Iform = 1

Block Format Keyword This material is able to handle up to three elasto plastic materials (solid, liquid, or gas). The material law is based on a diffusive interface technique.

To get sharper interfaces between submaterial zones, refer to /ALE/MUSCL.
Note: It is not recommended to use this law with Radioss single precision engine.
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 e x t
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 W + δ Q = ( Δ P + P e x t ) d V + δ Q

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

By default process is adiabatic δ Q = 0 . To enable thermal computation, refer to 6.

Deviatoric stresses are computed with a Johnson-Cook model:(5)
σ dev ={ Gεif in elastic domain ( α+b ε p n )( 1+cln ε ˙ ε ˙ 0 )( 1 ( T T 0 T melt T 0 ) m )others MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipCI8FfYlH80rFfeuY=Hhcbf9v8qqaqFr0xb9pg0xb9 qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=x frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa aaleaacaWGKbGaamyzaiaadAhaaeqaaOGaeyypa0Zaaiqacqaabeqa aiaaywW7caaMf8UaaGzbVlaaywW7caaMf8UaaGzbVlaaywW7caWGhb GaeqyTduMaaGzbVlaaywW7caaMf8UaaGzbVlaaywW7caaMf8UaaGzb VlaaywW7caaMf8UaaeyAaiaabAgacaqGGaGaaeyAaiaab6gacaqGGa GaaeyzaiaabYgacaqGHbGaae4CaiaabshacaqGPbGaae4yaiaabcca caqGKbGaae4Baiaab2gacaqGHbGaaeyAaiaab6gaaeaadaqadiqaai abeg7aHjabgUcaRiaadkgacqaH1oqzdaWgaaWcbaGaamiCaaqabaGc daahaaWcbeqaaiaad6gaaaaakiaawIcacaGLPaaacaaMc8+aaeWace aacaaIXaGaey4kaSIaam4yaiGacYgacaGGUbWaaSaaaeaacuaH1oqz gaGaaaqaaiqbew7aLzaacaWaaSbaaSqaaiaaicdaaeqaaaaaaOGaay jkaiaawMcaaiaaykW7caaMc8+aaeWaceaacaaIXaGaeyOeI0YaaeWa ceaadaWcaaqaaiaadsfacqGHsislcaWGubWaaSbaaSqaaiaaicdaae qaaaGcbaGaamivamaaBaaaleaacaWGTbGaamyzaiaadYgacaWG0baa beaakiabgkHiTiaadsfadaWgaaWcbaGaaGimaaqabaaaaaGccaGLOa GaayzkaaWaaWbaaSqabeaacaWGTbaaaaGccaGLOaGaayzkaaGaaGzb Vlaab+gacaqG0bGaaeiAaiaabwgacaqGYbGaae4CaaaacaGL7baaaa a@9AD1@

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 mat _ 1 ρ 0 mat _ 1 E 0 mat _ 1 Δ P min mat _ 1 C 0 mat _ 1
C 1 mat _ 1 C 2 mat _ 1 C 3 mat _ 1 C 4 mat _ 1 C 5 mat _ 1
G 1 mat _ 1 a mat _ 1 b mat _ 1 n mat _ 1    
c mat _ 1 ε ˙ 0 mat _ 1            
m mat _ 1 T 0 mat _ 1 T melt mat _ 1 T lim mat_1 ρ C v mat_1
ε p,max mat_1 σ max mat _ 1 K A mat _ 1 K B mat _ 1    
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 mat _ 2 ρ 0 mat _ 2 E 0 mat _ 2 Δ P min mat _ 2 C 0 mat _ 2
C 1 mat _ 2 C 2 mat _ 2 C 3 mat _ 2 C 4 mat _ 2 C 5 mat _ 2
G 1 mat _ 2 a mat _ 2 b mat _ 2 n mat _ 2    
c mat _ 2 ε ˙ 0 mat _ 2            
m mat _ 2 T 0 mat _ 2 T melt mat _ 2 T lim mat _ 2 ρ C v mat _ 2
ε p , max m a t _ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqqrFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda qhaaWcbaGaamiCaiaacYcaciGGTbGaaiyyaiaacIhaaeaacaWGTbGa amyyaiaadshacaaMi8Uaai4xaiaaigdacaaMi8oaaaaa@4576@ σ max mat _ 2 K A mat _ 2 K B mat _ 2    
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 mat _ 3 ρ 0 mat _ 3 E 0 mat _ 3 Δ P min mat _ 3 C 0 mat _ 3
C 1 mat _ 3 C 2 mat _ 3 C 3 mat _ 3 C 4 mat _ 3 C 5 mat _ 3
G 1 mat _ 3 a mat _ 3 b mat _ 3 n mat _ 3    
c mat _ 3 ε ˙ 0 mat _ 3            
m mat _ 3 T 0 mat _ 3 T m e l t mat _ 3 T lim mat _ 3 ρ C v mat _ 3
ε p , max m a t _ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqqrFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda qhaaWcbaGaamiCaiaacYcaciGGTbGaaiyyaiaacIhaaeaacaWGTbGa amyyaiaadshacaaMi8Uaai4xaiaaigdacaaMi8oaaaaa@4576@ σ max mat _ 3 K A mat _ 3 K B mat _ 3    

