Towards a new approach for modeling the behavior of granular materials: A mesoscopic-macroscopic change of scale

This paper constitutes a preliminary demonstration of the feasibility of a multi-scale approach for the definition of a constitutive law for granular materials. The case of two-dimensional granular materials was considered and the reasoning was built on 2D Discrete Element Method (DEM) simulations of 2D biaxial tests performed on sample made of disks. The change of scale relied on an intermediary local scale called the meso-scale which was based on the existence of meso-domains defined as closed loops of particles in contact. At the meso-scale, six sets of meso-domains or phases, with different properties in terms of local texture, have been defined. Then, an elastic-hardening-plastic model was designed at the phase scale and the identification of the model parameters was performed on a stress path denoted compression stress path. The model parameters defined for each phase were found correlated with the initial meso-texture of the considered phase and with the orientation of the loading path with respect to the phase orientation. The change of scale allowed us to obtain a modeling at the sample scale in good agreement with the DEM results on the compression stress path. Finally, the relevance of the model and of the approach were tested on a different stress path denoted unloading stress path. This was performed both at the level of the six phases and at the sample scale. The results were found to be in good agreement with the DEM simulations, which tends to validate the general approach presented in this paper, including the definition of the phases at the meso-scale, the design of a constitutive model at this scale, and the change of scale process to obtain the behavior of the material at the sample scale.