Metamaterials (mechanical and acoustic) and the concept of unit cell architecture
Although there is no universally accepted definition of metamaterials in mechanics and acoustics, it is accepted that "geometry" plays a fundamental role in determining their static and dynamic properties. While in the early 2000s, the shapes considered were rather canonical (matrix with circular or square inclusions, etc.), over time, increasingly complex geometries have been explored thanks to the increased computing power of computers and the evolution of manufacturing technologies. In this context, Nature, thanks to millions of years of evolution, is a great master of "material architecture" to obtain specific advanced properties and geometries focused on precise functionalities. Taking inspiration from hierarchical or fractal architectures, typical of the majority of biological systems, we show that by reproducing this structural enrichment at the mesoscale of metamaterials we induce behaviors of great richness, opening up new perspectives for the control of elastic waves based on the simultaneous activation of various wave attenuation mechanisms.
Metamaterials (mechanical and acoustic) and the concept of unit cell architecture
Although there is as yet no universally accepted definition of "mechanical and/or acoustic metamaterials", the scientific community tends to identify them as "composites with a periodic or quasi-periodic architecture, designed to produce an atypical static or dynamic response to specific stresses".
The "geometry" aspect therefore plays a fundamental role in determining the properties of metamaterials. For example, in dynamics, at filling fraction parity(1), the shape of the inclusions (or voids) and their distribution in the unit cell (circle-shaped, tile-shaped, cross-shaped, etc., centered, arranged at the edges, etc.) can lead to the opening of forbidden bands (frequencies in which wave propagation is strongly attenuated) or to curves with a negative slope in the dispersion diagram, and achieve atypical behaviors such as negative refraction, topological protection, perfect absorption, and so on.
Similarly, when local resonance effects are the main players responsible for the overall behavior of the metamaterial, the shape (and arrangement) of the resonators becomes essential. In this sense, we could say that metamaterials embody the concept of architecture.
At the beginning of the 2000s, the shapes considered were rather canonical (circular, square, etc.), but increasingly complex geometries have since been explored. This has been made possible by (i) the increased computing power of computers, and (ii) developments in manufacturing technologies. Two important examples are 3D printing, which makes it possible to produce increasingly complex shapes at reasonable prices, and (photo-)lithography, which offers unprecedented resolution over several length scales.
(1) Ratio of the volumes making up the matrix and the inclusion in a unit cell.
This paved the way for a new vision of the concept of "architecture" associated with metamaterials, i.e. "introducing, between the scale of the microstructure of the constituent material and that of the macrostructure, one or more other scales of organisation of matter". The hierarchical or fractal structures found in most biological systems, where the same geometry can be repeated in a 'self-similar' or 'non-self-similar' way on several scales, are clear examples. These scales, described as mesoscopic, may be weakly separated (coupled) from the macroscopic scale and to induce a wide range of effective behaviours.
Bio-inspiration in metamaterials: Nature, the grand master of material architecture
Although mankind has only recently begun to exploit complex architectures (mainly because of technological limitations), Naturethanks to millions of years of evolution, is a great master of 'hardware architecture' to obtain specific advanced properties and geometries focused on precise functionalities. In fact, the common feature leading to these surprising properties often lies in hierarchical organisation of matter on several scales (an organisation observed in many natural materials such as wood, bone, sponges, etc.). As a result, increasing attention has been devoted in recent years to the synthesis of artificial materials inspired by nature, but mainly targeting quasi-static performance. In contrast, the consideration of hierarchical organisation in the design of the elementary cell of phononic crystals and metamaterials (mechanical and acoustic)(2) is only very recent.
(2) Material architecture is understood here as "the organisation of a unit cell repeated on several levels of scale".
In this context, we presented a new type of metamaterial made up of a polymer matrix with non-self-similar cross-shaped holes repeated at several scale levels. This has enabled us to achieve highly attenuating behaviour compared with elastic waves on several frequency scales, thanks to the fact that the 'non-self-similar hierarchy' leads to the opening up of multiple (and wide) forbidden bands, including in the sub-wavelength regime (i.e. when the wavelength of the wave to be attenuated is much greater than the size of the structure itself).
By means of numerical models and scanning laser vibrometer measurements, we have revealed that the "non-self-similar" hierarchy allows the opening of such forbidden bands thanks to the simultaneous activation of multiple mitigation mechanisms Bragg scattering, local resonance and/or inertial amplification. These mechanisms have been clearly identified by analysing the imaginary part of the wavenumber. This multi-mechanism design approach leads to enriched dynamics at different scales (opening of additional band gaps, conservation of existing band gaps shifted in frequency, as well as the possibility of preserving the global deformation mechanisms of the previous hierarchical levels, despite the variation in the mass/rigidity ratio of the overall system).
In conclusion, the enrichment of the architecture of metamaterials at the mesoscale induces very rich effective behaviours, offering new perspectives for the control of elastic waves, favouring the simultaneous activation of various wave attenuation mechanisms.
References :
[1] Mazzotti, [...], Miniaci. Bio-inspired non-self-similar hierarchical elastic metamaterials. International Journal of Mechanical Sciences 241:107915 (2023).
[2] Miniaci et al. Bio-inspired hierarchical dissipative metamaterials, Physical Review Applied, 10, 024012 (2018).
