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Bounds on the effective conductivity of two‐dimensional N ‐component isotropic and symmetric cell mixtures
Author(s) -
Chinh Pham Duc
Publication year - 2004
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.200310135
Subject(s) - isotropy , conductivity , component (thermodynamics) , mathematics , perturbation (astronomy) , upper and lower bounds , mathematical analysis , yield (engineering) , subclass , geometry , physics , optics , thermodynamics , quantum mechanics , biology , antibody , immunology
Variational perturbation approach is applied to derive upper and lower bounds on the effective conductivity of two‐dimensional isotropic quasisymmetric (or symmetric cell) N ‐component media, which involve only the definite information about the volume proportions and properties of their components. The bounds appear to improve upon, or coincide (in case of circular cell subclass) with, the bounds constructed by an alternative variational approach. The general geometry‐dependent bounds for isotropic composites converge to yield the exact effective conductivity of the multi‐coated circles model.