0
research-article

Mixed finite elements for flexoelectric solids

[+] Author and Article Information
Feng Deng

State Key Laboratory for Strength and Vibration of Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
dengfeng12399@stu.xjtu.edu.cn

Qian Deng

State Key Laboratory for Strength and Vibration of Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
tonydqian@mail.xjtu.edu.cn

WenShan Yu

State Key Laboratory for Strength and Vibration of Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
wenshan@mail.xjtu.edu.cn

Shengping Shen

State Key Laboratory for Strength and Vibration of Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
sshen@mail.xjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4036939 History: Received April 18, 2017; Revised May 24, 2017

Abstract

Flexoelectricity refers to the two-way coupling between strain gradients and the electric field in dielectric materials, and is universal compare to piezoelectricity which is restricted to dielectrics with noncentralsymmetric crystalline structure. Involving strain gradients makes the phenomenon of flexoelectricity size dependent and more desirable for nanoscale applications. However, strain gradients involve higher order spatial derivate of displacements and bring difficulties to the solution of flexoelectric problems. This dilemma impedes the application of such universal phenomenon in multiple fields, such as sensors, actuators and nanogenerators. In this study, we develop a mixed finite element method (FEM) for the study of problems with both strain gradient elasticity and flexoelectricity being taken into account. To use C0 continuous elements in mixed FEM, the kinematic relationship between displacement field and its gradient is enforced by Lagrangian multipliers. Besides, four types of 2D mixed finite elements are developed to study the flexoelectric effect. Verification as well as validation of the present mixed FEM is performed through comparing numerical results with analytical solutions for an infinite tube problem. Finally, mixed FEM is used to simulate the electromechanical behavior of a 2D block subjected to concentrated force or voltage. This study proves that the present mixed FEM is an effective tool to explore the electromechancial behaviors of materials with the consideration of flexoelectricity.

Copyright (c) 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In