Conductivity of Particle-Reinforced Composites: Analytical Homogenization Approach

  • Igor V. AndrianovEmail author
  • Jan AwrejcewiczEmail author
  • Vladyslav V. DanishevskyyEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 77)


In this chapter, we consider the particle-reinforced composites consisting of infinite matrix \({{\varOmega }^{(1)}}\) and spherical inclusions \({{\varOmega }^{(2)}}\), composed of simple cubic (SC) (Fig. 4.1a) and body-centred cubic (BCC) (Fig. 4.1b) lattices.


Particle-reinforced Composites Boundary Perturbation Method Hashin Shtrikman High-contrast Composite Conductive Particles 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bakhvalov, N., and G. Panasenko. 1989. Averaging processes in periodic media mathematical problems in mechanics of composite materials. Kluwer: Dordrecht.Google Scholar
  2. 2.
    McKenzie, D.R., R.C. McPhedran, and G.H. Derrick. 1978. The conductivity of lattices of spheres. II. The body-centred and face-centred lattices. Proceedings of the Royal Society of London A 362: 211–232.Google Scholar
  3. 3.
    McPhedran, R.C., and D.R. McKenzie. 1978. The conductivity of lattices of spheres. 1. The simple cubic lattice. Proceedings of the Royal Society of London A 359: 45–63.Google Scholar
  4. 4.
    Batchelor, G.K., and R.W. O’Brien. 1977. Thermal or electrical conduction through a granular material. Proceedings of the Royal Society of London A 355: 313–333.CrossRefGoogle Scholar
  5. 5.
    Hashin, Z. 2001. Thin interphase/imperfect interface in conduction. Journal of Applied Physics 89: 2261–2267.CrossRefGoogle Scholar
  6. 6.
    McPhedran, R.C. 1986. Transport properties of cylinder pairs and of the square array of cylinders. Proceedings of the Royal Society of London A 408: 31–43.CrossRefGoogle Scholar
  7. 7.
    Berlyand, L., and V. Mityushev. 2005. Increase and decrease of the effective conductivity of two phase composites due to polydispersity. Journal of Statistical Physics 118: 481–509.Google Scholar
  8. 8.
    Kozlov, G.M. 1989. Geometrical aspects of averaging. Russian Mathematical Surveys 44 (2): 91–144.Google Scholar
  9. 9.
    Christensen, R.M. 2005. Mechanics of composite materials. Mineola, New York: Dover Publications.Google Scholar
  10. 10.
    De Gennes, P.G. 1976. On a relation between percolation theory and elasticity of gels. Journal of Physical Letters 37: 1–14.CrossRefGoogle Scholar
  11. 11.
    Shklovskii, B.I., and A.L. Efros. 1984. Electronic properties of doped semiconductors. Berlin, New York: Springer.CrossRefGoogle Scholar
  12. 12.
    Sotskov, V.A., and S.V. Karpenko. 2003. Electrical conduction in binary macrosystems: General rules. Technical Physics 48 (1): 100–103.CrossRefGoogle Scholar
  13. 13.
    Balagurov, B.Y., and V.A. Kashin. 1996. Quadratic effective characteristics of transport in two-component materials. Computer simulation of a three-dimensional disordered lattice. Journal of Experimental and Theoretical Physics 83 (3): 553–561.Google Scholar
  14. 14.
    Balagurov, B.Y., and V.A. Kashin. 2000. Conductivity of a two-dimensional system with a periodic distribution of circular inclusions. Journal of Experimental and Theoretical Physics. 90 (5): 850–860.Google Scholar
  15. 15.
    Balagurov, B.Y., and V.A. Kashin. 2005. Analytic properties of the effective dielectric constant of a two-dimensional Rayleigh model. Journal of Experimental and Theoretical Physics. 100 (4): 731–741.Google Scholar
  16. 16.
    Kazakov, V.A., and A.M. Satanin. 1981. A renormalization group approach for randomly distributed conductance. Physica Status Solidi B 108: 19–28.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Rayleigh, R.S. 1892. On the influence of obstacles arranged in rectangular order upon the properties of medium. Philosophical Magazine 34: 481–502.CrossRefzbMATHGoogle Scholar
  18. 18.
    Sangani, A.S., and A. Acrivos. 1983. The effective conductivity of a periodic array of spheres. Proceedings of the Royal Society of London A 386: 263–275.CrossRefGoogle Scholar
  19. 19.
    Batchelor, G.K. 1974. Transport properties of two-phase materials with random structure. Annual Review of Fluid Mechanics 6: 227–254.CrossRefzbMATHGoogle Scholar
  20. 20.
    Kharadly, M.M.Z., and W. Jackson. 1952. The properties of artificial dielectrics comprising arrays of conducting elements. Proceedings of Electrical Engineering 100: 199–212.Google Scholar
  21. 21.
    Meredith, R.E., and C.W. Tobias. 1960. Resistance to potential flow trough a cubical array of spheres. Journal of Applied Physics 31: 1270–1273.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institut für Allgemeine MechanikRWTH Aachen UniversityAachenGermany
  2. 2.Automation, Biomechanics and MechatronicsLodz University of TechnologyŁódźPoland
  3. 3.School of Computing and MathematicsKeele UniversityKeeleUK

Personalised recommendations