Highly Anisotropic Elements for Acoustic Pentamode Applications

Abstract

Pentamode metamaterials are a class of acoustic metafluids that are characterized by a divergence free modified stress tensor. Such materials have an unconventional anisotropic stiffness and isotropic mass density, which allow themselves to mimic other fluid domains. Here we present a pentamode design formed by an oblique honeycomb lattice and producing customizable anisotropic properties. It is shown that anisotropy in the stiffness can exceed three orders of magnitude, and that it can be realistically tailored for transformation acoustic applications. [16][17][18][19]. Such devices are defined as metafluids, which are effective materials with unconventional fluid-like properties whose particular bulk realization typically requires an anisotropic mass density. Experimental demonstration has been sparse, with most studies relying on a superlattice approach of alternating isotropic layers [20]. However, such an approach is difficult to realize and limited by the so-called mass catastrophe, which requires infinite mass density in the effective material profile.An alternative approach is to generalize the conventional stress strain relationship to include pentamode metamaterials. Pentamode materials [21][22][23] are metafluids that support five easy infinitesimal strains (i.e. there is only one non-zero eigenvalue of the elasticity tensor which is of a pure pressure type), and satisfies the invariance of the governing equations by virtue of maintaining a harmonic transformation. Pure pentamodes, in general, have an isotropic density and anisotropic stiffness with a negligible shear modulus. Recently, isotropic pentamode materials have become experimental reality, and it was shown that the structure's effective bulk modulus exceeded the shear modulus by three orders of magnitude [24]. However, it has yet to be reported that anisotropic pentamode metamaterials can be realistically implemented for specific applications, since an elastic solid with a zero shear modulus would have no stability and immediately flow away.In this Letter, we show that an oblique honeycomb lattice can be utilized as a simple yet versatile building block for pentamode device construction, which exerts highly anisotropic control over sound waves. The method presents a distinctly different approach to acoustic metamaterials, in that it does not require the difficult to achieve high value anisotropy in the effective mass density in addition to removing frequency bandwidth problems associated with inertial metafluids. Potential applications include extraordinary scattering reduction and arbitrary wave manipulation, low loss acoustic delay lines [25], and phase controlled logic gates [26].Anisotropy in pentamode metafluids. We consider elastic wave propagation in a microstructure having the general characteristics presented in Fig. 1. For simplicity we present our results in a two-dimensional (2D) plain strain space, however, the analysis can straightforwardly be extended to three dimensions. Only wavelengths much larger than the lattice constant...

Experiments on cloaking in optics, thermodynamics and mechanics

“…Their two-dimensional counterparts, i.e. bimode metamaterials, have also been discussed theoretically [56].…”

Vibrant times for mechanical metamaterials

“…Effective anisotropy can also be achieved by making the unit cell itself less symmetrical than the three-dimensional pentamode diamond lattice [46] (or the two-dimensional hexagonal lattice, [47] respectively). For example, one double-cone connection point can be shifted along the space diagonal of the facecentered cubic unit cell.…”

“…Anisotropic versions of pentamode [46] (and bimode [47] ) mechanical metamaterials as well as effectively anisotropic laminates composed of isotropic pentamode metamaterials have been considered as well. [45] As in any laminate metamaterial, [48] the anisotropy originates from the layering.…”

Design of arbitrary shaped pentamode acoustic cloak based on quasi-symmetric mapping gradient algorithm

“…By microstructure design, PM material can be made anisotropic in contrast to conventional fluids. 10,11 In addition, its effective property is obtained under a long wavelength condition without using a resonant mechanism and thus is basically broadband. Acoustic cloak using PM materials has advantages of finite mass, broadband efficiency, and solid nature, 7 is more promising for practical applications.…”

“…7 These findings stimulate an active study recently for this material conceived theoretically 2 decades ago. [8][9][10][11][12] PM material, including conventional fluid as a special case, is defined as an elastic material with only one non-zero eigenvalue of elasticity matrix, and supports only one kind of stress state. By microstructure design, PM material can be made anisotropic in contrast to conventional fluids.…”