Meso-scale signatures of inertial transitions in granular materials

Abstract

Granular materials have a complex collective behavior based on simple interactions between grains. The global behavior stems from dynamic rearrangements in the micro-structure. The local increase (resp. decrease) of the density generates jamming (resp. unjamming). In this paper, instabilities in the form of localized bursts of kinetic energy are studied at both the micro-scale (i.e. grain scale) and meso-scale (i.e. cluster scale). The bursts are defined from the variation of kinetic energy. The meso-domains (grain loops in 2D) are built from the tessellation of the medium. We analyze the gain and loss of mesostructures during a localized burst. Surprisingly, micro-structural reorganizations are able to keep the overall statistical equilibrium constant. The introduction of strain-like and stress-like quantities at the mesoscopic scale makes it possible to propose an expression that can be assimilated to mesoscopic second-order work. At this intermediate scale, the negative values of the second-order work are correlated to the appearance of bursts of kinetic energy, which stands for a meso-scale counterpart of Hill's macroscopic criterion of mechanical instability.

Configurational mechanics in granular media

“…5, where a biaxial loading path is simulated by using a discrete element method, stress fluctuations develop after the stress peak is reached, and become well marked in the critical state regime. As pointed out in Zhu et al (2016b) and Clerc et al (2021), these stress fluctuations stem from continuous microstructural reorganizations occurring within the assembly. Considering the evolution of two loop categories (loops with 3 grains, and loops with 6 grains), it can be observed in Fig.…”

Elastic–plastic intermittent re-arrangements of frictionless, soft granular matter under very slow isotropic deformations

“…While granular gases are better described by kinetic theory [5], dense granular fluids and granular solids are much harder to understand, in particular since they can transit from fluid-like flowing states to static, reversibly elastic states, dependent on the inflow and dissipation of energy. How and why they achieve this transition is still under debate, e.g., by irreversible plastic deformations [16][17][18][19][20][21][22][23][24][25], related also to creep/relaxation [11,[26][27][28], and many other studies, see Ref. [29] and references therein.…”

“…While slow shear shows evident stress drops due to mesoscale re-arrangements and deformations, see Refs. [21, [23][24][25], it was reported that there is only much weaker action under isotropic deformations in a small density window [21] for non-spherical, frictional particles. However, for frictionless spheres, a lot of re-arrangements are possible [4,6] and visible if only the compression rate is slow enough.…”

Incremental shear strain chain: a mesoscale concept for slip lines in 2D granular materials

“…To distinguish shear bands from local shear patterns in frictional granular materials, an intermediate scale, i.e., meso scale, between grain and sample scales is needed. At this scale, slip structures can be analyzed from both continuum and discrete points of views, provided that local stresses and strains are consistently defined [49][50][51].…”