Effective conductive and dielectric properties of matrix composites with inclusions of arbitrary shapes

International Journal of Engineering Science

Volumn 46, Issue 2, 2008, Pages 147-163

  Kanaun, S K ^a   Kochecksaraii, S Babaii ^a  

^a SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

Author keywords

Effective field method; Fast Fourier transform; Gaussian approximation functions; Homogenization problem; One particle problem; Toeplitze matrices; Two phase composite materials

Indexed keywords

ELECTRIC CONDUCTIVITY; FAST FOURIER TRANSFORMS; NUMERICAL METHODS; PERMITTIVITY; THERMAL CONDUCTIVITY;

EFFECTIVE FIELD METHOD; GAUSSIAN APPROXIMATION FUNCTIONS; HOMOGENIZATION PROBLEM; ONE PARTICLE PROBLEM; TOEPLITZE MATRICES; TWO PHASE COMPOSITE MATERIALS;

COMPOSITE MATERIALS;

EID: 37149050555     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2007.09.003     Document Type: Article

References (19)

1. Chew W.Ch. Waves and Fields in Inhomogeneous Media (1990), Van Nostrand Reinhold, Amsterdam
2. Foldy L.O. The multiple scattering of waves. Phys Rev 67 (1945) 107-119
3. Golub G.H., and Van Loan C.F. Matrix Computations (1993), Johns Hopkins University Press
4. Kanaun S., and Levin V. Effective field method on the mechanics of matrix composite materials. In: Markov K.Z. (Ed). Advances in Mathematical Modeling of Composite Materials, Series on Advances in Mathematics for Applied Sciences, vol. 15 (1994), World Scientific Publishing 1-58
5. Kanaun S. Effective field method in the linear problems of statics of composite media. Appl. Math. Mech. (PMM) 46 (1982) 655-665
6. Kanaun S. Elastic medium with random field of inhomogeneities. In: Kunin I.A. (Ed). Elastic Medium with Microstructure vol. 2 (1983), Springer-Verlag 165-228 (Chapter 7)
7. Kanaun S. Self-consistent schemes of averaging in the mechanics of matrix composite materials. Mech. Compos. Mater. 6 (1990) 984-994
8. Kanaun S. Dielectric properties of matrix composite materials with high volume concentration of inclusions (effective field approach). Int. J. Eng. Sci. 4 (2003) 1287-1312
9. Kunin I.A. Elastic Medium with Microstructure vol. 2 (1983), Springer-Verlag, Berlin, Heidelberg, NY
10. Lax M. Multiple scattering of waves. Rev. Mod. Phys. 23 (1951) 287-310
11. Lax M. Multiple scattering of waves. II. The effective field in dense systems. Phys. Rev. 85 (1952) 621-629
12. R. Landauer, Electrical conductivity in inhomogeneous media, in: Proceedings of the Conference on Electrical Transport and Optical Properties of Inhomogeneous Media (ETOPIM 1) 2 (AIP Conf. Proc.), 1978, pp. 2-46.
13. Maz'ya V. Approximate approximation. In: Whitman J.R. (Ed). The Mathematics of Finite Elements and Applications. Highlights (1993), Wiley, Chichester 77
14. Maz'ya V., and Schmidt G. On approximate approximations using Gaussian kernels. IMA J. Numer. Anal. 16 (1996) 13-30
15. Moulinec H., and Suquet P. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. C.R. Acad. Sci. Paris 318 (1994) 1417-1423
16. Kanaun S., and Babaii S. A numerical method for the solution of thermo- and electro-static problems for a medium with isolated inclusions. J. Comput. Phys. 192 (2003) 471-493
17. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in FORTRAN: The Art of Scientific Computing (1992), Cambridge University Press, Cambridge
18. Peterson A.F., Ray S.L., and Mittra R. Computational Methods for Electromagnetics (1997), IEEE Press, NY
19. Segurado J., and Llorca J. A numerical approximation to the elastic properties of sphere-reinforced composites. J. Mech. Phys. Solid 50 (2002) 2107-2121