Scattering Analysis and Optimization of Spherical Acoustic Cloak with Unideal Pentamode Material

The acoustic scattering is theoretically studied in this paper for three-dimensional spherical cloak composed of unideal pentamode material, for which small shear rigidity is always inevitable for a real designed microstructure. A theoretical formulation is developed to efficiently evaluate the cloaking performance. The generic scattering feature of the cloak and the effects of material imperfectness and inner cloak boundary constraints are systematically examined. The preferable constraint type and the critical imperfectness parameter of the material are identified for possible broadband invisibility. In addition, a very practical lining shell scheme is proposed to tune the constraint strength on the inner boundary. By combining the theoretical model with optimization algorithm, it is further proved that the cloak can be reduced by several piecewise-uniform layers and optimized to achieve excellent invisibility in targeted frequency bands. The study will provide valuable guidance for the future microstructural design of cloaks.