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`	`C`	`EPSPF`	`EPST1`	`EPST2`

If strain rate dependent material, at least 1 time, at most 10 times

(2)	(3)	(4)
`TID1`	`FSCA1`	`EPSR1`
`TID2`	`FSCA2`	`EPSR2`
etc	etc	etc

Example

(1)	(2)	(3)	(4)	(5)	(6)	(9)
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)
`C`	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 vs. plastic strain function corresponding to `EPSRi`. Separate functions must be defined for different strain rates. Integer > 0
`FSCAi`	Scale factor for i^th function. Default= 1.0 (Real)
`EPSRi`	Strain rate for i^th function. (Real)

Comments

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.
MATX43 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
The yield stress is defined by a user function and the yield stress is compared to equivalent stress. $σ_{eq} = \sqrt{A_{1} σ_{1}^{2} + A_{2} σ_{2}^{2} - A_{3} σ_{1} σ_{2} + A_{12} σ_{12}^{2}}$
Angles for Lankford parameters are defined with respect to orthotropic direction 1.
(1)
$\begin{array}{l} R = \frac{r_{00} + 2 r_{45} + r_{90}}{4} & H = \frac{R}{1 + R} \\ A_{1} = H (1 + \frac{1}{r_{00}}) & A_{2} = H (1 + \frac{1}{r_{90}}) \\ A_{3} = 2 H & A_{12} = 2 H (r_{45} + 0.5) (\frac{1}{r_{00}} + \frac{1}{r_{90}}) \\ r_{00} = \frac{A_{3}}{2 A_{1} - A_{3}} & r_{45} = \frac{1}{2} (\frac{A_{12}}{A_{1} + A_{2} - A_{3}} - 1) \\ r_{90} = \frac{A_{3}}{2 A_{2} - A_{3}} \end{array}$
The Lankford parameters r_α are determined from a simple tensile test at an angle α to the orthotropic direction 1.
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.
If plastic strain $\dot{ε}$ p reaches failure plastic strain $\dot{ε}$ p^max, the element is deleted.
If $\dot{ε}$ ₁ (largest principal strain) > $\dot{ε}$ _t1(EPST1), stress is reduced according to the following relation:
$σ = σ (\frac{ε_{t 2} - ε_{1}}{ε_{t 2} - ε_{t 1}})$
If $\dot{ε}$ ₁ (largest principal strain) > $\dot{ε}$ _t2(EPST2), the stress is reduced to be 0 (but the element is not deleted). If $\dot{ε} \leq {\dot{ε}}_{n}$ (EPSRn), yield is interpolated between ƒ_n and ƒ_n-1. If $\dot{ε} \leq {\dot{ε}}_{1}$ (EPSR1), function ƒ1 is used. Above $\dot{ε} \leq {\dot{ε}}_{max}$ , yield is extrapolated.

Figure 1.
This card is represented as extension to a MAT8 material in HyperMesh.