Strong-weak network anisotropy switching and hysteresis in three-dimensional granular materials

Abstract

We address hysteresis of three-dimensional polydisperse granular packs, comparing macro- and microscopic viewpoints, to reveal their elastic/inelastic mechanics and force network anisotropy. During the uniaxial loading-unloading cycle of an appropriately prepared pack, one can decompose the force network into weak and strong subnetworks. The first stages of loading exhibit arching, where all the fabric displays negative anisotropy. For later stages, the strong (weak) network shows positive (negative) anisotropy. On unloading, the force network progresses to a fabric wide hydrostatic point, where the anisotropies of the weak and strong subnetworks switch signs. During the loading stage, a Mohr circle analysis permits the identification of a well-defined macroscopic internal friction angle, whose value is larger than that of grain-grain interactions. To analyze unloading, a generalized local Coulomb-friction argument predicts a continuously changing friction angle, that vanishes at the hydrostatic point. A suggestive interplay between microscopic friction and fabric structure, at different loding stages, is proposed as the mechanism for the emergence of a macro internal friction angle.