State internal variables at different scales for the modeling of the behavior of granular materials

The main difficulty in modeling the behavior of a granular material arises from the discrete nature of this material. The precision of the description of phenomena requires complex developments able to trace important changes within the material throughout complex loadings. The works by Darve have tried to answer this question and have provided valuable results. Nevertheless, constitutive models still encounter difficulties in providing a correct prediction of the behavior in any case because the state variables of the models are not actual measurements of the internal state of the material. Scaling may help to bridge the gap between the behavior at the sample scale and local phenomena. Studies performed at the scale of the contact between grains and the scale of several grains, the so-called meso-scale, have provided interesting results to understand how the internal structure evolves throughout a loading and what local variables are, either geometrical or static, capable of explaining phenomena at the sample scale.