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 -λ 1n r) as r→0 or O(r -λ) 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.
Similar content being viewed by others
References
Bartholomew, P., Solution of elastic crack problems by superposition of finite elements and singular fields. Computer Methods Appl. Mech. Engng. 13 (1978) 59–78.
Strang, G. and Fix, G. J., An Analysis of the Finite Element Method, Prentice-Hall Inc., New Jersey (1973).
Jaswon, M. A. and Symm, G. T., Integral Equation Methods in Potential Theory and Elastostatics, Academic Press Inc., London (1977).
United States Air Force, Airplane damage tolerance design requirements. (1974) MIL-A-83444.
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.
Dundurs, J., Effect of elastic constants on stress in a composite under plane deformation. J. Composite Materials 1 (1967) 310–322.
Dundurs, J., Discussion of [10]. J. Appl. Mech. 36 (1969) 650–652.
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.
Bogy, D. B., Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. 38 (1971) 377–386.
Bogy, D. B., Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 35 (1968) 450–466.
Bogy, D. B., On the problem of edge-bonded elastic quarter planes loaded at the boundary. Int. J. Solids Structures 6 (1970) 1287–1313.
Hein, V. L. and Erdogan, F., Stress singularities in a two-material wedge. Int. J. Fract. Mech. 7 (1971) 317–330.
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.
Rao, A. K., Stress concentrations and singularities at interface corners. Z. angew. Math. Mech. 51 (1971) 395–406.
Dundurs, J. and Lee, M. S., Stress concentrations at a sharp edge in contact problems. J. Elasticity 2 (1972) 109–112.
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.
Comninou, M., Stress singularity at a sharp edge in contact problems with friction. Z. angew. Math. Phys. 27 (1976) 493–499.
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.
Dempsey, J. P., Stress singularities of the composite wedge. Ph.D. Dissertation, University of Auckland, New Zealand (1978).
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.
Bogy, D. B., On the plane elastostatic problem of a loaded crack terminating at a material interface. J. Appl. Mech. 38 (1971) 911–918.
Comninou, M. and Dundurs, J., A closed crack-tip terminating at an interface. J. Appl. Mech. 46 (1979) 97–100.
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00041942