Second-order computational homogenization of flexoelectric composites with isogeometric analysis

authored by: Bin Li, Ranran Zhang, Krzysztof Kamil Żur, Timon Rabczuk, Xiaoying Zhuang
Abstract: Flexoelectricity is an electromechanical coupling phenomenon in which electric polarization is generated in response to strain gradients. This effect is size-dependent and becomes increasingly significant at micro- and nanoscale dimensions. While heterogeneous flexoelectric materials demonstrate enhanced electromechanical properties, their effective application in nanotechnology requires robust homogenization methods. In this study, we propose a novel second-order computational homogenization framework for flexoelectricity, which combines isogeometric analysis and the finite cell method. Key innovations include the introduction of high-order periodic boundary conditions and homogenized high-order stresses, which ensure consistent multiscale analysis. Periodic boundary conditions are applied using penalty methods, and perturbation analysis is employed to efficiently compute equivalent material coefficients. The effectiveness of the proposed method is validated through numerical examples, demonstrating its ability to generate piezoelectric effects in flexoelectric microstructured materials.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Bialystok Technical University
Bauhaus-Universität Weimar
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 442
ISSN: 0045-7825
Publication date: 01.07.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2025.118031 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{9dbfb2a7e3cd484bb2c044ba8026fd4f,
title = "Second-order computational homogenization of flexoelectric composites with isogeometric analysis",
abstract = "Flexoelectricity is an electromechanical coupling phenomenon in which electric polarization is generated in response to strain gradients. This effect is size-dependent and becomes increasingly significant at micro- and nanoscale dimensions. While heterogeneous flexoelectric materials demonstrate enhanced electromechanical properties, their effective application in nanotechnology requires robust homogenization methods. In this study, we propose a novel second-order computational homogenization framework for flexoelectricity, which combines isogeometric analysis and the finite cell method. Key innovations include the introduction of high-order periodic boundary conditions and homogenized high-order stresses, which ensure consistent multiscale analysis. Periodic boundary conditions are applied using penalty methods, and perturbation analysis is employed to efficiently compute equivalent material coefficients. The effectiveness of the proposed method is validated through numerical examples, demonstrating its ability to generate piezoelectric effects in flexoelectric microstructured materials.",
keywords = "Finite cell method, Flexoelectricity, Isogeometric analysis, Perturbation analysis, Second-order homogenization",
author = "Bin Li and Ranran Zhang and {\.Z}ur, {Krzysztof Kamil} and Timon Rabczuk and Xiaoying Zhuang",
note = "Publisher Copyright: {\textcopyright} 2025",
year = "2025",
month = jul,
day = "1",
doi = "10.1016/j.cma.2025.118031",
language = "English",
volume = "442",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier BV",
}

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