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TECHNICAL PAPERS

Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method

[+] Author and Article Information
H. M. Shodja, A. S. Sarvestani

Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

J. Appl. Mech 68(1), 3-10 (Jun 14, 2000) (8 pages) doi:10.1115/1.1346680 History: Received October 07, 1999; Revised June 14, 2000
Copyright © 2001 by ASME
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References

Mura,  T., Shodja,  H. M., and Hirose,  Y., 1996, “Inclusion Problems,” Appl. Mech. Rev., 49, No. 10, Part 2, pp. S118–S127.
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Eshelby,  J. D., 1959, “The Elastic Field Outside an Ellipsoidal Inclusion,” Proc. R. Soc. London, Ser. A, A252, pp. 561–569.
Eshelby, J. D., 1961, “Elastic Inclusions and Inhomogeneities,” Progress in Solid Mechanics, Vol. 2, I. N. Sneddon and R. Hill, eds., North-Holland, Amsterdam, pp. 89–140.
Moschovidis,  Z. A., and Mura,  T., 1975, “Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method,” ASME J. Appl. Mech., 42, pp. 847–852.
Chen,  T., Dvorak,  G. J., and Benveniste,  Y., 1990, “Stress Fields in Composites Reinforced by Coated Cylindrically Orthotropic Fibers,” Mech. Mater., 9, pp. 17–32.
Walpole,  L. J., 1978, “A Coated Inclusion in an Elastic Medium,” Math. Proc. Cambridge Philos. Soc., 83, pp. 495–506.
Mikata,  Y., and Taya,  M., 1985, “Stress Field in and Around a Coated Short Fiber in an Infinite Matrix Subjected to Uniaxial and Biaxial Loadings,” ASME J. Appl. Mech., 52, pp. 19–24.
Benveniste,  Y., Dvorak,  G. J., and Chen,  T., 1989, “Stress Fields in Composites With Coated Inclusions,” Mech. Mater., 7, pp. 305–317.
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Hori,  M., and Nemat-Nasser,  S., 1993, “Double-Inclusion Model and Overall Moduli of Multi-Phase Composites,” Mech. Mater., 14, pp. 189–206.
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Tanaka,  K., and Mori,  T., 1972, “Note on Volume Integrals of the Elastic Field Around an Ellipsoidal Inclusion,” J. Elast., 2, pp. 199–200.
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Figures

Grahic Jump Location
Double inhomogeneity Σ=Ψ∪Ω embedded in an infinite medium Φ. Σ and Ω have arbitrary orientations, and C1,C2 and C are distinct
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Double inhomogeneity is replaced by an EDI with proper homogenizing polynomial eigenstrains
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Decomposition of the EDI problem to a domain under uniform far-field stress and three single-inclusion problems with proper polynomial eigenstrains
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A multi-inhomogeneity system consisting of n-layers of coatings
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A coated short fiber model considered by Mikata and Taya 8
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Variation of σz along r in the plane of z=0 obtained by the method of the EIM presented herein for the problem shown in Fig. 5
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A continuous coated fiber model under transverse loading considered by Benveniste et al. 9
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Stress distributions along the x-axis obtained by the method of the EIM presented herein for the problem shown in Fig. 7
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Stress distributions along the y-axis obtained by the method of the EIM presented herein for the problem shown in Fig. 7
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A double-inhomogeneity system consisting of a cavity Ω surrounded by a spherical inhomogeneity Σ which in turn is surrounded by an infinite domain, under far-field stress σx0
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Stress distributions along the x-axis for the problem depicted in Fig. 10

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