Electron. J. Diff. Eqns., Vol. 2006(2006), No. 137, pp. 1-11.

A property of the H-convergence for elasticity in perforated domains

Hamid Haddadou

Abstract:
In this article, we obtain the $H_{e}^{0}$-convergence as a limit case of the $H_{e}$-convergence. More precisely, if $\Omega_{\varepsilon}$ is a perforated domain with (admissible) holes $T_{\varepsilon}$ and $\chi_{\varepsilon}$ denote its characteristic function and if $(A^{\varepsilon},T_{\varepsilon}) \rightharpoonup A^{0}$, we show how the behavior as $(\varepsilon,\delta)\to(0,0)$ of the double sequence of tensors $A^{\varepsilon}_{\delta}=(\chi_{\varepsilon} +\delta(1-\chi_{\varepsilon})) A^{\varepsilon}$ is connected to $A^{0}$. These results extend those given by Cioranescu, Damlamian, Donato and Mascarenhas in [3] for the $H$-convergence of the scalar second elliptic operators to the linearized elasticity systems.

Submitted July 6, 2006. Published October 31, 2006.
Math Subject Classifications: 35B40, 74B05.
Key Words: Homogenization; H-convergence; linearized elasticity system; perforated domains.

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Hamid Haddadou
Institut Nationale de formation en Informatique
BP 68, Oued Smar, El Harrach
Alger, Algérie
email: h_haddadou@ini.dz

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