LINK BETWEEN THE CONDUCTIVITY AND ELASTIC-MODULI OF COMPOSITE-MATERIALS

We derive relations linking the conductivity sigma and elastic moduli of any two-dimensional, isotropic composite material. Specifically, u pper and lower bounds are derived on the effective bulk modulus kappa in terms of sigma and on the effective shear modulus mu* in terms of sigma. In some cases the bounds are attainable by certain microgeome tries and thus optimal. Knowledge of the conductivity can yield sharp estimates of the elastic moduli (and vice versa) even for infinite pha se contrast.