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Asymptotic study of imperfect interfaces in conduction through a granular composite material

Imperfect bonding between the constitutive components can greatly affect the properties of composite structures. We propose an asymptotic analysis of different types of imperfect interfaces arising in the problem of conduction through a simple cubic array of spherical inclusions. The performed study is based on the two-scale asymptotic homogenization method. The microscopic problem on the unit cell is solved using the underlying principles of the boundary-shape perturbation technique. The influence of the interface properties on the effective conductivity and on the local potential and flux fields is studied.