Vibrations d'un composite élastique comportant des inclusions granulaires très lourdes : effets de mémoire

Let Ω be a bounded open set of R3 and (ρε), (με), (λε) be sequences of ε-periodic functions on Ω, the function ρε taking very large values on a set of ε-periodically distributed balls of radius rε (rε≪ε). We study the asymptotic behaviour as ε→0 of the equation:{ρε∂2uε∂t2−div(σε(uε))=ρεfinΩ×(0,T)+boundary conditions,σε(uε)=λεtr(e(uε))I+2μεe(uε),e(uε)=12(∇uε+∇Tuε), and finally we find a non-local effective equation deduced from a homogenized system of hyperbolic equations. To cite this article: M. Bellieud, C. R. Acad. Sci. Paris, Ser. I 346 (2008).