# MAT3

Bulk Data Entry Defines the material properties for linear, temperature-independent, and orthotropic materials used by the CTAXI, CTRIAX6, and CQAXI axisymmetric elements, and CTPSTN and CQPSTN plane strain elements.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT3 MID EX ETH EZ NUXTH NUTHZ NUZX RHO
GZX AX ATH AZ TREF GE

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT3 17 3.0+7 3.1+7 3.2+7 0.33 0.28 0.30 2.0e-5
7.0+6 1.1e-4 1.1e-4 1.2e-4 35.5 0.19

## 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. 3

No default (Integer > 0 or <String>)

EX, ETH, EZ Young's moduli in the x, out-of-plane, and z directions, respectively.

No default (Real > 0.0)

NUXTH, NUTHZ, NUZX Poisson's ratios.
NUXTH
Poisson's ratio for strain in the out-of-plane direction, when stress is in the x direction.
NUTHZ
Poisson's ratio for strain in the z direction, when stress is in the out-of-plane direction.
NUZX
Poisson's ratio for strain in the x direction, when stress is in the z direction.

No default (Real)

RHO Mass density.

No default (Real)

GZX Shear modulus in the x-z plane.

No default (Real > 0.0)

AX, ATH, AZ Thermal expansion coefficient in the x, out-of-plane, and z directions, respectively.

No default (Real)

Default = blank (Real or blank)

GE Structural element damping coefficient. 8

No default (Real)

1. The indices of ‘z’ or ‘Z’ above represent (a) the in-plane z direction if the analysis is defined in x-z plane, or (b) the in-plane y direction if the analysis is defined in x-y plane. The out-of-plane index, ‘TH’ represents (a) the hoop direction $\theta$ in axisymmetric analysis, or (b) the direction of thickness in plane strain analyses, see Comment 7.
2. The material identification number/string must be unique for all MAT1, MAT2, MAT8 and MAT9 entries.
3. 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.
4. Values of all seven elastic constants, EX, ETH, EZ, NUXTH, NUTHZ, NUZX and GZX must be present.
5. A warning is issued if absolute value of NUXTH or NUTHZ is greater than 1.0.
6. The x, out-of-plane and z directions are principal material directions of the material coordinate system. The elements supported by MAT3 contains a THETA field to relate the principal material directions to the basic coordinate system.
7. The strain-stress relations are defined as:
1. axisymmetric analysis(1)
$\left\{\begin{array}{c}{\epsilon }_{x}\\ {\epsilon }_{y}\\ {\epsilon }_{z}\\ {\gamma }_{zx}\end{array}\right\}=\left[\begin{array}{cccc}\frac{1}{EX}& -\frac{NUTHX}{ETH}& -\frac{NUZX}{EZ}& 0\\ -\frac{NUXTH}{EX}& \frac{1}{ETH}& -\frac{NUZTH}{EZ}& 0\\ -\frac{NUXZ}{EX}& -\frac{NUTHZ}{ETH}& \frac{1}{EZ}& 0\\ 0& 0& 0& \frac{1}{GZX}\end{array}\right]\left\{\begin{array}{c}{\sigma }_{x}\\ {\sigma }_{\theta }\\ {\sigma }_{z}\\ {\tau }_{zx}\end{array}\right\}+\left(T-TREF\right)\left\{\begin{array}{c}AX\\ ATH\\ AZ\\ 0\end{array}\right\}$

with $\frac{NUXTH}{EX}=\frac{NUTHX}{ETH},\frac{NUXZ}{EX}=\frac{NUZX}{EZ}$ and $\frac{NUTHZ}{ETH}=\frac{NUZTH}{EZ}$ .

2. plain strain analysis(2)
$\left\{\begin{array}{c}{\epsilon }_{x}\\ {\epsilon }_{z}\\ {\gamma }_{zx}\end{array}\right\}=\left[\begin{array}{ccc}\frac{1}{EX}& -\frac{NUZX}{EZ}& 0\\ -\frac{NUXZ}{EX}& \frac{1}{EZ}& 0\\ 0& 0& \frac{1}{GZX}\end{array}\right]\left\{\begin{array}{c}{\sigma }_{x}\\ {\sigma }_{z}\\ {\tau }_{zx}\end{array}\right\}+\left(T-TREF\right)\left\{\begin{array}{c}AX\\ AZ\\ 0\end{array}\right\}$

with $\frac{NUXZ}{EX}=\frac{NUZX}{EZ}$ .

The material constants associated with ‘TH’ (i.e. $ETH$ , $NUXTH$ , $NUTHZ$ and $ATH$ ) are used to calculate the out-of-plane stress in plane strain analysis.(3)
${\sigma }_{th}=ETH\left[\frac{NUXTH}{EX}{\sigma }_{x}+\frac{NUZTH}{EZ}{\sigma }_{Z}-\left(T-TREF\right)ATH\right]$
Note: The strain and stress here are both defined in the material coordinate system.
8. To obtain the damping coefficient GE, multiply the critical damping ratio, $C/{C}_{0}$ by 2.0.
9. This card is represented as a material in HyperMesh.