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Broadband cloaking and shielding of elastic waves in solids.

Periodic Reporting for period 1 - METACLOAK (Broadband cloaking and shielding of elastic waves in solids.)

Reporting period: 2015-11-01 to 2017-10-31

This project dealt with the control of elastic waves in solid media using the metamaterial design concepts. Metamaterials are a particular type of structured media, usually artificial, whose properties are controlled less by the microscopic structure and more by the macroscopic arrangement of resonating elements characterizing the material. Those resonators are typically sub-wavelength, i.e. of size smaller than the propagating wavelength and they are arranged over a distance that allows coupling between each other. The effective properties emerge due to specific interactions with wave fields.

When this project started two years ago, it had the main goal of extending the cloaking concept (invisibility) in the field of seismic waves to conceal structures from destructive seismic waves. This was meant to be done with metamaterials, whose extraordinary wave control capacities only could deliver the correct property to build a cloak.
Practically I went much further extending metamaterial wave control capacities to both large scale (seismic metamaterials) and small scale (mechanical vibrations metamaterials).
From 2015, as a Marie Curie Fellow in Prof Craster’s group at Imperial College London I have developed the metamaterial concept to make practical devices to control mechanical waves across a wide range of scales from very low frequencies to very high frequencies; from: seismic waves (earthquakes) and ground vibrations (windfarms, trains, traffic and construction) all the way to nanostructures used in electronics, photonics and phononics.
My research has combined theoretical and numerical modelling and state of the art supercomputing with experiments in the laboratory and in the field (for seismic waves this has been literally in a field!). In these three years, I have validated prototypes that can be further developed and applied in research, industry and the environment. This can be applied in a wide range of areas, for instance: a meta forest (a plantation of trees) that can reduce ground borne vibrations, acoustic black holes (for absorbing unwanted sound, vibrations and resonances) and resonant nano-antenna which can be used as high sensitive nano detectors.
Since the beginning of the fellowship, the research work has advanced on three fronts simultaneously: The theoretical study of metamaterials properties, large scale simulations of metamaterials and experimental realisations.

Theoretical study of metamaterials properties
Inspired by early work on metamaterials during my previous postdoc, in 2015 at Imperial College London, I studied the effect of introducing local resonators to wave problems for elastic surfaces (elastic plates first and later to thick elastic substrate such as the earth surface). The metamaterial prototype was obtained by fixing several closely spaced slender beams (resonators) perpendicular to an elastic substrate (Figure 1a and b). From 2016 the research focused mainly on surface Rayleigh waves as this case was the most favorable for the development of seismic metamaterials and it was not yet been considered in literature because very challenging. The metamaterial’s dispersion curves showed unique characteristics such as subwavelength bandgaps and ultra fast/slow modes perfectly suited for wave control. This part of the work was carried out using a theoretical approach based on eigenvalue problems and homogenization theory. This theoretical study of the metamaterial physics has made possible to understand and reveal new phenomena such as the conversion of Rayleigh into shear waves or the lensing phenomena for elastic and seismic waves (Figure 1d).

Large scale simulations and metamaterials optimization
I have tested several new metamaterial designs in real applications featuring full-scale complexities. I have used SPECFEM3D, a state-of-the-art, open source, spectral element based code for elastodynamics problems. The High Performance Computing (HPC) CIMENT in Grenoble (France) and ARCHER in UK have been heavily used to compute the simulations. Starting from the basic resonant metamaterial studied in the theoretical part, the designs have been refined by exploring the parameter space through thousands of simulations. The aim was both improving the performances of the metamaterial (e.g. increase the effective bandwidth) and tailoring it to the specific seismic or laboratory scale (various examples in Figure 1).

Together with the theoretical and the numerical part, two experiments have been carried out during the 24 months. In both cases the results have been published (or are being published) in journal articles. For the seismic metamaterial I have co-organized the large-scale experiment on a forest using hundreds of seismometers and an active source of vibrations to validate the concept of resonant seismic metamaterials (Figure 2). The experiment required careful planning and a field trip that lasted two weeks in a forest located near Bordeaux (France). The second experiment was at a much smaller scale, in the ultrasound regime and was carried in the optic laboratory of the University of Nottingham. The aim of this second experiment was to validate the metamaterial design to convert surface wave into shear waves and explore possible use in mechanical engineering to reduce vibrations (Figure 1d).

Finally, the results produced in these 24 months have been also used to obtain funding and implement a large scale experiment on seismic metamaterials ( and more recently, to prepare a research proposal to fund my research group. I have obtained the funding and I will start my group from April 2018 in ETH Zurich.
This project has reset the state of the art in the development of seismic metamaterials. The study of the interaction between vertical resonators and a soft soil surface have demonstrated for the first time that seismic metamaterials can successfully attenuate vibrations from Surface waves. Thanks to the theoretical study and the numerical simulations, I have been able to design a large scale experiment to demonstrate that a forest can mimic the behaviour of resonant metamaterial and attenuate surface waves around 40-50 Hz (Figure 1b and Figure 2). This is the first experiment of this type showing the feasibility of seismic metamaterials (the experiment was co-fund through a grant of the French Research Council with french colleagues). With this result in hand, I can now move toward the design of ad-hoc resonant systems to be used in civil and geotechnical engineering against ground borne vibrations and maybe earthquakes (this is stil an open question).
The other great achievement of the past 24 months was the development of a novel metamaterial design (an elastic surface with rod like resonators of decreasing size) that converts surface waves into bulk shear waves. This adds another functionalities to metamaterials that could be used to reduce vibrations in mechanical components. This metamaterial is currently being tested for practical applications in mechanical engineering (Figure 1d).
Finally, I have initiated a collaborations with expert in nano fabrication and sensing to export the design of this metamaterial to nano-devices.
Figure 2, experiment on seismic metamaterials in a forest
Figure 1 showing various metamaterial designs studied in the 24 months