A topology optimization technique based on the topological derivative and the level set function is utilized to design/synthesize the micro-structure of a pentamode material for an acoustic cloaking device. The technique provides a micro-structure consisting of a honeycomb lattice composed of needle-like and joint members. The resulting metamaterial shows a highly anisotropic elastic response with effective properties displaying a ratio between bulk and shear moduli of almost 3 orders of magnitude. Furthermore, in accordance with previous works in the literature, it can be asserted that this kind of micro-structure can be realistically fabricated. The adoption of a topology optimization technique as a tool for the inverse design of metamaterials with applications to acoustic cloaking problems is one contribution of this paper. However, the most important achievement refers to the analysis and discussion revealing the key role of the external shape of the prescribed domain where the optimization problem is posed. The efficiency of the designed micro-structure is measured by comparing the scattering wave fields generated by acoustic plane waves impinging on bare and cloaked bodies.

Peer Reviewed