Get 20M+ Full-Text Papers For Less Than $1.50/day. Subscribe now for You or Your Team.

Learn More →

The J-integral in flexoelectric solids

The J-integral in flexoelectric solids The flexoelectric effect is a significant electromechanical coupling phenomenon between strain gradients and electric polarization. Since the design of materials with high flexoelectricity should be accompanied with stress concentration/intensity, the strength and fracture analysis of flexoelectric materials with large strain gradients is desired. The famous J-integral can be used to characterize the singularity at crack tips and predict the fracture behavior of flexoelectric solids. However, the definition of J-integral in flexoelectric solids is lacked or incomplete in the open literature. In this study, an explicit expression of J-integral associated with material configurational forces is derived from the gradient operation of electric enthalpy density function for centrosymmetric flexoelectric solids, where the electric enthalpy density depends not only on the strain and strain gradient, but also on the polarization and polarization gradient. The path-independence of J-integral in flexoelectric solids is also examined through the Gauss–Green’s theorem. Then the derived J-integral is applied to study a cylindrical cavity and a mode III crack problem in flexoelectric solids. The results indicate that, in flexoelectric solids, there is a conservation law of the J-integral. That is, the J-integral defined in a global coordinate system vanishes when the integration contour chosen to calculate the J-integral encloses whole cavity. The present complete expression of J-integral in flexoelectric solids is addressed from the self-consistent theory of flexoelectricity. It corrects the inaccurate definition of J-integral in the previous literature. The J-integral obtained in this paper will provide a useful way to study fracture problems in flexoelectric solids. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Fracture Springer Journals

The J-integral in flexoelectric solids

Loading next page...
 
/lp/springer-journals/the-j-integral-in-flexoelectric-solids-uS9R0zmJaY

References (52)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature B.V.
Subject
Materials Science; Characterization and Evaluation of Materials; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering
ISSN
0376-9429
eISSN
1573-2673
DOI
10.1007/s10704-018-0331-6
Publisher site
See Article on Publisher Site

Abstract

The flexoelectric effect is a significant electromechanical coupling phenomenon between strain gradients and electric polarization. Since the design of materials with high flexoelectricity should be accompanied with stress concentration/intensity, the strength and fracture analysis of flexoelectric materials with large strain gradients is desired. The famous J-integral can be used to characterize the singularity at crack tips and predict the fracture behavior of flexoelectric solids. However, the definition of J-integral in flexoelectric solids is lacked or incomplete in the open literature. In this study, an explicit expression of J-integral associated with material configurational forces is derived from the gradient operation of electric enthalpy density function for centrosymmetric flexoelectric solids, where the electric enthalpy density depends not only on the strain and strain gradient, but also on the polarization and polarization gradient. The path-independence of J-integral in flexoelectric solids is also examined through the Gauss–Green’s theorem. Then the derived J-integral is applied to study a cylindrical cavity and a mode III crack problem in flexoelectric solids. The results indicate that, in flexoelectric solids, there is a conservation law of the J-integral. That is, the J-integral defined in a global coordinate system vanishes when the integration contour chosen to calculate the J-integral encloses whole cavity. The present complete expression of J-integral in flexoelectric solids is addressed from the self-consistent theory of flexoelectricity. It corrects the inaccurate definition of J-integral in the previous literature. The J-integral obtained in this paper will provide a useful way to study fracture problems in flexoelectric solids.

Journal

International Journal of FractureSpringer Journals

Published: Nov 15, 2018

There are no references for this article.