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Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid axially symmetric conical die

Published online by Cambridge University Press:  24 October 2008

A. R. Robinson  and
J. C. Thompson
A. R. Robinson
Affiliation:
University of Illinois and University of Waterloo
J. C. Thompson
Affiliation:
University of Illinois and University of Waterloo
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Abstract

A solution which is exact within the framework of the classical theory of elasticity is obtained for the title problem assuming that the half space is homogeneous and isotropic, and that the die indents at a constant rate. If the shape of the die and the elastic medium are specified, the rate of indentation uniquely determines the outward speed of the edge of the expanding contact zone. The magnitude of this speed, relative to the speeds of the dilatational, rotational and Rayleigh waves in the elastic medium, determines which of four possible characteristic transient stress states will occur. Each of the four ranges of contact speed is solved by the method of rotational superposition of self-similar potentials which is briefly described in the Appendix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 369 - 379
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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