Auxetic-like metamaterials as novel earthquake protections

Bogdan Ungureanu,Sébastien Guenneau,Stefan Enoch,Younes Achaoui,Stéphane Brûlé,Argyropoulos Christos,Monti Alessio

doi:10.1051/epjam/2016001

Abstract

We propose that wave propagation through a class of mechanical metamaterials opens unprecedented avenues in seismic wave protection based on spectral properties of auxetic-like metamaterials. The elastic parameters of these metamaterials like the bulk and shear moduli, the mass density, and even the Poisson ratio, can exhibit negative values in elastic stop bands. We show here that the propagation of seismic waves with frequencies ranging from 1 Hz to 40 Hz can be influenced by a decameter scale version of auxetic-like metamaterials buried in the soil, with the combined effects of impedance mismatch, local resonances and Bragg stop bands. More precisely, we numerically examine and illustrate the markedly different behaviors between the propagation of seismic waves through a homogeneous isotropic elastic medium (concrete) and an auxetic-like metamaterial plate consisting of 43 cells (40 m × 40 m × 40 m), utilized here as a foundation of a building one would like to protect from seismic site effects. This novel class of seismic metamaterials opens band gaps at frequencies compatible with seismic waves when they are designed appropriately, what makes them interesting candidates for seismic isolation structures.

Highlights

One would like to design seismic metamaterials that have the ability to create band gaps for surface Rayleigh waves [5, 22, 23] and for all other elastic wave polarizations: within certain frequency ranges known as complete stop bands, an incoming mechanical wave would be completely reflected by the structure, whether the seismic wave signal propagates near the air-soil interface (Rayleigh or Love waves) or within the soil
We propose to use such auxetic-like composites in order to design elastic stop band metamaterials for seismic waves propagating in sedimentary soils at hertz frequencies [5]
The main conclusion of our study is that auxetic-like materials who have been widely studied for their special properties linked to a negative Poisson ratio m, have interesting stop band properties that can be used in the context of seismic wave protection

Summary

Introduction

One would like to design seismic metamaterials that have the ability to create band gaps for surface Rayleigh waves [5, 22, 23] and for all other elastic wave polarizations: within certain frequency ranges known as complete stop bands, an incoming mechanical wave would be completely reflected by the structure, whether the seismic wave signal propagates near the air-soil interface (Rayleigh or Love waves) or within the soil (coupled shear and pressure mechanical waves). A compression along the vertical axis z leads to a contraction of the shown bow-tie motif in Figure 1 along the horizontal x and y direction [4]. The Poisson ratio effectively changes if the modulus of the strain is not small compared to unity, i.e., if one leaves the linear mechanical regime and enters the nonlinear regime, in which the change in the angle a is no longer negligible [3]. This basic bow-tie motif can be assembled into two-dimensional model systems and into three-dimensional (anisotropic) mechanical metamaterials [4]. The quoted Poisson ratios m measured by this group

Stop band properties of auxetic-like metamaterials

Quantification of energy loss through auxetic-like metamaterials

Concluding remarks and perspectives on seismic metamaterials