High bulk modulus pentamodes: the three-dimensional metal water

Despite significant advances in the field of phononic crystals, the development of acoustic metafluids that replicate the behaviour of liquids in three dimensions remains elusive. For instance, water – the quintessential pentamode (PM) material – has a bulk modulus two orders of magnitude higher than current state-of-the-art PMs. The need for a low shear modulus inherently conflicts with the desire of high bulk modulus and density. In this letter, we shed light on the limitations of existing PM geometries and propose an innovative shape for the links that constitute the network. Inspired by the kinematics of ropes, these links are constructed from thin fibres and demonstrate the potential to create PMs with properties akin to those of liquids. As a prime example, we propose the design of the first metamaterial that fully deserves the name 3D metal water, since its acoustic properties in the low frequency regime are indistinguishable from water. Additionally, we highlight a shear band gap in the lattice dispersion diagram, and illustrate the influence of geometric parameters on the dynamic properties at higher frequencies. This novel design of metafluids holds promise for applications requiring anisotropic materials such as acoustic lenses, waveguides, and cloaks.