Abstract
We study the effective properties of an elastic composite medium under the assumption of small deformations. This composite is made of a periodic possibly disconnected subset filled up with a strong material surrounded by another material whose elastic coefficients are very small. The effective macroscopic behaviour obtained by homogenization turns out to be nonlocal and depends highly on the geometry of the strong component. In particular, second order derivative of the displacement appear in the limit energy when disconnected fibers are considered. These results were announced in [8].