MAT9OR

Bulk Data Entry Defines the material properties for linear, temperature-independent, and orthotropic materials for solid elements in terms of engineering constants.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MAT9OR	`MID`	`E1`	`E2`	`E3`	`NU12`	`NU23`	`NU31`	`RHO`
	`G12`	`G23`	`G31`	`A1`	`A2`	`A3`	`TREF`	`GE`

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MAT9OR	21	1e6	1e3	1e3	0.1	0.1		1e5
	1e3	1e3		1e-6	1e-6	1e-6

Definitions

Field	Contents	SI Unit Example
`MID`	Material identification number. Must be unique with respect to other MAT1, MAT2, MAT8, MAT9, and MAT9OR definitions. No default (Integer > 0)
`E1`	Elastic modulus in 1-direction. No default (Real)
`E2`	Elastic modulus in 2-direction. No default (Real)
`E3`	Elastic modulus in 3-direction. No default (Real)
`NU12`	Poisson's ratio for uniaxial loading in 1-direction. 3 No default (Real)
`NU23`	Poisson's ratio for uniaxial loading in 2-direction. 3 No default (Real)
`NU31`	Poisson's ratio for uniaxial loading in 3-direction. This field can be interpreted either as NU31 (default) or NU13, based on the optional SYSSETTING(MAT9ORT). 3 Default = Value of `NU23` field (Real)
`RHO`	Mass density. No default (Real)
`G12`	Shear modulus on plane 1-2.
`G23`	Shear modulus on plane 2-3.
`G31`	Shear modulus on plane 3-1.
`Ai`	Coefficient of thermal expansion in the i-direction Default =0.0 (Real)
`TREF`	Reference temperature for the calculation of thermal loads. Default = blank (Real or blank)
`GE`	Structural element damping coefficient. 5 Default = 0.0 (Real)

Comments

This input definition is internally converted to an equivalent MAT9 definition on reading (Comment 6). This is reflected in echoed (ECHO / ECHOON / ECHOOFF) input data and all messaging.
The material identification number must be unique for all MAT1, MAT2, MAT8, MAT9 and MAT9OR entries.
In general, $v$ $v$ ₁₂ is not the same as $v$ $v$ ₂₁, but they are related by $\frac{ν_{ij}}{E_{i}} = \frac{ν_{ji}}{E_{j}}$ $\frac{ν_{ij}}{E_{i}} = \frac{ν_{ji}}{E_{j}}$ .
Furthermore, material stability requires that:(1)
$E_{i} > ν_{ij}^{2} E_{j} and 1 - ν_{12} ν_{21} - ν_{23} ν_{32} - ν_{31} ν_{13} - 2 ν_{21} ν_{32} ν_{13} > 0$ $E_{i} > ν_{ij}^{2} E_{j} and 1 - ν_{12} ν_{21} - ν_{23} ν_{32} - ν_{31} ν_{13} - 2 ν_{21} ν_{32} ν_{13} > 0$
It may be difficult to find all nine orthotropic constants. In some practical problems, the material properties may be reduced to normal anisotropy in which the material is isotropic in a plane (for example, plane 1-2), and has different properties in the direction normal to this plane.
In the plane of isotropy, the properties are reduced to:(2)
$\begin{array}{l} E_{1} = E_{2} = E_{p} \\ ν_{31} = ν_{32} = ν_{np} \\ ν_{13} = ν_{23} = ν_{pn} \\ G_{13} = G_{23} = G_{n} \end{array}$
with $\frac{ν_{np}}{E_{n}} = \frac{ν_{pn}}{E_{p}}$ and $G_{p} = \frac{E_{p}}{2 (1 + ν_{p})}$

There are five independent material constants for normal anisotropy ( $E_{p}$ , $E_{n}$ , $v$ _pn, $v$ _np, and G_n).

In case the material has a planar anisotropy, in which the material is orthotropic only in a plane, the elastic constants are reduced to seven (E₁, E₂, E₃, $v$ ₁₂, G₁₂, G₂₃, and G₃₁).
To obtain the damping coefficient GE, multiply the critical damping ratio, $C / C_{0}$ by 2.0.
Internal conversion from MAT9OR to MAT9. The material property fields of the MAT9 entry are calculated internally from the MAT9OR entry using:(3)
$G_{11} = \frac{1 - ν_{23} ν_{32}}{E_{2} E_{3} Δ}$
(4)
$G_{22} = \frac{1 - ν_{31} ν_{13}}{E_{3} E_{1} Δ}$
(5)
$G_{33} = \frac{1 - ν_{12} ν_{21}}{E_{1} E_{2} Δ}$
(6)
$G_{44} = G_{12}$
(7)
$G_{55} = G_{23}$
(8)
$G_{66} = G_{31}$
(9)
$G_{12} = G_{21} = \frac{ν_{21} + ν_{31} ν_{23}}{E_{2} E_{3} Δ} = \frac{ν_{12} + ν_{13} ν_{32}}{E_{1} E_{3} Δ}$
(10)
$G_{13} = G_{31} = \frac{ν_{31} + ν_{21} ν_{32}}{E_{2} E_{3} Δ} = \frac{ν_{13} + ν_{12} ν_{23}}{E_{1} E_{2} Δ}$
(11)
$G_{23} = G_{32} = \frac{ν_{32} + ν_{31} ν_{12}}{E_{3} E_{1} Δ} = \frac{ν_{23} + ν_{13} ν_{21}}{E_{1} E_{2} Δ}$

Where,

$Δ = \frac{1}{E_{1} E_{2} E_{3}} | \begin{matrix} 1 & - ν_{21} & - ν_{31} \\ - ν_{12} & 1 & - ν_{32} \\ - ν_{13} & - ν_{23} & 1 \end{matrix} |$

The values of $v$ , E and G for the expressions in the above equations are taken from the NUij , Ei and Gij fields respectively of this MAT9OR entry; where i, j € {1,2,3} and the values of G₁₁, G₂₂, G₃₃, G₄₄, G₅₅, G₆₆, G₁₂, G₁₃, and G₂₃ (see above equations) are used to populate the G₁₁, G₂₂, G₃₃, G₄₄, G₅₅, G₆₆, G₁₂, G₁₃, and G₂₃ fields (G12=G21, G13=G31 and G23=G32 due to symmetry) of the MAT9 entry. The remaining elements of the MAT9 entry (that is G14, G15, G24, and so on) are equal to zero.