Tetramode Metamaterials as Phonon Polarizers

Abstract

In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are “easy”. Using Greek number words, this leads to hexamode (N = 6), pentamode (N = 5), tetramode (N = 4), trimode (N = 3), dimode (N = 2), and monomode (N = 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials (“meta‐fluids”) has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer‐based tetramode metamaterials are designed and characterized by numerical band‐structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated.

Dispersion Engineering by Hybridizing the Back‐Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes

“…Both techniques allow for the time‐resolved mapping of the displacement‐vector field with nanometer‐scale localization errors. [ 23,41 ] In this work, typical displacement amplitudes are roughly in the range of 2–40 nm (depending on frequency and component of the displacement vector). The band structure is derived from these data by Fourier transformation with respect to time t and with respect to coordinate vector r .…”

“…For the constituent polymer resulting from the 3D laser microprinting, the parameters of E = 4.19GPa for Young's modulus, ν = 0.4 for Poisson's ratio, and ρ = 1140 kgm −3 for mass density were chosen. [ 41 ]…”

Non-reciprocal and Non-Newtonian Mechanical Metamaterials

“…Metamaterials with tunable mechanical properties [11][12][13][14] , in particular having a rich dynamical behavior [15][16][17][18][19][20][21][22] or exhibiting non-reciprocity 23,24 , are extremely attractive for numerous applications, such as control of the propagation of acoustic and elastic waves [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . Beyond the homogenization limit, the idea of dynamic shear, bulk, or mass density is commonly used and accepted for waves 41 .…”

Three-Dimensional Optical Imaging of Internal Deformations in Polymeric Microscale Mechanical Metamaterials

“…However, they do not appear to have been applied in studies involving in situ mechanical compression. 27,28 Addressing this diagnostic gap, we develop and demonstrate a technique to image the deformation mechanics of microscale polymeric metamaterials during mechanical loading by using confocal microscopy. By capturing fluorescence from the polymerized material, we can produce high-fidelity threedimensional renderings of these structures.…”

“…Confocal imaging techniques have been recorded across literature to statically image three-dimensional microscale structures made with TPP. However, they do not appear to have been applied in studies involving in situ mechanical compression. , …”