Effective elastic moduli for 3D solid-solid phononic crystals of arbitraryanisotropy and oblique lattice structure are formulated analytically using theplane-wave expansion (PWE) method and the recently proposed monodromy-matrix(MM) method. The latter approach employs Fourier series in two dimensions withdirect numerical integration along the third direction. As a result, the MMmethod converges much quicker to the exact moduli in comparison with the PWE asthe number of Fourier coefficients increases. The MM method yields a moreexplicit formula than previous results, enabling a closed-form upper bound onthe effective Christoffel tensor. The MM approach significantly improves theefficiency and accuracy of evaluating effective wave speeds for high-contrastcomposites and for configurations of closely spaced inclusions, as demonstratedby three-dimensional examples.
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