Topology optimization design scheme for broadband non-resonant hyperbolic elastic metamaterials

Abstract

Metamaterials with hyperbolic equal-frequency contours possess unique properties, which offer novel means in elastic wave manipulation. The existing designs are either resonant-structure based that have large damping loss or have a relatively narrow working frequency range. In this paper, a topology optimization approach is developed to design non-resonant hyperbolic elastic metamaterials over a broad frequency range. Based on the physical nature of hyperbolic metamaterials, a two-step topology optimization design scheme is formulated and solved by a gradient-based optimizer. By engineering the dispersion band structure, non-resonant hyperbolic metamaterials have been successfully designed. Novel features such as negative refraction, wave partial focusing and super-resolution imaging have been numerically demonstrated.