Definition

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 mat _ i Initial volumetric fraction. 4

(Real)

 
ρ 0 mat _ i Initial density.

(Real)

[ kg m 3 ]
E 0 mat _ i Initial energy per unit volume.

(Real)

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

If fluid material ( G 1 mat _ 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 mat _ i 0 ), then default = -1e30.

(Real)

[ Pa ]
C 0 mat _ i Initial pressure.

(Real)

[ Pa ]
C 1 mat _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 2 mat _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 3 mat _ i Hydrodynamic coefficient.

(Real)

[ Pa ]
C 4 mat _ i Hydrodynamic coefficient.

(Real)

 
C 5 mat _ i Hydrodynamic coefficient.

(Real)

 
G 1 mat _ i Elasticity shear modulus.
= 0 (Default)
Fluid material

(Real)

[ Pa ]
a m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaacMgaaaaaaa@40ED@ Plasticity yield stress.

(Real)

[ Pa ]
b m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaacMgaaaaaaa@40ED@ Plasticity hardening parameter.

(Real)

[ Pa ]
n m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaacMgaaaaaaa@40ED@ Plasticity hardening exponent.

Default = 1.0 (Real)

 
c m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaacMgaaaaaaa@40ED@ Strain rate coefficient.
= 0
No strain rate effect

Default = 0.00 (Real)

 
ε ˙ 0 mat _ i Reference strain rate.

If ε ˙ ε ˙ 0 mat _ j , no strain rate effect

(Real)

[ 1 s ]
m m a t _ i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaacMgaaaaaaa@40ED@ Temperature exponent.

Default = 1.00 (Real)

 
T 0 mat _ i Initial temperature.

Default = 300 K (Real)

[ K ]
T m e l t mat _ i Melting temperature.
= 0
No temperature effect

Default = 1030 (Real)

[ K ]
T lim mat _ i Maximum temperature.

Default = 1030 (Real)

[ K ]
ρ C v mat _ i Specific heat per unit of volume. 7

(Real)

[ J m 3 K ]
ε p,max mat_i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipCI8FfYlH80rFfeuY=Hhcbf9v8qqaqFr0xb9pg0xb9 qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=x frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabew7aLnaaDa aaleaacaWGWbGaaiilaiGac2gacaGGHbGaaiiEaaqaaiaad2gacaWG HbGaamiDaiaayIW7caGGFbGaamyAaiaayIW7aaaaaa@44D6@ Failure plastic strain.

Default = 1030 (Real)

 
σ max mat _ i Plasticity maximum stress.

Default = 1030 (Real)

[ Pa ]
K A mat _ i Thermal conductivity coefficient 1. 8

(Real)

[ W m K ]
K B mat _ i Thermal conductivity coefficient 2. 8

(Real)

[ W m K 2 ]

