/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)	(3)	(5)	(7)	(8)	(9)
/MAT/LAW35/`mat_ID`/`unit_ID` or /MAT/FOAM_VISC/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`	$ν$	`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	$ν_{t}$	$η_{0}$	$λ$
`P`₀	$Φ$	$γ_{0}$

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)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus. (Real)	$[Pa]$
$ν$	Poisson's ratio. (Real)
`E`₁	Coefficient for Young's modulus update $E = E_{1} \dot{ε} + E_{2}$ . (Real)	$[Pa]$
`E`₂	Coefficient for Young's modulus update. (Real)	$[Pa]$
`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. = 0 Input is a pressure versus compression curve /MAT/LAW21 (DPRAG). = 1 Input is a function defining an "equivalent air pressure" that is removed from the system versus compression. This corresponds to an open cell foam formulation. (Integer)
`P`_min	Minimum pressure. (Real)	$[Pa]$
`fct_ID`_f	Curve identifier for pressure as function of volumetric strain volumetric strain is $γ = \frac{ρ_{0}}{ρ} - 1$ . (Integer)
`Fscale`_prs	Pressure function scale factor. Default = 1.0 (Real)
`F`_smooth	Smooth strain rate option flag. = 0 (Default) No strain rate smoothing. = 1 Strain rate smoothing active. (Integer)
`F`_cut	Cutoff frequency for the strain rate filtering. Default = 10000 Hz (Real)	$[Hz]$
`E`_t	Tangent modulus. (Real)	$[Pa]$
$ν_{t}$	Tangent Poisson's ratio. (Real)
$η_{0}$	Viscosity coefficient in pure shear (Navier's constant). (Real)	$[Pa \cdot s]$
$λ$	Navier's constant. (Real)	$[Pa \cdot s]$
`P`₀	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                    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
#---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

In all cases, for shear and bulk modulus calculation, the following value of the Young's modulus will be used:
$E = \max (E, E_{1} \dot{ε} + E_{2}) . {(\frac{V}{V_{0}})}^{n}$
If fct_ID_f = 0,
$\frac{d P}{d t} = C_{1} K {\dot{ε}}_{k k} - C_{2} [\frac{K + K_{t}}{3 λ + 2 η_{0}} σ_{k k}] + C_{3} [\frac{K K_{_{t}}}{3 λ + 2 η_{0}} ε_{k k}]$
Where,

$K = \frac{E}{3 (1 - 2 v)}$

$K_{t} = \frac{E_{t}}{3 (1 - 2 v_{t})}$

$P = - \frac{1}{3} σ_{k k}$

$ε_{k k} = \ln (\frac{V}{V_{0}})$
If fct_ID_f ≠ 0, the pressure is read from curve.
For closed cell polyurethane foam, the skeletal spherical stresses may be augmented by:
$P_{a i r} = - \frac{P_{0} \cdot γ}{1 + γ - Φ}$
The parameters F_smooth and F_cut allows you to enable strain-rate filtering. Three cases can be set:
- If F_smooth = 0 and F_cut = 0.0, the strain-rate filtering is turned off.
- If F_smooth = 1 and F_cut = 0.0, the strain-rate filtering uses a default cutoff frequency of 10 kHz.
- If F_cut ≠ 0, F_smooth is automatically set to 1 and the strain-rate filtering uses the cutoff frequency given by you.