This paper contains an asymptotic investigation - within the nonlinear theory of elastostatic plane stress - of the deformations and stresses near the tips of a traction-free interface-crack between two dissimilar semi-infinite Neo-Hookean sheets. The results obtained are free of oscillatory singularities of the kind predicted by the linearized theory, which would require the two deformed faces of an interface-crack to overlap in the vicinity of its tips. Instead, the crack is found to open smoothly near its ends, regardless of the specific loading at infinity.
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M.L. Williams, The stresses around a fault or crack in dissimilar media.Bulletin of the Seismological Societyof America 49(2) (1959) 199.
M. Knein, Zur Theorie des Druckversuchs,Zeitschrift für angewandte Mathematik und Mechanik 6 (1926) 43.
M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension.Journal of Applied Mechanics 19 (1952) 526.
A.H. England, A crack between dissimilar media.Journal of Applied Mechanics 32(2) (1965) 400.
J.R. Rice and G.C. Sih, Plane problems of cracks in dissimilar media.Journal of Applied Mechanics, 32(2) (1965) 418.
B.M. Malyshev and R.L. Salganik, The strength of adhesive joints using the theory of cracks.International Journal of Fracture Mechanics 1(2) (1965) 114.
M. Comninou, The interface crack.Journal of Applied Mechanics 44(4) (1977) 631.
M. Comninou, The interface crack in a shear field.Journal of Applied Mechanics, 5(2) (1978) 287.
J.D. Achenbach, L.M. Keer, R.P. Khetan, and S.H. Chen, Loss of adhesion at the tip of an interface crack.Journal of Elasticity 9(4) (1979) 397.
D.S. Dugdale, Yielding of steel sheets containing slits.Journal of the Mechanics and Physics of Solids 8 (1960) 100.
G.I. Barenblatt, The mathematical theory of equilibrium of cracks in brittle fracture. in:Advances in Applied Mechanics, VII, p. 55, Academic Press, New York, 1962.
J.K. Knowles, On some inherently nonlinear singular problems in finite elastostatics.Proceedings, Eighth U.S. National Congress of Applied Mechanics, UCLA, Western Periodicals Co., North Hollywood, 1978.
Eli Sternberg, On singular problems in linearized and finite elastostatics.Proceedings, 15th International Congress of Theoretical and Applied Mechanics, Toronto, North Holland, New York, 1980.
J.K. Knowles and Eli Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics.International Journal of Solids and Structures 11(11) (1975) 1173.
F.S. Wong and R.T. Shield, Large plane deformations of thin elastic sheets of Neo-Hookean material.Zeitschrift für angewandte Mathematik und Physik, 20(2) (1969) 176.
R.A. Stephenson, The equilibrium field near the tip of a crack for finite plante strain of incompressible elastic materials.Journal of Elasticity 12(1) (1982) 65.
J.K. Knowles, A nonlinear effect in Mode II crack problems.Engineering Fracture Mechanics 15(3–4) (1981) 469.
J.E. Adkins, A.E. Green, and G.C. Nicholas, Two-dimensional theory of elasticity for finite deformations.Philosophical Transactions, Royal Society of London, Series A, 247 (1954), 279.
The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.
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Knowles, J.K., Sternberg, E. Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. J Elasticity 13, 257–293 (1983). https://doi.org/10.1007/BF00042997
- Large Deformation
- Plane Stress
- Nonlinear Theory
- Specific Loading
- Asymptotic Investigation