The Construction and Investigation of Two-Dimensional Re-Entrant Multiphase Honeycomb Lattice Metafluid

Compared to conventional materials, underwater metamaterials possess numerous advantages in the manipulation of sound waves, which have garnered increasing attention. In terms of composition, commonly studied underwater wideband metamaterials can be classified into solid-phase pentamode metafluid and water–solid coupling metafluid. The concept of multiphase design in pentamode metafluid allows for decoupling the regulation of equivalent density from that of the equivalent bulk modulus, facilitating more convenient structural design. In typical auxetic metamaterial structure designs, the “re-entrant” mechanism is commonly employed; the skeleton is inwardly bent to a certain extent, enabling the design of a low volume-modulus for each cell. Consequently, a novel type of water–solid coupling metafluid is devised by combining the concepts of “multiphase” and “re-entrant”. Firstly, a straight-sided skeleton (referred to as “ss” skeletal) unit cell is designed, and its compression wave frequency band is determined through analysis of its band characteristics and related vibration modes. Subsequently, the “re-entrant” (referred to as “re”) mechanism is introduced into a unit cell, revealing an increase in equivalent density while decreasing the equivalent volume modulus due to this feature. The bent skeleton provides lower bulk modulus, while multiphase (referred to as “mp”) counterweighting offers higher equivalent density; their combination enables designing more impedance-matched metafluid. Then, a unit cell is designed utilizing both “re” and “mp” characteristics. Finally, acoustic performance simulations and analyses verify that both types exhibit excellent broadband water-like properties within the frequency range of 5000–27,000 Hz. In order to further validate the reliability of the design concept, two pairs of underwater metafluid cells with an impedance-matching effect were subsequently developed, demonstrating sound speeds that are half and one-third that of water, respectively. The skeleton thickness of the “re” cell was moderately enhanced compared to that of the straight side cell, thereby presenting an innovative approach for designing robust underwater metafluid cells.