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

Effect of the microstructure on the propagation velocity of ultrasound in magnetic powders

We analyze experimentally and theoretically the sound propagation velocity of P-waves in granular media made of micrometer-size magnetite particles under an external magnetic field. The sound velocity is measured in a coherent (long-wavelength) regime of propagation after a controlled sample preparation consisting of a fluidization and the application of a magnetic field. Several different procedures are applied and result in different but reproducible particle arrangements and preferential contact orientations affecting the measured sound velocity. Interestingly, we find that the sound velocity increases when the magnetic field is applied parallel to the sound propagation direction and decreases when the magnetic field is applied perpendicular to the sound propagation direction. The observed qualitative relationship between the changes in the particle arrangement and the sound velocity is analyzed theoretically based on an effective medium theory adapted to account for the effect of the magnetic field in the preparation procedure and its influence on the medium contact fabric.

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. 2) In addition to modeling grains as a gas of dissipative, rigid mass points, it is very helpful take grains as a thermal solid that has been sliced and diced. 3) General principles that appear invalid in granular media are repaired and restored once the true entropy is included. These abnormalities (such as invalidity of the fluctuation-dissipation theorem, granular temperatures failing to equilibrate, and grains at rest unable to explore the phase space) are consequences of the athermal approximation, not properties of granular media.

Ultrasonic evaluation of the morphological characteristics of metallic powders in the context of mechanical alloying

An ultrasonic method is proposed to characterize the morphological (geometrical) aspects of powders through the elastic modulus dependence of their packing on the factors of polydispersity, coordination number and particle shape. During the mechanical alloying process, the variation in geometrical characteristics of powders provides critical information. Ultrasonic parameters are shown to be sensitive not only to the average contact number per bead (i.e. the coordination number) but also to characteristics of the bead size distribution, when given the same sample preparation and confining pressure. These parameters, in turn, are sensitive to both the granular medium polydispersity and particle shapes. A non-monotonic behavior of the ultrasonic velocity (and of the derived compressional wave modulus) is observed throughout the alloying process, which thus offers possibilities for powder structure monitoring.

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. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

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. Therefore a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from 26^{∘} to the more realistic value of 30^{∘}. (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan, and Matsuoka-Nakai-realizing each, and interpolating between them, by shifting a single scalar parameter.

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. As the theory makes no reference to fabric anisotropy, the influence of which on sound is in doubt.

Comparison of hyperelastic models for granular materials

Three recently proposed hyperelastic models for granular materials are compared with experiment data. Though all three are formulated to give elastic moduli that are power law functions of the mean stress, they have rather different dependencies on individual stresses, and generally differ from well established experimental forms. Predicted static stress distributions are in qualitative agreement with experiments, but do not differ greatly from isotropic linear elasticity, and similarly fail to account for variability in experiment data that presumably occurs due to a preparation dependence of granular materials.