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Computational Modeling of Flexoelectricity—A Review

Author

Listed:
  • Xiaoying Zhuang

    (Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
    Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam)

  • Binh Huy Nguyen

    (Institute for Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany)

  • Subbiah Srivilliputtur Nanthakumar

    (Institute for Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany)

  • Thai Quoc Tran

    (Institute for Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany)

  • Naif Alajlan

    (Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia)

  • Timon Rabczuk

    (Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia)

Abstract

Electromechanical coupling devices have been playing an indispensable role in modern engineering. Particularly, flexoelectricity, an electromechanical coupling effect that involves strain gradients, has shown promising potential for future miniaturized electromechanical coupling devices. Therefore, simulation of flexoelectricity is necessary and inevitable. In this paper, we provide an overview of numerical procedures on modeling flexoelectricity. Specifically, we summarize a generalized formulation including the electrostatic stress tensor, which can be simplified to retrieve other formulations from the literature. We further show the weak and discretization forms of the boundary value problem for different numerical methods, including isogeometric analysis and mixed FEM. Several benchmark problems are presented to demonstrate the numerical implementation. The source code for the implementation can be utilized to analyze and develop more complex flexoelectric nano-devices.

Suggested Citation

  • Xiaoying Zhuang & Binh Huy Nguyen & Subbiah Srivilliputtur Nanthakumar & Thai Quoc Tran & Naif Alajlan & Timon Rabczuk, 2020. "Computational Modeling of Flexoelectricity—A Review," Energies, MDPI, vol. 13(6), pages 1-29, March.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:6:p:1326-:d:331747
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    References listed on IDEAS

    as
    1. Amir Abdollahi & Neus Domingo & Irene Arias & Gustau Catalan, 2019. "Converse flexoelectricity yields large piezoresponse force microscopy signals in non-piezoelectric materials," Nature Communications, Nature, vol. 10(1), pages 1-6, December.
    2. Bo He & Brahmanandam Javvaji & Xiaoying Zhuang, 2019. "Characterizing Flexoelectricity in Composite Material Using the Element-Free Galerkin Method," Energies, MDPI, vol. 12(2), pages 1-18, January.
    3. Nguyen, Vinh Phu & Anitescu, Cosmin & Bordas, Stéphane P.A. & Rabczuk, Timon, 2015. "Isogeometric analysis: An overview and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 89-116.
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