Modelling the Properties of Composites by Laminates

Laminate materials of the type introduced by Schulgasser [1] and Bruggeman [66,67] are studied and the extent to which they can simulate the transport properties of other composites is explored. Laminates with chirality, with especially high or low field concentrations, or which attain various bounds are constructed. The Hashin-Shtrikman bounds on the shear modulus are demonstrated to be optimal, being attained by a hierarchical laminate material. While the conductivity function of two-component composites can be simulated by laminates, an example suggests this does not extend to five-component composites. Attention is drawn to the connection between conductivity functions, Stieltjes functions, and bounds.