Stress-Strain Relations for a Simple Model of a Granular Medium

Abstract

Abstract A granular assemblage is represented by a model consisting of like spheres in contact arranged in a simple cubic lattice. Based on consideration of local contact forces and concomitant deformations, incremental stress-strain relations are derived and subsequently integrated, for certain types of loading, to yield total stress-strain relations. The integration is carried out for both a loading and an unloading process. A criterion of failure for the model is set up and the theory applied to a regimen of loading which gives rise to a plane state of stress.