Waves In Granular Materials Research Articles

Influence of Aspect Ratio on Wave Propagation in Granular Crystals Consisting of Ellipse-Shaped Particles

The behavior of waves in granular materials is very complex and closely related to the macro-micro properties such as particle shape, packing, and particle size distribution. In this study, the influence of the aspect ratio (AR) and confining stress on wave propagation in 2D granular crystals consisting of ellipse-shaped particles is investigated based on discrete element method. The energy attenuation, wave velocity, wavefront shape, and frequency dispersion are mainly focused. The results show that the energy attenuation exhibits an increasing trend with bigger confining stress and smaller AR in the direction of wave propagation. The wave velocities increase with increasing AR, and the relation between compressive wave velocities and the confining stress and AR is obtained. Wavefront has the elliptical shape which has the same AR as elliptical particles of specimen, and its analytical expression is also obtained. The dispersion is affected by AR, which is mainly reflected in the modified particle spacing in sine fitted frequency dispersion curve. Larger confining stress allows a larger maximum frequency, and produces stronger dispersion. The above conclusion can provide a reference for wave-guided granular crystals design.

Influence of packing density and stress on the dynamic response of granular materials

Laboratory geophysics tests including bender elements and acoustic emission measure the speed of propagation of stress or sound waves in granular materials to derive elastic stiffness parameters. This contribution builds on earlier studies to assess whether the received signal characteristics can provide additional information about either the material’s behaviour or the nature of the material itself. Specifically it considers the maximum frequency that the material can transmit; it also assesses whether there is a simple link between the spectrum of the received signal and the natural frequencies of the sample. Discrete element method (DEM) simulations of planar compression wave propagation were performed to generate the data for the study. Restricting consideration to uniform (monodisperse) spheres, the material fabric was varied by considering face-centred cubic lattice packings as well as random configurations with different packing densities. Supplemental analyses, in addition to the DEM simulations, were used to develop a more comprehensive understanding of the system dynamics. The assembly stiffness and mass matrices were extracted from the DEM model and these data were used in an eigenmode analysis that provided significant insight into the observed overall dynamic response. The close agreement of the wave velocities estimated using eigenmode analysis with the DEM results confirms that DEM wave propagation simulations can reliably be used to extract material stiffness data. The data show that increasing either stress or density allows higher frequencies to propagate through the media, but the low-pass wavelength is a function of packing density rather than stress level. Prior research which had hypothesised that there is a simple link between the spectrum of the received signal and the natural sample frequencies was not substantiated.

Rarefaction wave propagation in tapered granular columns

The study of stress waves in granular materials is of some importance in several industrial bulk materials handling systems. In particular, the growth in the magnitude of rarefaction waves due to friction has been thought to play an important role in the silo quaking phenomenon. To this end, this paper examines the propagation of rarefaction waves in granular columns subject to Coulomb wall friction, focusing on the effect of geometry by examining converging and diverging tapered columns. A one-dimensional dynamic model of these systems is developed and analytical solutions of this model are compared to a numerical model based on the Arbitrary Lagrangian–Eulerian formulation in a finite element analysis. This numerical model was first validated using the known behaviour of cylindrical columns. In all cases, the rarefaction waves examined in this work grew with the distance travelled up the column; however, the rate was shown to depend on the half-angle of the taper. Over a range of small angles, the analytical model was found to accurately predict this behaviour.

Shock waves in granular materials: Discrete and continuum comparisons

Small amplitude compression and shock waves in granular materials were examined from the point of view of an analytical model and discrete element simulations. The barotropic behaviour of granular materials was discussed in terms of the mechanisms behind the formation of shock fronts. This discussion leads to the development of a one dimensional continuum model which was used together with the method of characteristics to describe the nature of shock waves. The model provides a relationship between the states of the material on either side of a shock and an equation that defines the velocity of shock waves. Discrete Element Modelling was used to demonstrate the shock forming process in granular materials and to confirm the predictions of the analytical model. During this process it is demonstrated that an assembly based on a linear contact model does not show any barotropy and consequently cannot describe dynamics of granular materials in terms of shock forming mechanisms. This observation may have important consequences in the application of the linear contact model to dynamic systems. The Hertz–Mindlin contact model did not suffer from this issue and was able to demonstrate both barotropy and shock formation. The DEM assemblies were characterised in terms of the material properties of the analytical model which allowed direct comparisons to be made. In all respects the analytical model performed well, predicting the change in state of the material and the shock wave speed with a good deal of accuracy.

