Pentamode metamaterials with asymmetric double-cone elements

Pentamode metamaterials are a very interesting set of artificial solids. They are difficult to compress but flow easily, hence imitating somehow the behaviours of liquids. In this paper, three-dimensional (3D) pentamode metamaterials based on the asymmetric double-cone element (ADCE) are proposed. The ADCE is composed by two connected truncated cones with different thin diameters. The phonon band structures of the ADCEs pentamode metamaterials are numerically analysed by using the finite element method (FEM). Besides the single phonon mode, the complete 3D band gaps are also found in the phonon band structures. Here, the influence of the degree of asymmetry of ADCE to the figureof merit (FOM), which is the ratio of bulk modulus and shear modulus, is discussed. The FOM can be increased by 21-30% (at FOM≥ 10³) when the degree of asymmetry m ranges from 0.4 to 0.6.