Phonon band structures of the three dimensional latticed pentamode metamaterials

The artificially designed three-dimensional (3D) pentamode metamaterials have such an extraordinary characteristic that the solid materials behave like liquids. Meanwhile, the ideal structure of the pentamode metamaterials arranges in the same way as that of the diamond crystals. In the present research, we regard three types of pentamode metamaterials derived from the 3D crystal lattices as research objects. The phonon band structures of the candidate pentamode structures are calculated by using the finite element method (FEM). We illustrate the relation between the ratio of the bulk modulus B and the shear modulus G of different combinations of D and d. Finally, we find out the relationship between the phonon band structure and the structure parameters. It is useful for generating the phonon band structure and controlling elastic wave propagation.