Refinement of the Maxwell Formula for Composite Reinforced by Circular Cross-Section Fibers. Part II: Using Padé Approximants
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Date
2020
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Link
Abstract
EN: The effective properties of the fiber-reinforced composite materials with fibers of
circle cross section are investigated. The novel estimation for the effective coefficient of
thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic
homogenization is used. For an analytical solution of the periodically repeated cell problem the
Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S.
Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow,
especially for nondilute high-contrast composite materials. For improving this drawback we used
Padé approximations for various forms of SAP solutions with the following additive matching of
obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and
convenient form. They can be used even for a volume fraction of inclusion very near the physically
possible maximum value as well as for high-contrast composite constituents. The results are
confirmed by comparison with known numerical and asymptotic results.
Description
V. Gabrinets: ORCID 0000-0002-6115-7162, Jan Awrejcewicz: ORCID 0000-0003-0387-921X
Keywords
Maxwell formula, Padé approximants, circular cross-section fibers, КТ
Citation
Andrianov I. I., Awrejcewicz J., Starushenko G. A., Gabrinets V. A. Refinement of the Maxwell Formula for Composite Reinforced by Circular Cross-Section Fibers. Part I: Using Padé Approximants. Acta Mechanica. 2020. Vol. 231. URL: https://link.springer.com/article/10.1007%2Fs00707-020-02789-2 (27.01.2021). DOI: 10.1007/s00707-020-02789-2.