A micromechanical prediction of localization in a granular material

We predict localization in a strained, random aggregate of identical elasto-frictional particles. As triaxial compression proceeds, pairs of particles deform subject to local equilibrium and anisotropy develops because of contact deletion and the dependence of contact stiffness on the average strain. The combination of the deviations of the particle displacements from the average strain and the induced anisotropy results in a relation between increments in average strain and average stress that does not possess the major symmetry. This leads to the possibility of a discontinuity in a component of the incremental strain at a predicted value of the shear strain and a predicted orientation relative to the axis of greatest compression.