Flexoelectric effect is a universal and size-dependent electromechanical coupling between the strain gradient and electric field. The mathematical framework for flexoelectricity, which involves higher-order gradients of field quantities, is difficult to handle using traditional finite element method (FEM). Thus, it is important to develop an effective numerical method for flexoelectricity. In this paper, we develop a three-dimensional (3D) mixed finite element considering both flexoelectricity and strain gradient elasticity. To validate the developed element, we simulate the electromechanical behavior of a flexoelectric spherical shell subjected to inner pressure and compare the numerical results to analytical results. Their excellent agreement shows the reliability of the proposed FEM. The developed finite element is also used to simulate the electromechanical behavior of a nanometer-sized flexoelectric truncated pyramid. By decreasing the sample size, we observed the increase of its effective piezoelectricity. However, due to the effects of strain gradient elasticity and the influence of flexoelectricity on stiffness, the dependency of effective piezoelectricity on the sample size is not trivial. Numerical results indicate that, when the sample size is smaller than a certain value, the increase of effective piezoelectricity slows down. This finding also shows the importance of a numerical tool for the study of flexoelectric problems.
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March 2018
Research-Article
A Three-Dimensional Mixed Finite Element for Flexoelectricity
Feng Deng,
Feng Deng
State Key Laboratory for Strength and Vibration
of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
Search for other works by this author on:
Qian Deng,
Qian Deng
State Key Laboratory for Strength and
Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tonydqian@mail.xjtu.edu.cn
Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tonydqian@mail.xjtu.edu.cn
Search for other works by this author on:
Shengping Shen
Shengping Shen
State Key Laboratory for Strength
and Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn
and Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn
Search for other works by this author on:
Feng Deng
State Key Laboratory for Strength and Vibration
of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
Qian Deng
State Key Laboratory for Strength and
Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tonydqian@mail.xjtu.edu.cn
Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tonydqian@mail.xjtu.edu.cn
Shengping Shen
State Key Laboratory for Strength
and Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn
and Vibration of Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn
1Corresponding authors.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 17, 2017; final manuscript received December 30, 2017; published online January 24, 2018. Editor: Yonggang Huang.
J. Appl. Mech. Mar 2018, 85(3): 031009 (10 pages)
Published Online: January 24, 2018
Article history
Received:
November 17, 2017
Revised:
December 30, 2017
Citation
Deng, F., Deng, Q., and Shen, S. (January 24, 2018). "A Three-Dimensional Mixed Finite Element for Flexoelectricity." ASME. J. Appl. Mech. March 2018; 85(3): 031009. https://doi.org/10.1115/1.4038919
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