Variationally consistent Maxwell stress in flexoelectric structures under finite deformation and immersed in free space

authored by: Xiaoying Zhuang, Han Hu, S. S. Nanthakumar, Quoc Thai Tran, Yanpeng Gong, Timon Rabczuk
Abstract: Maxwell stress refers to the mechanical stress exerted on a dielectric material due to the presence of electric fields. It plays a significant role in the interaction between a dielectric material and the surrounding free space under finite deformation. Previous research on finite deformation of flexoelectricity mainly adopted a modified form of Maxwell stress, potentially not able to correctly capture some physical phenomena, such as the compression of a dielectric droplet in an electric field. In this work, we propose a consistent and complete variational principle for flexoelectricity, in which the Maxwell stress emerges naturally from the derivation, without introducing additional assumptions. An Isogeometric analysis-based numerical framework is developed accordingly and verified by both linear and nonlinear benchmark cases compared with experimental results. The present framework successfully captures and quantifies the behaviors of conductive liquids and soft dielectric solids subjected to an external electric field. Finally, a novel scenario is investigated in which a flexoelectric beam immersed in free space is analyzed, showing the interesting distribution of Maxwell stress-induced tractions at opposing boundaries. The test demonstrates that a higher dielectric constant can effectively enhance the material's stiffness in response to the external electric loading.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Los Alamos National Laboratory
Beijing University of Technology
Bauhaus-Universität Weimar
Type: Article
Journal: Applied mathematical modelling
Volume: 150
ISSN: 0307-904X
Publication date: 31.07.2025
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.apm.2025.116327 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{ed221b38f92643d19765b878334d910c,
title = "Variationally consistent Maxwell stress in flexoelectric structures under finite deformation and immersed in free space",
abstract = "Maxwell stress refers to the mechanical stress exerted on a dielectric material due to the presence of electric fields. It plays a significant role in the interaction between a dielectric material and the surrounding free space under finite deformation. Previous research on finite deformation of flexoelectricity mainly adopted a modified form of Maxwell stress, potentially not able to correctly capture some physical phenomena, such as the compression of a dielectric droplet in an electric field. In this work, we propose a consistent and complete variational principle for flexoelectricity, in which the Maxwell stress emerges naturally from the derivation, without introducing additional assumptions. An Isogeometric analysis-based numerical framework is developed accordingly and verified by both linear and nonlinear benchmark cases compared with experimental results. The present framework successfully captures and quantifies the behaviors of conductive liquids and soft dielectric solids subjected to an external electric field. Finally, a novel scenario is investigated in which a flexoelectric beam immersed in free space is analyzed, showing the interesting distribution of Maxwell stress-induced tractions at opposing boundaries. The test demonstrates that a higher dielectric constant can effectively enhance the material's stiffness in response to the external electric loading.",
keywords = "Bursting drop, Finite deformation, Flexoelectricity, Free space, Isogeometric analysis, Maxwell stress",
author = "Xiaoying Zhuang and Han Hu and Nanthakumar, {S. S.} and Tran, {Quoc Thai} and Yanpeng Gong and Timon Rabczuk",
note = "Publisher Copyright: {\textcopyright} 2025",
year = "2025",
month = jul,
day = "31",
doi = "10.1016/j.apm.2025.116327",
language = "English",
volume = "150",
journal = "Applied mathematical modelling",
issn = "0307-904X",
publisher = "Elsevier Inc.",
}

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