RIGOROUS LINK BETWEEN THE CONDUCTIVITY AND ELASTIC-MODULI OF FIBER-REINFORCED COMPOSITE-MATERIALS

We derive rigorous cross-property relations linking the effective tran sverse electrical conductivity sigma and the effective transverse ela stic moduli of any transversely isotropic, two-phase 'fibre-reinforced ' composite whose phase boundaries are cylindrical surfaces with gener ators parallel to one axis. Specifically upper and lower bounds are de rived on the effective transverse bulk modulus kappa in terms of sigm a and on the effective transverse shear modulus mu* in terms of sigma . These bounds enclose certain regions in the sigma*-kappa* and sigma -mu* planes, portions of which are attainable by certain microgeometr ies and thus optimal. Our bounds connecting the effective conductivity sigma to the effective bulk modulus kappa* apply as well to anisotro pic composites with square symmetry. The implications and utility of t he bounds are explored for some general situations, as well as for spe cific microgeometries, including regular and random arrays of circular cylinders, hierarchical geometries corresponding to effective-medium theories, and checkerboard models. It is shown that knowledge of the e ffective conductivity can yield sharp estimates of the effective elast ic moduli (and vice versa), even for infinite phase contrast.