Elastodynamic cloaking and field enhancement for soft spheres

TL;DR

This paper investigates the limitations of elastic cloaks in wave protection, revealing resonance-induced field enhancements at certain frequencies, and proposes mixed cloaks that combine invisibility with effective wave protection across a broad frequency range.

Contribution

It introduces non-singular asymmetric elastic cloaks with adjustable softness, analyzes resonance phenomena, and develops mixed cloaks that ensure both cloaking and protection over wide frequencies.

Findings

Cloaks reduce scattering but can cause resonance peaks.

Resonance peaks lead to large field enhancements inside cloaked spheres.

Mixed cloaks achieve both invisibility and wave protection across many frequencies.

Abstract

In this paper, we bring to the awareness of the scientific community and civil engineers, an important fact: the possible lack of wave protection of transformational elastic cloaks. To do so, we propose spherical cloaks described by a non-singular asymmetric elasticity tensor depending upon a small parameter $\eta,$ that defines the softness of a region one would like to conceal from elastodynamic waves. By varying $\eta$, we generate a class of soft spheres dressed by elastodynamic cloaks, which are shown to considerably reduce the soft spheres' scattering. Importantly, such cloaks also provide some wave protection except for a countable set of frequencies, for which some large elastic field enhancement (resonance peaks) can be observed within the cloaked soft spheres, hence entailing a possible lack of wave protection. We further present an investigation of trapped modes in elasticity via which we supply a good approximation of such Mie-type resonances by some transcendental equation. Next, after a detailed presentation of spherical elastodynamic PML of Cosserat type, we introduce a novel generation of cloaks, the mixed cloaks, as a solution to the lack of wave protection in elastodynamic cloaking. Indeed, mixed cloaks achieve both invisibility cloaking and protection throughout a large range of frequencies. We think, mixed cloaks will soon be generalized to other areas of physics and engineering and will in particular foster studies in experiments.