Skip to main content
SpringerLink
Log in

An explicit expression of the effective moduli for composite materials filled with coated inclusions

Acta Mechanica Sinica volume 14, pages 37–52 (1998)Cite this article

Abstract

The obvious shortcoming of the generalized self-consistent method (GSCM) is that the effective shear modulus of composite materials estimated by the method can not be expressed in an explicit form. This is inconvenient in engineering applications. In order to overcome that shortcoming of GSCM, a reformation of GSCM is made and a new micromechanical scheme is suggested in this paper. By means of this new scheme, both the effective bulk and shear moduli of an inclusion-matrix composite material can be obtained and be expressed in simple explicit forms. A comparison with the existing models and the rigorous Hashin-Shtrikman bounds demonstrates that the present scheme is accurate. By a two-step homogenization technique from the present new scheme, the effective moduli of the composite materials with coated spherical inclusions are obtained and can also be expressed in an explicit form. The comparison with the existing theoretical and experimental results shows that the present solutions are satisfactory. Moreover, a quantitative comparison of GSCM and the Mori-Tanaka method (MTM) is made based on a unified scheme.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Hill R. A self-consistent mechanics of composite materials.J Mech Phys Solids, 1965, 13: 213–222

    Article  Google Scholar 

  2. Budiansky B. On the elastic properties of some heterogeneous media.J Mech Phys Solids, 1965, 13: 223–227

    Article  Google Scholar 

  3. Mclaughlin R. A study of the differential scheme for composite materials.Int J Eng Sci, 1977, 15: 237–244

    Article  MATH  Google Scholar 

  4. Christensen RM, Lo KH. Solutions for effective shear properties of three phase sphere and cylinder models.J Mech Phys Solids, 1979, 27: 315–330

    Article  MATH  Google Scholar 

  5. Huang Y, Hu KX, Wei X. et al. A generalized self-consistent mechanics method for composite materials with multiphase inclusions.J Mech Phys Solids, 1994, 42: 491–504

    Article  MATH  Google Scholar 

  6. Weng GJ. Some elastic properties of reinforced solids with special reference to isotropic ones containing spherical inclusions.Int J Eng Sci, 1984, 22: 845–856

    Article  MATH  Google Scholar 

  7. Benveniste Y. A new approach to the application of Mori-Tanaka's theory in composites.Mech Mater, 1987, 6: 147–157

    Article  Google Scholar 

  8. Zheng QS, Du DX. Closed-form interacting solutions for composite materials with multi-phase inclusions, holes and microcracks.Key Eng Mater, 1998, 145–149: 479–488

    Article  Google Scholar 

  9. Christensen RM. A critical evaluation for a class of micromechanics models.J Mech Phys Solids, 1990, 38: 379–404

    Article  Google Scholar 

  10. Huang Y, Hwang KC, Hu KX et al. A unified energy approach to a class of micromechanical model for composite materials.Acta Mechanica Sinica, 1995, 11: 59–75

    Article  Google Scholar 

  11. Dvorak G, Benveniste Y. On transformation strains and uniform fields in multiphase elastic media.Proc R Soc Lond, 1992, A437: 291–310

    MathSciNet  Google Scholar 

  12. Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Solids. Amsterdam: Elsevier, 1993

    MATH  Google Scholar 

  13. Rodin G. The overall elastic response of materials containing spherical inhomogeneities.Int J Solids Structures, 1993, 30: 1849–1863

    Article  MATH  Google Scholar 

  14. Ponte Castaneda P, Suquet P. Nonlinear composites.Adv Appl Mech, 1997, 34: 171–301

    Article  Google Scholar 

  15. Walpole LJ. A coated inclusion in an elastic medium.Math Proc Camb Phil Soc, 1978, 83: 495–506

    MATH  MathSciNet  Google Scholar 

  16. Cherkaoui M, Sabar H, Berveiller M. Micromechanical approach of the coated inclusion problem and applications to composite materials.J Eng Mater Technol, 1994, 116: 274–278

    Google Scholar 

  17. Herve E, Zaoui A. N-layered inclusion-based micromechanical modeling.Int J Eng Sci, 1993, 31: 1–10

    Article  MATH  Google Scholar 

  18. Dederichs PH, Zeller R. Variational treatment of the elastic constants of disorder materials.Z Phys, 1973, 259: 103–116

    Article  Google Scholar 

  19. Kroner E. Statistical modeling. In: Gittus J, Zarka J eds. Small Deformations of Plasticity. London and New York: Elsevier Applied Science Pub. 1986

    Google Scholar 

  20. Love AEH. A Treatise on the Mathematical Theory of Elasticity. New York: Cambridge University Press, 1944

    MATH  Google Scholar 

  21. Lurie AL. Three-dimensional Problems of the Theory of Elasticity. New York: Interscience, 1964

    Google Scholar 

  22. Richard TG. The mechanical behaviour of a solid microsphere filled composites.J Comp Mater, 1975, 9: 108–114

    Google Scholar 

  23. Hashin Z, Shtrikman SA. A variation approach to the theory of the elastic behaviour of multiphase materials.J Mech Phys Solids, 1963, 11: 127–140

    Article  MATH  MathSciNet  Google Scholar 

  24. Huang JS, Gibson LJ. Elastic moduli of a composite of hollow sphere in a matrix.J Mech Phys Solids, 1993, 41: 55–75

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Peking University, 100871, Beijing, China

    Dai Lanhong, Huang Zhuping & Wang Ren

Authors
  1. Dai Lanhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huang Zhuping
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wang Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by the National Natural Science Foundation of China under the Contract NO. 19632030 and 19572008, and China Postdoctoral Science Foundation

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lanhong, D., Zhuping, H. & Ren, W. An explicit expression of the effective moduli for composite materials filled with coated inclusions. Acta Mech Sinica 14, 37–52 (1998). https://doi.org/10.1007/BF02486829

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02486829

Key Words

Search

Navigation