Ultrasound propagation in disordered granular media
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Ultrasound propagation in disordered granular media Xiaoping Jia Groupe de Physique des Solides, Université Paris 7 2 place Jussieu, 75251 Paris Cedex 05, FRANCE ABSTRACT We have identified, according to the ratio of the wavelength to the grain size, two distinct types of pulsed ultrasound transmission through a dry bead packing under stress: one corresponds to coherent ballistic waves characterized by the effective medium description, the other to the waves scattered by the inhomogeneous stress field within the granular medium. Over long distances of transport, the multiply scattered waves exhibit a diffusive character. Also we investigate the dynamics of the granular medium during a compaction under cyclic loadingunloading. Both the macroscopic deformation and the microscopic rearrangement have been measured, via an ultrasonic correlation technique using the multiple acoustic scattering very sensitive to the change of the system configuration. It is found that as the packing fraction increases, there is a continuous evolution of the system in response to external loading, from an irreversible behavior towards more elastic one. INTRODUCTION The study of granular media is of great current interest both scientifically and practically [1, 2]. In a static assembly of cohesionless grains, experimental observations (e.g., photoelastic visualization) [3, 4] and computer simulations [5] have shown very inhomogeneous spatial distributions of contact forces between particles, organized along force chains which extend over a scale of order 5-10 grains diameters. These force chains, carrying most of the forces in the system, involve only a small fraction of the total number of grains and are only marginally stable ("fragile matter"). Any external (thermal or mechanical) perturbation incompatible with the structure of the force chains or/and of sufficiently high amplitude, can lead to the plastic rearrangement of the system [1, 2]. Some new constitutive laws have been recently proposed to describe the static force transmission along the privileged force paths within granular systems and the instability of the force networks [6, 7]. In contrast to the conventional elastic description based on continuum mechanics, the equations governing the transmission of forces are hyperbolic instead elliptical, which lead to certain preferred directions as shown by experiments. Sound propagation in a disordered granular medium is of fundamental interest (multiple scattering). It also provides a very useful, and sometimes unique, probe of the internal structure such as force networks and the mechanical properties of real 3D granular packings [8, 9], where the coherent photoelastic methods become impracticable. In this paper, we investigate via ultrasound propagation, the dynamic force transmission at small amplitudes in glass bead packings under stress. Emphasis will be put on relevant length scales of observation for separating the different regimes of wave phenomena. Also the compaction of the granular packings under cyclic loading-unloading
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