Some challenges regarding cloaking and earthquake protection

Building upon analogies with cloaking of elastic waves in plates, a large scale experiment has demonstrated unprecedented control of surface seismic waves in structured soils. Here, we would like to review recent research advances and remaining challenges in the theory and applications of seismic metamaterials for cloaking and earthquake protection. We recall some results on transformation elastodynamics and introduce mathematical theory of near cloaking for elastic equations. The former is a natural framework for scattering problems in unbounded domains, while the latter addresses boundary measurements in bounded domains. These two fields of investigation bring complementary information on cloaking efficiency. Intimate links between cloaking and wave protection will be also discussed.