Bounds on the effective transport coefficients of two-phase media from discrete theoretical and experimental data

  • Stanisław Tokarzewski Institute of Fundamental Technological Research Polish Academy of Sciences
  • Andrzej Gałka Institute of Fundamental Technological Research Polish Academy of Sciences
  • Igor Andrianov Prydneprovie State Academy of Civil Engineering and Architecture

Abstract

By applying Pade approximants and continued fractions technique developed in [1, 2, 3, 24] we investigate a composite material of the effective modulus e(h) consisting of two components of real moduli 1 and 2, respectively, where h= 2/ 1. By starting from K power expansions of e(h) at fixed points h= h1, h2, ... ,hKthe infinite set of the general inequalities specifying explicitly the upper and lower bounds on e(h)/ 1 are derived. Our estimations generalize the previous bounds reported in [13, 17, 22] . The inequalities achieved are applied for the evaluation of the upper and lower bounds on e(h)/ 1 from the given experimental measurements.

Keywords

References

[1] G.A. Baker. Ess entials of Pade Approximants. Academic. Press, London, 1975.
[2] G.A. Baker, P. Graves-Morris. Pade Approximants. Part I: Basic Theory. Encyclopedia of Mathematics and its Applications, Vol. 13, Addison-Wesley Publ. Co., London, 1981.
[3] G.A. Baker, P. Graves-Morris. Pade Approximant.s, Part II: Extensions and Applications. Encyclopedia of Math· ematics and its Applications, Vol. 14, Addison-Wesley Publ. Co., London, 1981.
[4] D.J. Bergman. The dielectric constant of a composite material - A problem in classical physics. Phys. Report. C 43: 377- 407, 1978.
[5] D.J. Bergman. Bounds for the complex dielectric constants of two-component composite material. Phys.Rev. B23, 6: 3058- 3065, 1981.
Published
Jun 22, 2023
How to Cite
TOKARZEWSKI, Stanisław; GAŁKA, Andrzej; ANDRIANOV, Igor. Bounds on the effective transport coefficients of two-phase media from discrete theoretical and experimental data. Computer Assisted Methods in Engineering and Science, [S.l.], v. 4, n. 2, p. 229-241, june 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1404>. Date accessed: 17 may 2024.
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Vol 4 No 2 (1997)
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