The four possible forms for piezoelectric constitutive equations are shown below.
The names for each of the forms is arbitrary; they were taken from the two dependent
variables on the left-hand-side of each equation. Note that the Voltage and Electric Field
variables are related via a gradient.

Strain-Charge Form:

Stress-Charge Form:

Strain-Voltage Form:

Stress-Voltage Form:

Transformations

Matrix transformations for converting piezoelectric constitutive data from one form into another
form are shown below. Only 4 out of the 6 possible combinations are shown.

Strain-Charge to Stress-Charge:

Strain-Charge to Strain-Voltage:

Stress-Charge to Stress-Voltage:

Strain-Voltage to Stress-Voltage:

See the Symbol Definition page for the units and dimensions
of the constitutive matrices shown here.

See Subscript Definitions for an explanation
to the subscripts on the constitutive matrices.