Frequency dependent thermal expansion in binary viscoelastic composites

The effective thermal expansion coefficient β∗ of a binary viscoelastic composite is shown to be frequency dependent even if the thermal expansion coefficients βA and βB of both constituents are themselves frequency independent. Exact calculations for binary viscoelastic systems show that β∗ is related to constituent values βA,βB, volume fractions, and bulk moduli KA,KB, as well as to the overall bulk modulus K∗ of the composite system. Then, β∗ is determined for isotropic systems by first bounding (or measuring) K∗. For anisotropic systems with hexagonal symmetry, the principal values of the thermal expansion β⊥∗ and β∥∗ 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.