A semi-analytical model for oblique impacts of elastoplastic spheres

Chuan-yu Wu, Colin Thornton, Long-yuan Li

Research output: Contribution to journalArticle

70 Citations (Scopus)


Results of finite-element analysis (FEA) of oblique impacts of elastic and elastic, perfectly plastic spheres with an elastic. at substrate are presented. The FEA results are in excellent agreement with published data available in the literature. A simple model is proposed to predict rebound kinematics of the spheres during oblique impacts. In this model, the oblique impacts are classified into two regimes: (i) persistent sliding impact, in which sliding occurs throughout the impact, the effect of tangential (elastic or plastic) deformation is insignificant and the model reproduces the well-established theoretical solutions based on rigid body dynamics for predicting the rebound kinematics and (ii) non-persistent sliding impact, in which sliding does not occur throughout the impact duration and the rebound kinematics depends upon both Poisson's ratio and the normal coefficient of restitution (i. e. the yield stress of the materials). For non-persistent sliding impacts, the variation of impulse ratio with impact angle is approximated using an empirical equation with four parameters. These parameters are sensitive to the values of Poisson's ratio and the normal coefficient of restitution, but can be obtained by fitting numerical data. Consequently, a complete set of solutions is obtained for the rebound kinematics, including the tangential coefficient of restitution, the rebound velocity at the contact patch and the rebound rotational speed of the sphere during oblique impacts. The accuracy and robustness of this model is demonstrated by comparisons with FEA results and data published in the literature. The model is capable of predicting complete rebound behaviour of spheres for both elastic and elastoplastic oblique impacts.
Original languageEnglish
Pages (from-to)937-960
Number of pages24
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Issue number2103
Publication statusPublished - 1 Mar 2009


  • granular materials
  • contact mechanics
  • impact dynamics
  • oblique impact
  • coefficient of restitution


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