Local stress analysis in granular materials at a mesoscale

The purpose of this paper is to contribute to the change of scale techniques developed for granular materials. The proposed approach consists in considering an intermediate scale between the macroscales and microscales, called the mesoscale, using the classical homogenization scheme. In this approach, the mesoscale for 2D granular materials was defined at the level of local volumes, called mesodomains, which are local closed structures composed of particles in contact. In this paper, we focused on defining a local stress field at this scale. Two different methods are proposed, both based on the equivalent continuum mean stress but using different approximations of the mean stress tensor for each mesodomain. The two proposed methods were then compared to each other. Analyses performed on the stress field at the mesoscale show that this local field is heterogeneous and, in particular, that its heterogeneity is significantly structured at this scale. The distribution of the local mean stress (first invariant of the local stress tensor) is uniform in any mesodomain, whereas the distribution of the stress deviator (second invariant of the deviatoric part of the local stress tensor) is significantly dependent on the elongation direction and on the elongation degree of the mesodomains. The local stress ratio (ratio of the stress deviator to the mean stress) is higher within the mesodomains that are elongated in the global compression direction than that within the ones elongated in the global extension direction. Copyright (c) 2011 John Wiley & Sons, Ltd.