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.
E. Trefftz, ZAMM 13, 160 (1933)
M. A. Biot, Phil. Mag. 27, Ser. 7, 468 (1938)
- Maurice A. Biot, Elastizitätstheorie zweiter Ordnung mit Anwendungen, Z. Angew. Math. Mech. 20 (1940), 89–99 (German). MR 2311, DOI https://doi.org/10.1002/zamm.19400200202
- H. Neuber, Die grundgleichungen der elastischen Stabilität in allgemeinen Koordinaten und ihre Integration, Z. Angew. Math. Mech. 23 (1943), 321–330 (German). MR 12565, DOI https://doi.org/10.1002/zamm.19430230603
- A. E. Green, R. S. Rivlin, and R. T. Shield, General theory of small elastic deformations superposed on finite elastic deformations, Proc. Roy. Soc. London Ser. A 211 (1952), 128–154. MR 47486, DOI https://doi.org/10.1098/rspa.1952.0030
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
- Maurice A. Biot, Mechanics of incremental deformations. Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0185873
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)
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