Details
| Original language | English |
|---|---|
| Article number | 111170 |
| Journal | International Journal of Mechanical Sciences |
| Volume | 313 |
| Early online date | 12 Jan 2026 |
| Publication status | Published - 1 Mar 2026 |
Abstract
The distribution and propagation of cracks play a critical role in the design, fabrication, and optimization of high-sensitivity flexoelectric materials. Despite significant progress, the elucidation of the flexoelectric fracture mechanism remains an unresolved and challenging issue. In this study, a novel phase-field model addressing electromechanical fracture in both piezoelectric and flexoelectric materials is developed. Gradient elasticity and flexoelectricity are incorporated into the phase-field theory, with governing equations derived in the framework of thermodynamics. In light of the stress projection and the energetic failure criterion, the unsymmetric electromechanical fracture behavior can be reproduced. Different energy degradation strategies are introduced to account for the energy contributions from strain and strain gradients, enabling the accurate simulation of fractures influenced by flexoelectricity. Compared with conventional fracture models, this model reproduces the flexoelectric crack-tip effect during crack propagation for the first time. We performed numerical simulations of the crack evolution process in various flexoelectric materials and structures. The findings indicate that the gradient and flexoelectric effects can hinder the failure of solids for tensile fracture. Meanwhile, flexoelectricity can promote crack deflection toward the direction of the local electric field around the crack tip. Moreover, crack growth under mechanical loading is consistently accompanied by a continuous increase in the efficiency of energy conversion from mechanical to electrical form. However, excessive crack propagation weakens the capacity for dielectric energy storage in the material. This model not only provides a new perspective for the optimal design of efficient flexoelectric structures, but also offers a new framework for investigating the fracture behavior of electro-mechanical coupling materials with size effects.
Keywords
- Electromechanical fracture, Energy conversion, Flexoelectric effect, Gradient elasticity, Phase-field model
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Materials Science(all)
- General Materials Science
- Engineering(all)
- Aerospace Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Mechanical Sciences, Vol. 313, 111170, 01.03.2026.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A phase-field fracture model for flexoelectric structures
AU - Yue, Qiang
AU - Zhuang, Xiaoying
AU - Li, Bin
AU - Areias, Pedro
AU - Żur, Krzysztof Kamil
AU - Rabczuk, Timon
N1 - Publisher Copyright: © 2026
PY - 2026/3/1
Y1 - 2026/3/1
N2 - The distribution and propagation of cracks play a critical role in the design, fabrication, and optimization of high-sensitivity flexoelectric materials. Despite significant progress, the elucidation of the flexoelectric fracture mechanism remains an unresolved and challenging issue. In this study, a novel phase-field model addressing electromechanical fracture in both piezoelectric and flexoelectric materials is developed. Gradient elasticity and flexoelectricity are incorporated into the phase-field theory, with governing equations derived in the framework of thermodynamics. In light of the stress projection and the energetic failure criterion, the unsymmetric electromechanical fracture behavior can be reproduced. Different energy degradation strategies are introduced to account for the energy contributions from strain and strain gradients, enabling the accurate simulation of fractures influenced by flexoelectricity. Compared with conventional fracture models, this model reproduces the flexoelectric crack-tip effect during crack propagation for the first time. We performed numerical simulations of the crack evolution process in various flexoelectric materials and structures. The findings indicate that the gradient and flexoelectric effects can hinder the failure of solids for tensile fracture. Meanwhile, flexoelectricity can promote crack deflection toward the direction of the local electric field around the crack tip. Moreover, crack growth under mechanical loading is consistently accompanied by a continuous increase in the efficiency of energy conversion from mechanical to electrical form. However, excessive crack propagation weakens the capacity for dielectric energy storage in the material. This model not only provides a new perspective for the optimal design of efficient flexoelectric structures, but also offers a new framework for investigating the fracture behavior of electro-mechanical coupling materials with size effects.
AB - The distribution and propagation of cracks play a critical role in the design, fabrication, and optimization of high-sensitivity flexoelectric materials. Despite significant progress, the elucidation of the flexoelectric fracture mechanism remains an unresolved and challenging issue. In this study, a novel phase-field model addressing electromechanical fracture in both piezoelectric and flexoelectric materials is developed. Gradient elasticity and flexoelectricity are incorporated into the phase-field theory, with governing equations derived in the framework of thermodynamics. In light of the stress projection and the energetic failure criterion, the unsymmetric electromechanical fracture behavior can be reproduced. Different energy degradation strategies are introduced to account for the energy contributions from strain and strain gradients, enabling the accurate simulation of fractures influenced by flexoelectricity. Compared with conventional fracture models, this model reproduces the flexoelectric crack-tip effect during crack propagation for the first time. We performed numerical simulations of the crack evolution process in various flexoelectric materials and structures. The findings indicate that the gradient and flexoelectric effects can hinder the failure of solids for tensile fracture. Meanwhile, flexoelectricity can promote crack deflection toward the direction of the local electric field around the crack tip. Moreover, crack growth under mechanical loading is consistently accompanied by a continuous increase in the efficiency of energy conversion from mechanical to electrical form. However, excessive crack propagation weakens the capacity for dielectric energy storage in the material. This model not only provides a new perspective for the optimal design of efficient flexoelectric structures, but also offers a new framework for investigating the fracture behavior of electro-mechanical coupling materials with size effects.
KW - Electromechanical fracture
KW - Energy conversion
KW - Flexoelectric effect
KW - Gradient elasticity
KW - Phase-field model
UR - http://www.scopus.com/inward/record.url?scp=105028024239&partnerID=8YFLogxK
U2 - 10.1016/j.ijmecsci.2026.111170
DO - 10.1016/j.ijmecsci.2026.111170
M3 - Article
AN - SCOPUS:105028024239
VL - 313
JO - International Journal of Mechanical Sciences
JF - International Journal of Mechanical Sciences
SN - 0020-7403
M1 - 111170
ER -