  Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary
anisotropy and oblique lattice structure are formulated analytically using the
plane-wave expansion (PWE) method and the recently proposed monodromy-matrix
(MM) method. The latter approach employs Fourier series in two dimensions with
direct numerical integration along the third direction. As a result, the MM
method converges much quicker to the exact moduli in comparison with the PWE as
the number of Fourier coefficients increases. The MM method yields a more
explicit formula than previous results, enabling a closed-form upper bound on
the effective Christoffel tensor. The MM approach significantly improves the
efficiency and accuracy of evaluating effective wave speeds for high-contrast
composites and for configurations of closely spaced inclusions, as demonstrated
by three-dimensional examples.
