Effective conductivity of spheroidal particle composite with imperfect interfaces: Complete solutions for periodic and random micro structures

• The composites with periodic and random arrangement of spheroidal particles are considered.
• Effective conductivity of spheroidal particle composite with imperfect interfaces is studied.
• The complete solution of the conductivity problem has been obtained by the multipole expansion method.
• Combined effect of microstructure and interfaces on the effective conductivity of composite is evaluated.

The rigorous analytical approach to the conductivity homogenization problem for spheroidal particle composite with imperfect interfaces has been developed. The complete multipole series solution for a single inclusion with imperfect interface constitutes mathematical background of the work and provides a basic building block for the Maxwell and Rayleigh homogenization schemes. The low- and highly conducting spheroidal interface are considered in a unified way. The developed theory enables an analysis of composites of periodic and random micro structure with imperfect interfaces. Numerical study shows quite a significant combined effect of micro structure and imperfect interfaces on the macroscopic conductivity of composite. The obtained accurate solution serves as a benchmark for the known approximate theories. Their error due to neglecting the interaction effects and simplified treating the imperfect interfaces is estimated.