Quasistatic granular material rheology from particle simulations

We report on the quasistatic behaviour of model granular materials, as probed by DEM simulations of isotropic compression and triaxial compression tests, focussing on the macroscopic behaviour dependence on control parameters expressed in dimensionless forms that combine contact laws with test conditions, and on the influence of the initial state. A discussion of the microscopic origins of strain, which in some situations of small strains and stable contact networks are due to contact deflections, and in other cases results from the continuous breaking and repairing of networks under varying loads provides a useful classification of rheological regimes. Some guidelines for parameter choices in numerical simulations, and for some homogenization approaches, are inferre

Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach

We clarify the relation between the ergodicity breaking transition predicted by mode-coupling theory and the so-called dynamic transition predicted by the static replica approach. Following Franz and Parisi [Phys. Rev. Lett. 79, 2486 (1997)], we consider a system of particles in a metastable state characterized by non-trivial correlations with a quenched configuration. We show that the assumption that in a metastable state particle currents vanish leads to an expression for the replica off-diagonal direct correlation function in terms of a replica off-diagonal static four-point correlation function. A factorization approximation for this function results in an approximate closure for the replica off-diagonal direct correlation function. The replica off-diagonal Ornstein-Zernicke equation combined with this closure coincides with the equation for the non-ergodicity parameter derived using the mode-coupling theory.Comment: revised version; to be published in EP

Strain versus stress in a model granular material: a Devil's staircase

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 Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered throughout text, very close to published pape

Mobile particles in an immobile environment: Molecular Dynamics simulation of a binary Yukawa mixture

Molecular dynamics computer simulations are used to investigate thedynamics of a binary mixture of charged (Yukawa) particles with a size-ratio of 1:5. We find that the system undergoes a phase transition where the large particles crystallize while the small particles remain in a fluid-like (delocalized) phase. Upon decreasing temperature below the transition, the small particles become increasingly localized on intermediate time scales. This is reflected in the incoherent intermediate scattering functions by the appearance of a plateau with a growing height. At long times, the small particles show a diffusive hopping motion. We find that these transport properties are related to structural correlations and the single-particle potential energy distribution of the small particles.Comment: 7 pages, 5 figure

Numerical stress probing on a 2D model granular material

We use DEM simulations on a simple 2D model of a granular material to measure its deformation response to small stress increments of arbitrary directions (stress probes) and assess the applicability of the classical concepts of elastoplasticity. We impose stress increments in the space of principal stresses components, to numerical specimens selected at various intermediate states along the biaxial compression path. The elastic part of the incremental response is systematically identified by building the elastic stiffness matrix of well-equilibrated configurations. Plastic strain increments are computed standing on the partition hypothesis for strain increments into elastic- and plastic parts. The domain of validity of the partition hypothesis is discussed, playing extensively with the magnitude of the stress increments, in order to identify a range in which the incremental response is homogeneous of degree 1 and the essential features of plasticity models can be observed. We investigate in particular the existence of a plastic flow rule with a clearly defined plastic flow direction and yield criterion. The robustness of these features is tested over a range of contact stiffness levels and against the dominant deformation modes (i.e., based on contact deformation or network rearrangement)

Internal states of model isotropic granular packings. III. Elastic properties

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page

Equilibrium onions?

We demonstrate the possibility of a stable equilibrium multi-lamellar ("onion") phase in pure lamellar systems (no excess solvent) due to a sufficiently negative Gaussian curvature modulus. The onion phase is stabilized by non-linear elastic moduli coupled to a polydisperse size distribution (Apollonian packing) to allow space-filling without appreciable elastic distortion. This model is compared to experiments on copolymer-decorated lamellar surfactant systems, with reasonable qualitative agreement

Crop ontology in support of conservation and use of banana genetic resources

Poster presented at Workshop on Crop Ontology and Phenotyping Data Interoperability. Montpellier (France), 31 Mar-4 Apr 201