Piezoelectric Constitutive Equation |

Piezoelectricity is described mathematically within a material's constitutive equation,
which defines how the piezoelectric material's stress (T),
strain (S),
charge-density displacement (D),
and electric field (E) interact.
The piezoelectric constitutive law (in Strain-Charge form) is: |

The matrix
d contains the
piezoelectric coefficients for the material, and it appears
twice in the constitutive equation (the superscript t stands for matrix-transpose).
For a more detailed explanation of the constitutive variables, see the Symbol Definition page. For more on constitutive equations, visit the Constitutive Background page. |

Other Forms |

The four state variables
(S,
T,
D, and
E)
can be rearranged to give an additional 3 forms for a piezoelectric constitutive equation.
Instead of the coupling matrix
d, they contain the coupling matrices
e,
g, or
q.
It is possible to transform piezo constitutive data in one form to another form.
Why are these transformations important? A leading motivation is that
vendors typically publish material data for
To view the 4 piezoelectric constitutive equations and their mutual transformations, visit the Constitutive Transform page. |