Journal of Elasticity

, Volume 13, Issue 3, pp 257–293 | Cite as

Large deformations near a tip of an interface-crack between two Neo-Hookean sheets

  • J. K. Knowles
  • Eli Sternberg
Article

Abstract

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.

Keywords

Large Deformation Plane Stress Nonlinear Theory Specific Loading Asymptotic Investigation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.L. Williams, The stresses around a fault or crack in dissimilar media.Bulletin of the Seismological Societyof America 49(2) (1959) 199.Google Scholar
  2. [2]
    M. Knein, Zur Theorie des Druckversuchs,Zeitschrift für angewandte Mathematik und Mechanik 6 (1926) 43.Google Scholar
  3. [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.Google Scholar
  4. [4]
    A.H. England, A crack between dissimilar media.Journal of Applied Mechanics 32(2) (1965) 400.Google Scholar
  5. [5]
    J.R. Rice and G.C. Sih, Plane problems of cracks in dissimilar media.Journal of Applied Mechanics, 32(2) (1965) 418.Google Scholar
  6. [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.Google Scholar
  7. [7]
    M. Comninou, The interface crack.Journal of Applied Mechanics 44(4) (1977) 631.Google Scholar
  8. [8]
    M. Comninou, The interface crack in a shear field.Journal of Applied Mechanics, 5(2) (1978) 287.Google Scholar
  9. [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.Google Scholar
  10. [10]
    D.S. Dugdale, Yielding of steel sheets containing slits.Journal of the Mechanics and Physics of Solids 8 (1960) 100.Google Scholar
  11. [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.Google Scholar
  12. [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.Google Scholar
  13. [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.Google Scholar
  14. [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.Google Scholar
  15. [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.Google Scholar
  16. [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.Google Scholar
  17. [17]
    J.K. Knowles, A nonlinear effect in Mode II crack problems.Engineering Fracture Mechanics 15(3–4) (1981) 469.Google Scholar
  18. [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.Google Scholar

Copyright information

© Martinus Nijhoff Publishers 1983

Authors and Affiliations

  • J. K. Knowles
    • 1
  • Eli Sternberg
    • 1
  1. 1.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaU.S.A.

Personalised recommendations