Self-consistent averaging, using an auxiliary solution for an elliptical anisotropic viscous inclusion in an anisotropic viscous host, provides estimates of the principal bulk viscosities of a dispersion of aligned elliptical viscous clasts in an isotropic or anisotropic viscous matrix. Analysis and results are for a two-dimensional analog of a composite rock with clasts that are cylinders with axes normal to the plane of flow. The ratio of principal viscosities, ηn in clast parallel extension or shortening, ηs in clast-parallel shear, m = ηn/ηs, is smaller than that obtained using an auxiliary solution in which the host is isotropic. Results for the limiting case of rigid clasts indicates that the latter procedure overestimates the stress concentration in axis-parallel extension or shortening at intermediate clast volume fraction, f. If the matrix is anisotropic, bulk anisotropy derives from both the shape anisotropy and the intrinsic anisotropy of the matrix, and unsymmetrical relations for the principal viscosities and m (f) result. The results suggest that rheological anisotropy in rocks with a planar fabric is greatly reduced if the components are lenticular in form rather than continuous layers. A general solution is given for an elliptical inclusion for the case that the principal axes of anisotropy in both the host and the inclusion are oblique to the axes of the elliptical section and the host is subjected to homogeneous stress far from the inclusion.
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