Alaci Stelian, Filote Constantin, Ciornei Florina-Carmen



The Effect of Coefficient of Restitution for Two Collision Models

pdf PDF


The paper considers two models used in dynamic analysis of multibody system, describing the collision behaviour. One of the models accepts the internal friction work and the other, the plastic deformation work, but the common parameter is the coefficient of restitution. The effect of the coefficient of restitution is presented comparatively, in graphical manner, upon the normal approach, relative velocity versus time dependencies and phase maps. Following the different hypotheses, the dynamical system evolutions are significantly different. The two models studied represent the boundaries of a domain within which the actual system behaviour could be placed and the necessity of a complex model as amalgamation of the two models considered is emphasized.


coefficient of restitution, phase maps, plastic deformation


[1] K.L. Johnson, K. L., Contact Mechanics, Cambridge University Press, 1985.

[2] H.R. Hertz, 1882, “Ueber die Beruehrung elastischer Koerper” (“On Contact Between Elastic Bodies”), in Gesammelte Werke (Collected Works), Vol. 1, Leipzig, Germany, 1895.

[3] I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory, Wiley, 1966.

[4] Brach R.M., Mechanical Impact Dynamics, Rigid Body Collisions, New York: Wiley, 1991.

[5] S.P. Timoshenko, J.N. Goodier, Theory of elasticity. McGraw-Hill, New York, 1970.

[6] H.M. Lankarani, P.E. Nikravesh, Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, pp. 193– 207, 1994.

[7] P. Flores, M. Machado, M.T. Silva, J.M. Martins, “On the continuous contact force models for soft materials in multibody dynamics”, Multibody System Dynamics, vol. 25, pp. 357-375, 2011.

[8] S. Djerassi, Collision with friction; Part A: Newton’s hypothesis. Multibody Syst. Dyn. 21, pp. 37–54, 2009.

[9] H.M. Lankarani, P.E. Nikravesh, “A contact force model with hysteresis damping for impact analysis of multibody systems”, J. Mech. Des. 112, pp. 369-376, 1990.

[10] J. Grote; K. Makino; M. Berz, Verified computation of high-order Poincaré maps, WSEAS Transactions on Systems, 4(11), pp. 1986-1992, 2005.

[11] Y. Iskandarani, H.R Karimi, Hysteresis model parameters identification for the SAS rotational MR damper, Wseas Transactions on Systems And Control, Issue 10, Volume 6, pp. 371-381, October 2011.

[12] K.H. Hunt, F.R. Crossley, 'Coefficient of Restitution Interpreted as Damping in Vibroimpact’, Journal of Applied Mechanics, 7, pp. 440-445, 1975.

[13] B. N. Norden, On the Compression of a Cylinder in Contact with a Plane Surface, NBS Internal Report 73-243, 67 p., 1973.

[14] M. Machado, P. Moreira, P. Flores, H.M. Lankarani, Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mechanism and Machine Theory, Vol. 53, 99-121, 2012.

Cite this paper

Alaci Stelian, Filote Constantin, Ciornei Florina-Carmen. (2017) The Effect of Coefficient of Restitution for Two Collision Models. International Journal of Theoretical and Applied Mechanics, 2, 133-137


Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0