/MAT/LAW35 (FOAM_VISC)
Block Format Keyword This law describes a viscoelastic foam material using Generalized MaxwellKelvinVoigt model where viscosity is based on Navier equations.
This law is applicable only for shell and solid elements and can be used for open cell foams, polymers, elastomers, seat cushions and dummy paddings.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW35/mat_ID/unit_ID or /MAT/FOAM_VISC/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\nu $  E_{1}  E_{2}  n  
C_{1}  C_{2}  C_{3}  I_{Flag}  P_{min}  
fct_ID_{f}  Fscale_{prs}  F_{smooth}  F_{cut}  
E_{t}  ${\nu}_{t}$  ${\eta}_{0}$  $\lambda $  
P_{0}  $\Phi $  ${\gamma}_{0}$ 
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  Young's modulus (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's ratio (Real) 

E_{1}  Coefficient for Young's modulus update
$E={E}_{1}\dot{\epsilon}+{E}_{2}$
. (Real) 
$\left[\text{Pa}\right]$ 
E_{2}  Coefficient for Young's modulus
update. (Real) 
$\left[\text{Pa}\right]$ 
n  Exponent on relative
volume. (Real) 

C_{1}  Coefficient for pressure
calculation. (Real) 

C_{2}  Coefficient for pressure
calculation. (Real) 

C_{3}  Coefficient for pressure
calculation. (Real) 

I_{Flag}  Open cell foam flag.
(Integer) 

P_{min}  Minimum pressure. (Real) 
$\left[\text{Pa}\right]$ 
fct_ID_{f}  Curve identifier for pressure as
function of volumetric strain volumetric strain is
$\gamma =\frac{{\rho}_{0}}{\rho}1$
. (Integer) 

Fscale_{prs}  Pressure function scale
factor. Default = 1.0 (Real) 

F_{smooth}  Smooth strain rate option flag.


F_{cut}  Cutoff frequency for the strain rate
filtering. Default = 10000 Hz (Real) 
$\text{[Hz]}$ 
E_{t}  Tangent modulus. (Real) 
$\left[\text{Pa}\right]$ 
${\nu}_{t}$  Tangent Poisson's
ratio. (Real) 

${\eta}_{0}$  Viscosity coefficient in pure shear
(Navier's constant). (Real) 
$\left[\text{Pa}\cdot \text{s}\right]$ 
$\lambda $  Navier's constant. (Real) 
$\left[\text{Pa}\cdot \text{s}\right]$ 
P_{0}  Initial air
pressure. (Real) 
$\left[\text{Pa}\right]$ 
$\Phi $  Ratio of foam to polymer
density. (Real) 

${\gamma}_{0}$  Initial volumetric
strain. (Real) 
Example (Foam)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/FOAM_VISC/1/1
Foam
# RHO_I
4.3E11
# E Nu E1 E2 n
.2 0 0 0 0
# C1 C2 C3 Iflag Pmin
1 1 1 0 0
# func_IDf Fscale_prs Fsmooth Fcut
1076 0 1 15000.0
# Et Nu_t eta_0 Lamda
.25 0 10000 0
# P0 Phi gamma_0
0 0 0
#12345678910
# 3. FUNCTIONS:
#12345678910
/FUNCT/1076
Pressure function
# X Y
# Volumetric strain Pressure
100000 1000
10 1000
0 0
3000 7.633
209000 7.633
210000 18.5
#12345678910
#ENDDATA
/END
#12345678910
Comments
 In all cases, for shear and bulk
modulus calculation, the following value of the Young's modulus will be
used:
(1) $$E=\mathrm{max}(E,{E}_{1}\dot{\epsilon}+{E}_{2}).{\left(\frac{V}{{V}_{0}}\right)}^{n}$$  If
fct_ID_{f} =
0,
(2) $$\frac{dP}{dt}={C}_{1}K{\dot{\epsilon}}_{kk}{C}_{2}\left[\frac{K+{K}_{t}}{3\lambda +2{\eta}_{0}}{\sigma}_{kk}\right]+{C}_{3}\left[\frac{K{K}_{{}_{t}}}{3\lambda +2{\eta}_{0}}{\epsilon}_{kk}\right]$$Where, $K=\frac{E}{3\left(12v\right)}$
 ${K}_{t}=\frac{{E}_{t}}{3\left(12{v}_{t}\right)}$
 $P=\frac{1}{3}{\sigma}_{kk}$
 ${\epsilon}_{kk}=\mathrm{ln}\left(\frac{V}{{V}_{0}}\right)$
 If fct_ID_{f} ≠ 0, the pressure is read from curve.
 For closed cell polyurethane
foam, the skeletal spherical stresses may be augmented by:
(3) $${P}_{air}=\frac{{P}_{0}\cdot \gamma}{1+\gamma \Phi}$$  The parameters F_{smooth} and F_{cut}
allows you to enable strainrate filtering. Three cases can be set:
 If F_{smooth} = 0 and F_{cut} = 0.0, the strainrate filtering is turned off.
 If F_{smooth} = 1 and F_{cut} = 0.0, the strainrate filtering uses a default cutoff frequency of 10 kHz.
 If F_{cut} ≠ 0, F_{smooth} is automatically set to 1 and the strainrate filtering uses the cutoff frequency given by you.