/MAT/LAW90
Block Format Keyword This law describes the viscoelastic foam tabulated material. This material law can be used only with solid elements.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW90/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E_{0}  $\nu $  Tflag  
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}  ${\dot{\epsilon}}_{L}$  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) 

${\rho}_{i}$  Initial density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E_{0}  Initial Young's modulus. 3 (Real) 
$\left[\text{Pa}\right]$ 
Tflag  Tensile behavior flag.
(Integer) 

$\nu $  Poisson's ratio. (Real) 

I_{smooth}  Smooth strain rate option flag.
(Integer) 

F_{cut}  Cutoff frequency for strain rate
filtering. Default = 10^{30} (Real) 
$\text{[Hz]}$ 
N_{L}  Number of loading
functions. (Integer) 

fct_ID_{L}  Load function (in compression)
identifier. (Integer) 

${\dot{\epsilon}}_{L}$  Strain rate for load
function. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Fscale_{L}  Load function scale
factor. (Real) 
$\left[\text{Pa}\right]$ 
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
#12345678910
/UNIT/1
unit for mat
kg mm ms
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/LAW90/1/1
foam
# RHO_I
3E8
# EO NU Tflag
0.01 0 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
#12345678910
# 2. FUNCTIONS:
#12345678910
/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
#12345678910
/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
#12345678910
#ENDDATA
/END
#12345678910
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 quasistatic
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:$$\sigma =\left(1D\right)\sigma $$
With
$$D=\left(1Hys\right){\left(1{\left(\frac{{W}_{cur}}{{W}_{\mathrm{max}}}\right)}^{Shape}\right)}^{Alpha}$$Where, ${W}_{cur}$ and ${W}_{\mathrm{max}}$ are current and maximum quasistatic 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.
 The initial elastic modulus is set to the maximum value between ${E}_{0}$ and the initial tangent of the input curves. The maximum elastic modulus is minimum value between $100\xb7{E}_{0}$ and the maximum curve tangent.
 Specific material output variables:
 USR1: Equivalent stress
 USR2: Maximum for quasistatic energy, ${W}_{\mathrm{max}}$
 USR3: Equivalent strain rate
 USR4: Current energy, ${W}_{cur}$
 USR6: Equivalent strain
 USR7: Stress reduction factor, $D$
 /VISC/PRONY can be used with this material law to include viscous effects.