Summary
The problem of a rigid punch moving over a general anisotropic viscoelastic medium is considered both for the case where the medium is a finite layer and where it is an infinite half-space. Formal equations are derived, using Fourier Transform techniques, for the most general case where no assumptions are made concerning the shape of the punch. However, attention is then focussed on the case where the punch is uniformly infinite in one direction. Both the general inertial problem and the non-inertial approximation are considered for the half-plane problem. Previously known results are shown to emerge from the general formalism with relative ease. The general viscoelastic problem is shown to be formally identical to the isotropic problem treated in [1] though algebraically far more complex. In the non-inertial approximation, however, the extra complexity is not great, and in particular, if all the viscoelastic functions are assumed to have similar time behaviour, the resulting equations are essentially no more complex than the isotropic equations solved in [2]. For this case, the relationship between the hysteretic friction coefficients along the two axes of anisotropy on an orthotropic medium is quantified. Displacementtraction relationships are given for an isotropic layer, including inertial effects and some numerical results are given for the thick elastic layer problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Golden, J. M.: The problem of a rigid punch moving on a viscoelastic half-plane with inertial effects approximately included. J. Austral. Math. Soc.B 21, 198–229 (1979).
Golden, J. M.: The problem of a moving rigid punch on an unlubricated viscoelastic half-plane. Q. J. Mech. appl. Math.32, 25–52 (1979).
Golden, J. M.: Hysteretic friction of a plane punch on a half-plane with arbitrary viscoelastic behaviour. Q. J. Mech. appl. Math.30, 23 (1977).
Galin, L. A. (Moss, H., translator; Sneddon, I. N., ed.): Contact problems in the theory of elasticity. Raleigh: Department of Mathematics, North Carolina State College, 1961.
Willis, J. R.: Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids14, 163–176 (1966).
Willis, J. R.: Boussinesq problems for an anisotropic half-space. J. Mech. Phys. Solids15, 331–339 (1967).
Eason, G., Fulton, J., Sneddon, I. N.: The generation of waves in an infinite elastic solid by variable body forces. Phil. Trans. Roy. Soc. Lond.A 248, 575–607 (1956).
Eason, G.: The stresses produced in a semi-infinite solid by a moving surface force. Int. J. Engng. Sci.2, 581–609 (1965).
Alblas, J. B., Kuipers, M.: The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer — I. General considerations and thick layer asymptotics. Int. J. Solids Structures7, 99–109 (1971).
Alblas, J. B., Kuipers, M.: The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer — II. This layer asymptotics. Int. J. Solids Structures7, 225–237 (1971).
Alblas, J. B., Kuipers, M.: The contact problem of a rigid cylinder rolling on a thin viscoelastic layer. Int. J. Engng. Sci.8, 363–380 (1970).
Margetson, J.: Rolling contact of a rigid cylinder over a smooth elastic or viscoelastic layer. Acta Mech.13, 1–9 (1971).
Gradshteyn, I. S., Ryzhik, I. M.: Tables of integrals, series and products. New York: Academic Press 1965.
Author information
Authors and Affiliations
Additional information
With 1 Figure
Rights and permissions
About this article
Cite this article
Golden, J.M. The problem of a rigid punch sliding on an elastic or a viscoelastic layer. Acta Mechanica 43, 201–221 (1982). https://doi.org/10.1007/BF01176283
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01176283