MATPZO

Bulk Data Entry Defines the coupling terms between structural and dielectric materials for defining a piezoelectric coupling.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
MATPZO	`MID`	`PIEZO11`	`PIEZO12`	`PIEZO13`	`PIEZO14`	`PIEZO15`	`PIEZO16`	`FLAG`
		`PIEZO21`	`PIEZO22`	`PIEZO23`	`PIEZO24`	`PIEZO25`	`PIEZO26`
		`PIEZO31`	`PIEZO32`	`PIEZO33`	`PIEZO34`	`PIEZO35`	`PIEZO36`
	`DAMP`	`DPZO11`	`DPZO12`	`DPZO13`	`DPZO15`	`DPZO15`	`DPZO16`
		`DPZO21`	`DPZO22`	`DPZO23`	`DPZO25`	`DPZO25`	`DPZO26`
		`DPZO31`	`DPZO32`	`DPZO33`	`DPZO35`	`DPZO35`	`DPZO36`

Example

(1)	(2)	(3)	(4)	(5)	(6)	(8)	(9)
MATPZO	1	0.1			1.5	0.01	STRS
			0.01
				0.02

Definitions

Field	Contents	SI Unit Example
`MID`	Unique material identification number. No default (Integer > 0)
`PIEZOij`	Coupling terms for the piezoelectric material where `i` and `j` denote coordinate axes. 1 Default = 0.0 (Real)
`FLAG`	Flag to indicate the form of the coupling terms (`PIEZOij`). STRSCHG (Default) Stress-charge form STRNCHG Strain-charge form
`DAMP`	Flag to indicate the damping coefficients for piezoelectric coupling terms.
`DPZOij`	Coupling terms for the piezoelectric damping where `i` and `j` denote coordinate axes. Default = 0.0 (Real)

Comments

Values in PIEZOij and DPZOij can be blank, but at least one non-zero value of PIEZOij and DPZOij must be defined for a MATPZO Bulk Data Entry.
The material identification number can be the shared with structural materials (MAT1, MAT2, MAT8, MAT9 or MGASK), thermal materials (MAT4, MAT5), or electrical materials (MAT1EC, MAT2EC) but must be unique with respect to other dielectric materials (MAT1PT, MAT2PT).
MATPZO is supported for solid elements only.
The formulation is as follows:
- When FLAG=STRSCHG, the piezoelectric material matrix has the following form:(1)
  $[\begin{matrix} c_{E} & e^{T} \\ e & - ε_{S} \end{matrix}]$
  (2)
  $[e] = [\begin{matrix} e_{11} & e_{12} & e_{13} & e_{14} & e_{15} & e_{16} \\ e_{21} & e_{22} & e_{23} & e_{24} & e_{25} & e_{26} \\ e_{31} & e_{32} & e_{33} & e_{34} & e_{35} & e_{36} \end{matrix}]$
- When FLAG=STRNCHG, the coefficients form the coupling matrix $[d]$ as:(3)
  $[d] = [\begin{matrix} d_{11} & d_{12} & d_{13} & d_{14} & d_{15} & d_{16} \\ d_{21} & d_{22} & d_{23} & d_{24} & d_{25} & d_{26} \\ d_{31} & d_{32} & d_{33} & d_{34} & d_{35} & d_{36} \end{matrix}]$
  The $[d]$ matrix is converted to the $[e]$ matrix by:(4)
  $e = d c_{E}$
Where,

$c_{E}$

Elastic material matrix

$ε_{S}$

Permittivity matrix defined by MAT1PT or MAT2PT

$e_{i j}$

Refers to the coupling terms ( $P I E Z O_{i j}$ ) when FLAG=STRSCHG

$d_{i j}$

Refers to the coupling terms ( $P I E Z O_{i j}$ ) when FLAG=STRNCHG
For more information, refer to Piezoelectric Analysis in the User Guide.