Analysis of structure and strain at the meso-scale in 2D granular materials

In this paper, we introduce a new scale called the meso-scale in order to define an appropriate local scale for multi-scale kinematic analysis in granular materials. The proposed meso-scale corresponds to sub-domains obtained by subdividing a 2D granular assembly taking into account load-bearing contacts. For each sub-domain, a strain tensor is defined and a description of its structure is proposed. Our analysis, carried out on a biaxial compression test, reveals that strain is significantly related to the structure at the meso-scale: (1) strain in the major (respectively, minor) principal compression direction is largest within the sub-domains which are elongated in the minor (respectively, major) principal compression direction, and (2) contractancy takes place within the sub-domains which are elongated in the minor principal compression direction whereas dilatancy takes place within the sub-domains which are elongated in the major principal compression direction. Furthermore, we emphasize a relation between strain at the meso-scale and the induced anisotropy of granular materials during deviatoric loading.