WP4 | Theoretical approach

Heterogeneous anisotropic effective index of refraction for seismic surface waves inside a dense collection of vertical resonators (forest of trees or buried concrete columns).

Leader: Institut Fresnel, Marseille

It was theoretically shown by Farhat et al. (2009), and with subsequent experimental demonstration by Stenger et al. (2012), that a geometric transform in the Kirchhoff-Love plate equation leads to anisotropic Young’s modulus and isotropic density that both vary spatially.

1/ Designs of cloaks with artificially anisotropic soils using buried columns and/or forest of trees

Such metamaterial parameters make possible an invisibility cloak for flexural waves (in a plate), but one could envisage similar designs for surface seismic waves. One constraint is that strong anisotropy of the Young’s modulus is required on the inner circular boundary of the elastic cloak, as well as a vanishing density, to force the propagation of flexural waves around a cloaked region [i.e., a disk surrounded by a metamaterial ring ; see Fig. 1(g)]. However, the cloak parameters in (...)

2/ Designs of cloaks with gradient index soils using buried columns and/or forest of trees

Conformal platonics is an emerging topic of transformation elastodynamics using conformal mappings in order to ease the design of structured soils for civil engineering applications : one should first simplify the design of structured plates so as to prevent anisotropy in the metamaterial’s parameters. One way to do so is to extend the concept of conformal optics to platonics : the former was proposed in (Leonhardt, 2006) and is valid in the geometrical optics limit (when the wavelength is (...)