Fibered microstructures for some nonlocal Dirichlet forms

In this article we study the homogenization of some fibered microstructures in order to obtain prescribed nonlocal effects from strongly local conduction problems in a bounded open set S2 of R . According to the Beurling-Deny formula these nonlocal effects are represented by a so-called jumping measure defined on the product Q x Q. In particular we reach the measures of type j (dx, dy) = IE (dy) where E is a smooth open subset of Q. If the set E is connected the starting microstructure is only composed of high conductivity fibers. If the set E is not connected we also need a mixture of high and low conductivity fibers in the regions separating the components of E.