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)
MAT9	`MID`	`G11`	`G12`	`G13`	`G14`	`G15`	`G16`	`G22`
	`G23`	`G24`	`G25`	`G26`	`G33`	`G34`	`G35`	`G36`
	`G44`	`G45`	`G46`	`G55`	`G56`	`G66`	`RHO`	`A`
	`A`	`A`	`A`	`A`	`A`	`TREF`	`GE`
	`MODULI`	`MTIME`
	`RAYL`	`ALPHA`	`BETA`

Example


(1)	(2)	(3)	(5)	(6)	(7)	(8)	(9)
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. 10 No default (Real)
`MODULI`	Continuation line flag for moduli temporal property. 11
`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)

Comments

The material identification number/string must be unique for all MAT1, MAT2, MAT8, MAT9OR and MAT9 entries.
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.
The mass density, RHO, is used to automatically compute mass for all structural elements.
The convention for the Gij in fields 3 through 8 is represented by the matrix relationship.
${\begin{matrix} σ_{x} \\ σ_{y} \\ σ_{z} \\ τ_{xy} \\ τ_{yz} \\ τ_{zk} \end{matrix}} = [\begin{matrix} G 11 & G 12 & G 13 & G 14 & G 15 & G 16 \\ G 22 & G 23 & G 24 & G 25 & G 26 \\ G 33 & G 34 & G 35 & G 36 \\ G 44 & G 45 & G 46 \\ symmetric & G 55 & G 56 \\ G 66 \end{matrix}] ({\begin{matrix} ε_{x} \\ ε_{y} \\ ε_{z} \\ γ_{xy} \\ γ_{yz} \\ γ_{zx} \end{matrix}} - {\begin{matrix} A 1 \\ A 2 \\ A 3 \\ A 4 \\ A 5 \\ A 6 \end{matrix}} (T - TREF))$
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.
Unlike the MAT1 entry, data from the MAT9 entry is used directly, without adjustment of equivalent E, G, or NU values.
If material data is specified with the Engineering Constants E, E, E, NU12, NU13, NU23, G12, G23, and G13, use the MAT9OR data.
TREF is used as the reference temperature for the calculation of thermal loads.
The last continuation is optional.
Long field format can be used.
To obtain the damping coefficient GE, multiply the critical damping ratio, $C / C_{0}$ by 2.0.
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.
For material-dependent Rayleigh damping, the equivalent viscous damping, $C$ , is defined as:
$C = ALPHA * M + BETA * K$
Where,

ALPHA and BETA

Defined on the RAYL continuation line on the material entry

$M$

Mass matrix

$K$

Stiffness matrix

Supported solutions for material-dependent Rayleigh damping on MAT9:
- Direct Frequency Response
- Modal Frequency Response
- Direct Transient Response
- Modal Transient Response
- Nonlinear Transient Analysis
This card is represented as a material in HyperMesh.