# MAT9

Bulk Data Entry Defines the material properties for linear, temperature-independent, and anisotropic materials for solid elements.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT9 MID G11 G12 G13 G14 G15 G16 G22
G23 G24 G25 G26 G33 G34 G35 G36
G44 G45 G46 G55 G56 G66 RHO A1
A2 A3 A4 A5 A6 TREF GE
MODULI MTIME
RAYL ALPHA BETA

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT9 17 6.2+3           6.2+3
6.2+3
5.1+3     5.1+3   5.1+3 3.2 6.5-6
6.5-6         125.

## Definitions

Field Contents SI Unit Example
MID Unique material identification.
Integer
Specifies an identification number for this material.
<String>
Specifies a user-defined string label for this material entry. 2

No default (Integer > 0 or <String>)

Gij The material property matrix.

No default (Real)

RHO Mass density. Used to automatically compute mass for all structural elements.

No default (Real)

Ai Thermal expansion coefficient vector.

No default (Real)

TREF Reference temperature for the calculation of thermal loads.

Default = blank (Real or blank)

GE Structural element damping coefficient. 8

No default (Real)

MODULI Continuation line flag for moduli temporal property. 9
MTIME Material temporal property. This field controls the interpretation of the input material property for viscoelasticity.
INSTANT
This material property is considered as the Instantaneous material input for viscoelasticity on the MATVE entry.
LONG (Default)
This material property is considered as the Long-term relaxed material input for viscoelasticity on the MATVE entry.

RAYL Continuation line flag for material-dependent Rayleigh damping.
ALPHA Material-dependent Rayleigh Damping coefficient for the mass matrix.

Default = blank (Real ≥ 0.0)

BETA Material-dependent Rayleigh Damping coefficient for the stiffness matrix.

Default = blank (Real ≥ 0.0)

1. The material identification number/string must be unique for all MAT1, MAT2, MAT8, MAT9OR and MAT9 entries.
2. String based labels allow for easier visual identification of materials, including when being referenced by other cards. (example, the MID field of properties). For more details, refer to String Label Based Input File in the Bulk Data Input File.
3. The convention for the Gij in fields 3 through 8 is represented by the matrix relationship.(1)
$\left\{\begin{array}{c}{\sigma }_{x}\\ {\sigma }_{y}\\ {\sigma }_{z}\\ {\tau }_{\mathit{xy}}\\ {\tau }_{\mathit{yz}}\\ {\tau }_{\mathit{zk}}\end{array}\right\}=\left[\begin{array}{cccccc}G11& G12& G13& G14& G15& G16\\ & G22& G23& G24& G25& G26\\ & & G33& G34& G35& G36\\ & & & G44& G45& G46\\ & \mathit{symmetric}& & & G55& G56\\ & & & & & G66\end{array}\right] \left(\left\{\begin{array}{c}{\epsilon }_{x}\\ {\epsilon }_{y}\\ {\epsilon }_{z}\\ {\gamma }_{\mathit{xy}}\\ {\gamma }_{\mathit{yz}}\\ {\gamma }_{\mathit{zx}}\end{array}\right\}-\left\{\begin{array}{c}A1\\ A2\\ A3\\ A4\\ A5\\ A6\end{array}\right\}\left(T-\mathit{TREF}\right)\right)$

The subscripts 1 to 6 refer to x, y, z, xy, yz, and zx of the material coordinate system defined by the CORDM field on the PSOLID entry.

4. Unlike the MAT1 entry, data from the MAT9 entry is used directly, without adjustment of equivalent E, G, or NU values.
5. If material data is specified with the Engineering Constants E1, E2, E3, NU12, NU13, NU23, G12, G23, and G13, use the MAT9OR data.
6. The last continuation is optional.
7. Long field format can be used.
8. To obtain the damping coefficient GE, multiply the critical damping ratio, $C/{C}_{0}$ by 2.0.
9. MODULI continuation line is only applicable when used together with the MATVE entry. Refer to MATVE which provides additional information on how this material input is interpreted.
10. This card is represented as a material in HyperMesh.