Effective conductivity of materials with continuous curved fibers

Overall conductivity of composites reinforced with in-phase continuous sinusoidal fibers of circular cross-sections is investigated. The effects of the fiber/matrix conductivity contrast, crimp ratio and relative fiber radius are studied. Two approaches are employed for the analysis: direct finite element analysis based on curvilinear periodic unit cells, and micromechanical homogenization based on the conductivity contribution tensor combined with the non-interaction and Mori-Tanaka schemes. In addition, an approach to approximation of the conductivity contribution tensor of a single fiber using an equivalent set of ellipsoids is presented. Comparison of the direct numerical analysis results with micromechanical homogenization shows that the latter approach can be used to estimate all components of the effective conductivity tensor of the considered composite material system with good accuracy. However, the results also indicate that the choice of the micromechanical homogenization scheme for this type of reinforcement depends on the conductivity component being approximated and the fiber/matrix conductivity contrast.