An example flexoelectric piezoelectric material has a piezoelectric response, which may be a direct piezoelectric effect, a converse piezoelectric effect, both effects, or only one effect. A flexoelectric piezoelectric material comprises shaped elements of a material, which may be a substantially isotropic and centrosymmetric material. The shaped elements, such as cones, pyramids, wedges, or other tapered elements, may provide an electrical response in response to stress or strain gradients due to a flexoelectric effect in the material, and may provide a mechanical response in response to electric field gradients. Examples of the present invention include improved methods of fabricating devices comprising such shaped elements, and multi-layer devices having improved properties.