2023/12/09 by Zhuang, Xiaoying, Li, Bin, Nanthakumar, S. S. +1
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2312.05556
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.