Second‐order computational homogenization of flexoelectric composites

Abstract 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 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.