Dynamic Effective Mass of Granular Media

We develop the concept of frequency dependent effective mass, M[over ](omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M[over ](omega) provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation of acoustic waves in granular materials can be influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.

Acoustic waves in granular materials

The numerous sound propagation mechanisms in granular materials are rather complex and strongly depend on the material micro-scale parameters, such as inter-particle friction or damping. The use of DEM (Discrete Element Simulations) allows us to tune these parameters and hence to understand their influence. In both regular (crystal-like) and polydisperse (sand-like) systems of spheres, a small perturbation is created on one side of the simulation box and examined during its propagation and on arrival at the opposite side. Starting from a regular packing, a tiny size variation comparable to the typical contact deformation already changes sound propagation considerably [1]. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, mainly due to scattering effects. Furthermore, the wave propagation and transmission properties are studied on fully polydisperse, frictional and cohesive packings under increasing load until breakage of the material [2]. [1] O. Mouraille and S. Luding, Sound wave propagation in weakly polydisperse granular materials, Ultrasonics, submitted. [2] O. Mouraille, O. Herbst and S. Luding, Testing cohesive and frictional granular materials with the discrete element model, in preparation.

Wave Velocities in Granular Materials under Microgravity

Velocities of primary (P) and shear (S) waves in granular materials are highly dependent on confining stress. These wave velocities are related to mechanical properties of the materials such as stiffness, density, and stress history. Measurements of the wave velocities using piezoelectric sensors provide scientists and engineers a technique for nonintrusive characterization of those mechanical properties. For aerospace engineering, measuring the wave velocities under microgravity, which simulates low loading and stress conditions, has a number of potential applications. It can help the understanding of the soil mechanics and the development of appropriate materials handling technologies in extraterrestrial environments, which will be crucial to meeting NASA’s future space exploration goals. This paper presents the technique and results of experiments conducted at NASA Glenn Research Center using the 2.2s drop tower. Velocities of P and S waves in three sizes of glass beads and one size of alumina beads were measured under initially dense or loose compaction states. It was found that under microgravity, the wave signals were significantly weaker and the velocities were much slower. The material that makes up the beads has a strong influence on the wave velocities as well. The initial compaction state also has some influence on the wave velocities.

Pressure wave propagation in a granular bed

The transmission of pressure waves in granular materials is complicated by the heterogeneity and nonlinearity inherent in these systems. Such waves are propagated through particle contacts primarily along the "force chains" which carry most of the load in granular materials. These fragile and ephemeral chains coupled with irregular particle packing lead to the observed heterogeneity. Nonlinearity in these systems is largely the result of the force-deformation characteristic at particle contacts. Through experiments and simulations, we study the effects of heterogeneity and nonlinearity on the properties of pressure waves through a granular bed.

On solitons in microstructured solids and granular materials

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems — wave propagation in dilatant granular materials and wave propagation in shape-memory alloys — are studied. Model equations are KdV-like evolution equations in both cases. The types of solutions are determined and analysed. It has been found that waves in granular materials are composed by two concurrent ensembles of solitary waves and there exist a threshold parameter value governing the behaviour of stable waves in alloy type materials.

Elastoplastic Waves in Granular Materials

For a description of the deformation of materials with different resistances to tension and compression, the conventional rheological diagram is supplemented by a new element — rigid contact. It is used to construct a model of an ideal granular material possessing elastic and plastic properties. The loose state of the material is described by the Mises–Schleicher strength conditions, and transition to the plastic state is described by the Mises yield condition. The model proposed is employed to study the propagation of longitudinal elastic and plastic compression shock waves. It is shown that one- or two-wave configurations of discontinuities occur depending on the rate of compression and the degree of the initial loosening of the material.

