A micro-mechanical investigation of bifurcation in granular materials

In this paper, the notion of loss of sustainability of a mechanical state in a granular assembly is investigated. The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation. Then a link is established between the macroscopic second-order work on the specimen scale and a discrete local expression that introduces microscopic variables defined on each contact scale. This relation opens up a micro-mechanical interpretation allowing one to examine which micro-structural features are responsible for the vanishing of the macroscopic second-order work. Finally, it is established that both geometrical and material micro-structural origins may combine to induce the occurrence of bifurcation on a specimen scale.