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

Abstract

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.

Contact angle entropy and macroscopic friction in noncohesive two-dimensional granular packings

“…Particle rotations start to contribute as µ increases and become dominant for larger values of local friction. This leads to the saturation range which has been also obtained in bidimensional [11,43] and threedimensional simulations [15,44]. This clearly demonstrate that 2D simulations are able to reproduce important macroscopic properties, such as macroscopic friction, exhibited in 3D packings.…”

Memory of jamming–multiscale models for soft and granular matter

“…Recent works showed already that, along with the classical macroscopic properties (stress and volume fraction), the structural anisotropy is an important [41,45,46,[91][92][93][94] state-variable for granular materials, as quantified by the fabric tensor [43,68] that characterizes, on average, the geometric arrangement of the particles, the contacts and their network, i.e. the microstructure of the particle packing.…”

“…Around the jamming transition, these systems display considerable inhomogeneity, such as reflected by over-population of weak/soft/slow mechanical oscillation modes [11], forcenetworks [10,30,31], diverging correlation lengths and relaxation time-scales [9,13,22,[32][33][34][35], and some universal scaling behaviors [36,37]. Related to jamming, but at all densities, other phenomena occur, like shearstrain localization [12,16,[38][39][40], anisotropic evolution of structure and stress [7,9,11,13,30,31,[38][39][40][41][42][43][44][45][46], and force chain inhomogeneity [7,19,28]. To gain a better understanding of the jamming transition concept, one needs to consider both the structure (positions and contacts) and contact forces.…”

The role of gravity or pressure and contact stiffness in granular rheology

“…The deviatoric stress ratio, μ τ = p, is the effective macroscopic friction. The volumetric fabric F 3 v represents the contact number density, while the deviatoric fabric F dev quantifies the anisotropy of the contact network (as studied in detail in [53]).…”

“…F F 2 1 tends to positive values for larger p*, further establishing the difference between structure and stress tensors. However, in order to have a clear picture for the fabric tensor, the strong and weak subnetworks should be studied separately, since only the strong subnetwork carries almost all of the fabric anisotropy [53,69]. Along with a non-zero σ 2 eigenvalue we do expect other aspects to show up, like the non-collinearity of the stress/strain/fabric eigensystems, related to induced anisotropy.…”