Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces.

Layered composites constitute a class of composites of both theoretical and practical interest. Remarkably, analytical and exact expressions are available for the effective elastic moduli of a layered composite when the interface between any two of its neighboring layers is perfect and corresponds to a smooth plane. The objective of this work is to determine the effective elastic moduli of a layered composite of which the interface between any two neighboring layers remains perfect but oscillates fast about a plane and along one direction. To achieve this objective, a multiscale homogenization approach is elaborated. First, by carrying out an asymptotic analysis, it is shown that the zone in which a periodic rough interface is situated can be homogenized as an equivalent layer whose elastic properties admit coordinate-free analytical exact expressions. Next, the resulting layered composite is further homogenized and its macroscopic elastic moduli are determined in an exact and compact way. Examples are finally provided to illustrate and confirm the analytical results by comparing them with the corresponding numerical results obtained by the finite element method.