Does fabric tensor exist for a fabric?

It is shown that the mean intercept length distribution for planar fibre networks or for materials composed of a set of plates is not in general elliptic and cannot be expressed analytically in terms of a second-order tensor. However, our numerical computations indicate that the polar plot of the mean intercept length at the angle of measurement may become nearly ellipsoidal as the microstructure (fibres or plates) become less discretely organized, but yet remain orthotropic. The equations presented in this study may be used to obtain fibre (plate) orientation density functions from the experimental data on mean intercept length distribution.