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Two-dimensional elastic inclusion problems

Published online by Cambridge University Press:  24 October 2008

M. A. Jaswon
Affiliation:
Imperial CollegeLondon
R. D. Bhargava
Affiliation:
Imperial CollegeLondon

Abstract

An account is given of Eshelby's point-force method for solving elastic inclusion problems, and of his equations relating an in homogeneity to its equivalent inclusion. The introduction of complex variable formalism enables explicit solutions to be found in various two-dimensional cases. Strain energies are calculated. The equilibrium shape of an elliptic inclusion exhibits an interesting feature not previously expected. A fresh analysis of stress magnification effects is developed.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Frenkel, J.Kinetic theory of liquids (Oxford, 1946).Google Scholar
(2)Mott, N. F. and Nabarro, F. R. N.Proc. Phys. Soc. 52 (1940) 90.CrossRefGoogle Scholar
(3)Eshelby, J. D.Proc. Roy. Soc. A, 241 (1957) 376;Google Scholar
Eshelby, J. D.Proc. Roy. Soc. A, 252 (1959) 561.Google Scholar
(4)Mushkelishvili, N. I.Some basic problems of the mathematical theory of elasticity (Groningen, 1953).Google Scholar
(5)Green, A. E. and Zerna, W.Theoretical elasticity (Oxford, 1954).Google Scholar
(6)Bhargava, R. D. Ph.D. Thesis (London, 1959).Google Scholar
(7)Taylor, G. I.Proc. Roy. Soc. A, 145 (1934) 1.Google Scholar
(8)Jeffreys, H.Proc. Roy. Soc. A, 252 (1959) 431.Google Scholar
(9)Kröner, E.Acta Met. 2, (1954), 301.CrossRefGoogle Scholar
(10)Nabarro, F. R. N.Proc. Roy. Soc. A, 175 (1940) 519.Google Scholar