problem for a granular material that fills an hollow cylinder first isotropically compressed and then sheared under a rotatory motion. Next a small perturbation is applied on the boundaries of the specimen and we evaluate the corresponding stress distribution in the plane perpendicular to the axis of the cylinder.