content_image/356739.jpg content_image/356745.jpg content_image/356746.jpg
<img src='content_image/356739.jpg'>

where W is an energy density of deformation and polarization, a$_{ij}$ , b$_{ijkl}$ , c$_{ijkl}$ , d$_{ijk}$ , e$_{ijkl}$ , f$_{ijkl}$ , g$_{ijk}$ are the components of reciprocal dielectric susceptibility, polarization gradient- polarization gradient coupling tensor, elastic tensor, piezoelectric tensor, polarization gradient-strain coupling tensor, flexoelectric tensor, and polarization-polarization gradient coupling tensor, respectively, ϕ is the potential of electric field. 

Since the components of the stress tensor and the electric field vector E$_{i}$ = − ϕ ′ i are expressed as 

we have 

<img src='content_image/356745.jpg'>

<img src='content_image/356746.jpg'>

Compare (1), (2), and the second equation of (5), we conclude that flexoelectric tensor f$_{ijkl}$ 

