Details
| Original language | English |
|---|---|
| Article number | 116327 |
| Journal | Applied mathematical modelling |
| Volume | 150 |
| Early online date | 31 Jul 2025 |
| Publication status | Published - Feb 2026 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Applied mathematical modelling, Vol. 150, 116327, 02.2026.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variationally consistent Maxwell stress in flexoelectric structures under finite deformation and immersed in free space
AU - Zhuang, Xiaoying
AU - Hu, Han
AU - Nanthakumar, S. S.
AU - Tran, Quoc Thai
AU - Gong, Yanpeng
AU - Rabczuk, Timon
N1 - Publisher Copyright: © 2025
PY - 2026/2
Y1 - 2026/2
N2 - 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.
AB - 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.
KW - Bursting drop
KW - Finite deformation
KW - Flexoelectricity
KW - Free space
KW - Isogeometric analysis
KW - Maxwell stress
UR - http://www.scopus.com/inward/record.url?scp=105012594970&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2025.116327
DO - 10.1016/j.apm.2025.116327
M3 - Article
AN - SCOPUS:105012594970
VL - 150
JO - Applied mathematical modelling
JF - Applied mathematical modelling
SN - 0307-904X
M1 - 116327
ER -