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 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.
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