Approximate methods for numerical evaluation of the elastic moduli of composite and microheterogeneous materials

  • V. V. Skorokhod

Approximate methods for calculating the effective elastic moduli of microheterogeneous materials, including multiphase ones, are considered. These methods are based on the analogy between the electrostatic field in dielectrics and the field of elastic stresses and strains in solids. Formulas are derived for the quantitative evaluation, with accuracy sufficient for materials science practices, of the effective elastic moduli of composites with different structures as a function of the elastic moduli, morphology, and volume fraction of the phases. The method is validated by calculating the elastic characteristics of bodies with plane slit-like defects, including powder compacts.


effective elastic moduli multiphase materials composites electrostatic and elastic fields bodies with slit-like defects 


  1. 1.
    T. D. Shermergor, Theory of Elasticity of Microheterogeneous Materials [in Russian], Nauka, Moscow (1977).Google Scholar
  2. 2.
    G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1985).Google Scholar
  3. 3.
    G. A. Banushkin, V. Ya. Bulanov, and N. A. Sinitskii, Metal Composites: Introduction to Phenomenological Theory [in Russian], UNTs AN SSSR, Sverdlovsk (1987).Google Scholar
  4. 4.
    V. P. Privalko, V. V. Novikov, and Yu. G. Yanovskii, Basic Thermophysics and Rheophysics of Polymeric Materials [in Russian], Naukova Dumka, Kyiv (1991).Google Scholar
  5. 5.
    V. V. Skorokhod, “Calculating the isotropic elastic moduli of dispersed solid mixtures,” Poroshk. Metallurg., No. 1, 50–55 (1961).Google Scholar
  6. 6.
    J. K. Mackenzie, “The elastic constants of solid containing spherical holes,” Proc. Phys. Soc., Ser. B, 63, No. 1, 2–11 (1950).CrossRefGoogle Scholar
  7. 7.
    V. I. Odelevskii, “Calculating the generalized conductivity of heterogeneous systems,” Zh. Teor. Fiz., 21, No. 6, 666–685 (1951).Google Scholar
  8. 8.
    V. V. Skorokhod, Rheological Fundamentals of Sintering Theory [in Russian], Naukova Dumka, Kyiv (1972).Google Scholar
  9. 9.
    Z. Hashin, “The elastic moduli of heterogeneous materials,” Trans. ASME, J. Appl. Mech., 29, No. 1, 143–150 (1962).Google Scholar
  10. 10.
    Z. Hashin and S. Shtrikman, “A variational approach of the theory of the elastic behavior of multiphase materials,” J. Mech. Phys. Solids, 11, No. 2, 127–140 (1963).CrossRefGoogle Scholar
  11. 11.
    R. Hill, “A self-consistent mechanics of composite materials,” J. Mech. Phys. Solids, 13, No. 4, 213–222 (1965).CrossRefGoogle Scholar
  12. 12.
    B. Budiansky, “On the elastic moduli of some heterogeneous materials,” J. Mech. Phys. Solids, 13, No. 4, 223–227 (1965).CrossRefGoogle Scholar
  13. 13.
    L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media, Pergamon Press, Oxford (1984).Google Scholar
  14. 14.
    L. D. Landau and E. M. Lifshits, Theory of Elasticity, Butterworth-Heinemann, Maugin (1986).Google Scholar
  15. 15.
    H. Doi, Y. Fujiwara, K. Miyake, and Y. Oosawa, “A systematic investigation of elastic moduli of WC–Co alloys,” Met. Trans., 1, No. 5, 1417–1425 (1970).Google Scholar
  16. 16.
    V. V. Skorokhod, “Theory of the physical properties of porous and composite materials and the principles for control of their microstructure in manufacturing processes,” Powder Metall. Met. Ceram., 34, No. 1–2, 48–63 (1995).CrossRefGoogle Scholar
  17. 17.
    J. D. Eshelby, “The continuum theory of lattice defects,” in: F. Seitz and D. Turnbull (eds.), Progress in Solid State Physics, Vol. 3, Academic Press, New York (1956), pp. 79–303.Google Scholar
  18. 18.
    H. L. Frisch and R. Simha, “The viscosity of colloidal suspensions and macromolecular solutions,” in: F. R. Eirich (ed.), Rheology: Theory and Applications, Vol. 1, Academic Press, New York (1957), pp. 525–613.Google Scholar
  19. 19.
    R. L. Salganik, “Mechanics of bodies with a great number of cracks,” Mekh. Tverd. Tela, No. 4, 149–158 (1973).Google Scholar
  20. 20.
    O. V. Roman, V. V. Skorokhod, and G. R. Fridman, Ultrasonic and Resistometric Testing in Powder Metallurgy [in Russian], Vysheishaya Shkola, Minsk (1989).Google Scholar

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© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Frantsevich Institute for Problems of Materials Science, National Academy of Sciences of UkraineKievUkraine

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