Electroelastodynamics of flexoelectric energy conversion and harvesting in elastic dielectrics

Abstract

Flexoelectricity is the generation of electric polarization by the application of a non-uniform mechanical strain field, i.e., a strain gradient. This phenomenon is exhibited by all elastic dielectrics, but is expected to be significant only at very small scales. Energy harvesting is a potential future application area of flexoelectricity to enable next-generation ultra-low-power MEMS/NEMS devices by converting ambient vibrations into electricity. In this paper, an electroelastodynamic framework is presented and analyzed for flexoelectric energy harvesting from strain gradient fluctuations in centrosymmetric dielectrics, by accounting for the presence of a finite electrical load across the surface electrodes as well as two-way electromechanical coupling, and capturing the size effect. The flexoelectric energy harvester model is based on the Euler-Bernoulli beam theory and it assumes the main source of polarization to be static bulk flexoelectricity. Following recent efforts on the converse flexoelectric effect in finite samples, the proposed model properly accounts for thermodynamically consistent, symmetric direct and converse coupling terms. The transverse mode flexoelectric coupling coefficient (k) is obtained analytically as a direct measure of energy conversion; its dependence on the cantilever thickness and a material Figure of Merit (FoM) is shown. Size effects are further demonstrated by simulations of the electromechanical frequency response for a Strontium Titanate (STO) energy harvester at different geometric scales. It is obtained that the flexoelectric coupling coefficient of an STO cantilever for the fundamental bending mode increases from k≈3.5×10−7 to k≈0.33 as the thickness is reduced from mm- to nm-level. A critique of the experimentally identified large flexoelectric coefficient for Barium Strontium Titanate (BST) from the literature is also given with a coupling coefficient perspective.