Nonlinear Dynamics

, Volume 60, Issue 3, pp 217–229 | Cite as

Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres

  • Robert L. JacksonEmail author
  • Itzhak Green
  • Dan B. Marghitu
Original Paper


The current work presents a different methodology for modeling the impact between elasto-plastic spheres. Recent finite element results modeling the static deformation of an elasto-plastic sphere are used in conjunction with equations for the variation of kinetic energy to obtain predictions for the coefficient of restitution. A model is also needed to predict the residual deformation of the sphere during rebound, or unloading, of which several are available and compared in this work. The model predicts that a significant amount of energy will be dissipated in the form of plastic deformation such that as the speed at initial impact increases, the coefficient of restitution decreases. This work also derives a new equation for the initial critical speed which causes initial plastic deformation in the sphere that is different than that shown in previously derived equations and is strongly dependant on Poisson’s Ratio. For impacts occurring above this speed, the coefficient of restitution will be less than a value of one. This work also compares the predictions between several models that make significantly different predictions. The results of the current model also compare well with some existing experimental data. Empirical fits to the results are provided for use as a tool to predict the coefficient of restitution.


Nonlinear force Contact force Impact Elasto-plastic deformation Coefficient of restitution 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Robert L. Jackson
    • 1
    Email author
  • Itzhak Green
    • 2
  • Dan B. Marghitu
    • 1
  1. 1.Department of Mechanical EngineeringAuburn UniversityAuburnUSA
  2. 2.Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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