/MAT/LAW70 (FOAM_TAB)
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/LAW70/mat_ID/unit_ID or /MAT/FOAM_TAB/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E_{0}  v  E_{max}  ${\epsilon}_{\mathrm{max}}$  Itens  
F_{cut}  F_{smooth}  N_{L}  N_{uL}  Iflag  Shape  Hys 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{L}  ${\dot{\epsilon}}_{L}$  Fscale_{L} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{uL}  ${\dot{\epsilon}}_{uL}$  Fscale_{uL} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{T}  Fscale_{T} 
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) 
$\left[\text{Pa}\right]$ 
v  Poisson's ratio. (Real) 

E_{max}  Maximum Young's modulus. 3
(Real) 
$\left[\text{Pa}\right]$ 
${\epsilon}_{\mathrm{max}}$  Reference strain value for the maximum
Young's modulus usage. Default = 1 (Real) 

Itens  Flag to activate different behavior
between tensile and compression.
(Integer) 

F_{cut}  Cutoff frequency for strain rate
filtering. Default = 10^{30} (Real) 
$\text{[Hz]}$ 
F_{smooth}  Smooth strain rate option flag.
(Integer) 

N_{L}  Number of loading functions. 2 (Integer) 

N_{uL}  Number of unloading functions. 2 (Integer) 

Iflag  Flag to control the unloading response.
2
(Integer) 

Shape  Shape factor. Default = 1.0 (Real) 

Hys  Hysteresis unloading factor. Default = 1.0 (Real) 

fct_ID_{L}  Load function (in compression)
identifier. The first function must define the ${\dot{\epsilon}}_{L}=0$ strain rate. (Integer) 

${\dot{\epsilon}}_{L}$  Strain rate for load
function. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Fscale_{L}  Load function scale
factor. (Real) 
$\left[\text{Pa}\right]$ 
fct_ID_{uL}  Unload function (in compression)
identifier. The first function must define the ${\dot{\epsilon}}_{uL}=0$ strain rate. (Integer) 

${\dot{\epsilon}}_{uL}$  Strain rate for unload
function. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Fscale_{uL}  Unload function scale
factor. (Real) 
$\left[\text{Pa}\right]$ 
fct_ID_{T}  Scale factor function between tensile
and compression according strain. (Integer) 

