Processing math: 100%

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 ΔP . At each cycle:(1)
ΔP=ΔP1=ΔP2=ΔP3
Total pressure can be calculated with external pressure:(2)
P=ΔP+Pext
Where,
P
Positive for a compression and negative for traction.
Hydrostatic stresses are computed from Polynomial EOS:(3)
σm=ΔP=C0+C1μ+C'2μ2+C'3μ3+(C4+C5μ)E(μ)
(4)
dEint=(ΔP+Pext)dV

Where, E=Eint/V0,C'2=C2δμ0andC'3=C3δμ0 mean that the EOS is linear for an expansion and cubic for a compression.

Deviatoric stresses are computed with shear modulus:(5)
σdev=Gε

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 νvol        
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_10 ρmat_10 Emat_10 ΔPmat_1min Cmat_10
Cmat_11 Cmat_12 Cmat_13 Cmat_14 Cmat_15
Gmat_11                
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_20 ρmat_20 Emat_20 ΔPmat_2min Cmat_20
Cmat_21 Cmat_22 Cmat_23 Cmat_24 Cmat_25
Gmat_21                
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_30 ρmat_30 Emat_30 ΔPmat_3min Cmat_30
Cmat_31 Cmat_32 Cmat_33 Cmat_34 Cmat_35
Gmat_31                

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)

[m2s]
νvol Kinematic viscosity (volumetric), νvol=3λ+2μρ which corresponds to Stokes Hypothesis. 3

Default = 0 (Real)

[m2s]
αmat_i0 Initial volumetric fraction. 4

(Real)

 
ρmat_i0 Initial density.

(Real)

[kgm2]
Emat_i0 Initial energy per unit volume.

(Real)

[Jm3]
ΔPmat_imin Hydrodynamic cavitation pressure. 5

If fluid material ( Gmat_i1=0 ), then default = Pext .

If solid material ( Gmat_i10 ), then default = -1e30.

(Real)

[Pa]
Cmat_i0 Initial pressure.

(Real)

[Pa]
Cmat_i1 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i2 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i3 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i4 Hydrodynamic coefficient.

(Real)

 
Cmat_i5 Hydrodynamic coefficient.

(Real)

 
Gmat_i1 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 ΔP .(6)
    ΔP=max{ΔPmin,C0+C1μ+C'2μ2+C'3μ3+(C4+C5μ)E(μ)}

    However, total pressure is essential for energy integration ( dEint=PdV ). It can be computed with the external pressure flag Pext.

    P=ΔP+Pext leads to dEint=(Pext+ΔP)dV .

    This means that if Pext = 0, the computed pressure ΔP is also the total pressure: ΔP=P

  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
    νvol=3(λ+2μ3)ρ
    Kinematic volumetric viscosity
  4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

    For each material αmat_i0 must be defined between 0 and 1.

    Sum of initial volumetric fractions 3i=1αmat_i0 must be equal to 1.

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

  5. ΔPmat_imin flag is the minimum value for the computed pressure ΔP . It means that total pressure is also bounded to:(8)
    Pmat_imin=ΔPmat_imin+Pext

    For fluid materials and detonation products, Pmat_imin must remain positive to avoid any tensile strength so ΔPmat_imin must be set to Pext .

    For solid materials, default value ΔPmat_imin = 1e-30 is suitable but may be modified.

  6. Material tracking is possible through animation files:

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