# MATX43

Bulk Data Entry Defines additional material properties for Hill Orthotropic material for geometric nonlinear analysis. This law is only applicable to two-dimensional elements.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATX43 MID R00 R45 R90 CHARD EPSPF EPST1 EPST2
If strain rate dependent material, at least 1 time, at most 10 times
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TID1 FSCA1 EPSR1
TID2 FSCA2 EPSR2
etc etc etc

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT8 102 0.7173 0.7173 0.3 0.4     2.7
MATX43 102 1.0 1.0 2.0
1 1.0 0.1
2 1.0 0.05

## Definitions

Field Contents SI Unit Example
MID Material ID of the associated MAT8. 1

No default (Integer > 0)

R00 Lankford parameter at 0 degree.

Default = 1.0 (Real)

R45 Lankford parameter at 45 degrees.

Default = 1.0 (Real)

R90 Lankford parameter at 90 degrees.

Default = 1.0 (Real)

CHARD Hardening coefficient.
0.0 (Default)
The hardening is a full isotropic model.
1.0
Hardening uses the kinematic Prager-Ziegler model.
Between 0.0 and 1.0
Hardening is interpolated between the two models.

(1.0 ≥ Real ≥ 0.0)

EPSPF Failure plastic strain.

Default = 1030 (Real)

EPST1 Tensile failure strain.

Default = 1030 (Real)

EPST2 Tensile failure strain.

Default = 2.0*1030 (Real)

TIDi Identification number of a TABLES1 that defines the yield stress versus plastic strain function corresponding to EPSRi. Separate functions must be defined for different strain rates.

Integer > 0

FSCAi Scale factor for ith function.

Default= 1.0 (Real)

EPSRi Strain rate for ith function.

(Real)

1. The material identification number must be that of an existing MAT8 Bulk Data Entry. Only one MATX43 material extension can be associated with a particular MAT8. E1 must be equal to E2 on MAT8 that is extended by MATX43.
2. MATX43 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
3. The yield stress is defined by a user function and the yield stress is compared to equivalent stress. ${\sigma }_{\text{eq}}=\sqrt{{\text{A}}_{1}{\sigma }_{1}^{2}+{\text{A}}_{2}{\sigma }_{2}^{2}-{\text{A}}_{3}{\sigma }_{1}{\sigma }_{2}+{\text{A}}_{12}{\sigma }_{12}^{2}}$
4. Angles for Lankford parameters are defined with respect to orthotropic direction 1.
(1)
$\begin{array}{ll}\text{R}=\frac{{\text{r}}_{00}+2{\text{r}}_{45}+{\text{r}}_{90}}{4}\hfill & \text{H}=\frac{\text{R}}{1+\text{R}}\hfill \\ {\text{A}}_{1}=\text{H}\left(1+\frac{1}{{\text{r}}_{00}}\right)\hfill & {\text{A}}_{2}=\text{H}\left(1+\frac{1}{{\text{r}}_{90}}\right)\hfill \\ {\text{A}}_{3}=2\text{H}\hfill & {\text{A}}_{12}=2\text{H}\left({\text{r}}_{45}+0.5\right)\left(\frac{1}{{\text{r}}_{00}}+\frac{1}{{\text{r}}_{90}}\right)\hfill \\ {\text{r}}_{00}=\frac{{\text{A}}_{3}}{2{\text{A}}_{1}-{\text{A}}_{3}}\hfill & {\text{r}}_{45}=\frac{1}{2}\left(\frac{{\text{A}}_{12}}{{\text{A}}_{1}+{\text{A}}_{2}-{\text{A}}_{3}}-1\right)\hfill \\ {\text{r}}_{90}=\frac{{\text{A}}_{3}}{2{\text{A}}_{2}-{\text{A}}_{3}}\hfill & \hfill \end{array}$
5. The Lankford parameters rα are determined from a simple tensile test at an angle α to the orthotropic direction 1.
6. If the last point of the first (static) function equals 0 in stress, default value of failure plastic strain EPSPF is set to the corresponding value of plastic strain, p.
7. If plastic strain $\stackrel{˙}{\epsilon }$ p reaches failure plastic strain $\stackrel{˙}{\epsilon }$ pmax, the element is deleted.
8. If $\stackrel{˙}{\epsilon }$ 1 (largest principal strain) > $\stackrel{˙}{\epsilon }$ t1(EPST1), stress is reduced according to the following relation:

$\sigma =\sigma \left(\frac{{\epsilon }_{\text{t}2}-{\epsilon }_{1}}{{\epsilon }_{\text{t}2}-{\epsilon }_{\text{t}1}}\right)$

9. If $\stackrel{˙}{\epsilon }$ 1 (largest principal strain) > $\stackrel{˙}{\epsilon }$ t2(EPST2), the stress is reduced to be 0 (but the element is not deleted). If $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{\text{n}}$ (EPSRn), yield is interpolated between ƒn and ƒn-1. If $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{1}$ (EPSR1), function ƒ1 is used. Above $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{\text{max}}$ , yield is extrapolated.
10. This card is represented as extension to a MAT8 material in HyperMesh.