Fscale_{T}  Ordinate scale. (Real) 
Example (Foam)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
kg mm ms
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW70/1/1
Foam
# RHO_I
5E8
# EO NU E_max EPS_max Itens
.01 0 10 .8 0
# F_cut F_smooth N_L N_ul Iflag Shape Hys
.1 1 4 0 4 2 1E20
# fctID_L Eps_._L Fscale_L
1 0 .001
2 .01 .0015
3 .1 .002
3 1 .003
#12345678910
# 3. FUNCTIONS:
#12345678910
/FUNCT/1
Foam
# X Y
0 0
.03 .002
.04 .003
.14 .005
.46 .008
.63 .01
.82 .07
.83 .08
.93 1.4
.94 2.0
.95 3.0
.96 6
.97 10
.98 35
.99 300
#12345678910
/FUNCT/2
Foam
# X Y
0 0
.03 .002
.04 .003
.14 .005
.46 .008
.63 .01
.82 .07
.83 .08
.93 1.4
.94 2.0
.95 3.0
.96 6
.97 10
.98 35
.99 300
#12345678910
/FUNCT/3
Foam
# X Y
0 0
.03 .002
.04 .003
.14 .005
.46 .008
.63 .01
.82 .07
.83 .08
.93 1.4
.94 2.0
.95 3.0
.96 6
.97 10
.98 35
.99 300
#12345678910
#ENDDATA
/END
#12345678910
Comments
 This material is available for the
following parameters in the solid property:For Hexas:
Element I_{solid} I_{smstr} I_{frame} Hexa 1 1 1 1 1 2 1 11 1 1 11 2 17 11 1 17 11 2 14 11 N/A 18 11 2 24 11 2 Choice of formulation depends on particular load case. The best value I_{solid}, I_{smstr} and I_{frame} of form (refer to /DEF_SOLID). When hourglass appears, then fullyintegrated solid elements with I_{solid}=14, I_{smstr}=11 or I_{solid}= 17, I_{smstr}= 11, I_{frame}= 1 or 2 can be used.
For Tetras:Element I_{solid} I_{smstr} I_{frame} Tetra 1 1 1 1 11 1  Flag to control the unloading
response Iflag.
 If Iflag = 0, then N_{L} and N_{uL} must be greater than 0 (N_{L} ≥ 1 and N_{uL} ≥ 1).
 If Iflag =
1 or 2:
 N_{L} and N_{uL} must be greater than 0 (N_{L} ≥ 1 and N_{uL} ≥ 1)
 The first loading curve used for quasistatic
 D is computed as below:
(5) $$D=\left(\frac{{\sigma}_{\mathit{unloading}}}{{\sigma}_{\mathit{quasistatic}}}\right)$$Where, ${\sigma}_{\mathit{unloading}}$ and ${\sigma}_{\mathit{quasistatic}}$ are the current stresses computed, respectively.
 P is the pressure $P=\frac{1}{3}\left({\sigma}_{\mathit{xx}}+{\sigma}_{\mathit{yy}}+{\sigma}_{\mathit{zz}}\right)$
 If Iflag =
3 or 4:
 N_{uL} could be 0, because unloading curves are not used.
 D is computed as:
(6) $$D=\left(1\mathit{Hys}\right)\left(1{\left(\frac{{W}_{\mathit{cur}}}{{W}_{\mathrm{max}}}\right)}^{\mathit{Shape}}\right)$$Where, W_{curv} and W_{max} are current and maximum energy.
 When
${\epsilon}_{\mathrm{max}}$
is reached,
E_{max} is used whatever the curve
definition is.E_{0} and E_{max} used to calculate the current time step. According to current value of strain, Radioss interpolates Young's modulus between E_{0} and E_{max} linearly, where E_{0} is also used to calculate contact stiffness. Radioss automatically modifies E_{0} if it is less than the initial value according to the input stress/strain curves tangents.
 If E_{0} is not specified, use maximum initial slope of all stress strain loading curves as E_{0}.
 If E_{max} is not specified (or set default), use E_{max} as E_{0}. Specified value of E_{max} should be greater than E_{0}, otherwise also take = E_{0} as E_{max}.
 If ${\epsilon}_{\mathrm{max}}$ is not specified (or set default), take the strain where, E_{max} is reached for the first time on one of the loading curves.
 If both ${\epsilon}_{\mathrm{max}}$ and E_{max} are specified, take ${\epsilon}_{\mathrm{max}}$ where, E_{max} is reached for the first time on one of the loading curves.
 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.
 All curves need to be defined as positive abscissa and ordinate.
 Function fct_ID_{T} is used to scale specified stress strain curve in compression. Product of this function and specified stress strain function in compression gives the stress strain function in tension. Note that stress strain function in compression can be specified only until strain is equal to 1, which corresponds to full contraction of the foam. Therefore, the stress strain function in tension can be defined only until the tensile strain of 1.
 In order to recover the stress and
strain the initial state file, the following options have to be saved in the ASCII Output File (STYFile):
 /OUTP/STRESS/FULL
 /OUTP/STRAIN/FULL
 /OUTP/USERS/FULL
 Specific material output
variables:
 USR1: Modified equivalent strain* ( ${\epsilon}_{\mathit{eq}}^{*}={\epsilon}_{\mathit{eq}}\frac{{\sigma}_{y}}{E}$ )
 USR2: Max of internal energy
 USR3: Current Young's modulus
 USR4: Equivalent strain ${\epsilon}_{\mathit{eq}}$
 USR5: Status (1=loading; 1=unloading)
 USR6: Stress
 USR7: Strain rate
 USR8: Internal energy
 /VISC/PRONY can be used with this material law to include viscous effects.