Multiscale analysis of composite structures based on higher-order asymptotic homogenization with boundary layer correction

First-order homogenization generally becomes inaccurate for materials with a weak scale separation between characteristic lengths of the heterogeneities and the structural problem. It is also unable to provide a correct solution in the vicinity of the boundaries due to the loss of periodicity in these regions. In this article, we demonstrate the effectiveness of higher-order homogenization, up to the third-order, in estimating correctly the heterogeneous solution, for cases with a low scale separation in elastic composite materials. We also propose a higher-order general boundary layer method, effective for various boundary conditions (Dirichlet, Neumann or mixed), to correct the obtained estimation near the boundaries. The efficiency and accuracy of the proposed methods are studied on various numerical examples dealing with elastic laminates and fiber-matrix composites.