Granular medium impacted by a projectile: Experiment and model

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 d) onto 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 d(2) to the characteristic collision time tau(c). 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)).