A multi-scale approach to granular materials

It is now well established that the micro-structure of granular materials plays a significant role in their overall constitutive behavior. In the past few years, a great deal of theoretical and experimental research has been devoted to this domain, giving rise to constructive micro-mechanical approaches. However, constitutive models for granular materials based on a micro-mechanical approach remain scarce; solving practical engineering problems most often requires using phenomenological models, which often introduce numerous parameters with no physical meaning. This paper derives a “parameter-free” constitutive behavior of granular materials on the macroscopic level from a microscopic-scale description, taking a statistical description of the fabrics into account. In this approach, the location of each particle is ignored, but the probability of contact in a given direction is investigated. Modelling the creation or the loss of contacts in given directions makes it possible to analyze how the probability density of having contacts in these directions evolves, and thus a directional constitutive model can be developed. Highlighting micro-structural processes responsible for the transmission of local contact forces, the existence of two phases in the granular assembly was accounted for, giving rise to a partition of the stress tensor. The capability of the model is assessed from the simulation of standard tests, leading to satisfying preliminary qualitative results.