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Two-dimensional elliptic inclusions

Published online by Cambridge University Press:  24 October 2008

R. D. Bhargava  and
H. C. Radhakrishna
R. D. Bhargava
Affiliation:
Indian Institute of Technology, Kanpur, India
H. C. Radhakrishna
Affiliation:
Indian Institute of Technology, Kanpur, India
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Abstract

The simple concept of minimum potential energy of the classical theory of elasticity, first applied to solve inclusion problems (1) by one of the authors (R. D. B.), who considered spherical and circular inclusions, has now been extended to solve elliptic inclusion problems. The complex-variable method of determining the elastic field, first enunciated by A. C. Stevenson in the U.K. and N. I. Muskhelishvili in the U.S.S.R., has been used to determine the elastic field in the infinite material (the matrix) around the inclusion. Strain energies are calculated. The equilibrium size of an elliptic inclusion of elastic (Lamé's) constants λ1 and μ1, differing from those of matrix, for which the constants are λ and μ, has been determined.

An independent check on the calculations has been made by testing the continuity of normal and shearing stresses. The results also agree with the known results for the much simpler case when inclusion and matrix are of the same material.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 4 , October 1963 , pp. 811 - 820
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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