| In a piezoelectric material an applied uniform strain can induce an electric polarization or vice-versa. Crystallographic considerations restrict this technologically important property to non-centrosymmetric systems. It can, however, be shown both mathematically and physically, that a non-uniform strain can break the inversion symmetry and induce polarization even in non-piezoelectric materials. The key concept is that all crystalline dielectrics (including non-piezoelectric ones) exhibit the aforementioned coupling between strain gradient and polarization---an experimentally verified phenomenon known as the flexoelectric effect. This flexoelectric coupling, however, is generally very small and evades experimental detection unless very large strain gradients (or conversely polarization gradients) are present.;In this work, based on a field theoretic framework accounting for this phenomenon, the fundamental solutions (Green's functions) for the governing equations are developed and solutions to some illustrative boundary value problems are presented. The central contribution of this dissertation is the demonstration of the possibility of "designing piezoelectricity" by exploiting the large strain gradients present in the interior of composites containing nanoscale inhomogeneities to achieve an overall non-zero polarization even under a uniformly applied stress. The aforementioned effect may be realized only if both the shapes and distributions of the inhomogeneities are non-centrosymmetric. Simplest case of 1D layered superlattices consisting of non-piezoelectric (cubic) BaTiO3, SrTiO3 and MgO laminates are used to create the apparently piezoelectric 'meta material' which can achieve up to 11% of piezoelectric effect of quartz at thicknesses of 2 nm. Further, more complex geometries like periodic thin film with triangular voids are shown to induce averaged polarization up to 59.57% of quartz.;Finally, an asymptotic homogenization model for these apparently piezoelectric composites which will take into account not only the geometry and topological arrangement but also the electromechanical coupling between the constituents is presented. |
