Phonon band structures of three-dimensional pentamode metamaterials

TL;DR

This paper calculates phonon band structures of 3D pentamode metamaterials, revealing significant differences in wave velocities and the existence of wide frequency ranges with pure compression wave propagation, useful for advanced elastic wave control.

Contribution

It provides the first detailed phonon band structure analysis of 3D pentamode metamaterials, highlighting their potential for single-mode elastic wave applications.

Findings

Compression and shear wave velocities differ by over an order of magnitude.

Existence of frequency intervals with only compression waves due to a complete shear wave band gap.

Identification of wide bandwidths with purely single-mode compression wave behavior.

Abstract

Three-dimensional pentamode metamaterials are artificial solids that approximately behave like liquids, which have vanishing shear modulus. Pentamodes have recently become experimental reality. Here, we calculate their phonon band structures for various parameters. Consistent with static continuum mechanics, we find that compression and shear waves exhibit phase velocities that can realistically be different by more than one order of magnitude. Interestingly, we also find frequency intervals with more than two octaves bandwidth in which pure single-mode behavior is obtained. Herein, exclusively compression waves exist due to a complete three-dimensional band gap for shear waves and, hence, no coupling to shear modes is possible. Such single-mode behavior might, e.g., be interesting for transformation-elastodynamics architectures.