eFunda: Constitutive Transforms of Piezo Materials
engineering fundamentals Piezo: Constitutive Transforms
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All Constitutive Forms
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:
Constitutive Law: Strain-Charge Form Constitutive Law: Strain-Charge Form
Strain-Voltage Form: Stress-Voltage Form:
Constitutive Law: Strain-Voltage Form Constitutive Law: Stress-Voltage Form
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:
Transform: d to e Transform: d to g
Stress-Charge to Stress-Voltage: Strain-Voltage to Stress-Voltage:
Transform: e to q Transform: g to q
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.

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