Investigations on the performance of piezoelectric-flexoelectric energy harvesters

Flexoelectric electromechanical systems have received recent attention for their ability to harvest energy at the nanoscale where piezoelectric systems could not generate appreciable energy. The size-dependency of flexoelectric materials has been investigated; however, the piezoelectric effect has largely been neglected due to its low performance at the nanoscale. In this study, a piezoelectric-flexoelectric reduced-order model considering material structure, size dependency, and surface smoothness effects is developed in order to determine the performance of piezoelectric and/or flexoelectric systems at different scale levels. The size dependent effects are accounted using the classical couple stress theory with surface elasticity effects modeled using the Gurtin-Murdoch theory. The surface integrity modeling is implemented to include non-smooth surfaces due to the manufacturing precision at the nano-scale. A multi-phase model is introduced to model the material structure of the nanocrystalline substrate incorporating porosity effects. At nanoscale, the combined piezoelectric and flexoelectric configuration and the flexoelectric only configuration perform similarly with little variation; however, at transition scales, from nano to micro, the combined system outperforms either piezoelectric only or flexoelectric only configuration. A non-smooth surface increases the levels of the harvested power of the system in all cases. This study shows not only the performance of flexoelectric configurations at the nanoscale, but that a piezoelectric-flexoelectric system can generate more power than previously thought near the microscale.