/MAT/LAW90

Block Format Keyword This law describes the visco-elastic foam tabulated material. This material law can be used only with solid elements.

Format

(1)	(2)	(3)	(5)	(7)	(9)
/MAT/LAW90/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`₀		$ν$
`N`_L	`I`_smooth	`F`_cut	`Shape`	`Hys`	`Alpha`

If N_L ≠ 0, each loading function per line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_L	${\dot{ε}}_{L}$		`Fscale`_L

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`E`₀	Initial Young's modulus. 3 (Real)	$[Pa]$
$ν$	Poisson's ratio. (Real)
`I`_smooth	Smooth strain rate option flag. = 0 (Default) No strain rate smoothing. = 1 Strain rate smoothing active. (Integer)
`F`_cut	Cutoff frequency for strain rate filtering. Default = 10³⁰ (Real)	$[Hz]$
`N`_L	Number of loading functions. (Integer)
`fct_ID`_L	Load function (in compression) identifier. (Integer)
${\dot{ε}}_{L}$	Strain rate for load function. (Real)	$[\frac{1}{s}]$
`Fscale`_L	Load function scale factor. (Real)	$[Pa]$
`Shape`	Shape factor. Default = 1.0 (Real)
`Hys`	Hysteresis unloading factor. Default = 1.0 (Real)
`Alpha`	Exponent for unloading (used only if `Hys` > 0). Default = 1 (Real)

Example (Foam)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW90/1/1
foam
#              RHO_I
                3E-8
#                 EO                  NU 
                0.01                   0
#    Nload   Ismooth               F_cut               Shape                 Hys               Alpha
         3         1                  10                 10.                0.15                   0  
#  fct_IDL          Eps_._load          Fscaleload
        12                  .1                   0
        13                   1                   0
        13                 100                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/12
NULL
#                  X                   Y
              -0.300              -0.546					
              -0.200              -0.534					
              -0.100              -0.398					
               0.000               0.000					
               0.010               0.065					
               0.020               0.105					
               0.030               0.123					
               0.040               0.129					
               0.050               0.134					
               0.060               0.138					
               0.070               0.142					
               0.080               0.145					
               0.090               0.150					
               0.100               0.153					
               0.200               0.183					
               0.300               0.211					
               0.400               0.243					
               0.500               0.287					
               0.600               0.356					
               0.700               0.489					
               0.800               0.828					
               0.900               2.434					
               0.950              11.978					
               0.960              24.042					
               0.970              74.879					
               0.980             460.893					
               0.99             12810.97                                                           
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/13
NULL
#                  X                   Y
              -0.300              -0.546					
              -0.200              -0.534					
              -0.100              -0.398					
               0.000               0.000					
               0.010               0.065					
               0.020               0.105					
               0.030               0.123					
               0.040               0.129					
               0.050               0.134					
               0.060               0.138					
               0.070               0.142					
               0.080               0.145					
               0.090               0.150					
               0.100               0.153					
               0.200               0.183					
               0.300               0.211					
               0.400               0.243					
               0.500               0.287					
               0.600               0.356					
               0.700               0.489					
               0.800               0.828					
               0.900               2.434					
               0.950              11.978					
               0.960              24.042					
               0.970              74.879					
               0.980             460.893					
               0.99             12810.97                                                          
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Material behavior in tension and in compression is determined by strain rate dependent curves. The loading curve should be defined as:
- Positive abscissa and ordinate for the compression
- Negative abscissa and ordinate for traction (tension)
The unloading follows the quasi-static loading curve. This is the first curve of the set of strain rate dependent curves.
- If Hys = 0, the elastic modulus is used to switch from loading to unloading behavior.
- If Hys > 0, the following stress reduction factor $D$ is used to switch from loading to unloading behavior:(1)
  $σ = (1 - D) σ$
  
  With(2)
  $D = (1 - H y s) {(1 - {(\frac{W_{c u r}}{W_{\max}})}^{S h a p e})}^{A l p h a}$
  
  Where, $W_{c u r}$ and $W_{\max}$ are current and maximum quasi-static energy.
For stresses above the last load function, the behavior is extrapolated by using the last two load functions. To avoid huge stress values caused by the extrapolation, it is recommended to repeat the last load function.
Specific material output variables:
- USR1: Equivalent stress
- USR2: Maximum for quasi-static energy, $W_{\max}$
- USR3: Equivalent strain rate
- USR4: Current energy, $W_{c u r}$
- USR6: Equivalent strain
- USR7: Stress reduction factor, $D$
/VISC/PRONY can be used with this material law to include viscous effects.