Polarization versus Mori-Tanaka approximations for effective conductivity of isotropic composites

Nguyen Trung Kien, Pham Duc Chinh, Nguyen Thi Hai Duyen
Author affiliations

Authors

  • Nguyen Trung Kien University of Transport and Communications, Hanoi, Vietnam
  • Pham Duc Chinh Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Nguyen Thi Hai Duyen Thuyloi University, Hanoi, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/10572

Keywords:

effective conductivity, isotropic composite material, polarization approximation, Mori-Tanaka approximation

Abstract

Our polarization approximations for the effective conductivity of isotropic multicomponent materials, constructed recently as approximate solutions to the minimum energy principles, are compared with the widely used Mori-Tanaka approximation, derived as an approximate solution of the field equations. The similarities and differences, advantages and disadvantages of both approaches are analysed with illustrating numerical examples.

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References

R. M. Christensen. Mechanics of composite materials. Wiley, New York, (1979).

S. Torquato. Random heterogeneous media. Springer, New York, (2002).

T. Mori and K. Tanaka. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21, (5), (1973), pp. 571–574. doi:10.1016/0001-6160(73)90064-3.

H. Le-Quang, D. C. Pham, G. Bonnet, and Q. C. He. Estimations of the effective conductivity of anisotropic multiphase composites with imperfect interfaces. International Journal of Heat and Mass Transfer, 58, (1-2), (2013), pp. 175–187. doi:10.1016/j.ijheatmasstransfer.2012.11.028.

T. K. Nguyen, V. L. Nguyen, and D. C. Pham. Estimating effective conductivity of unidirectional transversely isotropic composites. Vietnam Journal of Mechanics, 35, (3), (2013), pp. 203–213. doi:10.15625/0866-7136/35/3/2767.

Q. H. Do, D. C. Pham, and A. B. Tran. Equivalent-inclusion approach for the conductivity of isotropic matrix composites with anisotropic inclusions. Vietnam Journal of Mechanics, 38, (4), (2016), pp. 239–248. doi:10.15625/0866-7136/6753.

D. C. Pham, A. B. Tran, and Q. H. Do. On the effective medium approximations for the properties of isotropic multicomponent matrix-based composites. International Journal of Engineering Science, 68, (2013), pp. 75–85. doi:10.1016/j.ijengsci.2013.03.007.

D. C. Pham and T. K. Nguyen. Polarization approximations for macroscopic conductivity of isotropic multicomponent materials. International Journal of Engineering Science, 97, (2015), pp. 26–39. doi:10.1016/j.ijengsci.2015.08.006.

A. Norris. An examination of the Mori–Tanaka effective medium approximation for multiphase composites. Journal of Applied Mechanics, 56, (1), (1989), pp. 83–88. doi:10.1115/1.3176070.

Z. Hashin and S. Shtrikman. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics, 33, (10), (1962), pp. 3125–3131. doi:10.1063/1.1728579.

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Published

27-03-2018

How to Cite

[1]
N. T. Kien, P. D. Chinh and N. T. H. Duyen, Polarization versus Mori-Tanaka approximations for effective conductivity of isotropic composites, Vietnam J. Mech. 40 (2018) 79–87. DOI: https://doi.org/10.15625/0866-7136/10572.

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Research Article