Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-30T05:45:07.820Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of a rigid sphere embedded in an adhering elastic or viscoelastic medium

Published online by Cambridge University Press:  20 January 2009

S. C. Hunter
S. C. Hunter
Affiliation:
University of Strathclyde, Now at Department of Applied Mathematics, and Computing Science, University of Sheffield.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The motion of a rigid sphere embedded in an adhering medium and subjected to an external force is analysed exactly in the context of classical elastodynamics. For the limiting case of an incompressible medium it is possible to write down a simple second order differential equation relating displacement of the ball to the external force.

The theory is generalised to the case of a viscoelastic solid and the results obtained are pertinent to recently developed experimental methods for testing the dynamical mechanical properties of very low modulus polymer gels.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 1 , June 1968 , pp. 55 - 69
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

REFERENCES

(1) Dobson, G. R. and Gordon, M., Theory of branching processes and statistics of rubber elasticity. J. Chem. Phys. 43 (1965), 705.CrossRefGoogle Scholar
(2) Dobson, G. R. and Gordon, M., Beitrage zur Verbessung der kautschukelastichen Zustandsgleichung. Plaste und Kautschuk, 13 (1966), 529.Google Scholar
(3) Erdelyi, A.et al., Higher Transcendental Functions, vol. II, Bateman Manuscripts Project (McGraw-Hill, 1953).Google Scholar
(4) Gordon, M., Hunter, S. C. and Ward, D., A rational geometry for measuring elastic and viscoelastic parameters, Nature, 217 (1968), 735.CrossRefGoogle Scholar
(5) Hunter, S. C., Viscoelastic Waves. Progress in Solid Mechanics I, editors Hill, R. and Sneddon, I. N. (North Holland Publishing Co., Amsterdam, pp. 1–59).Google Scholar
(6) Kolsky, H., The propagation of stress pulses in viscoelastic solids, Phil. Mag. 8, (1956), 693.CrossRefGoogle Scholar
(7) Leslie, F. M., The slow flow of a viscoelastic liquid past a sphere, Q.J.M.A.M. 14, part 1 (1961), 36.Google Scholar