Modified inelastic bouncing ball model of vibrated granular materials: Transmissibility and coefficient of restitution

Abstract

The modified Inelastic Bouncing Ball Model (mIBBM) was formulated by introducing transmissibility T_r, a compact parameter of the properties of the grains that accounts for the transmission efficiency of the force driving the granular materials because the earlier Inelastic Bouncing Ball Model (IBBM) is inadequate for describing the real-world dynamics of vibrated grains. However, we do not yet fully understand the relationship between T_r and the intrinsic grain properties and vibration parameters. Here, we study the relationship between the coefficient of restitution e of the individual grains and T_r. We performed a Discrete Element Method simulation of the vibrated monodisperse granular materials for different e values. We generated the bifurcation diagram (time-of-flight of the center-of-mass of the material versus dimensionless acceleration of the container) and then estimated the T_r value from the bifurcation point. T_r is constant for e ≤ 0.5 and indicates a decreasing value for larger e values. We cannot precisely determine T_r for larger e values because there is no bifurcation point in the high Γ regime where the granular materials are already fluidized. We have yet to explain why the flight times in the simulation are shorter than predicted by mIBBM and why lower e cases yield higher maximum height and longer times of flight. These deviations from the predictions are probably due to T_r being strongly dependent on other vibration parameters.