/MAT/LAW33 (FOAM_PLAS)

Block Format Keyword This law models a viscous-elastic 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
ρ i                
E Ka fct_IDf Fscalecrv        
P0 Φ γ 0        
A B C        
Read only if Ka = 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
E1 E2 Et η * η 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)

  
ρ i Initial density.

(Real)

 [ kg m 3 ]
E Young's modulus.

(Real)

 [ Pa ]
Ka Analysis type flag.
= 0
The skeletal behavior before yield is elastic.
= 1
The skeletal behavior before yield is visco-elastic.

(Integer)

  
fct_IDf Yield stress vs. volumetric strain curve function identifier.

(Integer)

  
Fscalecrv Scale factor for ordinate (stress) for fct_IDf.

Default = 1.0 (Real)

 [ Pa ]
P0 Initial air pressure. 5

(Real)

 [ Pa ]
Φ Ratio of foam to polymer density.

(Real)

  
γ 0 Initial volumetric strain.

(Real)

  
A Yield parameter.

(Real)

  
B Yield parameter.

(Real)

  
C Yield parameter.

(Real)

  
E1 Coefficient for Young's modulus update.

(Real)

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

(Real)

 [ Pa ]
Et Tangent modulus.

(Real)

 [ Pa ]
η * Viscosity coefficient in pure compression.

(Real)

  
η 0 Viscosity coefficient in pure shear.

(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_PLAS/1/1
Foam
#              RHO_I
               2E-10
#                  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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. If the limiting yield curve is not defined, then the material follows a Maxwell-Kelvin-Voight visco-elastic model.

    clip0061
    Figure 1.
  2. If the limiting yield curve is defined, then the material initially follows the visco-elastic law until it intersects the defined yield curve, which limits the visco-elastic stress in tension and compression. The material does not experience plasticity, but instead behaves in a visco hyperelastic way.
  3. If the yield function fct_IDf = 0, then(1)
    σ y = A + B ( 1 + C γ )
    Where, γ is the volumetric strain:(2)
    γ = V V 0 − 1 + γ 0 = ρ 0 ρ − 1 + γ 0 = − μ 1 + μ + γ 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHZoWzcq GH9aqpdaWcaaqaaiaadAfaaeaacaWGwbWaaSbaaSqaaiaaicdaaeqa aaaakiabgkHiTiaaigdacqGHRaWkcqaHZoWzdaWgaaWcbaGaaGimaa qabaGccqGH9aqpdaWcaaqaaiabeg8aYnaaBaaaleaacaaIWaaabeaa aOqaaiabeg8aYbaacqGHsislcaaIXaGaey4kaSIaeq4SdC2aaSbaaS qaaiaaicdaaeqaaOGaeyypa0ZaaSaaaeaacqGHsislcqaH8oqBaeaa caaIXaGaey4kaSIaeqiVd0gaaiabgUcaRiabeo7aNnaaBaaaleaaca aIWaaabeaaaaa@5604@
  4. If the yield function fct_IDf ≠ 0, then σ vs. γ is read from input of the curve idenfier fct_IDf. The curve can be defined for tensile ( γ > 0 ) and compression ( − 1 < γ < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeyOeI0IaaGymaiabgYda8iabeo7aNjabgYda8iaaicdaaaa@3C1D@ ). The input stress should be positive for both tension and compression.

    mat_law33_curve
    Figure 2.
  5. 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 a i r = − P 0 ⋅ γ 1 + γ − Φ
  6. Young’s modulus is used as the initial slope for unloading. It can be constant or variable, based on the strain rate.(4)
    E = max ( E , E 1 ε ˙ + E 2 )
  7. The unloading or the loading direction change (tensile <-> compression) is following the current elastic modulus, like an isotropic elastic-plastic material or highly viscous foam material. However, there is no plastic strain accumulation.


    Figure 3.