Analytical Solutions of Contact Impact Problems

[+] Author and Article Information
J. Jaeger

Ernst-Friedrich-Str 13, 76227 Karlsruhe, Germany

Appl. Mech. Rev 47(2), 35-54 (Feb 01, 1994) (20 pages) doi:10.1115/1.3111070 History: Online April 29, 2009


In this article, analytical solutions of the normal and tangential impact of half-spaces at low velocities are formulated. After a brief introduction, a classification of contact problems is proposed and some publications about impact are mentioned. The basic contact laws for monotonously increasing normal, tangential, and torsional contact have been found decades ago, while the general analytical solutions for tangential and torsional load histories, which are necessary for impact calculations, have only been found recently. Insertion of these contact laws into the equations of motion yields a system of nonlinear differential equations, which are uncoupled in the case of the oblique central impact. The normal solution of the uncoupled equations for Hertzian and some axisymmetric surfaces can be written as a hypergeometric function, which generalizes earlier solutions. Solutions in tangential direction for the compression phase and the restitution phase can be found for the case of complete adhesion. Finally, the kinematic coefficient of restitution is shown. This solutions may help to understand some open problems of the collision of rigid bodies, which are in contact on a small elastic domain, where a part of the kinetic energy is transformed into elastic energy and reconverted into kinetic energy in normal and tangential directions.

Copyright © 1994 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In