/MAT/LAW33 (FOAM_PLAS)
Block Format Keyword This law models a viscouselastic foam material with unloading/reloading like plastic behavior. This law is applicable only for solid elements and is typically used to model low density, closed cell polyurethane foams such as impact limiters.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW33/mat_ID/unit_ID or /MAT/FOAM_PLAS/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  K_{a}  fct_ID_{f}  Fscale_{crv}  
P_{0}  $\mathrm{\Phi}$  ${\gamma}_{0}$  
A  B  C 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

E_{1}  E_{2}  E_{t}  ${\eta}^{*}$  ${\eta}_{0}$ 
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young's modulus. (Real) 
$\left[\text{Pa}\right]$ 
K_{a}  Analysis type flag.
(Integer) 

fct_ID_{f}  Yield stress versus volumetric strain curve
function identifier. (Integer) 

Fscale_{crv}  Scale factor for ordinate (stress) for
fct_ID_{f}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
P_{0}  Initial air pressure. 5
(Real) 
$\left[\text{Pa}\right]$ 
$\mathrm{\Phi}$  Ratio of foam to polymer
density. (Real) 

${\gamma}_{0}$  Initial volumetric strain. (Real) 

A  Yield parameter. (Real) 

B  Yield parameter. (Real) 

C  Yield parameter. (Real) 

E_{1}  Coefficient for Young's modulus
update. (Real) 
$\left[\text{Pa}\cdot \text{s}\right]$ 
E_{2}  Coefficient for Young's modulus
update. (Real) 
$\left[\text{Pa}\right]$ 
E_{t}  Tangent modulus. (Real) 
$\left[\text{Pa}\right]$ 
${\eta}^{*}$  Viscosity coefficient in pure
compression. (Real) 

${\eta}_{0}$  Viscosity coefficient in pure
shear. (Real) 
Example (Foam)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/FOAM_PLAS/1/1
Foam
# RHO_I
2E10
# E Ka func_IDf Fscalecurv
200 1 0 1
# P0 Phi Gamma_0
0 0 0
# A B C
1E30 0 0
# E1 E2 Et eta_comp eta_shear
0 0 2 2E27 1E27
#12345678910
#ENDDATA
/END
#12345678910
Comments
 If the limiting yield curve is not defined, then the material follows a MaxwellKelvinVoight viscoelastic model.
 If the limiting yield curve is defined, then the material initially follows the viscoelastic law until it intersects the defined yield curve, which limits the viscoelastic stress in tension and compression. The material does not experience plasticity, but instead behaves in a visco hyperelastic way.
 If the yield function
fct_ID_{f}
= 0, then
(1) $${\sigma}_{y}=A+B(1+C\gamma )$$Where, $\gamma $ is the volumetric strain:(2) $$\gamma =\frac{V}{{V}_{0}}1+{\gamma}_{0}=\frac{{\rho}_{0}}{\rho}1+{\gamma}_{0}=\frac{\mu}{1+\mu}+{\gamma}_{0}$$  If the yield function fct_ID_{f} ≠ 0, then $\sigma $ versus $\gamma $ is read from input of the curve idenfier fct_ID_{f}. The curve can be defined for tensile ( $\gamma >0$ ) and compression ( $1<\gamma <0$ ). The input stress should be positive for both tension and compression.
 The optional air pressure, as a
function of the volumetric strain can be added to
the structural pressure. Pressure is applied only
on the spherical part of the stress
tensor.
(3) $${P}_{air}=\frac{{P}_{0}\cdot \gamma}{1+\gamma \mathrm{\Phi}}$$  Young’s modulus is used as the initial
slope for unloading. It can be constant or
variable, based on the strain
rate.
(4) $$E=\mathrm{max}(E,{E}_{1}\dot{\epsilon}+{E}_{2})$$  The unloading or the loading direction change (tensile <> compression) is following the current elastic modulus, like an isotropic elasticplastic material or highly viscous foam material. However, there is no plastic strain accumulation.