Second-order computational homogenization of flexoelectric composites

authored by: Xiaoying Zhuang, Bin Li, S. S. Nanthakumar, Thomas Böhlke
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 (Formula presented.) 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.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Karlsruhe Institute of Technology (KIT)
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 126
ISSN: 0029-5981
Publication date: 03.01.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.48550/arXiv.2312.05556 (Access: Open)
https://doi.org/10.1002/nme.7598 (Access: Open)

BibTeX

@article{d74bde608ad3401987a86da74ccb6c27,
title = "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 (Formula presented.) 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.",
keywords = "flexoelectricity, multiscale methods, second-order homogenization, size-dependent effects",
author = "Xiaoying Zhuang and Bin Li and Nanthakumar, {S. S.} and Thomas B{\"o}hlke",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s). International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.",
year = "2025",
month = jan,
day = "3",
doi = "10.48550/arXiv.2312.05556",
language = "English",
volume = "126",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "1",
}