A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

Y. L. Qu, G. Y. Zhang, Y. M. Fan, F. Jin

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

Original languageEnglish
Pages (from-to)1647-1659
Number of pages13
JournalMathematics and Mechanics of Solids
Volume26
Issue number11
DOIs
StatePublished - Nov 2021
Externally publishedYes

Keywords

  • couple stress theory
  • electric field gradient theory
  • flexoelectric effect
  • microstructure effect
  • Piezoelectric theory
  • quadrupole effect

Fingerprint

Dive into the research topics of 'A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory'. Together they form a unique fingerprint.

Cite this