/MAT/LAW35 (FOAM_VISC)

Block Format Keyword This law describes a visco-elastic foam material using Generalized Maxwell-Kelvin-Voigt 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
ρ i                
E ν E1 E2 n
C1 C2 C3   IFlag Pmin
fct_IDf   Fscaleprs            
Et νt η0 λ    
P0 Φ γ0        

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)

  
ρ i Initial density

(Real)

 [ kg m 3 ]
E Young's modulus

(Real)

 [ Pa ]
ν Poisson's ratio

(Real)

  
E1 Coefficient for Young's modulus update E = E 1 ε ˙ + E 2 .

(Real)

 [ Pa ]
E2 Coefficient for Young's modulus update.

(Real)

 [ Pa ]
n Exponent on relative volume.

(Real)

  
C1 Coefficient for pressure calculation.

(Real)

  
C2 Coefficient for pressure calculation.

(Real)

  
C3 Coefficient for pressure calculation.

(Real)

  
IFlag Open cell foam flag.
= 0
Input is a pressure vs. compression curve /MAT/LAW21 (DPRAG).
= 1
Input is a function defining an "equivalent air pressure" that is removed from the system vs. compression. This corresponds to an open cell foam formulation.

(Integer)

  
Pmin Minimum pressure

(Real)

 [ Pa ]
fct_IDf Curve identifier for pressure as function of volumetric strain volumetric strain is γ = ρ 0 ρ − 1 .

(Integer)

  
Fscaleprs Pressure function scale factor.

Default = 1.0 (Real)

  
Et Tangent modulus.

(Real)

 [ Pa ]
ν t Tangent Poisson's ratio.

(Real)

  
η 0 Viscosity coefficient in pure shear (Navier's constant).

(Real)

 [ Pa⋅s ]
λ Navier's constant.

(Real)

 [ Pa⋅s ]
P0 Initial air pressure.

(Real)

 [ Pa ]
Φ Ratio of foam to polymer density.

(Real)

  
γ 0 Initial volumetric strain.

(Real)

  

Example (Foam)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/FOAM_VISC/1/1
Foam
#              RHO_I
             4.3E-11                   
#                  E                  Nu                  E1                  E2                   n
                  .2                   0                   0                   0                   0
#                 C1                  C2                  C3               Iflag                Pmin
                   1                   1                   1                   0                   0
# func_IDf                    Fscalepres
      1076                             0
#                 Et                Nu_t               eta_0               Lamda
                 .25                   0               10000                   0
#                 P0                 Phi             gamma_0
                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1076
Pressure function
#                  X                   Y
#  Volumetric strain            Pressure
             -100000               -1000                                                            
                 -10               -1000                                                            
                   0                   0                                                            
                3000               7.633                                                            
              209000               7.633                                                            
              210000                18.5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. In all cases, for shear and bulk modulus calculation, the following value of the Young's modulus will be used:(1)
    E = max ( E , E 1 ε ˙ + E 2 ) . ( V V 0 ) n
  2. If fct_IDf = 0,(2)
    d P d t = C 1 K ε ˙ k k − C 2 [ K + K t 3 λ + 2 η 0 σ k k ] + C 3 [ K K t 3 λ + 2 η 0 ε k k ]
    Where,
    K = E 3 ( 1 − 2 v )
    K t = E t 3 ( 1 − 2 v t )
    P = − 1 3 σ k k
    ε k k = ln ( V V 0 )
  3. If fct_IDf ≠ 0, the pressure is read from curve.
  4. For closed cell polyurethane foam, the skeletal spherical stresses may be augmented by:(3)
    P a i r = − P 0 ⋅ γ 1 + γ − Φ