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Large deformations near a tip of an interface-crack between two Neo- Hookean sheets. (English) Zbl 0546.73079

The authors employ a nonlinear asymptotic theory of elastostatic plane stress problems for a traction-free interface crack between two otherwise bonded dissimilar semi-infinite Neo-Hookean sheets. The oscillatory singularities present in a linearized theory are shown to be absent in the nonlinear theory. Also, as a by-product, certain results in connection with the mode II crack problem for a single (homogeneous) Neo- Hookean sheet are presented.
Reviewer: M.N.L.Narasimhan

MSC:

74R05 Brittle damage
74E30 Composite and mixture properties
Full Text: DOI

References:

[1] M.L. Williams, The stresses around a fault or crack in dissimilar media.Bulletin of the Seismological Societyof America 49(2) (1959) 199.
[2] M. Knein, Zur Theorie des Druckversuchs,Zeitschrift für angewandte Mathematik und Mechanik 6 (1926) 43. · JFM 52.0843.05 · doi:10.1002/zamm.19260060104
[3] M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension.Journal of Applied Mechanics 19 (1952) 526.
[4] A.H. England, A crack between dissimilar media.Journal of Applied Mechanics 32(2) (1965) 400.
[5] J.R. Rice and G.C. Sih, Plane problems of cracks in dissimilar media.Journal of Applied Mechanics, 32(2) (1965) 418.
[6] 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. · doi:10.1007/BF00186749
[7] M. Comninou, The interface crack.Journal of Applied Mechanics 44(4) (1977) 631. · Zbl 0369.73092 · doi:10.1115/1.3424148
[8] M. Comninou, The interface crack in a shear field.Journal of Applied Mechanics, 5(2) (1978) 287. · Zbl 0386.73084 · doi:10.1115/1.3424289
[9] 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. · Zbl 0426.73081 · doi:10.1007/BF00044617
[10] D.S. Dugdale, Yielding of steel sheets containing slits.Journal of the Mechanics and Physics of Solids 8 (1960) 100. · doi:10.1016/0022-5096(60)90013-2
[11] 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.
[12] 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.
[13] 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. · Zbl 0457.73013
[14] 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. · Zbl 0348.73009 · doi:10.1016/0020-7683(75)90107-9
[15] 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. · Zbl 0179.55802 · doi:10.1007/BF01595559
[16] 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. · Zbl 0502.73079 · doi:10.1007/BF00043706
[17] J.K. Knowles, A nonlinear effect in Mode II crack problems.Engineering Fracture Mechanics 15(3-4) (1981) 469. · doi:10.1016/0013-7944(81)90072-2
[18] 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. · Zbl 0058.39603 · doi:10.1098/rsta.1954.0019
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