# MAT2PT

Bulk Data Entry Defines anisotropic permittivity and damping for dielectric materials

Note: This can be used along with the MATPZO Bulk Data Entry for defining piezoelectric coupling.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT2PT MID PMTVXX     PMTVYY   PMTVZZ DAMP
FLAG1 FLAG2

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT2PT 17 0.1     1.5   0.01
STRSCHG RELATIVE

## Definitions

Field Contents SI Unit Example
MID Unique material identification number.

No default (Integer > 0)

PMTVXX Defines the permittivity along the X direction.

No default (Real > 0.0)

PMTVYY Defines the permittivity along the Y direction.

Default = PMTVXX (Real > 0.0)

PMTVZZ Defines the permittivity along the Z direction.

Default = PMTVXX (Real > 0.0)

DAMP Damping term corresponding to the static electrical part.

Default = 1.0 (Real ≥ 0.0 and ≤ 1.0)

FLAG1 Flag to indicate the form of PMTVij coefficients.
STRNCHG (Default)
Indicates STRAIN-CHARGE form
STRSCHG
Indicates STRESS-CHARGE form

FLAG2 Flag to indicate type of permittivity.
ABSOLUTE (Default)
Absolute permittivity
RELATIVE
Relative permittivity
In this case, vacuum permittivity also needs to be provided by PARAM, VAPMTV.

1. 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).
2. MAT2PT is supported only for solid elements.
3. The electrical permittivity matrix has the following form:(1)
$\left[{\epsilon }_{S}\right]=\left[\begin{array}{ccc}{\epsilon }_{xx}& 0& 0\\ 0& {\epsilon }_{yy}& 0\\ 0& 0& {\epsilon }_{zz}\end{array}\right]=\left[\begin{array}{ccc}{\epsilon }_{0}{\epsilon }_{rxx}& 0& 0\\ 0& {\epsilon }_{0}{\epsilon }_{ryy}& 0\\ 0& 0& {\epsilon }_{0}{\epsilon }_{rzz}\end{array}\right]$
Where,
${\epsilon }_{0}$
Vacuum permittivity
${\epsilon }_{rxx}$
Relative permittivity defined by PMTVXX
${\epsilon }_{ryy}$
Relative permittivity defined by PMTVYY
${\epsilon }_{rzz}$
Relative permittivity defined by PMTVZZ
When FLAG=STRNCHG, the electrical permittivity matrix is expressed as:(2)
$\left[{\epsilon }_{T}\right]=\left[\begin{array}{ccc}{\epsilon }_{0}{\epsilon }_{rxx}& 0& 0\\ 0& {\epsilon }_{0}{\epsilon }_{ryy}& 0\\ 0& 0& {\epsilon }_{0}{\epsilon }_{rzz}\end{array}\right]$
The $\left[{\epsilon }_{T}\right]$ matrix is converted to the $\left[{\epsilon }_{S}\right]$ matrix by:(3)
${\epsilon }_{S}={\epsilon }_{T}-d{c}_{E}{d}^{T}$
Where,
${c}_{E}$
Elastic matrix
$d$
Piezoelectric coupling matrix defined in MATPZO
4. For more information, refer to Piezoelectric Analysis in the User Guide.