Decoupling design of compression modulus and density in pentamode metamaterials

Pentamode materials (PM) is a representative type of metamaterial capable of adjusting equivalent mechanical properties by tailoring its microstructure. Generally, there exists a significant correlation between its density (ρ) and compression modulus (E), which hinders meeting the needs of extreme mechanical cases, such as ultralight high-strength material and transformation acoustics. In this paper, an in-depth mechanical analysis by Timoshenko beam theory was conducted and an analytical expression was derived to intuitively capture the essence of the linkage between PM’s equivalent medium properties and geometric parameters. By this analytical equation, we theoretically proved an intrinsic decoupling relationship between the compression modulus and density. Based on it, we proposed a new microstructure configuration that can achieve perfect decoupling of compression modulus and density, as well as flexible adjustment of density and acoustic impedance over a large range can be implemented easily. Our results can support the developing of pentamode metamaterials with extreme-performing, further bolstering the versatility in shaping underwater acoustic waves.