/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)
/MAT/LAW90/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`₀		$ν$
`N`_L	`I`_smooth	`F`_cut	`Shape`	`Hys`

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

Definitions

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. 2 (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)

Example

#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----|
#-  2. MATERIALS:
/MAT/LAW90/1/1
foam
#              RHO_I
                3E-8
#                 EO                  NU 
                0.01                   0
#    Nload   Ismooth               F_cut               Shape                 Hys
         3         1                  10                 10.                0.15  
#  fct_IDL          Eps_._load          Fscaleload
        12                  .1                   0
        13                   1                   0
        13                 100                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. 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

Control of the unloading response: There are two ways for controlling the unloading:
- If Hys=0, follow the quasi-static loading curve for unloading.
- If Hys > 0, the loading curve are used for both loading and unloading behavior and the tensor unloading tensor stress is reduced by:(1)
  $σ = (1 - D) σ$
  
  With(2)
  $D = (1 - H y s) (1 - {(\frac{W_{c u r}}{W_{\max}})}^{S h a p e})$
  
  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 two last load functions. Then, in order to avoid huge stress values, it is recommended to repeat the last load function.
The loading curve should be defined as:
- Positive abscissa and ordinate for the compression
- Negative abscissa and ordinate for traction (tension)
In order to recover the stress and strain using initial state file, the following options have to be saved in ASCII Output File (STY-File):
- /OUTP/STRESS/FULL
- /OUTP/STRAIN/FULL
- /OUTP/USERS/FULL
Specific material output variables:
- USR2: Maximum for quasi-static energy $W_{\max}$
- USR3: Strain rate in principal direction 1
- USR4: Strain rate in principal direction 2
- USR5: Strain rate in principal direction 3
/VISC/PRONY can be used with this material law to include viscous effects.