Micromechanical analysis of second order work in granular media

This paper examines instabilities in granular materials from a microscopic point of view through numerical simulations conducted using a discrete element method on two three-dimensional specimens. The detection and the tracking of grain scale deformation mechanisms constitute the key point for a better understanding the failure process and puzzling out what lies behind the vanishing of the macroscopic second order work. For this purpose, the second order work from microscopic variables, involving contact force and branch vector, was introduced and tracked numerically. Then, all contacts depicting negative values of the second order work were deeply investigated, especially their spatial distribution (homogeneity, agglomeration, dispersion) within the specimen according to the density of the granular assembly and to the loading direction. A set of comparisons has been considered in this context in order to highlight how a specimen is populated with such contacts whether it is loaded along a direction included within the plastic tensorial zone or along a direction for which the specimen is likely to behave elastically (elastic tensorial zone). Moreover, these comparisons concerned also loading directions within the cone of instability so that links between the vanishing of both microscopic and macroscopic second order works can be established and the local mechanisms responsible for failure occurrence may be figured out.