Skip to main content
SpringerLink
Log in

Frictionless indentation by an elastic punch: a dynamic Hertzian contact problem

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

Frictionless indentation of an elastic half-plane by a relatively blunt, symmetric elastic punch at an ar: bitrary speed is analyzed by treating the more general problem of frictionless Hertzian contact between elastic solids. As in the quasi-static problem, the analysis assumes that the solid surface contours are approximately flat. In addition, the contact strip expands at a constant rate and the imposed rigid body motions and surface contours are represented by polynomial curves. Homogeneous function techniques allow analytic solutions to the basic mathematical problem. As an example, the general results are then applied to the uniformly accelerating parabolic punch on a half-plane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. RobinsonA. R. and ThompsonJ. C., Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid wedge-shaped die, Z. angew. Math. Mech. 54 (1974) 139.

    Google Scholar 

  2. CherepanovG. P. and Anfanas'evE. F., Some dynamic problems of the theory of elasticity—a review, Int. J. Engng. Sci. 12 (1974) 665.

    Google Scholar 

  3. BeddingR. J. and WillisJ. R., The dynamic indentation of an elastic half-space, J. Elasticity 3 (1973) 289.

    Google Scholar 

  4. BrockL. M., Symmetrical frictionless indentation over a uniformly expanding contact region—I. basic analysis, Int. J. Engng. Sci. 14 (1976) 191.

    Google Scholar 

  5. BrockL. M., Symmetrical indentation over a uniformly expanding contact region—II. perfect adhesion, Int. J. Engng. Sci. 15 (1977) 147.

    Google Scholar 

  6. MuskhelishviliN. I., Some basic problems of the mathematical theory of elasticity, Noordhoff International, Leyden 1975.

    Google Scholar 

  7. Smirnov, V. I. and Sobolev, S. L., Sur une méthode nouvelie dans le problème plan des vibrations élastiques, Trud. Inst. Seism. Akad. Nauk SSSR 20 (1932).

  8. MaueA. W., Die entspannungswelle bei plötzlichem einschnitt eines gespannten elastichen körpers, Z. angew. Math. Mech. 34 (1954) 1.

    Google Scholar 

  9. CarrierG. F., KrookM. and PearsonC. E., Functions of a complex variable, McGraw-Hill, New York 1966.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, University of Kentucky, 40506, Lexington, KY, U.S.A.

    L. M. Brock

Authors
  1. L. M. Brock
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brock, L.M. Frictionless indentation by an elastic punch: a dynamic Hertzian contact problem. J Elasticity 8, 381–392 (1978). https://doi.org/10.1007/BF00049188

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00049188

Keywords

Search

Navigation