The image above shows a Sierpinski carpet (the 2D version of a Menger sponge). Here, this plane fractal depicts a multi-scale material (i.e. an example of multiple-dynamic material - also known as "meta-material"). Reload the page to change the colors.
One should interpret meta-materials not as "materials of materials" but rather as materials featuring multiple dynamics1.
When designing this material, one tries to benefit from :
One one hand, the efficiency of the visco-thermal dissipation depends on the ratio between the acoustic wavelength and the pore size (or on the ratio between the viscous and thermal boundary layers and the pore size). This dissipation is of interest in a given frequency range only.
One the other hand, the multiple scattering effect depends on the ratio between the acoustic wavelength and the size of the scatterers. The acoustic dissipation associated with this scattering effect is also of interest only in a given frequency range.
Combining the two dynamics, one ends up with a material offering a sound dissipation in a larger frequency range than the porous alone or the scatterers alone.
The list below gives some examples of phenomena which can be added to the visco-thermal dynamic of usual porous materials to improve their behaviors in the case of acoustic excitations. The related frequencies of interest for these additional effects are also reported.
Some other phenomena are listed in the slides of a talk given during ICA 2019 in Aachen (Germany). References of experimental and modeling works are also reported in these slides.
The list above does not include active structures with "diode" effect (requiring a flow) or
black holes3, i.e. retardant structures (which are functionally graded materials i.e. non-homogeneous materials).
These latter phenomena might fall in other material categories (such as active materials and non-homogeneous materials).
Finally, one has to keep in mind that Periodicity adds Bragg interferences but is not necessary to take advantage of other phenomena. Materials for which the main involved phenomenon is Bragg interferences are usually called phononic crystals.