Constitutive Relationship

If a voltage is applied in the direction of poling electric field, the material elongates in that direction. The opposite effect is also present. On applying mechanical strain in the direction of poling electric field, a charge separation across the material (which is a dielectric) produces a voltage.

The constitutive equations for a piezoelectric material are

Actuation equation

(11.1)

                                                                                                           
Sensing equation 

(11.2)

Where  ε is mechanical strain,   σ is mechanical stress, S is the compliance at constant electric field,  d is the electro-mechanical coupling constant, E is electric field,  D is the electrical displacement (charge density),  is the dielectric constant of the piezoelectric material at constant stress. Without the piezoelectric coupling term, Equation 11.1 is simply Hooke’s law. Likewise, without the coupling term,, Equation 11.2 is simply the dielectric equation or a form of Gauss’ law for electricity. The piezoelectric coupling provides the medium for energy conservation. The electric field across the material affects its mechanics and the stress in the material affects its dielectric properties.

Piezoelectric materials are widely used as sensors in different environments. Lead Zirconate Titanate (commonly known as PZT) is the most prominent piezoelectric material as it could operate at a much higher temperature and possesses stronger piezoelectric effect relative to ferroelectric ceramics of other compositions.

Polystrene, polyvinylidene fluoride (PVDF), vinyl acetate and polyproplyene etc. are some polymers which show piezoelectric effect. Among them, PVDF shows strongest piezoelectricity. It refers to a class of materials based on the vinylidene fluoride monomer [-CF₂=CH₂-]. PVDF is the most popular piezoelectric polymer material for impact sensors. The present day development in smart structural technology is mainly centered around these two materials.