The piezoelectric constitutive law is defined by the two equations:

$$S=s T+dE\\ D=d T+\epsilon E$$

$S$: Strain. $T$: Stress. $E$: Electric field. $D$: electric charge-density displacement. $\epsilon$: Permittivity (evaluated at constant stress). $d$: piezoelectric strain constant. $s$: Elastic compliance (evaluated at constant electric field).

Apart from that we have the expression:


$g$ is piezoelectric voltage constant (or open-circuit constant).

For a piezoelectric material we can look up $g$, $d$, $\epsilon$ and $s$ in data tables, and let's assume that all other material data can be found likewise if needed. I also know the physical lenght/height $L$ of my material bulk. If I calculate the electric field generated at a certain applied stress $T$, then I can use that $E$ to find the voltage over the material piece:


BUT I am stuck trying to calculate the $E$. I feel that I do not know $D$ and $S$ in the above equations. I am even unsure of exactly what the $E$ in those equations is - isn't it the generated electric field?

Thank you in advance and good day.

  • $\begingroup$ I assume you have looked here? $\endgroup$ May 19, 2015 at 9:44
  • $\begingroup$ @honeste_vivere Sure. It doesn't explain or give an example of an actual calculation. For example a quote from the wikipedia page: a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500 V - how is this calculation performed? How is electric field found to calculate the voltage? $\endgroup$
    – Steeven
    May 19, 2015 at 10:52
  • $\begingroup$ I just sent the link because it defined the variables in the equations you showed and you asked for the definition of E. $\endgroup$ May 20, 2015 at 18:56

1 Answer 1


If the material is not connected to a circuit and doesn't have any external charges added then $D =0$ so you can use $$ D= dT + \epsilon E = 0 $$ along with the known stress $T$ to obtain $E$. Then use $V=EL$ to obtain the voltage $V$.

Here's a screenshot from Learnpiezo.org video series Lecture 3 Part F which covers the situation you described.

enter image description here


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