  Metamaterials are structures engineered at a small scale with respect to the
wavelength of the excitations they interact with. These structures behave as
artificial materials whose properties can be chosen by design, mocking and even
outperforming natural materials and making them the quintessential tool for
manipulation of wave systems. In this Letter we show how the acoustic
properties of a silicon nitride membrane can be affected by nanopatterning. The
degree of asymmetry in the pattern geometry induces an artificial anisotropic
elasticity, resulting in the splitting of otherwise degenerate mechanical
modes. The artificial material we introduce has a maximum Ledbetter-Migliori
anisotropy of 1.568, favorably comparing to most bulk natural crystals. With an
additional freedom in defining arbitrary asymmetry axes by pattern rotation,
our approach can be useful for fundamental investigation of material properties
as well as for devising improved sensors of light, mass or acceleration based
on micromechanical resonators.
