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General Integral Equations and Bounds of the Effective Moduli of Random Structure Composites

[+] Author Affiliations
Valeriy A. Buryachenko

Micromechanics & Composites LLC, Dayton, OH

Paper No. IMECE2017-70777, pp. V009T12A054; 3 pages
doi:10.1115/IMECE2017-70777
From:
  • ASME 2017 International Mechanical Engineering Congress and Exposition
  • Volume 9: Mechanics of Solids, Structures and Fluids; NDE, Structural Health Monitoring and Prognosis
  • Tampa, Florida, USA, November 3–9, 2017
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5844-8
  • Copyright © 2017 by ASME

abstract

One considers a linear elastic random structure composite material (CM) with a homogeneous matrix. The idea of the effective field hypothesis (EFH, H1) dates back to Faraday, Poisson, Mossotti, Clausius, and Maxwell (1830–1870, see for references and details [1], [2]) who pioneered the introduction of the effective field concept as a local homogeneous field acting on the inclusions and differing from the applied macroscopic one. It is proved that a concept of the EFH (even if this term is not mentioned) is a (first) background of all four groups of analytical methods in physics and mechanics of heterogeneous media (model methods, perturbation methods, self-consistent methods, and variational ones, see for refs. [1]). New GIEs essentially define the new (second) background (which does not use the EFH) of multiscale analysis offering the opportunities for a fundamental jump in multiscale research of random heterogeneous media with drastically improved accuracy of local field estimations (with possible change of sign of predicted local fields).

Estimates of the Hashin-Shtrikman (H-S) type are developed by extremizing of the classical variational functional involving either a classical GIE [1] or a new one. In the classical approach by Willis (1977), the H-S functional is extremized in the class of trial functions with a piece-wise constant polarisation tensors while in the current work we consider more general class of trial functions with a piece-wise constant effective fields. One demonstrates a better quality of proposed bounds, that is assessed from the difference between the upper and lower bounds for the concrete numerical examples.

Copyright © 2017 by ASME

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