Hi. You may find your answer in the following paper:

Article Investigating the behavior of smart thin beams with piezoele...

Adriaens, H.J.M.T.S.; De Koning, W.; Banning, R., "Modeling piezoelectric actuators," Mechatronics, IEEE/ASME Transactions on , vol.5, no.4, pp.331,341, Dec 2000

doi: 10.1109/3516.891044

Link to paper on IEEE Xplore

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=891044

Check this paper out

http://homepage.ntu.edu.tw/~yichung/power_harvesting_sms_2006.pdf

P=e*eo*V/(kt*d33*t)

P=pressure output, e=relative dielectric, eo=permittivity in vacuum, V= voltage applied, kt=coupling factor, d33=piezoelectric constant, t=thickness of piezoelectric layer

reference= https://www.amazon.com/Ultrasound-Piezoelectric-Physics-Engineers-Applications/dp/1793995389/ref=sr_1_3?keywords=henry+savage+piezoelectric&qid=1561056752&s=gateway&sr=8-3

Dear Sriphutkiat ,

Here is the formula I recently came to derive V=P/ne, where P is pressure, n number density of charges and e is the electron charge. If it works finely let me know.

Arbab

Here are the formulas you want (attached PDF).

Both forms no load and with load.

Yannapol Sriphutkiat, Henry Savage and A. I. Arbab

I have a piezo PZT pad (350nm thick and 20um diameter). I would like to measure the strain when the top and bottom are constrained. By constrained, I mean the bottom is fixed but the top side of the PZT is attached to a pillar which is flexible.

How do I calculate strain values in the case where the top side of PZT needs to push against some weight? I know the weight of the pillar. The sides of the piezo are free to move (no constraints). Please find the image of the structure I described.