Micro-macro correlations and anisotropy in granular assemblies under uniaxial loading and unloading

The influence of contact friction on the behavior of dense, polydisperse granular assemblies under uniaxial (oedometric) loading and unloading deformation is studied using discrete element simulations. Even though the uniaxial deformation protocol is one of the "simplest" element tests possible, the evolution of the structural anisotropy necessitates its careful analysis and understanding, since it is the source of interesting and unexpected observations. On the macroscopic, homogenized, continuum scale, the deviatoric stress ratio and the deviatoric fabric, i.e., the microstructure behave in a different fashion during uniaxial loading and unloading. The maximal stress ratio and strain increase with increasing contact friction. In contrast, the deviatoric fabric reaches its maximum at a unique strain level independent of friction, with the maximal value decreasing with friction. For unloading, both stress and fabric respond to unloading strain with a friction-dependent delay but at different strains. On the micro-level, a friction-dependent non-symmetry of the proportion of weak (strong) and sliding (sticking) contacts with respect to the total contacts during loading and unloading is observed. Coupled to this, from the directional probability distribution, the "memory" and history-dependent behavior of granular systems is confirmed. Surprisingly, while a rank-2 tensor is sufficient to describe the evolution of the normal force directions, a sixth order harmonic approximation is necessary to describe the probability distribution of contacts, tangential force, and mobilized friction. We conclude that the simple uniaxial deformation activates microscopic phenomena not only in the active Cartesian directions, but also at intermediate orientations, with the tilt angle being dependent on friction, so that this microstructural features cause the interesting, nontrivial macroscopic behavior.