/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 | |||||||||
ρiρi | |||||||||
E | νν | E1 | E2 | n | |||||
C1 | C2 | C3 | IFlag | Pmin | |||||
fct_IDf | Fscaleprs | Fsmooth | Fcut | ||||||
Et | νtνt | η0η0 | λλ | ||||||
P0 | ΦΦ | γ0γ0 |
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) |
|
ρiρi | Initial density (Real) |
[kgm3][kgm3] |
E | Young's modulus (Real) |
[Pa][Pa] |
νν | Poisson's ratio (Real) |
|
E1 | Coefficient for Young's modulus update
E=E1˙ε+E2E=E1˙ε+E2
. (Real) |
[Pa][Pa] |
E2 | Coefficient for Young's modulus
update. (Real) |
[Pa][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.
(Integer) |
|
Pmin | Minimum pressure. (Real) |
[Pa][Pa] |
fct_IDf | Curve identifier for pressure as
function of volumetric strain volumetric strain is
γ=ρ0ρ−1γ=ρ0ρ−1
. (Integer) |
|
Fscaleprs | Pressure function scale
factor. Default = 1.0 (Real) |
|
Fsmooth | Smooth strain rate option flag.
|
|
Fcut | Cutoff frequency for the strain rate
filtering. Default = 10000 Hz (Real) |
[Hz][Hz] |
Et | Tangent modulus. (Real) |
[Pa][Pa] |
νtνt | Tangent Poisson's
ratio. (Real) |
|
η0η0 | Viscosity coefficient in pure shear
(Navier's constant). (Real) |
[Pa⋅s][Pa⋅s] |
λλ | Navier's constant. (Real) |
[Pa⋅s][Pa⋅s] |
P0 | Initial air
pressure. (Real) |
[Pa][Pa] |
ΦΦ | Ratio of foam to polymer
density. (Real) |
|
γ0γ0 | 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:
(1) E=max(E,E1˙ε+E2).(VV0)nE=max(E,E1˙ε+E2).(VV0)n - If
fct_IDf =
0,
(2) dPdt=C1K˙εkk−C2[K+Kt3λ+2η0σkk]+C3[KKt3λ+2η0εkk]dPdt=C1K˙εkk−C2[K+Kt3λ+2η0σkk]+C3[KKt3λ+2η0εkk]Where,- K=E3(1−2v)K=E3(1−2v)
- Kt=Et3(1−2vt)Kt=Et3(1−2vt)
- P=−13σkkP=−13σkk
- εkk=ln(VV0)εkk=ln(VV0)
- If fct_IDf ≠ 0, the pressure is read from curve.
- For closed cell polyurethane
foam, the skeletal spherical stresses may be augmented by:
(3) Pair=−P0⋅γ1+γ−ΦPair=−P0⋅γ1+γ−Φ - The parameters Fsmooth and Fcut
allows you to enable strain-rate filtering. Three cases can be set:
- If Fsmooth = 0 and Fcut = 0.0, the strain-rate filtering is turned off.
- If Fsmooth = 1 and Fcut = 0.0, the strain-rate filtering uses a default cutoff frequency of 10 kHz.
- If Fcut ≠ 0, Fsmooth is automatically set to 1 and the strain-rate filtering uses the cutoff frequency given by you.