Enhanced micropolar model for wave propagation in ordered granular materials

Merkel, Aurélien; Luding, Stefan

doi:10.1016/j.ijsolstr.2016.11.029

Cited by 36 publications

(56 citation statements)

References 42 publications

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“…In Merkel et al (2010) it was seen that inclusion or removal of rotation does not significantly affect the longitudinal mode in an ordered granular crystal. However, the situation is different when rotations become prominent and other wave modes cannot be ignored (see Yang and Sutton, 2015;Merkel and Luding, 2017, and the references therein).…”

Section: R K Shrivastava and S Luding: Effect Of Disorder On Bulk mentioning

confidence: 99%

Effect of disorder on bulk sound wave speed: a multiscale spectral analysis

Shrivastava¹,

Luding²

2017

Nonlin. Processes Geophys.

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Abstract. Disorder of size (polydispersity) and mass of discrete elements or particles in randomly structured media (e.g., granular matter such as soil) has numerous effects on the materials' sound propagation characteristics. The influence of disorder on energy and momentum transport, the sound wave speed and its low-pass frequency-filtering characteristics is the subject of this study. The goal is understanding the connection between the particle-microscale disorder and dynamics and the system-macroscale wave propagation, which can be applied to nondestructive testing, seismic exploration of buried objects (oil, mineral, etc.) or to study the internal structure of the Earth. To isolate the longitudinal P-wave mode from shear and rotational modes, a one-dimensional system of equally sized elements or particles is used to study the effect of mass disorder alone via (direct and/or ensemble averaged) real time signals, signals in Fourier space, energy and dispersion curves. Increase in mass disorder (where disorder has been defined such that it is independent of the shape of the probability distribution of masses) decreases the sound wave speed along a granular chain. Energies associated with the eigenmodes can be used to obtain better quality dispersion relations for disordered chains; these dispersion relations confirm the decrease in pass frequency and wave speed with increasing disorder acting opposite to the wave acceleration close to the source.

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Section: R K Shrivastava and S Luding: Effect Of Disorder On Bulk mentioning

confidence: 99%

Effect of disorder on bulk sound wave speed: a multiscale spectral analysis

Shrivastava¹,

Luding²

2017

Nonlin. Processes Geophys.

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“…Figure 9A shows that the P-wave dispersion relation of the dry FCC packing is highly nonlinear, ie, the wave velocity decreases with the increase of the wavenumber and the frequency. 13,14 The group velocity approaches zero in the very high-frequency regime, as shown in Figure 9A. The amplitude spectrum of the particle velocity components along x 3 in Figure 9C highlights that the P-wave dispersion relation of the solid phase is identical to the one for the fluid phase of the saturated FCC packing (see Figure 8B).…”

Section: Time-domain and Frequency-domain Responsesmentioning

confidence: 73%

“…Figure A shows that the P‐wave dispersion relation of the dry FCC packing is highly nonlinear, ie, the wave velocity decreases with the increase of the wavenumber and the frequency . The group velocity approaches zero in the very high‐frequency regime, as shown in Figure A.…”

Section: Modeling Elastic Wave Propagation In Saturated Granular Crysmentioning

confidence: 90%

“…Unlike typical ultrasonic experiments in which wave velocities are inferred from the time evolution of signals, numerical simulations allow for direct measurements of wave velocities from dispersion branches in the frequency domain. 13,14 For dry granular materials, it is known that input frequencies affect the identification of travel time and travel distance from received signals and, in turn, wave velocities. Therefore, the wave velocities derived from dispersion branches, obtained from simulations, can be treated as the "ground truth."…”

Section: Effect Of Acoustic Sourcementioning

confidence: 99%

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Hydro‐micromechanical modeling of wave propagation in saturated granular crystals

Cheng

Luding

Rivas

et al. 2019

Num Anal Meth Geomechanics

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Summary Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro‐micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two‐way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore‐scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one‐dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face‐centered‐cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.

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“…The unique property of the waves propagating in the granular material is the attenuation or the localization due to the contribution of the randomness and the plasticity (dissipation) of the beads [5][6][7][8][9][10]. The localization or the attenuation of the waves due to either the disorder or the dissipation in granular matter are reported [14][15][16][17][18][19][20][21][22]. However, the theory on this kind of phenomena is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Localization of the small amplitude wave in three dimensional granular material

et al. 2020

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A general small amplitude wave equations are proposed for the granular material. It is shown that the wave is localized in a certain region which is in agreement with that found in both the analytical and the simulation results. The localization region depends on the wave frequency and the parameters of the granular material such as the bead radius, the magnitude of the initial prestress, the Young's modulus and the bead mass. Several examples are given which indicate that the attenuation rate of the wave depend on the permutation of the bead. It also depends on whether the wave is longitudinal or tangential.

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Enhanced micropolar model for wave propagation in ordered granular materials

Cited by 36 publications

References 42 publications

Effect of disorder on bulk sound wave speed: a multiscale spectral analysis

Effect of disorder on bulk sound wave speed: a multiscale spectral analysis

Hydro‐micromechanical modeling of wave propagation in saturated granular crystals

Localization of the small amplitude wave in three dimensional granular material

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