A Homogenization of Irrational Metamaterials

Abstract

Following the advent of electromagnetic metamaterials, researchers working in wave physics have translated concepts of engineered media to elastodynamics using analogies between Maxwell and Navier equations. Seismic metamaterials have emerged for soft soils structured at the meter scale, and have been tested ten years ago with full-scale experiments on holey soils to achieve shielding [1] and lensing [2] effects. Born in the soil, seismic metamaterials have emerged from the field of tuned-resonators buried in the soil, around building's foundations or near the soil-structure interface as local seismic isolators. Their designs are inspired e.g. by small scale mechanical metamaterials with a negative Poisson ratio, known as auxetic metamaterials [3]. Forests of trees have been interpreted as above-surface resonators, and coined natural seismic metamaterials [4]. Forest of trees not only have an effect on Rayleigh waves [4], but also on Love waves, that can be viewed as a counterpart of spoof plasmons in electromagnetics [5]. On the other hand, it is possible to control surface and volume seismic waves by structuring soft soils with columns of concrete clamped to the bedrock [6]. In this talk we will envision future developments of large scale auxetic metamaterials for building's foundations [3], above and below surface resonators for seismic protection [4, 5, 6] as well as metamaterial-like transformed urbanism at the city scale [7].