Advertisement

An Algorithm for Rigid Body Contact with Coulomb Friction

  • Lars Johansson
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 72)

Abstract

This paper is concerned with a numerical algorithm for the impact of rigid bodies against rigid obstacles. Some problems of this kind can be treated by specifying the quotient between the relative normal velocity of approach and separation, Newton [1], that is by introducing the classical coefficient of restitution. This is sometimes generalized to Poisson’s hypothesis, see Kilmister & Reeve [2]. In many cases, however, it is necessary to take both the normal and the tangential impulse at the impact into account to achieve reasonable agreement with observations. This class of problems has been the object of several recent studies, invariably leading to the introduction of one or more additional constitutive parameters, such as the coefficient of friction. Thus in Brach [3], a quotient between normal and tangential impulses is introduced, and several bounds based on physical assumptions, are derived for this quotient. In Stronge [4], the division of the impact process into a compression and an expansion phase is analyzed, and the problem is treated using a coefficient of restitution relating energies rather than velocities.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    I. Newton, Philosophiae Naturalis Principia Mathematica, Swedish translation by C.V.L. Charlier, Gleerups, Lund, 1927-31 and Liber, Malmö, 1986.Google Scholar
  2. [2]
    C.W. Kilmister & J.E. Reeve, Rational Mechanics, Longmans, London, 1966.zbMATHGoogle Scholar
  3. [3]
    R.M. Brach, Rigid Body Collisions, J. Appl. Mech., 56 (1989) 133–138.ADSCrossRefGoogle Scholar
  4. [4]
    W.J. Stronge, Rigid Body Collisions with Friction, Proc. R. Soc. Lond. A, 431 (1990) 169–181.MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. [5]
    J.J Moreau, Unilateral Contact and Dry Friction, in: J.J. Moreau & PD Panagiotopoulos, Nonsmooth Mechanics and Applications, CISM Courses and Lectures No. 302, Springer, Wien, 1988.Google Scholar
  6. [6]
    F. Pfeiffer & Ch. Glocker, Multibody Dynamics with Unilateral Contacts, Wiley, New York, 1996.zbMATHCrossRefGoogle Scholar
  7. [7]
    M. Anitescu, J.F Cremer & FA. Potra, Formulating 3D Contact Dynamics Problems, Reports on Computational Mathematics, No. 80/1995, Department of Mathematics, The University of Iowa.Google Scholar
  8. [8]
    J.J. Moreau, Some Numerical Methods in Multibody Dynamics: Application to Granular Materials, Eur. J. Mech., A/Solids, 13 (1994) 93–114.MathSciNetzbMATHGoogle Scholar
  9. [9]
    K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Heldermann, Berlin, 1988.zbMATHGoogle Scholar
  10. [10]
    P. Lötstedt, Coulomb Friction in Two-Dimensional Rigid Body Systems, ZAMM, 62 (1981) 605–615.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Lars Johansson
    • 1
  1. 1.Department of Mechanical Engineering Division of MechanicsLinköping UniversityLinköpingSweden

Personalised recommendations