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Scattering experiments can be leveraged to extract the effective propertiesof a heterogeneous metamaterial slab based on multi-point measurements insurrounding media. In this technique, two measurements are made in the ambientmedia on each side of a finite thickness micro-structured slab to decomposeincoming and outgoing waves. The method is applied to an example with locallyresonant micro-structured inclusions while paying close attention to parametersthat influence the extracted material parameters. It is observed that theextracted overall parameters converge to limiting values when the number ofunit cells across the slab thickness or ambient media modulus are increased.Dependence of extracted material parameters on the number of cells throughthickness or ambient media properties are attributed to the different responseof boundary (skin) and interior cells. A method is presented which represents afinite array with different effective properties for the skin regions vs. theinterior regions with great success in reproducing the scattering for differentslab thicknesses, and through which the interior regions properties becomeindependent of ambient media properties. In stop bands with lower materialloss, challenges arise that are associated with extremely small transmission.The assumption of continuity in transmission phase is enforceable to removephase ambiguity, although in certain cases (associated with nearly losslessspecimens) this assumption appears to fail. In such cases, interference fromcoupled shear modes may lead to apparent higher longitudinal transmissionwithin the stop band. This work provides a proof of concept for the developmentof an experimental methodology capable of extracting the effective propertiesand dispersion behavior of heterogeneous mechanical metamaterials without anyknowledge of the internal fields.

Multi-point Scattering Measurements for Effective Property Extraction from Metamaterials with Skin Effects