Homogenization of an elasticity problem in domains with a net of slender bars near surface

Abstract

We consider an elasticity problem in a domain Ω (ε)=Ω⧹F (ε) , where Ω is an open bounded domain in R 3, F (ε) is a connected nonperiodic set in Ω like a net of slender bars, and ε is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F ( ε) , i.e., for sufficiently small ε, the set F ( ε) is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).