Experimental validation of a broadband pentamode elliptical-shaped cloak for underwater acoustics

Design of arbitrarily shaped acoustic cloaks through PDE-constrained optimization satisfying sonic-metamaterial design requirements

“…Once the optimal required material properties are found, the inverse engineering problem of finding the microstructure geometry that exhibit those ρ and κ pairs has to be solved. This being a much more difficult problem than the direct one, it is usually tackled adopting optimization algorithms, either parametric of evolutionary, that employ as cost function the distance between the required desired material properties and those obtained by homogenization on the considered lattice [18,37]. In the case at hand, the simplicity of the geometry of the considered unit cells, which is univocally determined in both configurations by a pair of parameters, allows for a direct mapping of the whole C and C spaces into the ρ × κ one.…”

“…the material property distribution, with that of the microstructure that implements via long-wavelength homogenization the required density and bulk modulus, thus unlocking the marriage between the two stages of the design of such two-scale optimization problem. Indeed, the standard approach to implement inhomogeneous material property distributions in acoustic cloaking is to discretize them and fill each resulting sub-domain with an appropriately optimized microstructure [17,18,37]. This approach leads to sub-optimal solutions depending on the chosen discretization: provided that the sub-domains are sufficiently small compared to the wavelength considered, the wave "feels" a gradient of refraction index that might be different from the required one.…”