Simulating transmission through anisotropic pentamode materials submerged in water

Abstract

Interest has increased in recent years on the potential for underwater metallic metamaterials, which can be linked to the advancements in metal 3-D printing. One metamaterial of particular interest is an underwater anisotropic pentamode, i.e., a structure designed to support a single longitudinal wave for a broad-range of frequencies whose speed will change depending on its orientation relative to the incident acoustic wave. In an attempt to close the gap between experiment and theory, COMSOL simulations have been developed modeling the transmission and reflection of a normal plane wave incident on an anisotropic pentamode metamaterial consisting of tetrahedral unit cells. The utilization of the Floquet periodic boundary conditions allows for the replication of a semi-infinite medium response composed of repeating unit cells while only using a finite CAD drawing. Meshing techniques and geometric work-arounds are discussed in an attempt to achieve a cost-effective computation absent of numerical instabilities for a broad range of frequencies. Results show dynamic stress concentration is focused mainly at the joints of the unit cells. Plates designed to separate the fluid medium from the internal structure are shown to exhibit higher modes of vibrations, however contribute little to the far field due to energy flux conservation.