Why granular media are thermal, and quite normal, after all.

Two approaches exist to account for granular dynamics: The athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. Discrete element method (DEM), granular kinetic theory and athermal statistical mechanics (ASM) belong to the first, granular solid hydrodynamics (GSH) to the second one. A discussion of the conceptual differences between both is given here, leading, among others, to the following insights: 1) While DEM and granular kinetic theory are well justified to take grains as athermal, any entropic consideration is far less likely to succeed.

Transient elasticity and the rheology of polymeric fluids with large amplitude deformations.

Transient elasticity is a systematic generalization of viscoelasticity. Its purpose is to give a coherent description of non-Newtonian effects displayed by soft-matter systems, especially polymer melts and solutions. Using the concept of transient elasticity we describe here a hydrodynamic model for polymeric fluids, which is applicable for large amplitude deformations.

Transient elasticity and polymeric fluids: Small-amplitude deformations.

Transient elasticity (TE) is a concept useful for a systematic generalization of viscoelasticity. Due to its thermodynamic consistency, it naturally leads to a simple description of non-Newtonian effects displayed by polymeric fluids, granular media, and other soft matter. We employ a continuum-mechanical theory that is derived from TE and tailored to polymeric fluids, showing how it captures a surprisingly large number of phenomena in shear and elongational flows, including stationary, oscillatory, and transient ones, as well as the flow down an inclined channel.

Applying GSH to a wide range of experiments in granular media.

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, whose wide range of applicability is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: i) static stress distribution, clogging; ii) elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; iii) rapid dense flow: the μ-rheology, Bagnold scaling and the stress minimum; iv) elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and non-local fluidization.

Hydrodynamics of granular gases with a two-peak distribution.

Vibrating walls, frequently employed to maintain the temperature (i.e., average velocity) in a granular gas, modify the system strongly, rendering it dissimilar to a molecular one in various aspects.

Dip of the granular shear stress.

Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcing a constant volume does not prevent the local density to vary, and a stress dip may still occur.

Expression for the granular elastic energy.

Granular solid hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some drawbacks.

Elastic waves in the presence of a granular shear band formed by direct shear.

The propagation of elastic waves in a box under direct shear, filled with glass beads and being sheared at constant rates, is studied experimentally and theoretically. The respective velocities are shown to be essentially unchanged from that in a static granular system under the same pressure and shear stress but without a shear band. Influence of shear band on sound behaviors are also briefly discussed.

Propagation of elastic waves in granular solid hydrodynamics.

The anisotropic stress-dependent velocity of elastic waves in glass beads--as observed by Khidas and Jia [Phys. Rev. E 81, 021303 (2010)]--is shown to be well accounted for by "granular solid hydrodynamics," a broad-range macroscopic theory of granular behavior.

Inconsistency of a dissipative contribution to the mass flux in hydrodynamics.

The possibility of dissipative contributions to the mass flux is considered in detail. A general thermodynamically consistent framework is developed to obtain such terms, the compatibility of which with general principles is then checked-including Galilean invariance, the possibility of steady rigid rotation and uniform center-of-mass motion, the existence of a locally conserved angular momentum, and material objectivity. All previously discussed scenarios of dissipative mass fluxes are found to be ruled out by some combinations of these principles but not a new one that includes a smoothed velocity field v[over ] .

Incremental stress-strain relation from granular elasticity: comparison to experiments.

Granular media are reversible and elastic if the stress increments are small enough. An elastic stress-strain relation, employed previously to determine static stress distributions, in this paper is compared to experiments by Kuwano and Jardine [Geotechnique 52, 727 (2002)] on incremental stress-strain relations, and shown to yield satisfactory agreement. In addition, the yield condition is given a firmer footing.

Hydrodynamic theory of polydisperse chain-forming ferrofluids.

The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the chain-forming particles, while accounting for the free magnetic particles by dissipative terms in the Maxwell equations.

From elasticity to hypoplasticity: dynamics of granular solids.

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics.

Granular elasticity: stress distributions in silos and under point loads.

An elastic-strain-stress relation, the result of granular elasticity as introduced in the preceding paper, is employed here to calculate the stress distribution (a) in cylindrical silos and (b) under point loads assuming uniform density. In silos, the ratio k{J} between the horizontal and vertical stress is found to be constant (as conjectured by Janssen) and given as k{J}=1-sin phi (with phi the Coulomb yield angle), in agreement with a construction industry standard usually referred to as the Jaky formula. Next, the stress distribution at the bottom of a granular layer exposed to a point force at its top is calculated.

Granular elasticity: general considerations and the stress dip in sand piles.

Granular materials are predominantly plastic, incrementally nonlinear, preparation-dependent, and anisotropic under shear. Nevertheless, their static stress distribution is well accounted for, in the whole range up to the point of failure, by a judiciously tailored isotropic nonanalytic elasticity theory termed granular elasticity. The first purpose of this paper is to carefully expound this view.

Energetic instability unjams sand and suspension.

Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions, and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain relation is derived that captures many relevant features of sand, including especially the Coulomb yield surface and a third-order jamming transition.

Granular elasticity without the Coulomb condition.

A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.

Sound damping in ferrofluids: magnetically enhanced compressional viscosity.

The damping of sound waves in magnetized ferrofluids is investigated and shown to be considerably higher than in the nonmagnetized case. This fact may be interpreted as a field-enhanced, effective compressional viscosity-in analogy to the ubiquitous field-enhanced shear viscosity that is known to be the reason for many unusual behaviors of ferrofluids under shear.

Shear-excited sound in magnetic fluid.

Perceptible sound is shown to be excited in ferrofluids by the shear motion of a rigid plate, if the fluid is exposed to a magnetic field oblique both to the plate and to the direction of propagation. This is in contrast to other fluids, including anisotropic ones such as nematic liquids.