Abstract
The asymptotic-shielding effect and the asymptotic behavior of the conductivity of a medium containing closely spaced, perfectly conducting inclusions. It is proved that in the presence of asymptotic shielding for pairs of adjacent particles, the original continuous problem can be approximated by a finite-dimensional problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
J-L. Lions, “Some computational aspects of the homogenization method in composite materials,” in: Computational Methods in Mathematics, Geophysics, and Optimum Control [Russian translation], Nauka, Novosibirsk (1978), pp. 5–19.
L. Borcea and G. Papanicolaou, “Network approximation for transport properties of high contrast materials,” SIAM J. Appl. Math., 58, No. 2, 501–539 (1998).
L. V. Berlyand and A. G. Kolpakov, “Network approximation in the limit of small interparticle distance of the effective properties of a high contrast random dispersed composite,” Arch. Rational Mech. Anal., No. 3, 179–227 (2001).
J. C. Maxwell, Treatise on Electricity and Magnetismus, Vol. 1, Oxford Univ. Press, Oxford (1873).
J. B. Keller, “Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders,” J. Appl. Phys., 34, No. 4, 991–993 (1963).
I. E. Tamm, Foundations of Electricity Theory [in Russian], Nauka, Moscow (1976).
W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, New York-Toronto-London (1950).
N. N. Medvedev, Vorornoi-Delaunay Method and the Structure of Noncrystalline Systems [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (2000).
O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptical Equations [in Russian], Nauka, Moscow (1964).
V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1976).
M. Sahimi, Heterogeneous Materials, Springer-Verlag, Berlin-Heidelberg-New York (2003).
Yu. N. Rabotnov, Mechanics of Deformable Solids [in Russian], Nauka, Moscow (1979).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 128–140, May–June, 2005.
Rights and permissions
About this article
Cite this article
Kolpakov, A.G. Asymptotic behavior of the conducting properties of high-contrast media. J Appl Mech Tech Phys 46, 412–422 (2005). https://doi.org/10.1007/s10808-005-0091-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10808-005-0091-8