Flexoelectricity shows promising applications for self-powered devices with its increased power density. This paper presents a second-order computational homogenization strategy for flexoelectric composite. The macro-micro scale transition, Hill-Mandel energy condition, periodic boundary conditions, and macroscopic constitutive tangents for the two-scale electromechanical coupling are investigated and considered in the homogenization formulation. The macrostructure and microstructure are discretized using C1 triangular finite elements. The second-order multiscale solution scheme is implemented using ABAQUS with user subroutines. Finally, we present numerical examples including parametric analysis of a square plate with holes and the design of piezoelectric materials made of non-piezoelectric materials to demonstrate the numerical implementation and the size-dependent effects of flexoelectricity.
@article{arxiv.2312.05556,
title = {Second-order computational homogenization of flexoelectric composites},
author = {Xiaoying Zhuang and Bin Li and S. S. Nanthakumar and Thomas Bohlke},
journal= {arXiv preprint arXiv:2312.05556},
year = {2023}
}