Exploiting Buckling-induced Symmetry Breaking for Tunable Wave Propagation through Elastic Phononic Crystals

Elastic phononic crystals (EPC) are metamaterials that have periodic modulations in material properties such as shear modulus, bulk modulus, and density, while being flexible to deformations. In EPCs, wave propagation is affected not only by material properties but also by symmetry properties of the crystal. In the past, it has been shown that buckling of compressed EPCs could tune wave propagation – for example, by changing the number of intersections in the band diagram, potentially leading to the opening of band gaps. From the theoretical standpoint of representation theory of symmetry groups, we can trace such changes in band diagrams to changes in symmetries of deformed phononic crystals. This helps us predict, which band intersections are protected by symmetry and their degree of degeneracy. We anticipate that buckling, in addition to causing a state of stress in the EPC, also leads to a change in the unit cell symmetry. In this work, we take a closer look at buckling-induced symmetry breaking and extend the representation theory formalism for different loading conditions. We then have the potential to predict how different loading paths affect the symmetries of EPCs and hence their wave propagation properties, which would be helpful for a rational design of tunable EPCs.