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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Mura,  T., Shodja,  H. M., and Hirose,  Y., 1996, “Inclusion Problems,” Appl. Mech. Rev., 49, No. 10, Part 2, pp. S118–S127.
Eshelby,  J. D., 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. London, Ser. A, A241, pp. 376–396.
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.
Christensen,  R. M., and Lo,  K. H., 1979, “Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” J. Mech. Phys. Solids, 27, pp. 315–330.
Hill, R., 1972, “An Invariant Treatment of Interfacial Discontinuities in Elastic Composites,” Continuum Mechanics and Related Problems of Analysis, L. I. Sedov, ed., Academy of Sciences USSR, Moscow, pp. 597–604.
Benveniste,  Y., 1987, “A New Approach of Mori-Tanaka’s Theory in Composite Materials,” Mech. Mater., 6, pp. 147–157.
Hori,  M., and Nemat-Nasser,  S., 1993, “Double-Inclusion Model and Overall Moduli of Multi-Phase Composites,” Mech. Mater., 14, pp. 189–206.
Nemat-Nasser, S., and Hori, M., 1993, Micromechanics: Overall Properties of Heterogeneous Solids, Elsevier, Amsterdam.
Tanaka,  K., and Mori,  T., 1972, “Note on Volume Integrals of the Elastic Field Around an Ellipsoidal Inclusion,” J. Elast., 2, pp. 199–200.
Mura, T., 1987, Micromechanics of Defects in Solids 2nd Edition, Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
Asaro,  R. J., and Barnett,  D. M., 1975, “The Non-uniform Transformation Strain Problem for an Anisotropic Ellipsoidal Inclusion,” J. Mech. Phys. Solids, 23, pp. 77–83.
Mikata,  Y., and Taya,  M., 1985b, “Stress Field in a Coated Continuous Fiber Composite Subjected to Thermomechanical Loadings,” J. Compos. Mater., 19, pp. 554–578.


Grahic Jump Location
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
Grahic Jump Location
Stress distributions along the x-axis for the problem depicted in Fig. 10
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
Grahic Jump Location
Double inhomogeneity is replaced by an EDI with proper homogenizing polynomial eigenstrains
Grahic Jump Location
Decomposition of the EDI problem to a domain under uniform far-field stress and three single-inclusion problems with proper polynomial eigenstrains
Grahic Jump Location
A multi-inhomogeneity system consisting of n-layers of coatings
Grahic Jump Location
A coated short fiber model considered by Mikata and Taya 8
Grahic Jump Location
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
Grahic Jump Location
A continuous coated fiber model under transverse loading considered by Benveniste et al. 9
Grahic Jump Location
Stress distributions along the x-axis obtained by the method of the EIM presented herein for the problem shown in Fig. 7
Grahic Jump Location
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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