We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.

This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction ΦRCP ≃ 0.639 with a high coordination number: z * ≃ 6 on the force-carrying backbone. If compressed with a realistic coefficient of friction µ = 0.3 packings stabilize in a loose state with Φ ≃ 0.593 and z * ≃ 4.5. And, more surprisingly, an idealized "vibration" procedure, which maintains an agitated, collisional régime up to high densities results in equally small values of z * while Φ is close to the maximum value ΦRCP. Low coordination packings have a large proportion (>10%) of rattlers -grains carrying no force -the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized "floppy modes" associated with divalent grains. Low pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.

The statement of the title is shown by numerical simulation of homogeneously sheared assemblies of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate gamma[over ] in the limit of small gamma[over ] and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle phi , equal to 5.76 degrees +/-0.22 degrees in simple shear, is independent of average pressure P in the rigid limit and stems from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, similar to the effective friction of a frictionless slider on a bumpy surface. Solid fraction Phi remains equal to the random close packing value approximately 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit. Defining the inertial number as I=gamma radical m/(aP), with m the grain mass and a its diameter, both internal friction coefficient mu*=tan phi and volume 1/Phi increase as powers of I in the quasistatic limit of vanishing I , in which all mechanical properties are determined by contact network geometry. The microstructure of the sheared material is characterized with a suitable parametrization of the fabric tensor and measurements of coordination numbers.

Model granular assemblies, in which grains are assumed rigid and frictionless, at equilibrium under some prescribed external load, are shown to possess, under generic conditions, several remarkable mechanical properties, related to isostaticity and potential energy minimization. Isostaticity -the uniqueness of the contact forces, once the list of contacts is known-is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to small load increments, even though grains are perfectly rigid. In general, one gets an upper bound on the contact coordination number. The approximation of small displacements, that is introduced and discussed, allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation in rearrangements of the network of contacts. Plasticity and hysteresis are related to the lack of such uniqueness, which can be traced back, apart from intergranular friction, to non-reversible rearrangements of small but finite extent, in which the system jumps between two distinct potential energy minima in configuration space, or to bounded tensile forces, deriving from a non-convex potential, in the contacts. Properties of response functions to load increments are discussed. On the basis of past numerical studies, it is argued that, provided the approximation of small displacements is valid, displacements due to the rearrangements of the rigid grains in response to small load increments, once averaged on the macroscopic scale, are solutions to elliptic boundary value problems (similar to the Stokes problem for viscous incompressible flow).

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

A series of viscosimetric and small-angle neutron scattering experiments on asphaltenes diluted in mixed toluene/heptane solvents has been conducted, with the purpose of characterizing the size, molecular weight, and internal structure of asphaltene aggregates as a function of solvent conditions. With increasing flocculant (i.e., heptane) content in the solvent, the intrinsic viscosities of asphaltene aggregates first decreased, went through a minimum for heptane fractions ≈ 10−20%, and then increased at the approach of flocculation. These variations paralleled those of the volume of aggregate occupied per unit mass of asphaltene, a behavior reminiscent of the Flory−Fox relationship for polymers in a solvent. This volume, proportional to the cubed radius of gyration of the aggregates divided by their molecular weight, was determined from the neutron scattering data. For increasing heptane fractions in the solvent, the molecular weight of the aggregates increased with their radius of gyration according to a power law, the exponent being in the range of 2. This exponent also characterized the self-similar internal structure of the asphaltene aggregates. With due care to the possible systematic effects of the strong polydispersity of these aggregates, these results are discussed in light of recent models of colloidal aggregation.

The structure of asphaltene solutions in toluene was studied by small-angle neutron scattering (SANS) as a function of temperature and concentration. Temperature alters solvent quality, flocculation being expected at low temperature. SANS measurements were carried out at four different temperatures (from 73 down to 8 °C) for solute (asphaltene) volume fractions Φ ranging from =0.3 to ∼10%. Asphaltenes were found to form nanometric aggregates, whose average masses (Mw) and radii of gyration (RGZ) increased as temperature decreased. These parameters hardly varied with concentration in the dilute regime Φ e 3-4%, in which no evidence of dissociation was found. At higher Φ, apparent values of the same parameters (Mw and RGZ) decreased as repulsive interactions or aggregate interpenetration reduced the normalized intensity, I/Φ, a phenomenon reminiscent of the semidilute regime of polymers and fractal aggregates. At the two lowest temperatures studied, 8 and 20 °C, a strong scattering at low q signaled flocculation, as some of the asphaltenes formed dense domains of micronic size. This phenomenon occurred throughout the studied concentration range and entailed some limited hysteresis for time scales of the order of a few hours.

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wavefront followed by random oscillations made of multiply scattered waves. We find that the coherent wavefront is insensitive to details of the packing: force chains do not play an important role in determining this wavefront. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse-propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wavefront scales with pressure as p 1/6 ; we compare this result with experimental data on various granular systems where deviations from the p 1/6 behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.