Extremal micropolar materials for elastic wave cloaking

TL;DR

This paper introduces extremal micropolar materials as a new approach to elastic wave cloaking, demonstrating their design, simulation, and potential for controlling elastic waves using asymmetric elasticity transformation.

Contribution

It establishes a novel connection between micropolar continuum theory and asymmetric elasticity transformation for elastic cloaking, including a practical metamaterial design and numerical verification.

Findings

Successful design of a 2D elastic cloak using extremal micropolar metamaterials

Numerical simulations show excellent agreement with effective-medium calculations

Unveils new strategies for elastic wave control via micropolar media

Abstract

The asymmetric transformation elasticity offers a promising method to control elastic waves. However, this method requires elastic materials that support asymmetric stresses, which is not objective within the Cauchy elasticity framework. Nevertheless, asymmetric stress tensor is a typical feature of micropolar continuum theory. Yet, possible connection between micropolar continuum theory and the asymmetric elasticity transformation has remained elusive. Here, we demonstrate that extremal micropolar media, which refer to micropolar media with easy deformation modes, can be used to design elastic cloaks following the asymmetric transformation method. A metamaterial model is proposed to achieve the required extremal micropolar parameters for cloaking. We further design a two-dimensional metamaterial cloak and verify its cloaking performance numerically. An excellent agreement between the metamaterial cloak simulation and an effective-medium calculation is obtained. This study unveils a novel strategy for controlling elastic waves through micropolar media and also sheds light on interesting properties of extremal micropolar materials.