Spanning the scales of mechanical metamaterials using time domain simulations in transformed crystals, graphene flakes and structured soils

Abstract

We begin with a brief historical survey of discoveries of quasi-crystals and graphene, and then introduce the concept of transformation crystallography, which consists of the application of geometric transforms to periodic structures. We consider motifs with three-fold, four-fold and six-fold symmetries according to the crystallographic restriction theorem. Furthermore, we define motifs with five-fold symmetry such as quasi-crystals generated by a cut-and-projection method from periodic structures in higher-dimensional space. We analyze elastic wave propagation in the transformed crystals and (Penrose-type) quasi-crystals with the finite difference time domain freeware SimSonic. We consider geometric transforms underpinning the design of seismic cloaks with square, circular, elliptical and peanut shapes in the context of honeycomb crystals that can be viewed as scaled-up versions of graphene. Interestingly, the use of morphing techniques leads to the design of cloaks with interpolated geometries reminiscent of Victor Vasarely's artwork. Employing the case of transformed graphene-like (honeycomb) structures allows one to draw useful analogies between large-scale seismic metamaterials such as soils structured with columns of concrete or grout with soil and nanoscale biochemical metamaterials. We further identify similarities in designs of cloaks for elastodynamic and hydrodynamic waves and cloaks for diffusion (heat or mass) processes, as these are underpinned by geometric transforms. Experimental data extracted from field test analysis of soil structured with boreholes demonstrates the application of crystallography to large scale phononic crystals, coined as seismic metamaterials, as they might exhibit low frequency stop bands. This brings us to the outlook of mechanical metamaterials, with control of phonon emission in graphene through extreme anisotropy, attenuation of vibrations of suspension bridges via low frequency stop bands and the concept of transformed meta-cities. We conclude that these novel materials hold strong applications spanning different disciplines or across different scales from biophysics to geophysics.

Emergence of seismic metamaterials: Current state and future perspectives

“…The first type includes structured soils made of cylindrical voids ( [4], [5] and [40]) or rigid inclusions ( [41] and [42]), including seismic metamaterials. We can call this historical first group, "Seismic Soil-Metamaterials" or SSM (FIG.…”

“…The physical process is the interference of waves (body or surface waves) scattered from surfaces or objects. The effects of the dynamic anisotropy are reinforced by the local resonance of implemented, which are disposed along a grid according to transformation elastodynamics ( [40] and [43]) and morphing tools [42] that could theoretically lead to an ideal cloak detouring waves around a protected area (FIG. 9).…”

A Review of Research on Seismic Metamaterials

“…[44] Considering the geometric transformation of seismic cloaks with different shapes in the context of different crystals, Aznavourian et al, in 2017, analyzed the elastic wave propagation in the transformed crystals and quasicrystals. [45] The experimental data extracted from the field test analysis of soil structured with boreholes show that the bioinspired SMs have great application value.…”

“…It can reroute and reconstruct plane seismic surface waves around a region that must remain protected, as shown in Figure 14. [45] In addition to the aforementioned classical regulation mechanism, in 2017, Achaoui et al achieved elastic surface wave reflectors at very large wavelengths in structured soils modeled as a fully elastic layer, periodically clamped to bedrock. It was highlighted that the existence of zero-frequency stop-band media mechanism can be used to obtain shielding effects.…”

Role of nanophotonics in the birth of seismic megastructures

“…The first type includes structured soils made of cylindrical voids ( [2] and [3]) or rigid inclusions ( [5] and [6]), including seismic metamaterials. This group is called "Seismic Soil-Metamaterials" or SSM in short.…”