Mechanical metamaterials with anisotropic and negative effective mass‐density tensor made from one constituent material

If one replaces the bulk masses in a three‐dimensional (3D) mass‐and‐spring model of a solid by composite masses made of different springs connected to a heavy internal mass, one obtains a paradigm for a metamaterial with an effectively frequency‐dependent and anisotropic mass‐density tensor. Besides the different internal eigenfrequencies, components of this tensor can become negative. Today, such structures can be fabricated by using 3D printing – usually, however, only out of one constituent material and with constraints regarding the maximum ratio of unit cell size to minimum feature size. Here, we use numerical phonon band structure calculations to study what performance can be expected with current fabrication technology.