The Matched Asymptotic Expansion for the Computation of the Effective Behavior of an Elastic Structure With a Thin Layer of Holes

In the framework of matched asymptotic expansions we introduce a new efficient and robust method to approximate the behavior of a structure containing a thin layer with periodically distributed micro-holes. A surface (in three dimensions) or a line (in two dimensions), on which particular jumping conditions are defined, substitutes for the initial problem.