Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites

The paper addresses the problem of modeling of fiber reinforced composites with imperfect bonding between the matrix and the inhomogeneities. The imperfections of different kinds are usually modeled as either layered inhomogeneities or by springs of certain stiffnesses distributed along the matrix/fiber interfaces. We compare the two approaches for the case of incompressible layer between the phases and calculate effective properties of fiber reinforced composites with periodic square arrays of fibers possessing imperfect contact with the surrounding material. We identify the interval of thickness at which the interphase does not influence the effective properties and show how the imperfection effects described by different models can be expressed in terms of each other.