The Maxwell modified method of determination of effective constants of heterogeneous materials

1Kushch, VI
1Maystrenko, AL
1Chernobai, VS
1V.N. Bakul Institute for Superhard Materials of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 2:35-41
Section: Materials Science
Language: Ukrainian

The Maxwell modified method of determination of effective constants is formulated in terms of the dipole moments of a real piece of a composite and the equivalent inclusion. The method is rigorous in the sense that the evaluation of an effective constant converges to the exact value with increasing the cluster size. For example, the problem of determining the thermal conductivity of a fiber composite shows that the method provides the calculation of effective constants with high accuracy for composites with periodic or disordered micro structure.

Keywords: composite, dipole moment, effective constants, Maxwell method
  1. Maxwell, J. C. (1892.). A treatise on electricity and magnetism. Vol. 1. Oxford: Clarendon Press.
  2. Kachanov, M. and Sevostianov, I., (Eds.). (2013). Effective Properties of Heterogeneous Materials. Berlin: Springer.
  3. Milton, G. W. (2002). The Theory of Composites. Cambridge: Cambridge Univ. Press.
  4. Mogilevskaya, S. G., Crouch, S. L., Stolarski, H. K., Benusiglio, A. (2010). Int. J. Solids and Structures. 47, pp. 407-418.
  5. Mogilevskaya, S. G., Stolarski, H. K., Crouch, S. L. (2012).J. of Mech. and Phys. of Solids, 60, pp. 391-417.
  6. Mogilevskaya, S. G., Kushch, V. I., Koroteeva, O., Crouch, S. L. (2012).J. Mech. Mater. and Struct., 7, pp. 103-117.
  7. Kushch, V. I., Sevostianov, I. (2016). Int. J. Eng. Sci., 98, pp. 36-50.
  8. Landau, L. D., Lifshitz, E. M. (2001). Theory of Fields. Izd. 8-e, stereot. Moscow, Fismatlit (in Russian).
  9. Kushch, V. I., Sevostianov, I. (2014). Int. J. Eng. Sci., 74, pp. 15-34.
  10. Golovchan, V. T., Guz, A. N., Kohanenko, Yu. V., Kushch, V. I. (1993). Mechanics of composites. Vol. 1. Kyiv: Naukova Dumka (in Russian).
  11. Kushch, V. I. (2013). Micromechanics of composites: multipole expansion approach. Amsterdam, Elsevier.
  12. Avelin, J., Sharma, R., Hanninen, I., Sihvola, A. H. (2001). IEEE Transactions on antennas and propagation, 49, pp. 451-457.
  13. Perrins, W. T., McKenzie, D. R., McPhedran, R. C. (1979). Proc. of Royal Society of London. Ser. A, 369, pp. 207-225.
  14. Cheng, H., Greengard, L. (1997).J. Computational Physics, 136, pp. 629-639.