Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions

We discuss the modeling of the coefficient of restitution as a function of the incoming velocity in elasto-plastic collisions with normal frictionless impact, and compare the results from nonlinear finite-element analysis to those of two recent normal force displacement models: One by Thornton (ASME J. Appl. Mech. 64 (1997) 383) and one by Vu-Quoc and Zhang (Proc. R. Soc. London, Ser. A 455 (1999) 4013) which is the displacement-driven counterpart of the force-driven model proposed by Vu-Quoc, Zhang, and Lesburg (ASME. J. Appl. Mech. 67 (2000) 363). The resulting values of the coefficient of restitution are also compared to those from the model proposed in Stronge (in: R.C. Batra, A.K. Mal, G.P. MacSithigh (Eds.), Impact Waves and Fractures, ASME AMD 205 (1995) 351). The relationships among the coefficient of restitution, the incoming velocity, the collision time, the contact force/displacement, the normal pressure distribution are presented and discussed. These results establish the better accuracy provided by the model proposed by Vu-Quoc, Zhang, and Lesburg, when compared to previously proposed models.