Skip to main content
Log in

On the singular behavior at the vertex of a bi-material wedge

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

Information on the singular behavior at the vertex of a bi-material wedge is the objective of this paper. A summary of the necessary conditions, which depend heavily on the associated eigenvalue equation, for stress singularities of O(r 1n r) as r→0 or O(r ) as r→0 is stated. The eigenvalue equations arising from a wide range of boundary and interface conditions are then provided. Bi-material wedge problems that have been subjected to singularity analyses of some generality in the literature are briefly reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bartholomew, P., Solution of elastic crack problems by superposition of finite elements and singular fields. Computer Methods Appl. Mech. Engng. 13 (1978) 59–78.

    Google Scholar 

  2. Strang, G. and Fix, G. J., An Analysis of the Finite Element Method, Prentice-Hall Inc., New Jersey (1973).

    Google Scholar 

  3. Jaswon, M. A. and Symm, G. T., Integral Equation Methods in Potential Theory and Elastostatics, Academic Press Inc., London (1977).

    Google Scholar 

  4. United States Air Force, Airplane damage tolerance design requirements. (1974) MIL-A-83444.

  5. Dempsey, J. P. and Sinclair, G. B., On the stress singularities in the plane elasticity of the composite wedge. J. Elasticity 9 (1979) 373–391.

    Google Scholar 

  6. Dundurs, J., Effect of elastic constants on stress in a composite under plane deformation. J. Composite Materials 1 (1967) 310–322.

    Google Scholar 

  7. Dundurs, J., Discussion of [10]. J. Appl. Mech. 36 (1969) 650–652.

    Google Scholar 

  8. Dundurs, J., Properties of elastic bodies in contact. The Mechanics of the Contact Between Deformable Bodies, eds. de Pater, A. D., and Kalker, J. J., Delft University Press, (1975), pp. 54–66.

  9. Bogy, D. B., Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. 38 (1971) 377–386.

    Google Scholar 

  10. Bogy, D. B., Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 35 (1968) 450–466.

    Google Scholar 

  11. Bogy, D. B., On the problem of edge-bonded elastic quarter planes loaded at the boundary. Int. J. Solids Structures 6 (1970) 1287–1313.

    Google Scholar 

  12. Hein, V. L. and Erdogan, F., Stress singularities in a two-material wedge. Int. J. Fract. Mech. 7 (1971) 317–330.

    Google Scholar 

  13. Gdoutos, E. E. and Theocaris, P. S., Stress concentrations at the apex of a plane indenter acting on an elastic half-plane. J. Appl. Mech. 42 (1975) 688–692.

    Google Scholar 

  14. Rao, A. K., Stress concentrations and singularities at interface corners. Z. angew. Math. Mech. 51 (1971) 395–406.

    Google Scholar 

  15. Dundurs, J. and Lee, M. S., Stress concentrations at a sharp edge in contact problems. J. Elasticity 2 (1972) 109–112.

    Google Scholar 

  16. Theocaris, P. S. and Godoutos, E. E., Stress singularities at vertices of composite plates with smooth or rough interfaces. Arch. Mech. Stosow 28 (1976) 693–704.

    Google Scholar 

  17. Comninou, M., Stress singularity at a sharp edge in contact problems with friction. Z. angew. Math. Phys. 27 (1976) 493–499.

    Google Scholar 

  18. Bogy, D. B. and Wang, K. C., Stress singularities at interface corners in bonded dissimilar isotropic elastic materials. Int. J. Solids Structures 7 (1971) 993–1005.

    Google Scholar 

  19. Dempsey, J. P., Stress singularities of the composite wedge. Ph.D. Dissertation, University of Auckland, New Zealand (1978).

  20. Avetisian, A. G. and Chobanian, K. S., On the nature of stresses in the fixed vicinity of the junction surface brink of a composite elastic body loaded in conditions of a plane problem of the elasticity theory (in Russian). Akad. Nauk. Arm. SSR. Erivan Izv. Mekh. 25 (1972) 13–25.

    Google Scholar 

  21. Bogy, D. B., On the plane elastostatic problem of a loaded crack terminating at a material interface. J. Appl. Mech. 38 (1971) 911–918.

    Google Scholar 

  22. Comninou, M. and Dundurs, J., A closed crack-tip terminating at an interface. J. Appl. Mech. 46 (1979) 97–100.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dempsey, J.P., Sinclair, G.B. On the singular behavior at the vertex of a bi-material wedge. J Elasticity 11, 317–327 (1981). https://doi.org/10.1007/BF00041942

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00041942

Keywords

Navigation