Asymptotic solution of a crack in a vanishingly thin elliptic inhomogeneity
Author:
Chien H. Wu
Journal:
Quart. Appl. Math. 48 (1990), 233-249
MSC:
Primary 73M25; Secondary 73B27
DOI:
https://doi.org/10.1090/qam/1052134
MathSciNet review:
MR1052134
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Abstract: When a crack of finite size is wholly surrounded by a thin inhomogeneity, the behavior of the solution near a crack tip is the same as that of a semi-infinite crack surrounded by a semi-infinite inhomogeneity. The analytical structure of the solution for the latter problem is established via the consideration of the title problem. It is shown that the standard Fast Fourier Transform Algorithm may be applied for the determination of the coefficients involved in the analytically structured series solution. An approximate but explicit solution is also derived for the title problem.
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C. H. Wu, A Semi-infinite crack penetrating an inclusion, J. Appl. Mech. 55, 736–738 (1988)
C. H. Wu and C. H. Chen, A crack in a confocal elliptic inhomogeneity embeded in an infinite medium, J. Appl. Mech., to appear
J. Dundurs, Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading—discussion, J. Appl. Mech. 36, 650–652 (1969)
A. H. England, Complex Variable Method in Elasticity, Wiley-Interscience, New York, 1971
J. D. Eshelby, The force on an elastic singularity, Philos. Trans. Roy. Soc. London A 224, 87–112 (1951)
J. W. Hutchinson, Crack Tip Shielding by Micro-Cracking in Brittle Solids, Mech-87, Harvard University, 1986
P. S. Steif, A semi-infinite crack partially penetrating a circular inclusion, J. Appl. Mech. 54, 87–92 (1987)
M. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, 1975
C. H. Wu, A Semi-infinite crack penetrating an inclusion, J. Appl. Mech. 55, 736–738 (1988)
C. H. Wu and C. H. Chen, A crack in a confocal elliptic inhomogeneity embeded in an infinite medium, J. Appl. Mech., to appear
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Article copyright:
© Copyright 1990
American Mathematical Society
