Acoustic waves in granular materials

Dynamic simulations with discrete elements are used to obtain more insight into the wave propagation in dense granular media. A small perturbation is created on one side of a dense, static packing and examined during its propagation until it arrives at the opposite side. The influence of polydispersity is studied by randomly varying the particle sizes by a tiny amount. A size variation comparable to (or larger than) the typical contact deformation, considerably changes sound propagation, i.e., the transmission spectrum becomes discontinuous and lower frequencies are transmitted better in the polydisperse packing. The inter-particle friction affects the dispersion relation, it increases the propagation speed and leads to an extended linear, large wavelength regime

Sound propagation in dry granular materials : discrete element simulations, theory, and experiments

In this study sound wave propagation through different types of dry confined\ud granular systems is studied. With three-dimensional discrete element simulations, theory and experiments, the influence of several micro-scale properties: friction, dissipation, particle rotation, and contact disorder, on the macro-scale sound wave propagation characteristics are investigated. Experiments, analyzed with the “Spectral Ratio Technique”, make it possible\ud to extract frequency-dependent propagation velocities and attenuation. An improved set-up for future investigations is proposed in order to better understand dispersion and propagation of sound in granular materials.\ud The full dispersion relation of a Face-Centered-Cubic lattice is derived from a\ud theoretical analysis that involves translations, tangential elasticity, and rotations. The additional displacement and rotation modes and the energy conversion between them is studied using discrete element simulations. Simulations and theory are in perfect quantitative agreement for the regular lattices examined. As a first small step away from order, systems with weak geometrical disorder (system structure) but strong contact disorder, i.e. with an inhomogeneous contact force distribution, are studied next. They reveal nicely the dispersive nature of granular materials and show strong frequency filtering. Low frequencies propagate, whereas high frequencies vanish exponentially. A more detailed study of how energy is transfered between different wavenumber bands shows linearly increasing transfer rates for increasing wavenumbers. A first theoretical approach using a linear Master Equation leads to a quantitative prediction of the energy evolution per band for short times.\ud A bigger second step in complexity is made by investigating the sound propagation in a realistic tablet made of a sintered frictional and cohesive polydisperse powder and prepared in different ways. These simulations nicely display history dependence and the effect of different material parameters.\ud As a conclusion, simulations were found to be a valuable tool to complement theoretical and experimental approaches towards the understanding of complex phenomena, such as sound propagation in (dry) granular materials. However, many open issues, in particular concerning the modeling, still remain

Sound propagation in isotropically and uni-axially compressed cohesive, frictional granular solids

Using an advanced contact model in DEM simulations, involving elasto-plasticity, adhesion, and friction, pressure-sintered tablets are formed from primary particles and prepared for unconfined tests. Sound propagation in such packings is studied under various friction and adhesion conditions. Small differences can be explained by differences in the structure that are due to the sensitivity of the packing on the contact properties during preparation history. In some cases the signals show unexpected propagation behaviour, but the power-spectra are similar for all values of adhesion and friction tested. Furthermore, one of these tablets is compressed uni-axially and under unconfined conditions and the sound propagation characteristics are examined at different strains: (i) in the elastic regime, (ii) during failure, and (iii) during critical flow: the results vary astonishingly little for packings at different externally applied strains

The influence of particle surface roughness on elastic stiffness and dynamic response

Discrete-element method (DEM) simulations of planar wave propagation are used to examine the effect of particle surface roughness on the stiffness and dynamic response of granular materials. A new contact model that considers particle surface roughness is implemented in the DEM simulations. Face-centred cubic lattice packings and random configurations are used; uniform spheres are considered in both cases to isolate fabric and contact model effects from inertia effects. For the range of values considered here surface roughness caused a significant reduction in stiffness, particularly at lower confining stresses. The simulations confirm that surface roughness effects can at least partially explain the value of the exponent in the relationship between stiffness and mean confining stress for an assembly of spherical particles. Frequency domain analyses showed that the maximum frequency transmitted through the sample is reduced when surface roughness is considered. The assumption of homogeneity of stress and contacts in analytical micromechanical models is shown to lead to an overestimation of stiffness

Numerical determination of the material properties of porous dust cakes

The formation of planetesimals requires the growth of dust particles through collisions. Micron-sized particles must grow by many orders of magnitude in mass. In order to understand and model the processes during this growth, the mechanical properties, and the interaction cross sections of aggregates with surrounding gas must be well understood. Recent advances in experimental (laboratory) studies now provide the background for pushing numerical aggregate models onto a new level. We present the calibration of a previously tested model of aggregate dynamics. We use plastic deformation of surface asperities as the physical model to bring critical velocities for sticking into accordance with experimental results. The modified code is then used to compute compression strength and the velocity of sound in the aggregate at different densities. We compare these predictions with experimental results and conclude that the new code is capable of studying the properties of small aggregates.Comment: Accepted for publication in A&

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