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 \( \tau_{c}^{}\) . 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)).
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Valance, A., Crassous, J. Granular medium impacted by a projectile: Experiment and model. Eur. Phys. J. E 30, 43–54 (2009). https://doi.org/10.1140/epje/i2009-10504-9
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DOI: https://doi.org/10.1140/epje/i2009-10504-9