The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitudes, the dependence of the resulting strain on stress direction is a Lévy flight in the thermodynamic limit. The mechanical properties of granular media are currently an active field of research, both in the condensed matter physics and in the mechanics and engineering communities [1, 2,3].Granular packings close to mechanical equilibrium are traditionnally modelled, in the framework of continuum mechanics, with elastoplastic constitutive laws [3,4], i.e., incremental stress-strain relations. Such laws, despite their practical success, were never clearly related to grain-level mechanics. Moreover, cohesionless granular systems seem to be quite different from ordinary solids. Many experimental, theoretical and numerical studies [2,5,6,7,8] have recently been devoted to the peculiar features of stress transmission in granular systems at equilibrium, with correlations over length scales significantly larger than the grain size.Observations of displacement fields and strains, as the system moves from one equilibrium to another, are scarcer. Systems of rigid grains are expected to deform because of rearrangements of the packing, rather than contact elasticity. How such rearrangements average to produce a macroscopic strain, related to stress variations, remains rather mysterious. The rather singular, unilateral form of the local interaction in such systems led some authors [9] to expect quite unusual macroscopic properties, for which the very concept of strain, so familiar in mechanics of solids, would be irrelevant.Direct grain-level approaches are, in principle, possible by numerical simulations. However, one has then to define a complete mechanical model to enable a calculation of particle trajectories. In practice, dynamical parameters ruling energy dissipation are often chosen according to computational convenience as much as physical accuracy. It would be desirable to assess the influence of such choices on the results.The present numerical study addresses those problems, as follows.Disordered, dense assemblies of rigid, circular, frictionless discs, are prepared by isotropic compaction. The force law reduces to the condition that contacts transmit repulsive normal forces of unknown magnitude. Then, the direction of the load is gradually altered, thus simulating the biaxial test of fig.

Features of rheological laws applied to solid-like granular materials are recalled and confronted to microscopic approaches via discrete numerical simulations. We give examples of model systems with very similar equilibrium stress transport properties -- the much-studied force chains and force distribution -- but qualitatively different strain responses to stress increments. Results on the stability of elastoplastic contact networks lead to the definition of two different rheological regimes, according to whether a macroscopic fragility property (propensity to rearrange under arbitrary small stress increments in the thermodynamic limit) applies. Possible consequences are discussed.Comment: Published in special issue of "Comptes-Rendus Physique" on granular material

In this letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent, α. We experimentally validate a particular case of the so-called Tsallis-Bukman scaling law, α = 2/(3 − q), where q is obtained by fitting the probability density function (PDF) of the measured fluctuations with a q-Gaussian distribution, and the diffusion exponent is measured independently during the experiment. Applying an original technique, we are able to evince a transition from an anomalous diffusion regime to a Brownian behavior as a function of the length of the strain-window used to calculate the displacements of grains in experiments. The outstanding conformity of fitting curves to a massive amount of experimental data shows a clear broadening of the fluctuation PDFs as the length of the strain-window decreases, and an increment in the value of the diffusion exponent -anomalous diffusion. Regardless of the size of the strain-window considered in the measurements, we show that the Tsallis-Bukman scaling law remains valid, which is the first experimental verification of this relationship for a classical system at different diffusion regimes. We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials. Turbulence is one of the most complex, but ubiquitous, phenomena observed in Nature and it is related with the underlying mechanisms responsible for the micro-macro upscale causing wide-ranging effects on classical systems, like macroscopic friction in granular solids or turbulent flow regime in fluids [1][2][3][4]. The presence of multiple scales in time and space is an additional defy to a comprehensive theoretical description, and a particular effort is made in the literature to perform experiments and simulations in order to validate the proposed theoretical descriptions, particularly Tsallis nonextensive (NE) statistical mechanics [5][6][7][8].A paradigmatic work relating anomalous diffusion and turbulent-like behavior in confined granular media was presented by Radjai and Roux [4], using numerical simulations, and confirmed qualitatively by experiments by Combe and collaborators [7,8]. Radjai and Roux coined a new expression to characterize the analogies between fluctuations of particle velocities in quasistatic granular flows and the velocity fields observed in turbulent fluid flow in high Reynolds number regime, the "granulence". Most of the evidences of the granulence are based in simulations using discrete element method (DEM) but, unfortunately, one can verify a lack of quantitative experimental verification in the last years, limiting the knowledge of the micromechanics of this system based almost exclusively on numerical evidences.In the present work, we aim exactly to fill this gap by contributing with the experiment...

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This paper is concerned with micromechanics of Schneebeli material specimens composed of wooden roller stacks. Several laboratory tests are carried out to analyse the material behaviour under complex loading conditions, involving loading–unloading cycles and principal axes rotations. In order to characterize micromechanical deformation features and structure evolution, a series of pictures is taken during loading. Pictures are then digitized using a stereo device, obtaining the position of each roller. Starting from these data a number of computer programs, conceived for the purpose, allow us to measure micromechanical variables and to analyse their evolution. In the following, after the description of the devices employed in this research, macromechanical results are analysed to evaluate the reliability of the laboratory model. Then, local variables are introduced and the use of continuum mechanics to describe granular materials behaviour is discussed. Finally, the evolution of local kinematic variables is described, focusing interest on the evolution of specimen anisotropy. © 1997 by John Wiley & Sons, Ltd. Mech. cohesive‐frictional mater. 2, 121–163 (1997)

In a granular material, a macroscopically homogeneous deformation does not correspond to a homogeneous displacement field when looking at the individual grains. The deviation of a grain displacement from the value dictated by the continuum field (referred to as 'fluctuation') is likely to hold valuable information about the characteristic length(s) involved in the grains' rearrangement, which is the principal mechanism of irreversible deformation for granular materials. This paper shows a selection of results from a series of shear tests on a two-dimensional analogue granular material. The route opened by the pioneering work of Radjaï and Roux is followed, and the same framework is used to analyse the experimental data on displacement fluctuations. Digital image correlation has been used to measure and characterise the displacement fluctuations. The analysis of their spatial organisation reveals the emergence of a minimum-length scale; that is, in the order of 10 times the mean particle size.

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