# /MAT/LAW70 (FOAM_TAB)

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) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW70/mat_ID/unit_ID or /MAT/FOAM_TAB/mat_ID/unit_ID
mat_title
${\rho }_{i}$
E0 v Emax ${\epsilon }_{\mathrm{max}}$ Itens
Fcut Fsmooth NL NuL Iflag Shape Hys
If ${N}_{L}>0$ , define ${N}_{L}$ loading function per line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDL ${\stackrel{˙}{\epsilon }}_{L}$ FscaleL
If ${N}_{uL}>0$ , define ${N}_{uL}$ unloading function per line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDuL ${\stackrel{˙}{\epsilon }}_{uL}$ FscaleuL
If Itens = 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDT FscaleT

## 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)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
E0 Initial Young's modulus. 3
= 0 (Default)
E0 maximum initial slope of the loading functions.

(Real)

$\left[\text{Pa}\right]$
v Poisson's ratio.

(Real)

Emax Maximum Young's modulus. 3
= 0 (Default)
Emax maximum slope of the loading functions.

(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.
= 0 (Default)
Same behavior between the compression tensile.
= 1
Different behavior between compression tensile. The tensile behavior is the compression curve multiply by Scale factor, which is defined in fct_IDT.

(Integer)

Fcut Cutoff frequency for strain rate filtering.

Default = 1030 (Real)

$\text{[Hz]}$
Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

(Integer)

(Integer)

Iflag Flag to control the unloading response. 2
= 0 (Default)
= 1
The material behavior follows NL loading curves (only first curve is used for quasi-static) and NuL loading curves. For unloading the deviatoric stress is reduced by using the quasi-static unloading curve:
$\mathbf{\sigma }=\left(1-D\right) \left(\mathbf{\sigma }+P\right)-P$
with $D=\left(\frac{{\sigma }_{\mathit{unloading}}}{{\sigma }_{\mathit{quasi-static}}}\right)$
= 2
The material behavior follows NL loading curves (only first curve used for quasi-static) and NuL unloading curves. For unloading the tensor stress is reduced by using the quasi-static unloading curve:
$\mathbf{\sigma }=\left(1-D\right)\mathbf{\sigma }$
with, $D=\left(\frac{{\sigma }_{\mathit{unloading}}}{{\sigma }_{\mathit{quasi-static}}}\right)$
3
$\mathbf{\sigma }=\left(1-D\right) \left(\mathbf{\sigma }+P\right)-P$
with $D=\left(1-\mathit{Hys}\right)\left(1-{\left(\frac{{W}_{\mathit{cur}}}{{W}_{\mathrm{max}}}\right)}^{\mathit{Shape}}\right)$
= 4
$\mathbf{\sigma }=\left(1-D\right)\mathbf{\sigma }$
with $D=\left(1-\mathit{Hys}\right)\left(1-{\left(\frac{{W}_{\mathit{cur}}}{{W}_{\mathrm{max}}}\right)}^{\mathit{Shape}}\right)$

(Integer)

Shape Shape factor.

Default = 1.0 (Real)

Default = 1.0 (Real)

fct_IDL Load function (in compression) identifier.

The first function must define the ${\stackrel{˙}{\epsilon }}_{L}=0$ strain rate.

(Integer)

${\stackrel{˙}{\epsilon }}_{L}$ Strain rate for load function.

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
FscaleL Load function scale factor.

(Real)

$\left[\text{Pa}\right]$
fct_IDuL Unload function (in compression) identifier.

The first function must define the ${\stackrel{˙}{\epsilon }}_{uL}=0$ strain rate.

(Integer)

${\stackrel{˙}{\epsilon }}_{uL}$ Strain rate for unload function.

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
FscaleuL Unload function scale factor.

(Real)

$\left[\text{Pa}\right]$
fct_IDT Scale factor function between tensile and compression according strain.

(Integer)

FscaleT Ordinate scale.

(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----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW70/1/1
Foam
#              RHO_I
5E-8
#                 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               1E-20
#  fctID_L             Eps_._L            Fscale_L
1                   0                .001
2                 .01               .0015
3                  .1                .002
3                   1                .003
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

1. This material is available for the following parameters in the solid property:
For Hexas:
Element Isolid Ismstr Iframe
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 Isolid, Ismstr and Iframe of form (refer to /DEF_SOLID). When hourglass appears, then fully-integrated solid elements with Isolid=14, Ismstr=11 or Isolid= 17, Ismstr= 11, Iframe= 1 or 2 can be used.

For Tetras:
Element Isolid Ismstr Iframe
Tetra 1 1 1
1 11 1
2. Flag to control the unloading response Iflag.
• If Iflag = 0, then NL and NuL must be greater than 0 (NL1 and NuL1).
• If Iflag = 1 or 2:
• NL and NuL must be greater than 0 (NL1 and NuL1)
• The first loading curve used for quasi-static
• D is computed as below:
$D=\left(\frac{{\sigma }_{\mathit{unloading}}}{{\sigma }_{\mathit{quasi-static}}}\right)$

Where, ${\sigma }_{\mathit{unloading}}$ and ${\sigma }_{\mathit{quasi-static}}$ 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:
• NuL could be 0, because unloading curves are not used.
• D is computed as:
$D=\left(1-\mathit{Hys}\right)\left(1-{\left(\frac{{W}_{\mathit{cur}}}{{W}_{\mathrm{max}}}\right)}^{\mathit{Shape}}\right)$

Where, Wcurv and Wmax are current and maximum energy.

3. When ${\epsilon }_{\mathrm{max}}$ is reached, Emax is used whatever the curve definition is.
E0 and Emax used to calculate the current time step. According to current value of strain, Radioss interpolates Young's modulus between E0 and Emax linearly, where E0 is also used to calculate contact stiffness. Radioss automatically modifies E0 if it is less than the initial value according to the input stress/strain curves tangents.
• If E0 is not specified (or set to 0), use maximum initial slope of all stress strain loading curves as E0.
• If Emax is not specified (or set to 0), use maximum slope of all stress strain loading curves.
• If ${\epsilon }_{\mathrm{max}}$ is not specified (or set default), take the strain where, Emax is reached for the first time on one of the loading curves.
• If both ${\epsilon }_{\mathrm{max}}$ and Emax are specified, take ${\epsilon }_{\mathrm{max}}$ where, Emax is reached for the first time on one of the loading curves.
4. 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.
5. All curves need to be defined as positive abscissa and ordinate. The curves are smoothed, re-sampled and dis-intersected, if necessary. The modified curves are printed in the Starter output file.
6. Function fct_IDT 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.
7. In order to recover the stress and strain the initial state file, the following options have to be saved in the Initial State (STA-file):
• /STATE/BRICK/EREF
• /STATE/BRICK/STRAIN/FULL
• /STATE/BRICK/STRES/FULL
• /STATE/BRICK/AUX/FULL
8. Specific material output variables:
• USR1: Modified equivalent strain* ( ${\epsilon }_{\mathit{eq}}^{*}={\epsilon }_{\mathit{eq}}-\frac{{\sigma }_{y}}{E}$ )
• USR2:
• Maximum internal energy for Iform > 0
• Equivalent stress for the other formulations for Iform = 0
• USR3: Current Young's modulus
• USR4: Equivalent strain ${\epsilon }_{\mathit{eq}}$