*PIEZOELECTRIC

Optional parameters

DEPENDENCIES: Set this parameter equal to the number of field variables included in the definition of the piezoelectric properties. If this parameter is omitted, the piezoelectric properties are assumed not to depend on any field variables but may still depend on temperature. See Material Data Definition for more information.
TYPE: Set TYPE=S (default) to specify stress material coefficients for the piezoelectric property. Set TYPE=E to specify strain material coefficients for the piezoelectric property.

Data lines to define the piezoelectric stress coefficient matrix (TYPE=S)

First line

$e_{1 11}^{φ}$ . (Units of FL⁻¹ $φ$ ⁻¹.)
$e_{1 22}^{φ}$ .
$e_{1 33}^{φ}$ .
$e_{1 12}^{φ}$ .
$e_{1 13}^{φ}$ .
$e_{1 23}^{φ}$ .
$e_{2 11}^{φ}$ .
$e_{2 22}^{φ}$ .

Second line

$e_{2 33}^{φ}$ .
$e_{2 12}^{φ}$ .
$e_{2 13}^{φ}$ .
$e_{2 23}^{φ}$ .
$e_{3 11}^{φ}$ .
$e_{3 22}^{φ}$ .
$e_{3 33}^{φ}$ .
$e_{3 12}^{φ}$ .

Third line

$e_{3 13}^{φ}$ .
$e_{3 23}^{φ}$ .
Temperature, $θ$ .
First field variable.
Second field variable.
Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)

Sixth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the piezoelectric properties as a function of temperature and other predefined field variables.

Data lines to define the piezoelectric strain coefficient matrix (TYPE=E; for the shear components these coefficients relate the engineering, and not the tensorial, shear strain components to the components of the potential gradient vector)

First line

$d_{1 11}^{φ}$ . (Units of L $φ$ ⁻¹.)
$d_{1 22}^{φ}$ .
$d_{1 33}^{φ}$ .
$d_{1 12}^{φ}$ .
$d_{1 13}^{φ}$ .
$d_{1 23}^{φ}$ .
$d_{2 11}^{φ}$ .
$d_{2 22}^{φ}$ .

Second line

$d_{2 33}^{φ}$ .
$d_{2 12}^{φ}$ .
$d_{2 13}^{φ}$ .
$d_{2 23}^{φ}$ .
$d_{3 11}^{φ}$ .
$d_{3 22}^{φ}$ .
$d_{3 33}^{φ}$ .
$d_{3 12}^{φ}$ .

Third line

$d_{3 13}^{φ}$ .
$d_{3 23}^{φ}$ .
Temperature, $θ$ .
First field variable.
Second field variable.
Etc., up to five field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than five)

Sixth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the piezoelectric properties as a function of temperature and other predefined field variables.