On the extension of the grain loop concept from 2D to 3D granular assemblies

In the field of granular materials, a link between the microscopic variables (contact force and displacement) and macroscopic variables (stress and strain) requires an intermediate scale called the mesoscopic scale. An important class of mesostructure is the so-called loops, which are closed chains of grains in contact. In two dimensions (2D), these structures tessellate a material domain into elementary partitions that account for the physics of granular materials. However, this property no longer applies in three dimensions (3D). In this paper, we propose to identify 3D mesostructures that generalize the 2D properties of loops and their ability to account for the deformability of granular materials. To do so, a weighted Delaunay tessellation is used to partition a 3D specimen into tetrahedra. These tetrahedra are then merged through a criterion defined consistently with the one used to identify loops in 2D. As the 3D structures do not match the mathematical definition of loops, they are named clusters. A series of 3D DEM triaxial tests were performed to analyze the statistics of clusters during the loading path. It is shown that clusters behave analogously to loops, promoting an increase in the number of denser mesostructures during the strain contraction phase and looser ones during dilation. Furthermore, increasing amounts of looser clusters appear around force chains, promoting a decrease in the stability of the chained structures. Clusters are more diverse in shape and topology compared with loops. Thus, additional metrics besides the number of grains forming them are needed to characterize these structures. In this respect, we propose the concepts of order (number of external frontiers) and deformability.