Effective conductivity of composite with imperfect contact between elliptic fibers and matrix: Maxwell’s homogenization scheme

In the present paper, we use Maxwell homogenization scheme to calculate effective transverse conductivity of a fibrous composite with imperfect contact between the matrix and the parallel elliptic fibers. The developed theory extends the Hasselman–Johnson formula to the composites with elliptic fibers. The complete solution of the conductivity problem for single elliptic inclusion with imperfect interface provides the mathematical background of the method. In the Maxwell homogenization scheme, the effective inclusion is an ellipse with aspect ratio governed by the orientation distribution of elliptic fibers. The formula for effective conductivity is derived by equating the induced dipole moment of effective inclusion to the total dipole moment of individual inhomogeneities. In addition to the usual shape of inclusions, their volume content and phase conductivities, our model accounts also for the interface conductivity and orientation distribution of fibers. The obtained solution has been verified by comparison with the available in literature analytical solutions and numerical data for the particular cases. The reported numerical data validate the equivalent inhomogeneity shape choice. The interface conductivity and fiber orientation statistics are shown to be of primary importance for the effective conductivity of composite.