Lawrence Berkeley National Laboratory

The effective thermal expansion coefficient beta* of a binary viscoelastic composite is shown to be frequency dependent even if the thermal expansion coefficients beta A and beta B of both constituents are themselves frequency independent. Exact calculations for binary viscoelastic systems show that beta* is related to constituent values beta A, beta B, volume fractions, and bulk moduli KA, KB, as well as to the overall bulk modulus K* of the composite system. Then, beta* is determined for isotropic systems by first bounding (or measuring) K* and therefore beta*. For anisotropic systems with hexagonal symmetry, the principal values of the thermal expansion beta*perp and beta*para can be determined exactly when the constituents form a layered system. In all the examples studied, it is shown explicitly that the eigenvectors of the thermoviscoelastic system possess non-negative dissipation -- despite the complicated analytical behavior of the frequency dependent thermal expansivities themselves. Methods presented have a variety of applications from fluid-fluid mixtures to fluid-solid suspensions, and from fluid-saturated porous media to viscoelastic solid-solid composites.