LEAST-SQUARES METHODS FOR THE MECHANICS OF NONHOMOGENEOUS GRANULAR ASSEMBLIES

Using least squares methods consistent averages for stress and strain of a nonhomogeneous granular assembly are derived. The expression for the average of the strain increment serves as a constraint in a functional approach to solving the displacements and spins of particles of a granular assembly in a statistical manner. The method shows directly what microscopic angular distributions are needed to describe the internal state of an assembly. They are the distribution of contacts, the distribution of both the averages and the variations in the interactive properties of the grains. The method is then applied to an assembly with normal-interacting circular grains in two dimensions. The incremental stiffness and the average displacement of the contacts as a function of the angle are obtained for the case of non-rotating strains. The results show clearly that for this case the sliding mode of motion is the most relevant one for deviatoric loading.