Transport and elastic properties of fractal media

We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modelling of both surface-fractal and mass-fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough interface has a relatively strong influence on the properties of composites. In contrast a fractal volume (mass) has little effect on material properties.