Homogenizing media containing a highly conductive honeycomb substructure

Article type: Research Article

Authors: Gruais, Isabelle^; | Poliševski, Dan

Affiliations: Université de Rennes 1, I.R.M.A.R., Campus de Beaulieu, 35042 Rennes Cedex, France | I.M.A.R., P.O. Box 1-764, RO-014700 Bucharest, Romania

Note: [] Corresponding author. E-mail: [email protected]

Abstract: The present paper deals with the homogenization of the heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a rectangular honeycomb structure formed by a set of thin layers crossing orthogonally and periodically. We consider the case when the conductivity of the thin layers is in inverse proportion to the vanishing volume of the rectangular honeycomb structure. We find the system that governs the asymptotic behaviour of the temperature distribution of this binary medium. The dependence with respect to the thicknesses of the layers is also emphasized. We use an energetic method associated to a natural control-zone of the vanishing domain.

Keywords: homogenization, conduction, fine-scale, honeycomb structure

DOI: 10.3233/ASY-2009-0970

Journal: Asymptotic Analysis, vol. 67, no. 1-2, pp. 33-43, 2010