Quasi-laminate and quasi-columnate modeling of dielectric and piezoelectric properties of cubic-cell metamaterials

Abstract

Dielectric and piezoelectric properties of closed-cell or open-cell metamaterials with cubic cells are predicted analytically via quasi-laminate / Q-lam and quasi-columnate / Q-col models. For dielectric properties also numerical results are given. Model predictions of relative permittivity are within the Wiener bounds. Q-lam model predictions are higher than Q-col model predictions (and even exceed the Hashin-Shtrikman upper bound), but the numerical results are in between these two predictions. Closed-cell metamaterials exhibit higher permittivity than open-cell metamaterials. The classical predictions by Rittenmyer et al. and Banno correspond to the Q-col model predictions for open-cell and closed-cell metamaterials, respectively. Model predictions for longitudinal piezoelectric charge coefficients are close to Newnham’s parallel model, i.e. relatively constant over a wide range of porosity, with a steep decrease as the porosity approaches 100 %. Brief comments are given on the transverse piezoelectric charge coefficient, the hydrostatic piezoelectric charge coefficient and the piezoelectric voltage coefficient.