Size effect in through-thickness conductivity of heterogeneous plates

• The exact Green operator is explicitly derived with the help of the fast Fourier transform (FFT) for heterogeneous plates.
• The second-order bounds and a third-order correlation approximation are obtained for the effective conductivity.
• The size effect of the effective through-thickness conductivity is shown to be more significant than the one in-plane.
• The results obtained in the present work are directly applicable to other physically analogous transport phenomena.

In this work, the size effect on the effective through-thickness conductivity of heterogeneous plates expressed in second-order Hashin–Shtrikman bounds and a third-order correlation approximation is studied. By taking into account the homogeneous temperature boundary conditions, the exact Green operator for the plate is first established. Then, the respective bounds and correlation approximation are constructed. With the help of the method based on the fast Fourier transform (FFT), the bounds and correlation approximation for the effective through-thickness conductivity are computed for the plates reinforced or weaken randomly either by spherical particles or unidirectional fibers. The numerical results show that the size effect of the effective through-thickness conductivity is more significant than the one of the effective in-plane conductivity.