Dilatancy-Induced P Waves as Evidence for Nonlinear Soil Behavior

A much-discussed topic in seismology deals with how and under which loading conditions soil shows nonlinear behavior and how this can be verified from seismograms. Seismologists have been seriously searching for signatures of nonlinear soil response to earthquakes for about two decades. A mechanism explaining the dispersion in the P -wave spectra due to the interaction between compressional ( P ) and shear ( S ) waves is presented. Shear waves in granular materials induce longitudinal dilatancy waves (so-called Δ waves) with approximately double frequency. This can be explained with dilatancy and contractancy, which is characteristic of granulates under shear deformations. The predicted dispersion is observed in laboratory experiments and verified by comparing accelerograms from hard-rock and soil stations from the Vrancea region, Romania. The arrival-time difference between Δ waves and S waves may theoretically be indicative of the thickness of nonsaturated granular layers. These results, modeled with nonlinear constitutive relations of the rate type, show a specific type of nonlinearity in granular sediments also for earthquakes of moderate magnitudes.

Effect of seawater salt on compressional wave in dry beach sand

At the previous ASA meeting, quantitative results were presented revealing the effect of water content on compressional wave velocity in beach sand. New ultrasonic compressional wave results are presented demonstrating the effect of salt crystals bonding beach sand grains as seawater is evaporated. Wave velocity and attenuation results are compared with beach sand rinsed with distilled water. Although the salinity of seawater is only about 35 parts per thousand, the salt concentration increases rapidly as the seawater is evaporated. The sand grains become covered with a glaze and solid salt bonds are formed connecting the grains. The acoustic properties of salt crystals (compressional wave velocity 4.53 km/s, and density 2.165×103 kg/m3) are close to those of a sand grain. Results from controlled experiments using spherical particles and plates bonded with evaporated salt water are also discussed. The author is not aware of any publication describing the adhesion of sea salt to beach sand. The new findings contribute to understanding the propagation of high-frequency compressional waves in granular materials leading to reliable seismoacoustic detection of buried objects in beach sand. [Work supported by ONR.]

Observation of nonlinear interaction of acoustic waves in granular materials: demodulation process

Experimental study of the demodulation effect of ultrasonic waves in glass beads are reported. Both impulsive (burst) and continuous regime have been studied for amplitude modulated signals with its carrier frequency of 100 kHz. It is shown that two low frequency acoustical modes corresponding to the modulation frequency (in the range of few kHz) are excited due to the nonlinear processes in the granular medium. The excitation of a first mode propagating mainly through the beads (solid-based mode) and the excitation of a second mode propagating mainly through the air saturating the granular material (fluid-based mode) are observed. Possible physical mechanisms of generation and regimes of propagation in the granular assemblages are discussed.

Model for Subharmonic Waves in Granular Materials

Here, we present a model explaining the instability onset of granular surface waves. Our model is based on the fact that lateral motion of grains at large scale takes place when the layer is in free flight, whereas, thickness relaxation occurs only during the layer-plate collision. A master equation is introduced to take into account the mass motion while simple arguments allow us to write down a diffusion equation for the layer thickness. Numerical simulation shows that square patterns are selected by the nonlinearities introduced in this model and localized structures are observed when the local dilation in the layer becomes small with respect to the particle diameter. Figure 1 is a side view of the experimental cell showing the time evolution of the waves close to the layer-container collison. During the collision, thickness modulations relax until the layer takes off. Each layer modulation splits into two sand packets which move laterally. They subsequently collide and form new modulations shifted in space by half the pattern wavelength. The pattern is then subharmonic, oscillating at one half the drive frequency. Lateral motion of grains takes place during every cycle of the external excitation. This motion is similar to that of a fluid particle in a standing surface wave. However, there is one important difference: In the fluid case, the lateral transfer of mass is induced by the gradient of hydrostatic pressure which exists at all times (6). In the granular case, the pressure gradient exists only during the collision and is a result of the transfer of momentum from the plate to the grain network. In our analysis, we, therefore, consider the effective drive to be composed of a series of impulsive accelerations that only occur when the layer collides with the plate. The dynamics of the layer described in the continuum limit using two variables: , the local layer thickness, and , the horizontal component of the grain velocity ( represents the horizontal coordinates and is the time). We consider to be independent of the vertical coordinate. With these variables, the

