Enhanced converse flexoelectricity in piezoelectric composites by coupling topology optimization with homogenization

Abstract

We demonstrate that large apparent converse flexoelectric properties can be obtained in piezoelectric composites using theoretical approaches. To do so, we first present a numerical homogenization method accounting for all electromechanical terms related to strain and the electric field gradient. We then evaluate the coefficients of the model by numerical simulations on periodic piezoelectric composites. After combining the homogenization approach with topology optimization to enhance the converse properties of the composite, we present numerical results that reveal that the apparent converse flexoelectric coefficients, as well as those associated with the higher order coupling terms involving the electric field gradient, are of the same order as the direct flexoelectric properties of the local constituents. These results suggest that both converse and higher order electromechanical coupling effects may contribute strongly to the flexoelectric response and properties of piezoelectric composites. Finally, we show that it is theoretically possible to obtain optimized designs of composites with apparent converse flexoelectric properties 1-2 orders of magnitude larger than ones obtained with naïve guess designs.