Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 137, pp. 1-11.
Title: A property of the H-convergence for elasticity in perforated domains
Author: Hamid Haddadou (Institut Nationale de formation, Algerie)
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
$(A^{\varepsilon},T_{\varepsilon})\overset{H_{e}^{0}}{\rightharpoonup}A^{0}$,
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.