Direct piezoelectric effect

Linear electrical-displacement response to mechanical stress in a suitable piezoelectric material. It is distinct from the converse effect, in which an applied electric field causes strain. The measured voltage also depends on electrical loading and mechanical constraints.

For electrically isolated electrodes with unchanged free charge, the increment of normal electric displacement field is approximately zero. A constitutive relation such as $D_3=d_{31}({\sigma }_1+{\sigma }_2)+ϵE_3$ then gives an induced field that balances stress-induced displacement. Finite leakage and input capacitance modify the voltage response.

A tensor coefficient relating an increment of electrical displacement to stress, or the corresponding converse strain response to electric field, under stated constitutive conventions. Charge-per-force units $\mathrm{C}{\mathrm{N}}^{-1}$ are equivalent to displacement-per-voltage units $\mathrm{m}{\mathrm{V}}^{-1}$ for the usual $d$ coefficients.