Optimal Design Methodology for Maximum Electro-Momentum Coupling in Piezoelectric Metamaterial Scatterers

As an elastodynamic bianisotropy, Willis coupling has been widely employed for acoustic metamaterials in which the linear momentum is additionally coupled to strain at the macroscale while it is coupled only to velocity by mass density at the microscale. Recently, a novel coupling, called electro-momentum coupling, is discovered for piezoelectric materials responding to electric fields such that the macroscopic momentum can also be coupled with electric stimuli. This electromechanical bianisotropy implies the possibility of programmable functionality in piezoelectric metamaterial devices as electro-momentum coupling can be smartly controlled by modulation of external stimuli, <i>i.e.,</i> active wave manipulation by stimulus modulation. However, the theory of how the electro-momentum coupling coefficient depends on external stimuli has not been developed in the previous literature. At the same time, how to rationally design microstructures with consideration for their sensitivity to the coupling coefficient has not been widely studied for two-dimensional cases. In this work, we aim to propose a general, optimal design methodology to design microstructures of piezoelectric metamaterials with external stimuli that can reach the theoretical maximum bianisotropic performance of scattering proposed in our previous work for piezoelectric metamaterial scatterers. Additionally, machine learning algorithms will be used to efficiently complement computational approaches in the design framework as well as to overcome the intrinsic nonlinearities of coupling.