Wave Propagation in Granular Rod Using High-Gradient Theory

Based on a microstructural approach, granular material can be represented by an equivalent continuum of the high-gradient type. The high-gradient model is used in this paper to study the effect of microstructure on the propagation of waves in granular material. The constitutive coefficients of the high-gradient continuum are expressed in explicit functions of interparticle stiffness. Based on the high-gradient model, a fourth-order partial differential equation is formulated for the wave propagation in granular medium. Hamilton's principle is employed to devise the additional boundary conditions involved in the differential equation. The differential equation is solved for wave propagation in a finite rod of granular material with specified boundary conditions. The present results show that the dynamic behavior of a rod of granular solid is very different from the behavior of a rod of classical continuum. The predicted phenomena are in agreement with the simulation results from discrete element methods and with the experimental observations from a chain of photoelastic disks subjected to an impact load.

Density waves in dry granular media falling through a vertical pipe.

We report experimental measurements of density waves in granular materials flowing down in a capillary tube. The density wave regime occurs at intermediate flow rates between a low density free fall regime and a high compactness slower flow. We observe this intermediate state when the ratio of the tube diameter to the particle size lies between 6 and 30. The propagation velocity of the waves is constant along the tube length and increases linearly with the total mass flow rate $\ensuremath{\Phi}$. The wave structures include compact clogs (lengths are independent of $\ensuremath{\Phi}$) and bubbles of low compactness (lengths increase with $\ensuremath{\Phi}$). Both length distributions are invariant along the tube length. A model assuming a free fall regime in the bubbles and a compactness of 35% inside the clogs allows to account for the mass distribution in the flow.

Density patterns in two-dimensional hoppers.

Recent experiments by Baxter et al. [Phys. Rev. Lett. 62, 2825 (1989)] showed the existence of density waves in granular material flowing out of a hopper. We show, using molecular dynamics simulations, that this effect is a consequence of static friction and find that these density fluctuations follow a 1/${\mathit{f}}^{\mathrm{\ensuremath{\alpha}}}$ spectrum. The effect is enhanced when the opening angle of the hopper decreases.

Recurrent clogging and density waves in granular material flowing through a narrow pipe

We report on density waves in granular material, investigated both experimentally and numerically. When granular material falls through a long narrow pipe one observes recurrent clogging. The kinetic energy of the falling particles increases up to a characteristic threshold corresponding to the onset of recurrent clogging and density waves of no definite wavelength. The distances between regions of high density depend strongly on the initial conditions. They vary irregularly without any characteristic time and length scale. The particle-flow was investigated using 2D Molecular Dynamics simulations. Experimental investigations lead to equivalent results.

Experimental and computational modeling of wave propagation in granular materials

A hybrid experimental-computational study has been conducted in order to determine the propagational characteristics of mechanical waves in granular materials. The experimental investigation has used the method of dynamic photoelasticity to collect photographic data which provide information on the wave speeds, integranular contact loadings, and wave-spreading characteristics. The computational study employed the use of the distinct-element method whereby the motion of each granule in the material is modeled by rigid-body dynamics assuming each particle interaction has particular frictionless stiffness and damping forces. The experimental results provide special dynamic material constants necessary for the computational modeling, and they also provide data for comparison purposes. Results from the experimental and computational studies compare well with each other and indicate that local microstructure plays an important role in the wave propagation through such materials.

Numerical Studies of Dynamic Compaction of Inert and Energetic Granular Materials

In this paper a numerical study of dynamic compaction of granular materials is presented. A multiphase mixture model treating two-phase nonequilibrium flow is applied to describe dynamic compaction experiments. Compaction is modeled using a description of grain distortion driven by pressure differences. Various energetic and inert granular materials including HMX, Fluid A (Nitrocellulose), Melamine, and Teflon are studied for various piston-impact conditions and compared to existing data. Numerical analysis of a ramp-wave piston-impact experiment is also examined. The multiphase mixture model predicts reasonably well the observed steady compaction wave characteristics. Dynamic compaction experiments with detailed resolution are needed to better address the transient behavior of compaction waves in granular materials.