# /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

## 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)

${\rho }_{i}$ Initial density

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
E0 Initial Young's modulus. 3

(Real)

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

(Real)

Emax Maximum Young's modulus. 3
= 0
Emax is equal to E0 (default).

(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)

= 0 (Default)
= 1
$\mathbf{\sigma }=\left(1-D\right) \left(\mathbf{\sigma }+P\right)-P$
with $D=\left(\frac{{\sigma }_{\mathit{unloading}}}{{\sigma }_{\mathit{quasi-static}}}\right)$
= 2
$\mathbf{\sigma }=\left(1-D\right)\mathbf{\sigma }$
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)

$\left[\frac{\text{1}}{\text{s}}\right]$

(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)

$\left[\frac{\text{1}}{\text{s}}\right]$

(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
• 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)
• D is computed as below:(5)
$D=\left(\frac{{\sigma }_{\mathit{unloading}}}{{\sigma }_{\mathit{quasi-static}}}\right)$

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:
• 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, 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, use maximum initial slope of all stress strain loading curves as E0.
• If Emax is not specified (or set default), use Emax as E0. Specified value of Emax should be greater than E0, otherwise also take = E0 as Emax.
• 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.
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 ASCII Output File (STY-File):
• /OUTP/STRESS/FULL
• /OUTP/STRAIN/FULL
• /OUTP/USERS/FULL
8. 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 ${\epsilon }_{\mathit{eq}}$
• USR6: Stress
• USR7: Strain rate
• USR8: Internal energy
9. /VISC/PRONY can be used with this material law to include viscous effects.