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Modeling of Imperfect Viscoelastic Interfaces in Composite Materials

The present work deals with hierarchical composites in three dimensions, whose constituents behave as non-aging linear viscoelastic materials. We model the influence that imperfect viscoelastic interfaces have on the macroscopic effective response of these structures. As an initial approach, the problem of two bodies in adhesion is studied and in particular the case of soft viscoelastic interface at zero-order is considered. We deduce the integral form of the viscoelastic interface by applying the matched asymptotic expansion method, the correspondence principle, and the Laplace–Carson transform. Then, by adapting the integral form previously obtained, we address a heterogeneous problem for periodic structures. Here, theoretical results obtained for perfect interfaces are extended to the formal viscoelastic counterpart of the spring-type imperfect interface model. Finally, we show the potential of the proposed approach by performing calculations of effective properties in heterogeneous structures with two- and three-scale geometrical configurations and imperfect viscoelastic interfaces.