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.

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

“…3, we can see that the three optimized unit cells obtained by K 1111 , K 2211 and K 1212 have similar topologies. Finally, we note that the optimized microstructures are similar to the ones obtained by optimizing the direct flexoelectric constants F 1221 and F 2112 for the PZT/PZT case 36 .…”

“…This is a well-known issue in strain gradient homogenization problem, which can cause a dependence to the number of unit cells within the RVE and to non-vanishing higher-order properties in the case of materials which do not have local gradient effects (see a discussion in 32 ). In our previous work 36 , we have introduced appropriate body forces to balance these non-equilibrated terms. It has also been shown in the context of purely mechanical gradient effects that such procedure is consistent with asymptotic homogenization 37 .…”

“…The detailed expression can be found following the procedure described in our previous work on the topology optimization of direct flexoelectric properties 36 . The optimization problem ( 22) is solved by the Conservative Convex Separable Approximations (CCSA) optimizer 48 based on the adjoint sensitivity.…”

Dynamic analysis of flexoelectric systems in the frequency domain with isogeometric analysis

“…In this example, the effects of flexoelectricity on dynamic voltage, power and dis- Then, in this work, ℓ d was chosen as ℓ d = 10ℓ. The modal damping ratios in (61) are found as ξ 1 = ξ 2 = 0.01. For the close-circuit of Fig.…”

Explicit topology optimization for graded lattice flexoelectric nanostructures via ersatz material model

“…To achieve lattice structure design, representative volume element (RVE)‐based computational approach is popular in small‐scale calculation. With the use of RVE, Chen et al 23 proposed a SIMP‐based topology optimization approach for flexoelectric composites, where the analysis and optimization are only carried out in an element. Zheng et al 24 simulated an isotropic matrix filled with spherical flexoelectric inclusions by RVE.…”