Effective medium approximation for conductivity of coated-inclusion composites with anisotropic coating

Tran Bao Viet, Nguyen Thi Huong Giang, Pham Duc Chinh


Effective medium approximations are constructed in this paper to estimate the macroscopic conductivity of coated-inclusion composites with thin anisotropic coating. The two-phase coated-inclusion are substituted by equivalent one-phase inclusion, using the multi-coated spheres assemblage and the differential substitution approaches. Then, the usual effective medium approximation schemes are applied to the equivalent medium to estimate the conductivity of original three-phase composites. The results obtained were compared with the numerical simulation by finite element method in 2D show the effectiveness of the methods.


Coated-inclusion; effective conductivity; equivalent-inclusion approach; anisotropic coating

Full Text:



E. Hervé and A. Zaoui. Elastic behaviour of multiply coated fibre-reinforced composites. International Journal of Engineering Science, 33, (10), (1995), pp. 1419–1433. https://doi.org/10.1016/0020-7225(95)00008-l.

Y. P. Qiu and G. J. Weng. Elastic moduli of thickly coated particle and fiber-reinforced composites. Journal of Applied Mechanics, 58, (2), (1991), pp. 388–398. https://doi.org/10.1115/1.2897198.

C.-W. Nan, R. Birringer, D. R. Clarke, and H. Gleiter. Effective thermal conductivity of particulate composites with interfacial thermal resistance. Journal of Applied Physics, 81, (10), (1997), pp. 6692–6699. https://doi.org/10.1063/1.365209.

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. https://doi.org/10.1016/j.ijheatmasstransfer.2012.11.028.

I. V. Andrianov, A. L. Kalamkarov, and G. A. Starushenko. Three-phase model for a fiber-reinforced composite material. Composite Structures, 95, (2013), pp. 95–104. https://doi.org/10.1016/j.compstruct.2012.07.003.

M. Hori and S. Nemat-Nasser. Double-inclusion model and overall moduli of multi-phase composites. Mechanics of Materials, 14, (3), (1993), pp. 189–206. https://doi.org/10.1115/1.2904292.

D. S. Liu and D. Y. Chiou. Modeling of inclusions with interphases in heterogeneous material using the infinite element method. Computational Materials Science, 31, (3-4), (2004), pp. 405–420. https://doi.org/10.1016/j.commatsci.2004.05.002.

Y. M. Shabana. A micromechanical model for composites containing multi-layered interphases. Composite Structures, 101, (2013), pp. 265–273. https://doi.org/10.1016/j.compstruct.2013.02.008.

P. D. Chinh and T. A. Binh. Equivalent-inclusion approach for the conductivity of isotropic matrix composites with anisotropic inclusions. Vietnam Journal of Mechanics, 38, (4), (2016), pp. 239–248. https://doi.org/10.15625/0866-7136/6753.

T. K. Nguyen and D. C. Pham. Equivalent-inclusion approach and effective medium estimates for elastic moduli of two-dimensional suspensions of compound inclusions. Philosophical Magazine, 94, (36), (2014), pp. 4138–4156. https://doi.org/10.1080/14786435.2014.978831.

D. C. Pham and B. V. Tran. Equivalent-inclusion approach and effective medium approximations for conductivity of coated-inclusion composites. European Journal of Mechanics-A/Solids, 47, (2014), pp. 341–348. https://doi.org/10.1016/j.euromechsol.2014.05.010.

B. V. Tran, D. C. Pham, and T. H. G. Nguyen. Equivalent-inclusion approach and effective medium approximations for elastic moduli of compound-inclusion composites. Archive of Applied Mechanics, 85, (12), (2015), pp. 1983–1995. https://doi.org/10.1007/s00419-015-1031-6.

T. N. Quyet, P. D. Chinh, and T. A. Binh. Equivalent-inclusion approach for estimating the elastic moduli of matrix composites with non-circular inclusions. Vietnam Journal of Mechanics, 37, (2), (2015), pp. 123–132. https://doi.org/10.15625/0866-7136/37/2/5659.

B.-V. Tran, D.-C. Pham, and T.-H.-G. Nguyen. Effective medium approximation for conductivity of unidirectional coated-fiber composites. Computational Thermal Sciences: An International Journal, 9, (1), (2017), pp. 63–76. https://doi.org/10.1615/computthermalscien.2017015911.

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. https://doi.org/10.1063/1.1728579.

D. C. Pham. Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems. Zeitschrift fur angewandte Mathematik und Physik, 69, (1), (2018), p. 13. https://doi.org/10.1007/s00033-017-0905-6.

DOI: https://doi.org/10.15625/0866-7136/13717 Display counter: Abstract : 305 views. PDF : 70 views.


  • There are currently no refbacks.

Copyright (c) 2019 Vietnam Academy of Science and Technology


Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam
Tel: (+84) 24 3791 7103
Email: vjmech@vjs.ac.vn