Connection overlap deviation analysis of pentamode metamaterials

The adjacent double-cones of the pentamode metamaterials form a connection overlap for the non-180° angle connection, and the overlap leads to a connection overlap deviation between the actual effective narrow touch diameters d′ and the defined narrow touch diameters d. The connection overlap deviation increases with the increasing of wide touch diameters D of the double-cones of the pentamode metamaterials with linear outside profile cones. In order to decrease the influence of the connection overlap deviation on the pentamode metamaterials, three types of pentamode metamaterials with small connection overlap (second and third order polynomial outside profile cones structures and the cones stacked by the cylinders-frustums) are proposed and studied in this paper. The connection overlap deviations of pentamode metamaterials with different outside profile cones are analyzed, the phononic band structures are calculated, and the ratio of bulk modulus B to shear modulus G are analyzed for evaluating fluid property. The results show that the pentamode metamaterials proposed by us have smaller connection overlap deviation and more excellent fluid properties than the pentamode metamaterials with linear outside profile cones. The ratio of bulk modulus to shear modulus can be increased by 7.47%-215.92% with the increasing of D from 1 mm to 9.6 mm.