Quasi-static deformation of particulate media

Quasi-static shear deformation of granular media is examined by performing numerical simulations on polydisperse systems of elastic spheres in a periodic cell. Results of axisymmetric compression test simulations are reported for both a dense and a loose system of spheres sheared under constant mean stress conditions. At the macroscopic scale, the simulated stress-strain-dilation responses are in excellent qualitative agreement with the mechanical behaviour of sand observed in real experiments. Numerical simulation permits a detailed examination of the evolution of internal variables associated with the micromechanical processes occurring at the particle scale. In this context, we present and discuss the evolution of the induced structural anisotropy, the percentage of sliding contacts, the average coordination number and the normal and tangential contact-force contributions to the stress tensor. Encouraged by recent research published by physicists working on granular media, we show how the distribution of normal contact forces evolves during shear, and how it is affected by changing the particle modulus and stress level. This work has led us to consider two types of interparticle contacts: (1) the contacts carrying below-average normal contact forces; and (2) the contacts carrying above-average normal contact forces. We examine how these two different categories contribute to the stress tensor and the structural anisotropy tensor. As a consequence, we present information that provides new insights into the physics of granular media and clarifies some previous findings.