Homogenization of layered media based on scattering response and field integration

The stress wave scattering off of any finite slab may be used as a physical approach to determining some or all of the overall dynamic constitutive parameters of such a specimen. In this paper, this approach is applied to normal incidence of symmetric and asymmetric layered structures with elastic or viscoelastic layers. The method determines all of the overall constitutive constants of a Willis-type material (including zero and non-zero coupling parameters) for all frequencies, even in stop bands of elastic structures, exactly. The ambiguity in phase velocity calculation is overcome using continuity considerations. Symmetries in coupling constants and the restrictions due to energy conservation and dissipation are presented. Integrating the wave equations directly leads to a proposed micro-structural scheme for determination of the overall constitutive parameters. The results of this method are identical to those derived based on the scattering response for all frequencies, including stop bands, and beyond the long wavelength limit of traditional homogenization techniques. The proposed approach has the potential to be applied to 3D-structured unit cells, oblique incidences, and simultaneous scattering of multiple waves.