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.
Similar content being viewed by others
References
N. V. Brilliantov, Phys. A 231 (1996), p. 417
D. Elata, & J. G. Barryman, Mechanics of Materials 24 (1996), p. 229
C. Thornton, & W. Randall, Micromechanics of Granular Materials, M. Satake and J.T. Jenkins, Eds., Elsevier, 1988
M. H. Sadd, Q. Tai, & A. Shukla, Int. J. Non-Linear Mechanics 28(2) (1993), p. 251
K. Tanaka, M. Nishida, T. Kunimochi, & T. Takagi, Handbook of Conveying and Handling of Particulate Solids, A. Levy and H. Kalman, Eds., Elsevier, 2001
P. A. Cundall & O. D. Strack, Geotecnique 29 (1979), p. 47
O. Vinogradov, Computer Modeling and Simulation in Engineering 4(3) (1999), p. 287
S. Luding, Private communication
S. Chapman, Am. J. Phys. 28 (1960), p. 705
K. L. Johnson, Contact Mechanics. Cambridge University Press, 1985
W. J. Stronge, Contact Mechanics. Cambridge University Press, 2000
N. Minorsky, Nonlinear Oscillations, Krieger, 1974
S. Wolfram, The Mathematica Book. Cambridge University Press, 1999
O. Vinogradov, Proc. ASME Int. Mech. Eng. Congress and Exposition, New York, PVP-25205 (2001), p. 1–5
Author information
Authors and Affiliations
Corresponding author
Additional information
The financial assistance provided by the National Science and Engineering Research Council of Canada is gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Vinogradov, O. Equivalent normal stiffness of the ball in granular dynamics simulations. GM 5, 153–158 (2003). https://doi.org/10.1007/s10035-003-0134-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10035-003-0134-x