Artificially engineered materials, designed to interact with propagating waves, have been proposed to protect isolated buildings, infrastructure systems for nuclear industry or urbanized areas from incoming seismic waves and represent a breakthrough for the safety and for the preservation of historic and strategic infrastructures (e.g., hospitals, power plants, etc.). These materials, originally introduced as seismic metamaterials [1], are inspired by physical concepts well established in the domains of phononic crystals and resonant metamaterials. Phononic crystals and resonant metamaterials allow manipulating the propagation of waves at different scales, ranging from thermal [2] to infrasound vibrations [3].

In particular, phononic crystals are periodic materials that can exhibit large band gaps [4], i.e. frequency regions, where the propagation of waves with wavelengths in the order of material periodicity is hindered. For instance, large scale experiments showed that phononic crystals made of cylindrical holes in sedimentary soil can reflect seismic elastic energy, achieving attenuation of ground accelerations at a frequency range around 50 Hz. More recently, it has been shown that a similar concept can be used to realize seismic lenses with large (≈ 100 m) gradient index able to reroute surface waves around buildings [5]. Although revolutionary in their conception, implementation of these systems at the low frequencies characteristic of seismic events (<30 Hz) requires very large structures, as the seismic wavelengths can be of several meters or decameters.

Conversely, a resonant metamaterial consists of a medium with embedded locally resonant units able to interact with propagating waves at a sub-wavelength scale [4]. Therefore, for seismic waves characterized by long wavelengths, resonant metamaterials allow for construction of more viable devices, i.e. of smaller and feasible spatial dimensions. On the basis of this paradigm, sub-wavelength structures, in the form of resonant metafoundations [7] or resonant metabarriers [8] have been proposed in recent years to isolate nuclear power plants from incoming seismic longitudinal and shear waves and to shield buildings from surface Rayleigh waves, respectively.

The idea of a resonant metabarrier, in particular, is motivated by the fact that far from the epicenter Rayleigh waves carry most of the earthquake energy [9] and that existing structures may be hard to be retrofitted with innovative foundation systems. The resonant metabarrier founds its operating principle on the interaction between purposely designed resonant units with surface waves in the low frequency regime (<10 Hz). The resonant units, to be buried below the soil surface, are passive devices (mass-stiffness systems) activated by the vertical component of the Rayleigh wave motion. Once activated, the normal stresses exerted on the soil by the resonant units redirect part of the elastic Rayleigh wave energy into the interior of the soil deposit as vertically polarized shear waves.

The physics of these resonant systems has been predicted analytically and verified numerically at different wave scales, or in other words at different frequencies, whereas its occurence has been proven experimentally only in very few works.

For instance, the surface-to-shear conversion has been observed in the MHz range, for microspheres [10] and micropillars [11] and at the kHz range with a test on an array of small scale steel resonators embedded in a resin block [8]. However, even if measurements at the geophisical scale have shown a reduction of the surface motion due to the resonance of forest trees [12], the experimental proof of the metabarrier concept in the Hz range is still absent.

One of the main reason is probably related to the cost of the test needed to prove a 1:1 scale metabarrier for Raylegh waves as well as for the significant resonating mass needed to activate the wave conversion. As such recent reserach discoveries can be applied to reduce the dimension and weight of the metabarrier, like rainbow trapping [13], multi-mass resonators [14], negative stiffness [15] and hyper damping phenomena [16].

As the idea of the metabarrier has been recently extended also to Love waves [17], a proficient result of this proposal could potentially open also to metabarriers for horizonally polarized surface waves.

[1] Brûlé, S., Javelaud, E. H., Enoch, S. & Guenneau, S. Experiments on Seismic Metamaterials: Molding Surface Waves. Phys. Rev. Lett. 112, 133901 (2014).

[2] Maldovan, M. Phonon wave interference and thermal bandgap materials. Nat. Mater. 14, 667–674 (2015).

[3] Shi, Z., Cheng, Z. & Xiong, C. A New Seismic Isolation Method by Using a Periodic Foundation. Earth Sp. 2586–2594 (2010).

[4] Deymier, P. Acoustic metamaterials and phononic crystals (2013).

[5] Colombi, A., Guenneau, S., Roux, P. & Richard, C. Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves. Nat. Publ. Gr. 9, 1–19 (2015).

[6] Kadic, M., Bückmann, T., Schittny, R. & Wegener, M. Metamaterials beyond electromagnetism. Rep. Prog. Phys. 76, 126501 (2013).

[7] Cheng Z. and Shi, Z. Novel composite periodic structures with attenuation zones. Eng. Struct. 56, 1271–1282 (2013).

[8] A. Palermo, S. Krodel, A. Marzani, C. Daraio, Engineered metabarrier as shield from seismic surface waves, Scientific Reports 6 (2016), Article number: 39356.

[9] Graff, K. F. Wave motion in elastic solids. Wave motion in elastic solids (1991).

[10] N. Boechler, J. Eliason, A. Kumar, A. Maznev, K. Nelson, N. Fang, Interaction of a contact resonance of microspheres with surface acoustic waves, Physical review letters 111 (3) (2013) 036103.

[11] S. Benchabane, A. Khelif, J.-Y. Rauch, L. Robert, V. Laude, Evidence for complete surface wave band gap in a piezoelectric phononic crystal, Physical Review E 73 (6) (2006) 065601.

[12] A. Colombi, P. Roux, S. Guenneau, P. Gueguen, R. V. Craster, Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances, Scientic reports 6 (19238) (2016).

[13] Krödel, S., Thomé, N., Daraio, C. “Wide band-gap seismic metastructures”. Extrem. Mech. Lett. 4, 111–117 (2015).

[14] Palermo, A., Vitali, M., Marzani, A. “Metabarriers with multi-mass locally resonating units for broad band Rayleigh waves attenuation”, Soil Dynamics and Earthquake Engineering, 113, 265-277 (2018).

[15] Antoniadis, I.A., Kanarachos, S.A., Gryllias, K. Sapountzakis.I. ”KDamping: A Stiffness Based Vibration Absorption Concept”, Journal of Vibration and Control, DOI: 10.1177/1077546316646514. 2016.

[16] I. Antoniadis, D. Chronopoulos, V. Spitas, D. Koulocheris, Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element, Journal of Sound and Vibration 346 (2015) 37–52.

[17] Palermo, A., Marzani, A. “Control of Love waves by resonant metasurfaces”, Scientific Reports, 7234 (2018)