Iform = 0

Block Format Keyword The material law is based on a diffusive interface technique.

To get sharper interfaces between submaterial zones, refer to /ALE/MUSCL.

LAW51 is based on equilibrium between each material present inside the element. Radioss computes and outputs a relative pressure Δ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaeiLdiaadcfaaaa@3B95@ . At each cycle:(1)
Δ P = Δ P 1 = Δ P 2 = Δ P 3
Total pressure can be calculated with external pressure:(2)
P = Δ P + P ext
Where,
P
Positive for a compression and negative for traction.
Hydrostatic stresses are computed from Polynomial EOS:(3)
σ m = Δ P = C 0 + C 1 μ + C 2 ' μ 2 + C 3 ' μ 3 + ( C 4 + C 5 μ ) E ( μ )
(4)
d E int = ( Δ P + P e x t ) d V

Where, E = E int / V 0 , C 2 ' = C 2 δ μ 0 a n d C 3 ' = C 3 δ μ 0 mean that the EOS is linear for an expansion and cubic for a compression.

Deviatoric stresses are computed with shear modulus:(5)
σ d e v = G ε

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW51/mat_ID/unit_ID
mat_title
Blank
Iform                  
#Global Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Pext ν ν v o l        
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 m a t _ 1 ρ 0 m a t _ 1 E 0 m a t _ 1 Δ P min m a t _ 1 C 0 m a t _ 1
C 1 m a t _ 1 C 2 m a t _ 1 C 3 m a t _ 1 C 4 m a t _ 1 C 5 m a t _ 1
G 1 m a t _ 1                
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 m a t _ 2 ρ 0 m a t _ 2 E 0 m a t _ 2 Δ P min m a t _ 2 C 0 m a t _ 2
C 1 m a t _ 2 C 2 m a t _ 2 C 3 m a t _ 2 C 4 m a t _ 2 C 5 m a t _ 2
G 1 m a t _ 2                
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 m a t _ 3 ρ 0 m a t _ 3 E 0 m a t _ 3 Δ P min m a t _ 3 C 0 m a t _ 3
C 1 m a t _ 3 C 2 m a t _ 3 C 3 m a t _ 3 C 4 m a t _ 3 C 5 m a t _ 3
G 1 m a t _ 3                

Definitions

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier.

(Interger, maximum 10 digits)

 
mat_title Material title.

(Character, maximum 100 characters)

 
Iform Formulation flag.

(Integer)

 
Pext External pressure. 2

Default = 0 (Real)

[ Pa ]
ν Kinematic viscosity shear ν = μ / ρ . 3

Default = 0 (Real)

[ m 2 s ]
ν v o l Kinematic viscosity (volumetric), ν v o l = 3 λ + 2 μ ρ which corresponds to Stokes Hypothesis. 3

Default = 0 (Real)

[ m 2 s ]
α 0 m a t _ i Initial volumetric fraction. 4

(Real)

 
ρ 0 m a t _ i Initial density.

(Real)

[ kg m 2 ]
E 0 m a t _ i Initial energy per unit volume.

(Real)

[ J m 3 ]
Δ P min m a t _ i Hydrodynamic cavitation pressure. 5

If fluid material ( G 1 m a t _ i = 0 ), then default = P e x t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeyOeI0IaamiuamaaBaaaleaacaWGLbGaamiEaiaadshaaeqaaaaa @3E74@ .

If solid material ( G 1 m a t _ i 0 ), then default = -1e30.

(Real)

[ Pa ]
C 0 m a t _ i Initial pressure.

(Real)

[ Pa ]
C 1 m a t _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 2 m a t _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 3 m a t _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 4 m a t _ i Hydrodynamic coefficient.

(Real)

 
C 5 m a t _ i Hydrodynamic coefficient.

(Real)

 
G 1 m a t _ i Elasticity shear modulus.
= 0 (Default)
Fluid material

(Real)

[ Pa ]

Example

/MAT/LAW51/1
99.99% Water + 0.01% Air-MULTIMAT: AIR+WATER,units{kg,m,s,Pa}
#(output is total pressure:Pext=0)
#--------------------------------------------------------------------------------------------------#
#                    Material Law No 51. MULTI-MATERIAL SOLID LIQUID GAS  ALE-CFD-SPH               
#--------------------------------------------------------------------------------------------------#
#     Blank format

