An inclusion at a bi-material elastic interface

Journal of Engineering Mathematics

Volumn 37, Issue 1-3, 2000, Pages 155-170

  Selvadurai, A P S ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Bi material interface; Embedded inclusion; Integral equations; Stiffness bounds

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELASTICITY; INCLUSIONS; INTEGRAL EQUATIONS; SOLIDS; STIFFNESS; TRACTION (FRICTION);

BIMATERIAL INTERFACE; EMBEDDED INCLUSION; STIFFNESS BOUNDS;

INTERFACES (MATERIALS);

DISPLACEMENT; ELASTIC BODY; INCLUSION;

EID: 0034143647     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004782110718     Document Type: Article

References (35)

1. J. N. Goodier, Concentration of stress around spherical and cylindrical inclusions and flaws. J. Appl. Mech. Trans. ASME 55 (1933) 39-44.
2. J. M. Dewey, Elastic constants of materials loaded with non-rigid fillers. J. Appl. Phys. 18 (1947) 578-584.
3. R. H. Edwards, Stress concentration around spherical inclusions and cavities. J. Appl. Mech. Trans. ASME 18 (1951) 19-30.
4. J. D. Eshelby, Elastic inclusions and inhomogeneities. In: I.N. Sneddon and R. Hill (eds.), Progress in Solid Mechanics, 2. Amsterdam: North Holland (1961) pp. 89-146.
5. A. I. Lur'e, Elastostatic problem for a triaxial ellipsoid. Mech. Tverdogo Tela. 1 (1967) 80-83.
6. G. de Josselin de Jong, Application of stress functions to consolidation problems. Proc. 4th Int. Conf. Soil Mech. Fdn. Engng. 3 (1957) 320-323.
7. R. P. Kanwal and D. L. Sharma, Singularity methods for elastostatics, J. Elasticity 6 (1976) 405-418.
8. A. P. S. Selvadurai, Load-deflexion characteristics of a deep anchor in an elastic medium. Geotechnique 26 (1976) 405-418.
9. A. H. Zureick, Transversely isotropic medium with a rigid spheroidal inclusion under an axial pull. J. Appl. Mech. Trans. ASME 55 (1988) 495-497.
10. J. R. Willis, Variational and related methods for the overall properties of composites. In: C.-S. Yih (ed.), Advances in Applied Mechanics. New York: Academic Press 21 (1981) 1-78.
11. L. J. Walpole, Elastic behaviour of composite materials: theoretical foundations. In: C.-S. Yih (ed.), Advances in Applied Mechanics. New York: Academic Press 21 (1981) 169-242.
12. T. Mura, Micromechanics of Defects in Solids. Sijthoff and Noordhoff, The Netherlands (1981) 494 pp.
13. T. Mura, Inclusion problems. Appl. Mech. Rev.. 41 (1988) 15-20.
14. W. D. Collins, Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks. I, Cracks in an infinite solid and a thick plate. Proc. R. Soc. London A203 (1962) 359-386.
15. L. M. Keer, A note on the solution of two asymmetric boundary value problems. Int. J. Solids Struct. 1 (1965) 257-264.
16. M. K. Kassir and G. C. Sih, Some three-dimensional inclusion problems in elasticity theory. Int. J. Solids Struct 4 (1968) 225-241.
17. A. P. S. Selvadurai, Analytical methods for embedded flat anchor problems in geomechanics. In: H. J. Siriwardane and M. M. Zaman (eds.), Computer Methods and Advances in Geomechanics. Rotterdam: A. A. Balkema 1 (1994) 305-321.
18. M. L. Williams, Stresses around a fault or crack in dissimilar media. Bull. Seism. Soc. Amer 49 (1959) 199-204.
19. A. H. England, On stress singularities in linear elasticity, Int. J. Engng. Sci. 9 (1971) 571-585.
20. J. R. Willis, The penny-shaped crack on an interface. Q. J. Mech. Appl. Math. 25 (1972) 367-385.
21. G. C. Sih and E. P. Chen, Cracks in Composite Materials. In: G.C. Sih (ed.), Mechanics of Fracture, Vol. 6. The Hague: Martinus Nijhoff Publ. (1981). 537 pp.
22. Ia. S. Ufliand, The contact problem of the theory of elasticity for a die, circular in its plane, in the presence of adhesion. Prikl. Mekh. 20 (1956) 578-587.
23. V. I. Mossakovskii, The fundamental mixed boundary problem of the theory of elasticity for a halfspace with a circular line separating the boundary conditions. Prikl. Math. Mekh 18 (1954) 187-196.
24. L. M. Keer, Mixed boundary value problems for a penny-shaped cut. J. Elasticity 5 (1975) 89-98.
25. G. M. L. Gladwell, Contact Problems in the Classical Theory of Elasticity. The Netherlands Sijthoff and Noordhoff (1980) 716 pp.
26. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity. London: Cambridge University Press (1927) 643 pp.
27. A. P. S. Selvadurai, Elastostatic bounds for the stiffness of an elliptical disc inclusion embedded at a transversely isotropic bi-material interface. J. Appl. Math. Phys. (ZAMP) 35 (1984) 13-23.
28. I. N. Sneddon, The Use of Integral Transforms. New York: McGraw Hill (1972) 539 pp.
29. I. N. Sneddon, Mixed Boundary Value Problems in Potential Theory. Amsterdam: North-Holland (1996) 283 pp.
30. K. E. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second-Kind. Philadelphia: Soc. Ind. Appl. Math. (1976) 230 pp.
31. C. T. H. Baker, The Numerical Treatment of Integral Equations. Oxford: Clarendon Press (1977) 1034 pp.
32. L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations. Canbridge: Cambridge Univ. Press (1985) 376 pp.
33. A. W. Skempton, The pore pressure coefficients A and B. Geotechnique 4 (1954) 143-147.
34. J. R. Rice and M. P. Cleary, Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents. Rev. Geophys. Space Phys. 14 (1976) 227-241.
35. A. P. S. Selvadurai (ed.), Mechanics of Poroelastic Media, Solid Mechanics and its Applications, 35. Dordrecht: Kluwer Academic Publishers (1996) 389 pp.