Tuning of band diagrams via elastic deformation of 2D phononic crystals

Phononic crystals are macroscopic elastic metamaterials that have periodic modulations in material properties such as shear modulus, bulk modulus, and density. Propagation of acoustic waves through phononic crystals depends not just on material properties but also on the symmetry properties of the crystal. In the past, it was demonstrated that buckling of compressed phononic crystals could tune wave propagation properties. To explain these observations, we employ a representation theory-based formalism by drawing an analogy between band theory in electronic systems and that in phononic systems. In particular, we use representation theory to predict the lifting of degeneracies in band diagrams due to changes in phononic crystal symmetries upon elastic deformation. These predictions were confirmed in numerical calculations of band diagrams for compressed 2D phononic crystals. This holds the potential to better inform design strategies for the development of deformable phononic devices.