[TTPrograms]

I think in mechanical metamaterials the characteristic length defining the "metamaterial region" is rather the wavelength of pressure waves in the material you're considering - much like in electromagnetics you want the patterning (cell) length to be much less than the wavelength of radiation. In work like this they are effectively looking at 0.1 Hz or lower - near static loading - so I think pattern size can be quite large (around 600 m wavelength in bulk rubber for 0.1 Hz). This interpretation also replicates the localized behavior in the shock experiment videos. When the platform is dropped an impulse is applied with frequencies above the metamaterial regime for the material, so you see highly asymmetric response through the material - implying that the macroscopic "metamaterial" property characterization is insufficient to predict response, and so analysis must be done at feature scales rather than wavelength scales. The idea being that a "metamaterial" is a structure that can be treated as a bulk continuous material with a particular defined response as long as the interacting frequencies are all sufficiently low (far below the characteristic wavelength of the material).

I think the bending analysis you cite can determine the relative feature sizes desirable for certain "micro-scale" mechanical behavior, but it's possible to build a mechanical "metamaterial" much larger than that as well.