MICROSTRUCTURE AND CONDUCTIVITY OF HIERARCHICAL LAMINATE COMPOSITES

Certain hierarchical laminates with a wide separation of length scales are known theoretically to have optimal transport and mechanical prop erties. We derive analytical expressions for the n-point probability f unctions that statistically characterize the microstructure for more g eneral hierarchical laminates with an arbitrary number of stages and a finite separation of length scales. Using two-point probability infor mation, we rigorously bound the effective conductivity (or dielectric constant) tensor for macroscopically anisotropic laminates and study h ow the separation of length scales affects the effective properties.