Extremal Micropolar Materials for Elastic Wave Cloaking

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 linearized Cauchy elasticity for small deformations. 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.

Keywords: asymmetric transformation elasticity, extremal micropolar media, easy deformation modes, micropolar metamaterials, elastic cloak