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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 fi...