Structurally Rigid Elastic Composites for Acoustic Imaging Countermeasures

We explore the possibilities coming from transformation acoustics and beyond for creating rigid elastic composite shells capable of suppressing the total scattering cross-section of acoustically large objects. The reported design methodology is based on generalized shape and topology optimization, and the outcomes are suitable for rapid prototyping techniques. Acoustic cloaking has been a subject of interest to the phononics community since the advent of transformation acoustics (TA). TA methodology is based on the form-invariance of the scalar Helmholtz equation describing acoustic pressure waves in fluids. Much of the past effort in TA was focused on the so-called acoustic metaflu- ids 1 , 2 , 3 , which are materials with vanishingly small shear modulus. The acoustics of metafluids is mathematical- ly almost as simple as acoustics of regular fluids, with the only complication that the density is anisotropic and described by a rank-2 tensor. This explains why virtually all recent effort (with a few exceptions) in transfor- mation acoustics was devoted to metafluids 1 , 2 , 3 . Unfortunately, the structural properties of metafluids are not particularly suitable for deployable acoustic devic- es. Fluids (and metafluids) are unable to support any amount of shear stress: an infinitesimal amount of shear stress leads to a finite deformation. This presents a fundamental difficulty in integrating them with any on-board devices mounted on air vehicles, or even on stationary platforms that are subject to wind or streaming water. This lack of structural robustness was overcome in the proof-of-concept demonstrations involving acoustic met- afluids by restricting device geometries to two-dimensional (in-plane) propagation. These geometries allowed the use of metafluids formed by arrays of rigid inclusions (rods, bars) which are mechanically disconnected from each other and embedded in a homogeneous fluid (air, water, etc.) By construction, such a metamaterial geometry does not support in-plane shear wave propagation and therefore acts as a two-dimensional metafluid. The difficulty with generalizing this strategy into three dimensions is so fundamental that no demonstration of a non-trivially three-dimensional transformation acoustical device has been offered to date, even as merely a proof-of-concept experiment. The need for structural integrity and rigidity calls for the development of elastic metamaterials with a suitably large shear modulus. Such media would be capable of tolerating finite stress in arbitrary directions, whose amount is limited only by their yield or fracture properties.