Energy dissipation and dispersion effects in granular media.

The strong interactions between particles will make the energy within the granular materials propagate through the network of contacts and be partly dissipated. Establishing a model that can clearly classify the dissipation and dispersion effects is crucial for the understanding of the global behaviors in the granular materials. For particles with rate-independent material, the dissipation effects come from the local plastic deformation and can be constrained at the energy level by using energetic restitution coefficients. On the other hand, the dispersion effects should depend on the intrinsic nature of the interaction law between two particles. In terms of a bistiffness compliant contact model that obeys the energetical constraint defined by the energetic coefficients, our recent work related to the issue of multiple impacts indicates that the propagation of energy during collisions can be represented by a distributing law. In particular, this law shows that the dispersion effects are dominated by the relative contact stiffness and the relative potential energy stored at the contact points. In this paper, we will apply our theory to the investigation of the wave behavior in granular chain systems. The comparisons between our numerical results and the experimental ones by Falcon, [Eur. Phys. J. B 5, 111 (1998)] for a column of beads colliding against a wall show very good agreement and confirm some conclusions proposed by Falcon Other numerical results associated with the case of several particles impacting a chain, and the collisions between two so-called solitary waves in a Hertzian type chain are also presented.