BOUNDS ON THE COMPLEX BULK MODULUS OF A 2-PHASE VISCOELASTIC COMPOSITE WITH ARBITRARY VOLUME FRACTIONS OF THE COMPONENTS

The complex bulk modulus of an isotropic two phase composite material is analyzed in terms of the complex moduli of its phases. Bounds are d eveloped for the complex bulk modulus kappa = kappa*' + ikappa*'' of the composite with arbitrary volume fractions of phases. These bounds enclose a region in the complex plane (kappa', kappa*'') or in a stif fness loss map (\kappa\, kappa*''/kappa*' = tan delta). The frequency range is assumed to be well below frequencies associated with the ine rtial terms; the acoustic wavelength is much larger than the inhomogen eities. The bounds are obtained from the bulk modulus bounds by Gibian sky and Milton (1993, Proc. R. Soc. London A440, 163-188) for the two phase composites with fixed volume fractions of phases. The composite bulk modulus is shown to be constrained to a lens shaped region of the complex (kappa', kappa*'') plane by the outermost pair of several ci rcular arcs, which depend on the component material properties. The bo unds are investigated numerically to explore conditions which give ris e to high loss combined with high stiffness. Composite microstructures corresponding to various points on the circular arcs are identified.