d33 piezoelectric coefficient

Electromechanical properties of polarized piezoelectric materials 

Polarized piezoelectric materials are characterized by several coefficients and relationships.
In simplified form, the basic relationships between the electrical and elastic properties can be represented as follows:

D: electric flux density
d: piezoelectric charge coefficient
T: mechanical stress
εT : permittivity (for T = constant )
E electric field

S:mechanical strain
sE: Compliance or elasticity coefficient (for E = constant)


These relationships apply only to small electrical and mechanical amplitudes,
so-called small signal values. In this range, the relationships between
mechanical, elastic deformation S or stress T and electrical field E
or electrical flux density D are linear, and the values for the coefficients are constant.

Piezoelectric Charge Coefficient, Piezoelectric Deformation Coefficient, Piezo Modulus d

The piezo modulus is the ratio of induced electric charge to mechanical stress
or of achievable mechanical stress to electric field applied (T = constant).

For piezo actuators, the piezo modules is also referred to as deformation coefficient.
The unit of coefficient is usually pC/N (pico Colomb per Newton)

Example:

Strain produced per unit of applied electrical field in V/m or charge density in C/m2 per unit of pressure in N/m2, each in the polarization direction

reference:
PIceramic