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Conductivity of two‐dimensional composites with randomly distributed elliptical inclusions
Author(s) -
Mityushev V.,
Rylko N.,
Bryła M.
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700236
Subject(s) - composite material , materials science , conductivity , electrical resistivity and conductivity , physics , engineering , electrical engineering , quantum mechanics
Analytical approximate formulae for the effective conductivity tensor of the two‐dimensional composites with elliptical inclusions are derived in the form of polynomial approximations in concentration. New formulae explain the seeming contradiction between various formulae derived in the framework of self consistent methods. Random composites with high conducting inclusions of two different shapes (elliptical and circle) of the same area are compared. It is established that greater relative concentration of ellipses increases the effective conductivity.