Eur. Phys. J. E (2009) 30: 43-54
https://doi.org/10.1140/epje/i2009-10504-9

Regular Article

Granular medium impacted by a projectile: Experiment and model

Institut de Physique de Rennes, UMR UR1-CNRS 6251, Université de Rennes 1, Campus de Beaulieu, F-35042, RENNES Cedex, France

^* e-mail: alexandre.valance@univ-rennes1.fr

Received: 29 January 2009
Revised: 12 June 2009
Accepted: 30 July 2009
Published online: 18 September 2009

Abstract

We present a minimal discrete model for the propagation of energy through a 3D granular medium impacted by a particulate projectile. In this model, energy is transferred from grain to grain via binary collision events. This description can be successfully applied to the analysis of the collision process of a single spherical particle (of diameter donto a half space of granular medium composed of similarly sized particles. The model reproduces remarkably well the experimental observations. Besides, the present model provides a clear picture of the mechanism of energy propagation. A continuum version of the model, where the energy propagation from bead to bead is characterized by a diffusion equation, is derived. The diffusion coefficient is found to be proportional to the ratio of d² to the characteristic collision time . The numerical value of the coefficient of proportionality is essentially governed by the geometry of the packing. This paper constitutes an extension of a previously published letter (J. Crassous, D. Beladjine, A. Valance, Phys. Rev. Lett. 99, 248001 (2007)).