Novel Anisotropic Metamaterials for Manipulating Multi-Modal Elastic Waves at Oblique Incidence

The manipulation of elastic waves, such as perfect transmission across dissimilar media, is challenging not just because of impedance mismatch but also because of the existence of multiple elastic wave modes, longitudinal and transverse. Thereby, elastic wave manipulation requires elaborate simultaneous control of longitudinal and transverse waves having different impedances and phase velocities. The situation becomes more complicated when an elastic wave is obliquely incident at an interface because the oblique incidence always couples longitudinal and transverse waves. The constitutive relation that requires a fourth-order elasticity tensor also complicates the analysis of elastic waves. On the other hand, the higher-order tensor offers more freedom to 'design' the constitutive relation. Among others, we focus on a wide range of anisotropy of the elasticity tensor and propose to utilize the anisotropy of an elastic medium as much as possible to find novel anisotropic metamaterials for the desired wave manipulation. After presenting the derived conditions of anisotropy for some wave manipulation problems, we present an example of perfect retroreflection of an elastic wave using anisotropic metamaterials and experimental results performed with the realized metamaterials that are made on an aluminum plate with elaborate void drilling. The practical significance of the designed anisotropic metamaterials is also demonstrated.