Comparative study of the pentamodal property of four potential pentamode microstructures

In this paper, a numerical comparative study is presented on the pentamodal property of four potential pentamode microstructures (three based on simple cubic and one on body-centered cubic structures) based on phonon band calculations. The finite-element method is employed to calculate the band structures, and the two essential factors of the ratio of bulk modulus B to shear modulus G and the single-mode band gap (SBG) are analyzed to quantitatively evaluate the pentamodal property. The results show that all four structures possess a higher B/G ratio than traditional materials. One of the simple cubic structures exhibits the incomplete SBG, while the three other structures exhibit complete SBG to decouple the compression and shear waves in all propagation directions. Further parametric analyses are presented investigating the effects of geometrical and material parameters on the pentamodal property of these structures. This study provides guidelines for the future design of novel pentamode microstructures possessing a high B/G ratio and a low-frequency broadband SBG.