On the evolution of stress and microstructure during general 3D deviatoric straining of granular media

The paper presents results of periodic cell simulations on a polydisperse system of 27 000 elastic spheres. In order to explore general three-dimensional stress space an initially isotropically compressed system is subjected to radial deviatoric strain paths and the corresponding stress and fabric responses are illustrated. It is shown that two parameters can be identified that characterise the stress and fabric respectively during general three-dimensional straining. Each parameter, when plotted against deviatoric strain, provides a unique evolution curve, irrespective of the loading direction. It is demonstrated that, for general states of stress, the magnitude of the deviatoric stress is entirely due to the strong force chains that constitute the sub-network of contacts transmitting greater than average contact forces. It is also demonstrated that the relationship between the Lode angle for stress and the Lode angle for strain can be characterised by the curvature of a circular arc and, for radial deviatoric straining, this constitutes a flow rule that defines the relationship between the directions of the stress and strain-rate vectors. Furthermore, by plotting the characteristic stress parameter against the curvature of the circular arc flow rule, a simple scaling law is obtained.