Refinement of the Maxwell Formula for Composite Reinforced by Circular Cross-Section Fibers. Part I: Using the Schwarz Alternating Method
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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 circular 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 analytical
solution of the periodically repeated cell problem, the Schwarz alternating process is employed. The principal
term of the refined formula coincides with the classical Maxwell formula. On the other hand, the refined
formula can be used far beyond the area of applicability of the Maxwell formula. It can be used for dilute and
non-dilute composites. It is 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, circular cross-section fibers, Schwarz alternating method, 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 the Schwarz Alternating Method. Acta Mechanica. 2020. Vol. 231. URL: https://link.springer.com/article/10.1007%2Fs00707-020-02788-3 (27.01.2021). DOI: 10.1007/s00707-020-02788-3.