Frequency band gaps in dielectric granular metamaterials modulated by electric field

Wave propagation in granular materials is known to be dispersive. Micromorphic continuum model based upon granular micromechanics (Misra, A. and P. Poorsolhjouy, Continuum Mech. Thermodyn, 2016. 28(1-2): p. 215-234.) has the ability to describe this dispersion behavior. In this pa- per we show that the dispersive behavior can be modulated by using electric field when the grains have dielectric properties. To this end, we apply the recently enhanced model that incorporates electro-elastic coupling by connecting microstrain to electric dipole and quadrupole densities due to bound charges in dielectric grains (Romeo, M., Mech. Res. Commun., 2018. 91: p. 33-38.). We particularly investigate the effect of induced polarization that arises due to an imposed electric field. Two cases of dielectric one dimensional infinite rods with the same micromorphic properties have been studied, where case 1 and 2 are in null and nonzero external electric fields, respectively. Parametric studies are performed to under- stand the contribution of the polarizability (dipole effect), intrinsic quadrupole density, and external elec- tric field on the dispersive behavior of granular media. Results predict an acoustic and an optical branch in the dispersive curve. Polarizability and external electric field are mainly affecting small wavenum- ber behavior of the wave branches, while quadrupole density alters the behavior of the material at large wavenumbers. A possibility of altering the optical branch to an acoustic branch is also observed, for which instability or attenuation occurs depending upon the direction of the imposed electric field with respect to the wave propagation direction. We find that the location and the width of the frequency band gaps can be altered using external electric field. The possibility of creating or removing frequency band gaps is also shown to exist. The extended theory accounting for electro-elasticity can therefore be utilized as a tool to analyze existing granular media, or to design granular metamaterials, as it systematizes the design process and eliminates ad-hoc manners leading to large data libraries.