Extremal micropolar materials for elastic wave cloaking

The asymmetric transformation elasticity provides a promising method for controlling elastic waves. However, it requires elastic materials capable of supporting asymmetric stresses, which are not admissible within the linearized Cauchy elasticity under small deformations. In contrast, asymmetric stress tensors naturally arise in micropolar continuum theory, yet the connection between micropolar media and the asymmetric transformation elasticity has remained largely unexplored. In this work, we demonstrate that extremal micropolar media, which are micropolar materials exhibiting soft modes, can be used to design elastic cloaks via asymmetric transformation elasticity. Our first contribution is to establish a rigorous theoretical formulation of the asymmetric transformation method within the micropolar continuum framework. Second, we propose a micropolar metamaterial model that exhibits required soft modes for cloaking. A two-dimensional metamaterial cloak is then constructed and its cloaking performance is verified through full-wave numerical simulations. This study unveils a novel strategy for controlling elastic waves through micropolar media and also sheds light on interesting physical properties of extremal micropolar materials.