Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials

Fabric tensors are commonly used in the study of granular materials as internal variables to quantify anisotropic fabrics. Fabric tensors can be constructed based on different microstructural entities in the material, such as particle long axis orientations, inter-particle contact normal directions, and orientations of void shapes. The current study explores the relationship between these different fabric tensors. Using two-dimensional discrete element method (DEM) simulations, we discover a simple and strong linear correlation between contact normal- and void vector-based fabric tensors for granular materials composed of non-elongated particles. This correlation holds true independent of the variations of all parameters and conditions exhaustively considered in this study, including the material’s packing density, stress state, inter-particle friction angle, particle size distribution, and particle shape. We also perform a preliminary and exploratory study of materials consisting of significantly elongated particles. The limited results show that the change of void vector-based fabric tensor appears to be affected by the corresponding components of the particle orientation-based fabric tensor and contact normal-based fabric tensor. Meanwhile, the normal component of the particle orientation-based fabric tensor and the corresponding component of contact normal-based fabric tensor are negatively correlated.