#    IFORM
         0
#---Global parameters------------------------------------------------------------------------------#
#              P_EXT                  NU               LAMDA
                   0                   0                   0
#---Material#1:AIR(PerfectGas)---------------------------------------------------------------------#
#            ALPHA_1             RHO_0_1               E_0_1             P_MIN_1              C_0_1
              0.0001                 1.2             2.5E+05                   0                  0
#              C_1_1               C_2_1               C_3_1               C_4_1              C_5_1
                   0                   0                   0                 0.4                0.4
#                G_1
                   0
#---Material#2:WATER(Linear_Incompressible)--------------------------------------------------------#
#            ALPHA_2             RHO_0_2               E_0_2             P_MIN_2               C_0_2
              0.9999              1000.0                   0                   0                   0
#              C_1_2               C_2_2               C_3_2               C_4_2               C_5_2
             2.25E+9                   0                   0                   0                   0
#                G_2
                   0
#---Material#3:not defined-------------------------------------------------------------------------#
#            ALPHA_3             RHO_0_3               E_0_3             P_MIN_3               C_0_3
                 0.0                   0                   0                   0                   0
#              C_1_3               C_2_3               C_3_3               C_4_3               C_5_3
                   0                   0                   0                   0                   0
#                G_3
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW51/1
99.99% Water + 0.01% Air-MULTIMAT: AIR+WATER,units{kg,m,s,Pa}
#(output is relative pressure to Pext=1E+5Pa)
#--------------------------------------------------------------------------------------------------#
#                    Material Law No 51. MULTI-MATERIAL SOLID LIQUID GAS -ALE-CFD-SPH               
#--------------------------------------------------------------------------------------------------#
#     Blank format

#    IFORM
         0
#---Global parameters------------------------------------------------------------------------------#
#              P_EXT                  NU               LAMDA
                1E+5                   0                   0
#---Material#1:AIR(PerfectGas)---------------------------------------------------------------------#
#            ALPHA_1             RHO_0_1               E_0_1             P_MIN_1               C_0_1
              0.0001                 1.2             2.5E+05                   0               -1E+5
#              C_1_1               C_2_1               C_3_1               C_4_1               C_5_1
                   0                   0                   0                 0.4                 0.4
#                G_1
                   0
#---Material#2:WATER(Linear_Incompressible)--------------------------------------------------------#
#            ALPHA_2             RHO_0_2               E_0_2             P_MIN_2               C_0_2
              0.9999              1000.0                   0                   0                   0
#              C_1_2               C_2_2               C_3_2               C_4_2               C_5_2
             2.25E+9                   0                   0                   0                   0
#                G_2
                   0
#---Material#3:not defined-------------------------------------------------------------------------#
#            ALPHA_3             RHO_0_3               E_0_3             P_MIN_3               C_0_3
                 0.0                   0                   0                   0                   0
#              C_1_3               C_2_3               C_3_3               C_4_3               C_5_3
                   0                   0                   0                   0                   0
#                G_3
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Numerical diffusion can be improved using the second order method for volume fraction convection, /ALE/MUSCL. The previous /UPWIND used to limit diffusion is now obsolete
  2. Radioss computes and outputs a relative pressure Δ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaeiLdiaadcfaaaa@3B95@ .(6)
    Δ P = max { Δ P min , C 0 + C 1 μ + C 2 ' μ 2 + C 3 ' μ 3 + ( C 4 + C 5 μ ) E ( μ ) }

    However, total pressure is essential for energy integration ( d E int = P d V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamizaiaadweadaWgaaWcbaGaciyAaiaac6gacaGG0baabeaakiab g2da9iabgkHiTiaadcfacaWGKbGaamOvaaaa@42F4@ ). It can be computed with the external pressure flag Pext.

    P = Δ P + P e x t leads to d E int = ( P e x t + Δ P ) d V .

    This means that if Pext = 0, the computed pressure Δ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaeiLdiaadcfaaaa@3B95@ is also the total pressure: Δ P = P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaeiLdiaadcfacqGH9aqpcaWGqbaaaa@3D70@

  3. Kinematic viscosities are global and is not specific to each material. It allows computing viscous stress tensor:(7)
    τ = μ [ ( V ) + t ( V ) ] + λ ( V ) I
    Where,
    ν = μ / ρ
    Kinematic viscosity in shear
    ν v o l = 3 ( λ + 2 μ 3 ) ρ
    Kinematic volumetric viscosity
  4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

    For each material α 0 m a t _ i must be defined between 0 and 1.

    Sum of initial volumetric fractions i = 1 3 α 0 m a t _ i must be equal to 1.

    For automatic initial fraction of the volume, refer to the /INIVOL card.

  5. Δ P min m a t _ i flag is the minimum value for the computed pressure Δ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaeiLdiaadcfaaaa@3B95@ . It means that total pressure is also bounded to:(8)
    P min m a t _ i = Δ P min m a t _ i + P e x t

    For fluid materials and detonation products, P min m a t _ i must remain positive to avoid any tensile strength so Δ P min m a t _ i must be set to P e x t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeyOeI0IaamiuamaaBaaaleaacaWGLbGaamiEaiaadshaaeqaaaaa @3E74@ .

    For solid materials, default value Δ P min m a t _ i = 1e-30 is suitable but may be modified.

  6. Material tracking is possible through animation files:

    /ANIM/BRIC/VFRAC (All material volumetric fractions)