Determination of the effective conductivity of composites with spherical and spheroidal anisotropic particles and imperfect interfaces

• A micromechanical scheme to estimate the effective conductivity of composites is developed.
• The imperfect interface can be either highly conducting or resistive.
• The inhomogeneity can be spherical or spheroidal.
• The inhomogeneity phases can be anisotropic.
• Size- and shape-dependent effective conductivities of composites are studied.

The present work aims to develop a micromechanical scheme to estimate the effective conductivity of isotropic particulate multiphase composites with imperfect interfaces between the matrix and inhomogeneity phases. The interface can be either highly conducting or resistive, the inhomogeneities can be spherical or spheroidal, and the matrix phase is isotropic but the inhomogeneity phases can be anisotropic. By applying the generalized Mori–Tanaka (GMT) model based on the morphologically representative pattern (MRP) approach and by using the solution results obtained for auxiliary problems accounting for imperfect interfaces, the closed-form expression for the effective conductivity is obtained. Numerical results are provided to illustrate the dependence of the effective conductivity on the size and shape of inhomogeneities and to compare the estimations with the relevant upper and lower bounds.