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

TitleThe Maxwell modified method of determination of effective constants of heterogeneous materials
Publication TypeJournal Article
Year of Publication2017
AuthorsKushch, VI, Maystrenko, AL, Chernobai, VS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.02.035
Issue2
SectionMaterials Science
Pagination35-41
Date Published2/2017
LanguageUkrainian
Abstract

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.

Keywordscomposite, dipole moment, effective constants, Maxwell method
References: 
  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. https://doi.org/10.1007/978-94-007-5715-8
  3. Milton, G. W. (2002). The Theory of Composites. Cambridge: Cambridge Univ. Press. https://doi.org/10.1017/CBO9780511613357
  4. Mogilevskaya, S. G., Crouch, S. L., Stolarski, H. K., Benusiglio, A. (2010). Int. J. Solids and Structures. 47, pp. 407-418. https://doi.org/10.1016/j.ijsolstr.2009.10.007
  5. Mogilevskaya, S. G., Stolarski, H. K., Crouch, S. L. (2012).J. of Mech. and Phys. of Solids, 60, pp. 391-417. https://doi.org/10.1016/j.jmps.2011.12.008
  6. Mogilevskaya, S. G., Kushch, V. I., Koroteeva, O., Crouch, S. L. (2012).J. Mech. Mater. and Struct., 7, pp. 103-117. https://doi.org/10.2140/jomms.2012.7.103
  7. Kushch, V. I., Sevostianov, I. (2016). Int. J. Eng. Sci., 98, pp. 36-50. https://doi.org/10.1016/j.ijengsci.2015.07.003
  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. https://doi.org/10.1016/j.ijengsci.2013.08.002
  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. https://doi.org/10.1109/8.918620
  13. Perrins, W. T., McKenzie, D. R., McPhedran, R. C. (1979). Proc. of Royal Society of London. Ser. A, 369, pp. 207-225. https://doi.org/10.1098/rspa.1979.0160
  14. Cheng, H., Greengard, L. (1997).J. Computational Physics, 136, pp. 629-639. https://doi.org/10.1006/jcph.1997.5787