MATX70

Bulk Data Entry Defines additional material properties for tabulated visco-elastic foam material for explicit dynamic analysis.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATX70	`MID`	`EMAX`	`EPSMAX`	`FSMOOTH`	`F`	`NLOAD`	`NULOAD`	`I`

If NLOAD ≥ 1, NLOAD times

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	`TIDL`	`EPSRL`	`FSCALL`

If NULOAD ≥ NULOAD times

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	`TIDU`	`EPSRU`	`FSCALU`

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
MATX1	170	0.1		0.1	9.9E-07
MAT70	170	1.0	0.8			1	4

	2

Definitions

Field	Contents	SI Unit Example
`MID`	Material ID of the associated MAT1. 1 No default (Integer > 0)
`EMAX`	Maximum young modulus. (Real > 0)
`EPSMAX`	Maximum plastic (failure) strain. (Real > 0)
`FSMOOTH`	Strain rate smoothing flag. OFF (Default) ON
`F`	Cutoff frequency for strain rate filtering. Default = 1.E30 (Real ≥ 0)
`NLOAD`	Number of loading stress-strain function. Default = 1 (Integer ≥ 1)
`NULOAD`	Number of unloading stress-strain function. If `IFLAG` in this card is 1, 2, 3, or 4, `NULOAD` must be 0. Default = 1, if `IFLAG` = 0 Default = 0, if `IFLAG` = 1, 2, 3, 4 (Integer > 0)
`I`	Flag to control the loading/unloading behavior. 5 0 (Default) Behavior follows the loading and unloading curves respectively. 1 Behavior follows the loading/unloading curves. For unloading, the deviatoric stress is modified. 2 Behavior follows the loading/unloading curves. For unloading, the stress tensor is modified. 3 The loading curve is used for both loading and unloading. For unloading, the deviatoric stress is modified. The unloading curves are ignored. 4 The loading curve is used for both loading and unloading. For unloading, the stress tensor is modified. The unloading curves are ignored. (Integer)
	Shape factor. Default = 1.0 (Real)
	Hysteresis unloading factor. Default = 1.0 (Real)
`TIDL`	Identification number of TABLES1 entry that defines the loading function. (Integer > 0)
`EPSRL`	Strain rate for loading function. Default = 0.0 (Real)
`FSCALL`	Scale factor for loading function. Default = 1.0 (Real)
`TIDU`	Identification number of TABLES1 entry that defines the unloading function. No default (Integer > 0)
`EPSRU`	Strain rate for unloading function. Default = 0.0 (Real)
`FSCALU`	Scale factor for unloading function. Default = 1.0 (Real)

Comments

The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT1.
MATX70 is only applied in explicit dynamic analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
This material law can be used only with solid elements. The corresponding PSOLIDX property must define I = 1 (Belytschko element), I = 1 (small strain), and I = OFF (not co-rotational).
The loading and unloading functions use engineering stress-strain curve.

Figure 1. Loading and Unloading Stress-Strain Curves
The loading and unloading behavior is determined by IFLAG.
- IFLAG = 0 - The material behavior follows the defined curves for loading and unloading. NLOAD and NULOAD must be greater than 0.
- I = 1 - Both loading curves are used respectively. For unloading, the deviatoric stress is modified by using the quasi-static unloading curve.(1)
  $σ = (1 - D) (σ + p \cdot l) - p \cdot l$
  
  Where, $D$ is calculated from the quasi-static unloading curve.
  
  $D = (\frac{σ_{unloading}}{σ_{quasi-static}}), σ_{unloading}, σ_{quasi-static}$ are the current stresses computed respectively from the unloading and quasi-static curves.
  
  The pressure is: (2)
  $p = - (σ_{x x} + σ_{y y} + σ_{z z}) / 3$
- I = 2 - Both loading and unloading curves are used respectively. For unloading, the stress tensor is modified using the quasi-static unloading curve $σ$ = (1 - D) $σ$ , where, D is calculated from the quasi-static unloading curve.
  $D = (\frac{σ_{unloading}}{σ_{quasi-static}}), σ_{unloading}, σ_{quasi-static}$ are the current stresses computed respectively from the unloading and quasi-static curves.
- I = 3 - The loading curves are used for both loading and unloading behavior. The unloading curve is ignored. The deviatoric unloading stress is modified using:(3)
  $σ = (1 - D) (σ + p \cdot I) - p \cdot I$
  (4)
  $D = (1 - H y s) (1 - {(\frac{W_{c u r}}{W_{\max}})}^{S h a p e})$
  
  Where, W_cur and W_max are the current and maximum energy, respectively.
- I = 4 - The loading curves are used for both loading and unloading behavior. The unloading curve is ignored. The unloading stress tensor is modified using $σ = (1 - D) σ$ (5)
  $D = (1 - H y s) (1 - {(\frac{W_{c u r}}{W_{\max}})}^{S h a p e})$
  
  Where, W_cur and W_max are the current and maximum energy, respectively.
- For I = 3, 4 the unloading curves are not used
For stresses above the last load function, the behavior is extrapolated by using the two last load functions. In order to avoid huge stress values, it is recommended to repeat the last load function.
When maximum plastic strain EPSMAX is reached, EMAX is used whatever the curve definition is.
If EMAX is blank, EMAX is set and equal to Young modulus on MAT1 card.
If EPSMAX is blank, it will be calculated automatically if EMAX is less than the maximum tangent according to the input stress-strain curves.
Young's modulus E on MAT1 card would be modified automatically if it is less than the initial value according to the input stress-strain curves' tangents.
This card is represented as a material in HyperMesh.