MAT3

Format

Example

Definitions

Comments

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 seven elastic constants, EX, ETH, EZ, NUXTH, NUTHZ, NUZX and GZX must be present. GTHZ and GXTH are only effective for general axisymmetric elements CTAXIG and CQAXIG.
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. 2D axisymmetry(1)
      $$\{\begin{array}{c}{\epsilon }_x\\ {\epsilon }_y\\ {\epsilon }_z\\ {\gamma }_{zx}\end{array}\}=\left[\begin{array}{cccc}\frac{1}{EX}& -\frac{NUTHX}{ETH}& -\frac{NUZX}{EZ}& 0\\ -\frac{NUXTH}{EX}& \frac{1}{ETH}& -\frac{NUZTH}{EZ}& 0\\ -\frac{NUXZ}{EX}& -\frac{NUTHZ}{ETH}& \frac{1}{EZ}& 0\\ 0& 0& 0& \frac{1}{GZX}\end{array}\right]\{\begin{array}{c}{\sigma }_x\\ {\sigma }_{\theta }\\ {\sigma }_z\\ {\tau }_{zx}\end{array}\}+(T-TREF)\{\begin{array}{c}AX\\ ATH\\ AZ\\ 0\end{array}\}$$

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

   2. general axisymmetry(2)
      $$\left\{\left.\begin{array}{c}{\epsilon }_x\\ {\epsilon }_{\theta }\\ {\epsilon }_z\\ \begin{array}{l}{\gamma }_{x\theta }\\ {\gamma }_{\theta z}\\ {\gamma }_{zx}\end{array}\end{array}\right\}\right.=\left[\begin{array}{cccccc}\frac{1}{EX}& -\frac{NUTHX}{ETH}& -\frac{NUZX}{EZ}& 0& 0& 0\\ -\frac{NUXTH}{EX}& \frac{1}{ETH}& -\frac{NUZTH}{EZ}& 0& 0& 0\\ -\frac{NUXZ}{EX}& -\frac{NUTHZ}{ETH}& \frac{1}{EZ}& 0& 0& 0\\ 0& 0& 0& \frac{1}{GXTH}& 0& 0\\ 0& 0& 0& 0& \frac{1}{GTHZ}& 0\\ 0& 0& 0& 0& 0& \frac{1}{GZX}\end{array}\right]\left\{\left.\begin{array}{c}{\sigma }_x\\ {\sigma }_{\theta }\\ {\sigma }_z\\ \begin{array}{l}{\tau }_{x\theta }\\ {\tau }_{\theta z}\\ {\tau }_{zx}\end{array}\end{array}\right\}\right.+(T-TREF)\left\{\left.\begin{array}{c}AX\\ ATH\\ AZ\\ \begin{array}{l}0\\ 0\\ 0\end{array}\end{array}\right\}\right.$$

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

   3. plain strain analysis(3)
      $$\left\{\begin{array}{c}{\epsilon }_x\\ {\epsilon }_z\\ {\gamma }_{zx}\end{array}\right\}=\left[\begin{array}{ccc}\frac{1}{EX}& -\frac{NUZX}{EZ}& 0\\ -\frac{NUXZ}{EX}& \frac{1}{EZ}& 0\\ 0& 0& \frac{1}{GZX}\end{array}\right]\left\{\begin{array}{c}{\sigma }_x\\ {\sigma }_z\\ {\tau }_{zx}\end{array}\right\}+(T-TREF)\left\{\begin{array}{c}AX\\ AZ\\ 0\end{array}\right\}$$

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

   The material constants associated with ‘TH’ (that is, $ETH$ , $NUXTH$ , $NUTHZ$ and $ATH$ ) are used to calculate the out-of-plane stress in plane strain analysis.(4)

   $${\sigma }_{th}=ETH\left[\frac{NUXTH}{EX}{\sigma }_x+\frac{NUZTH}{EZ}{\sigma }_Z-(T-TREF)ATH\right]$$
   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.