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: | ||

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. |