Voltage vs thickness of Piezo

Hi,

I am trying to see the variation of voltage generated by a free piezo with varying thickness of piezo, under given strain.

I expect the variation to be linearly proportional, I am attaching the equations (Voltage_Vs_Thickness.png file, available at C:\Program Files\COMSOL\COMSOL43b\doc\pdf\MEMS_Module\MEMSModuleUsersGuide) used by COMSOl and supporting calculations (calculations.jpg file) required further.

I modelled the free PZT and swept the thickness of piezo (study 3) but unfortunately the behavior is coming otherwise.

Please clarify.

Thank you in advance.

Regards,
Naveet.