Document 
Free access article
Eur. Phys. J. B 7, 155-168
On the validity of Hertz contact law for
granular
material acoustics
C. Coste - B. Gilles
Laboratoire de Physique, École Normale
Supérieure de Lyon,
46 allée d'Italie, 69364 Lyon Cedex 07, France
coste@physique.ens-lyon.fr
Revised: 28 May 1998 / Accepted: 27 July 1998
Abstract
We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical
spherical beads. In this geometry, we are able to test quantitatively alternative models to the
Hertz theory of contact between elastic solids. We compare the predictions of the different models
to experimental results that concern linear sound wave propagation in the chain submitted to a
static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic,
elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we
also use oxidized metallic beads. We demonstrate experimentally that at
low static forces, for all types of beads, the linear
acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after
onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian
behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the
predictions of Hertz theory.
PACS
83.70.Fn Granular solids
- 83.10.Pp Particle dynamics -
43.25.Cb Macrosonic
propagation, finite amplitude sound; shock waves
|
|
|
Contents
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag