# Dynamic behavior of mechanical cloaks designed by direct lattice transformation

## TL;DR

This paper extends a direct-lattice-transformation method to dynamic elastic waves, achieving broadband cloaking with significant scattering reduction, validated through an effective-medium approach.

## Contribution

It introduces a novel application of the direct-lattice-transformation approach to elastic wave cloaking in the dynamic regime, demonstrating broadband scattering suppression.

## Key findings

- Achieved over fivefold reduction in elastic wave scattering.
- Demonstrated effectiveness of cubic coordinate transformations over linear ones.
- Validated cloaking performance using an effective-medium approach.

## Abstract

Steering waves in elastic solids is more demanding than steering waves in electromagnetism or acoustics. As a result, designing material distributions which are the counterpart of optical invisibility cloaks in elasticity poses a major challenge. Waves of all polarizations should be guided around an obstacle to emerge on the downstream side as though no obstacle were there. Recently, we have introduced the direct-lattice-transformation approach. This simple and explicit construction procedure led to extremely good cloaking results in the static case. Here, we transfer this approach to the dynamic case, i.e., to elastic waves or phonons. We demonstrate broadband reduction of scattering, with best suppressions exceeding a factor of five when using cubic coordinate transformations instead of linear ones. To reliably and quantitatively test these cloaks efficiency, we use an effective-medium approach.