Generalized locally-exact homogenization theory for evaluation of electric conductivity and resistance of multiphase materials

Abstract The locally-exact homogenization theory is further extended to investigate the homogenized and localized electric behavior of unidirectional composite and porous materials. Distinct from the classical and numerical micromechanics models, the present technique is advantageous by developing exact analytical solutions of repeating unit cells (RUC) with hexagonal and rhomboid geometries that satisfy the internal governing equations and fiber/matrix interfacial continuities in a point-wise manner. A balanced variational principle is proposed to impose the periodic boundary conditions on mirror faces of an RUC, ensuring rapid convergence of homogenized and localized responses. The present simulations are validated against the generalized Eshelby solution with electric capability and the finite-volume direct averaging micromechanics, where excellent agreements are obtained. Several micromechanical parameters are then tested of their effects on the responses of composites, such as the fiber/matrix ratio and RUC geometry. The efficiency of the theory is also proved and only a few seconds are required to generate a full set of properties and concomitant local electric fields in an uncompiled MATLAB environment. Finally, the related programs may be encapsulated with an input/output (I/O) interface such that even non-professionals can execute the programs without learning the mathematical details.