Equivalent normal stiffness of the ball in granular dynamics simulations

Abstract

In the paper a concept of an equivalent normal ball stiffness based on averaging the work done by the nonlinear Hertz force during the impact is introduced and a numerical assessment is made on its efficiency in simulating collinear collisions. The systems of balls investigated, ranging from 2 to 30, are considered to be coupled and conservative. The energy and momentum conservation principles are used to assess the accuracy of simulation results. The effect of the time step for both linear and nonlinear models is investigated and it is shown that the linear model allows an increased time step compared to a nonlinear one while meeting energy and momentum conservation requirements with the same accuracy. In the paper also the pattern of break up for both models and different number of balls is investigated. It is found that for both models the pattern is the same: the balls are disconnected one at the time with constant rate and this rate does not depend on the number of balls.