Lucas Pomot, PhD

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Seismic Metamaterial: geometrical transformation, homogenization and experiment

Lucas Pomot will defend his PhD Thesis entitled ""Seismic Metamaterial: geometrical transformation, homogenization and experiment"" on October 30, 2019 at 02:00 pm in Amphitheater François Canac (LMA).

PhD panel :
- PhD advisor : M. Cédric PAYAN, Aix Marseille University / LMA
- Referee : M. Philippe ROUX, Isterre
- Referee : Mme Agnès MAUREL Institut Langevin
- External Examiner : M. Abdelkrim KHELIF FEMTO-ST
- PhD Co-advisor : M. Sébastien GUENNEAU Institut Fresnel
- Invited Member : M. Stéphane Bourgeois, AMU/LMA,
- Invited Member : M. Marcel Rémillieux, Los Alamos National Laboratory

Abstract : The results obtained during these studies can be split into three different axes. First, a general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows to perform cloaking. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. These cloaks have parameters compatible with existing technology and they mimic the behavior of the transformed material. Numerical simulations have been performed to qualitatively and quantitatively study the cloaking efficiency of these metamaterials. In a second part we apply the previous result on elastic waves. Controlling elastic waves in plates is a major challenge previously addressed without energy considerations. We propose an energy approach for the design of plate cloaks, which prevents any unphysical features. Within this framework, it is shown that the Kirchhoff-Love equation for anisotropic heterogeneous plates is form invariant for a class of transformations with a vanishing Hessian. This formalism is detailed and numerically validated with three-dimensional simulations in the time domain. Our approach opens new avenues in the control of mechanical vibrations with applications ranging from sensing in ultrasonics to earthquake protection in civil engineering. In the last part we perfom a experimental campaign at the Loas Alamos National Laboratory. We studied the propagation of seismic waves through an array of resonators using a 3D laser vibrometer. This type of instrument allowed us to study in great detail the interactions between the seismic wave and the resonators.

Keywords: métamatériaux, transformation géométrique, homogénéisation, approche expérimentale