Open Access

ARTICLE

Electric Field Gradient Theory with Surface Effect for Nano-Dielectrics

Shuling Hu¹, Shengping Shen^1,2

1 MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an, Shaanxi 710049, P.R. China
2 Corresponding author. Tel & Fax: 86-29-82660977; E-mail: sshen@mail.xjtu.edu.cn

Computers, Materials & Continua 2009, 13(1), 63-88. https://doi.org/10.3970/cmc.2009.013.063

Abstract

The electric field gradient effect is very strong for nanoscale dielectrics. In addition, neither the surface effect nor electrostatic force can be ignored. In this paper, the electric Gibbs free energy variational principle for nanosized dielectrics is established with the strain/electric field gradient effects, as well as the effects of surface and electrostatic force. As regards the surface effects both the surface stress and surface polarization are considered. From this variational principle, the governing equations and the generalized electromechanical Young-Laplace equations, which take into account the effects of strain/electric field gradient, surface and electrostatic force, are derived. The generalized bulk and surface electrostatic stress are obtained from the variational principle naturally. The form are different from those derived from the flexoelectric theory. Based on the present theory, the size-dependent electromechanical phenomenon in nano-dielectrics can be predicted.

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Keywords

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