Theoretical verification of three-dimensional manufacturable pentamode metamaterial microstructure

A special kind of pentamode metamaterial, which is composed of double-cone elements and forms simple-cubic lattice, is investigated in this paper. Based on finite-element method, the phonon band structure and the transmission spectrum of the pentamode metamaterial are calculated, and then the pentamodal behavior of this structure is theoretically verified from two aspects, i.e. the physical properties and the mathematical definition. Results show that in the phonon band structure, there is a wider single-mode band gap, corresponding to the remarkable loss in the transmission spectrum. The ratio of bulk modulusBto shear modulusGis more than 300, which is obviously larger than that of traditional materials. Except for the isotropic bulk modulusB, the other mechanical moduli are all anisotropic. Five of six eigenvalues of elastic coefficient matrix are nearly zero for the microstructure, and only one is non-zero. These results demonstrate that this metamaterial microstructure performs excellent pentamodal characteristics, and also conforms to the mathematical definition of 'pentamode'.