Wave propagation in granular rod using high-gradient theory

Based on a microstructural approach, granular material can be represented by an equivalent continuum of the high-gradient type. The high-gradient model is used in this paper to study the effect of microstructure on the propagation of waves in granular material. The constitutive coefficients of the high-gradient continuum are expressed in explicit functions of interparticle stiffness. Based on the high-gradient model, a fourth-order partial differential equation is formulated for the wave propagation in granular medium. Hamilton's principle is employed to devise the additional boundary conditions involved in the differential equation. The differential equation is solved for wave propagation in a finite rod of granular material with specified boundary conditions. The present results show that the dynamic behavior of a rod of granular solid is very different from the behavior of a rod of classical continuum. The predicted phenomena are in agreement with the simulation results from discrete element methods and with the experimental observations from a chain of photoelastic disks subjected to an impact load.