Summary
This paper provides a general series solution to the problem of interacting circular inhomogeneities in plane elastostatics. The analysis is based upon the use of the complex stress potentials of Muskhelishvili and the Laurent series expansion method. The general forms of the complex potentials are derived explicitly for the circular inhomogeneity problem under arbitrary plane loading. Using the superposition principle, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing any number ofarbitrarily located inhomogeneities. The above procedure reduces the problem to a set of linear algebraic equations which are solved with the aid of a perturbation technique. The current method is shown to be capable of yielding approximate closed-form solutions for multiple inhomogeneities, thus providing the explicit dependence of the solution upon the partinent parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. (London)A 241, 376–396 (1957).
Jaswon, M. A., Bhargava, R. D.: Two-dimensional elastic inclusion problems. Proc. Cambridge Phil. Soc.57, 669–680 (1961).
Theocaris, P. S., Ioakimidis, N. I.: The inclusion problem in plane elasticity. Q. J. Mech. Appl. Math.30, 437–448 (1977).
Yang, H. C., Chou, Y. T.: Generalized plane problems of elastic inclusions in anisotropic solids. J. Appl. Mech.44, 437–441 (1976).
Honein, T., Hermann, G.: On the bonded inclusions with circular or straight boundaries in plane elastostatics. J. Appl. Mech.57, 850–856 (1990).
Hashin, Z.: Analysis of composite materials. J. Appl. Mech.50, 481–505 (1983).
Willis, J. R.: The overall elastic response of composite materials. J. Appl. Mech.50, 1202–1209 (1983).
Weng, G. J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci.22, 845–856 (1984).
Isida, M., Igawa, H.: Analysis of a zig-zag array of circular inclusions in a solid under uniaxial tension. Int. J. Solids Struct.27, 1515–1535 (1991).
Tandon, G. P., Weng, G. J.: Stress distribution in and around spheroidal inclusions and voids at finite concentration. J. Appl. Mech.53, 511–518 (1986).
Moschovidis, Z. A., Mura, T.: Two-ellipsoidal inhomogeneities by the equivalent inclusion method. J. Appl. Mech.42, 847–852 (1975).
Rodin, G. J., Hwang, G. J.: On the problem of linear elasticity for an infinite region containing a finite number of non-intersecting spherical inhomogeneities. Int. J. Solids Struct.27, 145–159 (1991).
Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff 1953.
Isida, M.: Method of Laurent series expansion for internal crack problems. In: Methods of analysis and solutions of crack problems (Sih, G. C., ed.), pp. 56–130. London: Noordhoff 1973.
Gong, S. X., Meguid, S. A.: A general solution to the antiplane problem of an arbitrarily located elliptical hole near the tip of a main crack. Int. J. Solids Struct.28, 249–263 (1991).
Gong, S. X., Meguid, S. A.: On the effect of the release of residual stresses due to near-tip microcracking. Int. J. Fract.52, 257–274 (1991).
Meguid, S. A., Gong, S. X., Gaultier, P. E.: Main crack-microcrack interaction under mode I, II and III loadings: shielding and amplification. Int. J. Mech. Sci.33, 351–359 (1991).
Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. In: Mathematical theory of dislocations (Mura, T., ed.), pp. 70–115. New York: ASME 1968.
Haddon, R. A. W.: Stresses in an infinite plate with two unequal circular holes. Q. J. Mech. Appl. Math.20, 277–291 (1967).
Gong, S. X., Meguid, S. A.: A general treatment of the elastic field of an elliptical inhomogeneity under antiplane shear. J. Appl. Mech.59, 131–135 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gong, S.X., Meguid, S.A. Interacting circular inhomogeneities in plane elastostatics. Acta Mechanica 99, 49–60 (1993). https://doi.org/10.1007/BF01177234
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01177234