Topology optimization of flexoelectric composites using computational homogenization

Abstract We present a topology optimization framework to design periodic composites comprised of piezoelectric constituents that exhibit large flexoelectric constants. The novelty of the approach is that it leverages a representative volume element (RVE)-based computational homogenization approach that enables the analysis of periodic composites where the characteristic dimensions of the microstructure are significantly smaller than those of the structure, and as such requires only the optimization of a single RVE rather than that of the entire structure. We utilize this approach to analyze the enhancement in flexoelectric constants that can be achieved in different types of PZT-based composites, including hard–hard (PZT–PZT), and hard–soft (PZT–polymer composite, and porous PZT) structures. In all cases, significant enhancements are observed, with improvements between 2 and 15 times those of a naive guess, with some designs reaching a factor of one order of magnitude larger than BTO. We identify different mechanisms governing the enhanced electromechanical couplings, which can arise either from an enhancement of effective piezoelectricity in the RVE for PZT–PZT composites, or from a more subtle interplay involving the enhancement of effective piezoelectric and dielectric properties coupled with a reduction in mechanical compliance for PZT–polymer and porous PZT RVEs.