Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions.

World Pumps

Major news, innovation and real-life applications for pumps and ancillary equipment.

Wind Systems

Towers, turbines, gearboxes; processes for shaping and finishing component parts.

more free magazines
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
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:
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.