Computational Modeling of Flexoelectricity—A Review

Xiaoying Zhuang, Binh Huy Nguyen, Subbiah Srivilliputtur Nanthakumar, Thai Quoc Tran, Naif Alajlan and Timon Rabczuk
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Xiaoying Zhuang: Division of Computational Mechanics, 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

Energies, 2020, vol. 13, issue 6, 1-29

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.

Keywords: flexoelectricity; numerical methods; modeling (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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