Plane strain problem of two coplanar cracks in an initially stressed neo-Hookean anisotropic infinite medium
Authors:
Brij M. Singh and Ranjit S. Dhaliwal
Journal:
Quart. Appl. Math. 37 (1980), 451-457
DOI:
https://doi.org/10.1090/qam/99631
MathSciNet review:
QAM99631
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Abstract: We consider the plane strain problem of determining the crack energy in an initially stressed neo-Hookean anisotropic infinite medium containing two coplanar cracks. We assume that the cracks are opened by a constant internal pressure. By using a Fourier transform solution of the equilibrium equations the problem is reduced to solving a set of triple integral equations with a cosine kernel. These integral equations are solved and a closed-form expression for the crack energy $W$ is obtained. The numerical values of $W$ are graphed in Figs. 1, 2.
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E. Trefftz, ZAMM 13, 160 (1933)
M. A. Biot, Phil. Mag. 27, Ser. 7, 468 (1938)
M. A. Biot, ZAMM 20, 89 (1940)
H. Neuber, ZAMM 23, 321 (1943)
A. E. Green, R. S. Rivlin and R. T. Shield, Proc. Roy. Soc. London A211, 128 (1952)
A. E. Green and W. Zerna, Theoretical elasticity, Oxford, Clarenton Press, 114 (1954)
M. A. Biot, Mechanics of incremental deformations, John Wiley, New York (1965)
K. N. Srivastava and M. Lowengrub, Proc. Roy. Soc. Edinb. A68, 309 (1969)
M. Lowengrub and K. N. Srivastava, Int. J. Engng. Sci. 6, 359 (1968)
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Article copyright:
© Copyright 1980
American Mathematical Society