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW51/1
99.99% Water + 0.01% Air-MULTIMAT:AIR+WATER+COPPER,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
         1
#---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           SIGMA_Y_1                BB_1                 N_1
                   0                   0                   0                   0
#               CC_1     EPSILON_DOT_0_1
                   0                   0
#               CM_1                T_10             T_1MELT            T_1LIMIT             RHOCV_1
                   0                   0                   0                   0                   0
#      EPSILON_MAX_1         SIGMA_MAX_1               K_A_1               K_B_1
                   0                   0                   0                   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           SIGMA_Y_2                BB_2                 N_2
                   0                   0                   0                   0
#               CC_2     EPSILON_DOT_0_2
                   0                   0
#               CM_2                T_20             T_2MELT            T_2LIMIT             RHOCV_2
                   0                   0                   0                   0                   0
#      EPSILON_MAX_2         SIGMA_MAX_2               K_A_2               K_B_2
                   0                   0                   0                   0
#---Material#3:OFHC COPPER(elastic plastic solid:Mie_Gruneisen+JCook)------------------------------#
#            ALPHA_3             RHO_0_3               E_0_3             P_MIN_3               C_0_3
                 0.0              8930.0                   0                   0                   0
#              C_1_3               C_2_3               C_3_3               C_4_3               C_5_3
           1.389E+11           1.379E+11          -0.351E+11                0.97                0.97
#                G_3           SIGMA_Y_3                BB_3                 N_3
             47.7E+9              120E+6              292E+6                0.31
#               CC_3     EPSILON_DOT_0_3
               0.025                   1
#               CM_3                T_30             T_3MELT            T_3LIMIT             RHOCV_3
                1.09                 300                1790                   0          3.42019E+6
#      EPSILON_MAX_3         SIGMA_MAX_3               K_A_3               K_B_3
                   0              1.2E+9                   0                   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 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaCiXdiabg2da9iabeY7aTnaadmGabaWaaeWaceaacqGHhis0cqGH xkcXcaWHwbaacaGLOaGaayzkaaGaey4kaSIaaGPaVpaaCaaaleqaba GaamiDaaaakiaaygW7daqadiqaaiabgEGirlabgEPielaahAfaaiaa wIcacaGLPaaaaiaawUfacaGLDbaacqGHRaWkcqaH7oaBdaqadiqaai abgEGirlaahAfaaiaawIcacaGLPaaacaWHjbaaaa@5817@
    Where,
    ν = μ / ρ
    Cinematic shear viscosity flag
    ν v o l = 3 ( λ + 2 μ 3 ) ρ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyVd42aaSbaaSqaaiaadAhacaWGVbGaamiBaaqabaGccqGH9aqp daWcaaqaaiaaiodadaqadiqaaiabeU7aSjabgUcaRmaalaaabaGaaG OmaiabeY7aTbqaaiaaiodaaaaacaGLOaGaayzkaaaabaGaeqyWdiha aaaa@4967@
    Cinematic volumetric viscosity flag
  4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

    For each material α 0 mat _ i must be defined between 0 and 1.

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

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

  5. Δ P min mat _ 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 mat _ i = Δ P min mat _ i + P e x t

    For fluid materials and detonation products, P min mat _ i must remain positive to avoid any tensile strength so Δ P min mat _ 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 mat _ i = 1e-30 is suitable but may be modified.

  6. Heat contribution is computed only if the thermal card is associated to the material law (/HEAT/MAT).
    In this case, δ Q = ρ C V V d T and the parameters for thermal diffusion are read for each material:(9)
    ρ C V mat _ i , K A mat _ i , K B mat _ i and T 0 mat _ i

    For solids and liquids, C ν C p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qamaaBaaaleaacqaH9oGBaeqaaOGaeyisISRaam4qamaaBaaa leaacaWGWbaabeaaaaa@3FF6@ for perfect gas: γ = C p / C ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4SdCMaeyypa0Jaam4qamaaBaaaleaacaWGWbaabeaakiaac+ca caWGdbWaaSbaaSqaaiabe27aUbqabaaaaa@41A5@

  7. The temperature evolution in the Johnson-Cook model is computed with the flag ρ C V mat _ i , even if the thermal card (/HEAT/MAT) is not defined.
  8. Thermal conductivity, K MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaci4saaaa@3A77@ , is linearly dependent on the temperature:(10)
    K ( T ) = K A + K B T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaci4samaabmGabaGaamivaaGaayjkaiaawMcaaiabg2da9iaadUea daWgaaWcbaGaamyqaaqabaGccqGHRaWkcaWGlbWaaSbaaSqaaiaadk eaaeqaaOGaamivaaaa@4335@
  9. Material tracking is possible through animation files:

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