Where the first term corresponds to the direct piezoelectric effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.
2.
Here, the flexoelectric coefficient, \ mu _ { ijkl }, is a fourth-rank polar tensor and d _ { ijk } is the coefficient corresponding to the direct piezoelectric effect.
3.
The reversible process in that materials exhibiting the direct piezoelectric effect ( the internal generation of electrical charge resulting from an applied mechanical force ) also exhibit the reverse piezoelectric effect ( the internal generation of a mechanical strain resulting from an applied electrical field ).
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