NONLINEAR ELASTIC WAVES IN A GRANULAR MEDIUM (original) (raw)
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Towards a Mathematical Model for Elastic Wave Propagation in Granular Materials
Engineering, 2012
A theoretical model for the propagation of acoustic waves in dry granular media is presented within the framework of the nonlinear granular elasticity. An essential ingredient is the dependence of the elastic moduli on compression. For the purpose of illustration, we analyze the case of a time-harmonic plane wave propagation under isotropic compression. We derive explicit relations for the wave speed dependence with the confining pressure. The present approach provides an accurate description of acoustic wave propagation in granular packings and represents a powerful tool to interpret the results of current experiments.
Transitional nonlinear elastic behaviour in dense granular media
2008
Nonlinear sound propagation in a stressed glass bead pack is investigated via amplitude measurements of harmonic generation. We evidence two distinct regimes of sound-matter interaction: reversible and irreversible, as a function of the ratio r s between dynamic strain and static one. In the reversible regime, the higher harmonics generated agree well with a mean-field model based on the Hertz contact theory, and the coefficient of nonlinearity b deduced from the measured amplitude of second-harmonic is consistent with that deduced from the acoustoelastic measurement. Beyond a certain threshold (r s > 3%), the interaction of sound wave with granular matter becomes irreversible, accompanied by a small compaction of the medium.
Elastic wave propagation in confined granular systems
Physical Review E, 2005
We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wavefront followed by random oscillations made of multiply scattered waves. We find that the coherent wavefront is insensitive to details of the packing: force chains do not play an important role in determining this wavefront. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse-propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wavefront scales with pressure as p 1/6 ; we compare this result with experimental data on various granular systems where deviations from the p 1/6 behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.
Model for Dissipative Highly Nonlinear Waves in Dry Granular Systems
Physical Review Letters, 2010
A model is presented for the characterization of dissipative effects on highly nonlinear waves in one-dimensional dry granular media. The model includes three terms: Hertzian, viscoelastic, and a term proportional to the square of the relative velocity of particles. The model outcomes are confronted with different experiments where the granular system is subject to several constraints for different materials. Excellent qualitative and quantitative agreement between theory and experiments is found.
Propagation of elastic waves in granular solid hydrodynamics
Physical Review E, 2010
The anisotropic, stress-dependent velocity of elastic waves in glass beads-as observed by Y. Khidas and X. Jia, see [Phys. Rev. E, 81:021303, Feb. 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.
Wave propagation in elasto-plastic granular systems
Granular Matter, 2013
Due to the nonlinear nature of the inter-particle contact, granular chains made of elastic spheres are known to transmit solitary waves under impulse loading. However, the localized contact between spherical granules leads to stress concentration, resulting in plastic behavior even for small forces. In this work, we investigate the effects of plasticity in wave propagation in elasto-plastic granular systems. In the first part of this work, a force-displacement law between contacting elastic-perfectly plastic spheres is developed using a nonlinear finite element analysis. In the second part, this force-displacement law is used to simulate wave propagation in one-dimensional granular chains. In elasto-plastic chains, energy dissipation leads to the formation and merging of wave trains, which have characteristics very different from those of elastic chains. Scaling laws for peak force at each contact point along the chain, velocity of the leading wave, local contact and total dissipation are developed.
Wave propagation in confined granular systems
arXiv (Cornell University), 2004
We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wavefront followed by random oscillations made of multiply scattered waves. We find that the coherent wavefront is insensitive to details of the packing: force chains do not play an important role in determining this wavefront. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse-propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wavefront scales with pressure as p 1/6 ; we compare this result with experimental data on various granular systems where deviations from the p 1/6 behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.
Granular packings: Nonlinear elasticity, sound propagation, and collective relaxation dynamics
Physical Review E, 2004
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter.
Acta Acustica united with Acustica, 2008
The problem of the nonlinear reflection of acoustic waves from a mechanically free surface of an unconsolidated granular layer under gravity is solved analytically using the successive approximations method. The theory revealed specific dependencies of the characteristics of the generated acoustic harmonics of longitudinal and shear waves on frequency and the thickness of the granular layer, which are related to a power-law gravity-induced depth stratification of linear and nonlinear mechanical properties of the granular layer. The developed theory could be useful for the analysis of the acoustic experiments directed to the investigation of fundamental mechanical properties of unconsolidated granular media near the jamming transition taking place at zero confining pressure.