Maximizing electro-momentum coupling in generalized 2D Willis Metamaterials

The coupling of momentum to strain in elastic metamaterials, known as the Willis coupling, has been widely studied in recent years for its potential in enabling novel phenomena in wave propagation. More recent work has shown that in piezoelectric composites, the momentum can also be coupled to the electrical stimulus, resulting in a new form of electro-momentum coupling, which offers a new approach to controlling elastic wave phenomena through a non-mechanical stimulus. In this study, we present a topology optimization approach to maximize the electro-momentum coupling in piezoelectric composites, where dynamic homogenization is utilized to obtain the effective mechanical, electrical, and electro-mechanical constitutive relations. We first validate the approach in one-dimension, then demonstrate that the electro-momentum coupling can enable asymmetric wave propagation in two-dimensions, both through mechanical and electrical loadings. This approach can enable the design of piezoelectric composites that support novel wave phenomena that can be excited through non-mechanical means.