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.

The Sayers and Kachanov (1991) crack-influence parameters are shown to be directly related to Thomsen (1986) weak-anisotropy seismic parameters for fractured reservoirs when the crack density is small enough. These results are then applied to seismic wave propagation in reservoirs having HTI symmetry due to aligned vertical fractures. The approach suggests a method of inverting for fracture density from wave speed data.

A model study on fractured systems was performed using a concept that treats isotropic cracked systems as ensembles of cracked grains by analogy to isotropic polycrystalline elastic media. The approach has two advantages: (a) Averaging performed is ensemble averaging, thus avoiding the criticism legitimately leveled at most effective medium theories of quasistatic elastic behavior for cracked media based on volume concentrations of inclusions. Since crack effects are largely independent of the volume they occupy in the composite, such a non-volume-based method offers an appealingly simple modeling alternative. (b) The second advantage is that both polycrystals and fractured media are stiffer than might otherwise be expected, due to natural bridging effects of the strong components. These same effects have also often been interpreted as crack-crack screening in high-crack-density fractured media, but there is no inherent conflict between these two interpretations of this phenomenon. Results of the study are somewhat mixed. The spread in elastic constants observed in a set of numerical experiments is found to be very comparable to the spread in values contained between the Reuss and Voigt bounds for the polycrystal model. However, computed Hashin-Shtrikman bounds are much too tight to be in agreement with the numerical data, showing that polycrystals of cracked grains tend to violate some implicit assumptions of the Hashin-Shtrikman bounding approach. However, the self-consistent estimates obtained for the random polycrystal model are nevertheless very good estimators of the observed average behavior.