Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation

We investigate the effective conductivity (${\sigma }_e$) of a class of amorphous media defined by the level-cut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate ${\sigma }_e$ for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in ${\sigma }_e$ are observed between the Gaussian media and the identical overlapping sphere model used previously as a `model’ amorphous medium. In contrast ${\sigma }_e$ shows little variability between different Gaussian media.