An elastodynamic Willis meta-slab with strong directional-dependent absorption

TL;DR

This paper explores how Willis coupling in elastic slabs with specific microstructures leads to strong, directional-dependent absorption at low frequencies, advancing understanding of elastodynamic metamaterials.

Contribution

It demonstrates the emergence of Willis coupling in heterogeneous elastic slabs with asymmetric microstructures, enabling tailored low-frequency absorption properties.

Findings

Willis coupling appears in elastic slabs with asymmetric void arrays.

The slabs exhibit strong directional-dependent absorption at low frequencies.

Inclusion of loss maintains reciprocity while enhancing absorption.

Abstract

Electromagnetic bi-anisotropy finds an analogy in acoustic metamaterial science as Willis coupling. Its impact and emergence in the field of elastodynamic metamaterials is not as well understood however, given the coupling between compressional and shear waves. Here we discuss the emergence of Willis coupling in heterogeneous elastic slabs embedded in an acoustic fluid. The microstructure of the slab comprises circular cylindrical voids and asymmetry is present via two neighbouring line arrays, each with a repeating void of differing radius. The slab matrix is soft, with Poisson ratio close to $1/2$ so that the voids act as Giant Monopole Resonators, and induce a strong dynamic response at low frequency. The incorporation of Willis constitutive coupling ensures that a unique set of effective material properties can be assigned to the slab up to a maximum frequency defined by the periodic spacing of the voids and the elastic properties of the substrate. Including loss in the elastic medium via its shear modulus induces strong directional-dependent absorption at low frequency, whilst of course maintaining reciprocity.