Details
| Original language | English |
|---|---|
| Pages (from-to) | 718-739 |
| Number of pages | 22 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 341 |
| Early online date | 31 May 2018 |
| Publication status | Published - 1 Nov 2018 |
Abstract
We propose an isogeometric approach for flexoelectricity in soft dielectric materials at finite deformations accounting for Maxwell stresses on the surface between two different media. In contrast to piezoelectricity where there is a linear dependence between mechanical strain and electric polarization, in flexoelectricity the polarization is related to strain gradients which requires a C1 continuous finite element framework. In electro-mechanical materials, the Maxwell stress emerges as a consequence of the coupling effect between electrostatics and mechanics. If a solid body is embedded in a surrounding medium such as air or vacuum, the Maxwell stress acting on the surfaces governs the interaction between electric fields and deformable media. This is quite difficult to handle due to the surface discontinuity and the traction electrical forces still have to satisfy some certain continuity conditions, hence an appropriate numerical framework is required for the treatment. Here, we employed Non-Uniform Rational B-spline (NURBS) functions with knot insertion technique in order to introduce discontinuities across material interfaces while still maintaining C1 continuity in the domain to evaluate the coupling effect of strain gradient and electric polarization in the regime of finite deformation. The accuracy and robustness of our IGA approach for flexoelectric soft materials are demonstrated in some benchmark numerical examples.
Keywords
- Finite deformation, Flexoelectricity, IGA - C continuity, Maxwell stress, Soft dielectric
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 341, 01.11.2018, p. 718-739.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A large deformation isogeometric approach for flexoelectricity and soft materials
AU - Thai, Tran Quoc
AU - Rabczuk, Timon
AU - Zhuang, Xiaoying
N1 - Funding information: The author would like to acknowledge the financial support from the Sofja Kovalevskaja Prize of the Alexander von Humboldt Foundation (Germany) .
PY - 2018/11/1
Y1 - 2018/11/1
N2 - We propose an isogeometric approach for flexoelectricity in soft dielectric materials at finite deformations accounting for Maxwell stresses on the surface between two different media. In contrast to piezoelectricity where there is a linear dependence between mechanical strain and electric polarization, in flexoelectricity the polarization is related to strain gradients which requires a C1 continuous finite element framework. In electro-mechanical materials, the Maxwell stress emerges as a consequence of the coupling effect between electrostatics and mechanics. If a solid body is embedded in a surrounding medium such as air or vacuum, the Maxwell stress acting on the surfaces governs the interaction between electric fields and deformable media. This is quite difficult to handle due to the surface discontinuity and the traction electrical forces still have to satisfy some certain continuity conditions, hence an appropriate numerical framework is required for the treatment. Here, we employed Non-Uniform Rational B-spline (NURBS) functions with knot insertion technique in order to introduce discontinuities across material interfaces while still maintaining C1 continuity in the domain to evaluate the coupling effect of strain gradient and electric polarization in the regime of finite deformation. The accuracy and robustness of our IGA approach for flexoelectric soft materials are demonstrated in some benchmark numerical examples.
AB - We propose an isogeometric approach for flexoelectricity in soft dielectric materials at finite deformations accounting for Maxwell stresses on the surface between two different media. In contrast to piezoelectricity where there is a linear dependence between mechanical strain and electric polarization, in flexoelectricity the polarization is related to strain gradients which requires a C1 continuous finite element framework. In electro-mechanical materials, the Maxwell stress emerges as a consequence of the coupling effect between electrostatics and mechanics. If a solid body is embedded in a surrounding medium such as air or vacuum, the Maxwell stress acting on the surfaces governs the interaction between electric fields and deformable media. This is quite difficult to handle due to the surface discontinuity and the traction electrical forces still have to satisfy some certain continuity conditions, hence an appropriate numerical framework is required for the treatment. Here, we employed Non-Uniform Rational B-spline (NURBS) functions with knot insertion technique in order to introduce discontinuities across material interfaces while still maintaining C1 continuity in the domain to evaluate the coupling effect of strain gradient and electric polarization in the regime of finite deformation. The accuracy and robustness of our IGA approach for flexoelectric soft materials are demonstrated in some benchmark numerical examples.
KW - Finite deformation
KW - Flexoelectricity
KW - IGA - C continuity
KW - Maxwell stress
KW - Soft dielectric
UR - http://www.scopus.com/inward/record.url?scp=85050655262&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.05.019
DO - 10.1016/j.cma.2018.05.019
M3 - Article
AN - SCOPUS:85050655262
VL - 341
SP - 718
EP - 739
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -