Iform = 10

Block Format Keyword Able to handle up to four materials: Three elasto-plastic materials (solid, liquid, or gas), and one high explosive material (JWL EOS).

The material law is based on a diffusive interface technique. For sharper interfaces between submaterial zone, refer to /ALE/MUSCL.

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)
ΔP=ΔP 1 =ΔP 2 =ΔP = 3 ΔP 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeuiLdqKaamiuaiabg2da9iabfs5aejaadcfacaaMi8+aaSbaaSqa aiaaigdaaeqaaOGaeyypa0JaeuiLdqKaamiuaiaayIW7daWgaaWcba GaaGOmaaqabaGccqGH9aqpcqqHuoarcaWGqbWaaSraaSqaaiaaioda aeqaaOGaeyypa0JaeuiLdqKaamiuaiaayIW7daWgaaWcbaGaaGinaa qabaaaaa@5159@
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 a n d C 3 ' = C 3 δ μ 0 mean that the EOS is linear for an expansion and cubic for a compression.

By default, the 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 σ VM α ( α+b ε p n )( 1+cln ε ˙ ε ˙ 0 )( 1 ( T T 0 T melt T 0 ) m )if σ VM >α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aaSbaaSqaaiaadsgacaWGLbGaamODaaqabaGccqGH9aqp daGabiabaeqabaGaaGzbVlaaywW7caaMf8UaaGzbVlaaywW7caaMf8 UaaGzbVlaadEeacqaH1oqzcaaMf8UaaGzbVlaaywW7caaMf8UaaGzb VlaaywW7caaMf8UaaGzbVlaaywW7caWGPbGaamOzaiaaysW7cqaHdp WCdaWgaaWcbaGaamOvaiaad2eaaeqaaOGaeyizImQaaGjbVlabeg7a HbqaamaabmGabaGaeqySdeMaey4kaSIaamOyaiabew7aLnaaBaaale aacaWGWbaabeaakmaaCaaaleqabaGaamOBaaaaaOGaayjkaiaawMca aiaaykW7daqadiqaaiaaigdacqGHRaWkcaWGJbGaciiBaiaac6gada Wcaaqaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGim aaqabaaaaaGccaGLOaGaayzkaaGaaGPaVlaaykW7daqadiqaaiaaig dacqGHsisldaqadiqaamaalaaabaGaamivaiabgkHiTiaadsfadaWg aaWcbaGaaGimaaqabaaakeaacaWGubWaaSbaaSqaaiaad2gacaWGLb GaamiBaiaadshaaeqaaOGaeyOeI0IaamivamaaBaaaleaacaaIWaaa beaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaad2gaaaaakiaawI cacaGLPaaacaaMf8UaamyAaiaadAgacaaMe8Uaeq4Wdm3aaSbaaSqa aiaadAfacaWGnbaabeaakiabg6da+iaaysW7cqaHXoqyaaGaay5Eaa aaaa@9D99@
High explosive material is modeled with linear EOS if unreacted and JWL EOS for detonation products:(6)
ΔP={ C 0 + C 1 μifT< T det A( 1 ω R 1 V ) e R 1 V +B( 1 ω R 2 V ) e R 2 V +ω E V if σ VM >α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeuiLdqKaamiuaiabg2da9maaceGaeaqabeaacaaMf8UaaGzbVlaa ywW7caaMf8UaaGzbVlaaywW7caaMf8Uaam4qamaaBaaaleaacaaIWa aabeaakiabgUcaRiaadoeadaWgaaWcbaGaaGymaaqabaGccqaH8oqB caaMf8UaaGzbVlaaywW7caaMf8UaaGzbVlaaywW7caaMe8UaaGjbVl aaywW7caWGPbGaamOzaiaaysW7caWGubGaeyipaWJaaGjbVlaadsfa daWgaaWcbaGaciizaiaacwgacaGG0baabeaaaOqaaiaadgeadaqadi qaaiaaigdacqGHsisldaWcaaqaaiabeM8a3bqaaiaadkfadaWgaaWc baGaaGymaaqabaGccaWGwbaaaaGaayjkaiaawMcaaiaaykW7caWGLb WaaWbaaSqabeaacqGHsislcaWGsbWaaSbaaWqaaiaaigdaaeqaaSGa amOvaaaakiabgUcaRiaadkeadaqadiqaaiaaigdacqGHsisldaWcaa qaaiabeM8a3bqaaiaadkfadaWgaaWcbaGaaGOmaaqabaGccaWGwbaa aaGaayjkaiaawMcaaiaadwgadaahaaWcbeqaaiabgkHiTiaadkfada WgaaadbaGaaGOmaaqabaWccaWGwbaaaOGaey4kaSIaeqyYdC3aaSaa aeaacaWGfbaabaGaamOvaaaacaaMf8UaamyAaiaadAgacaaMe8Uaeq 4Wdm3aaSbaaSqaaiaadAfacaWGnbaabeaakiabg6da+iaaysW7cqaH XoqyaaGaay5Eaaaaaa@9595@

Where, V is relative volume: V = V o l u m e / V 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamOvaiabg2da9iaadAfacaWGVbGaamiBaiaadwhacaWGTbGaamyz aiaac+cacaWGwbWaaSbaaSqaaiaaicdaaeqaaaaa@4391@ and E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaamyraaaa@3A70@ is the internal energy per unit initial volume: E = E int / V 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaamyraiabg2da9iaadweadaWgaaWcbaGaciyAaiaac6gacaGG0baa beaakiaac+cacaWGwbWaaSbaaSqaaiaaicdaaeqaaaaa@41C3@ . 9 to 13

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 amat_1 bmat_1 nmat_1    
cmat_1 ε ˙ 0 m a t _ 1            
m m a t _ 1 T 0 m a t _ 1 T m e l t m a t _ 1 T lim m a t _ 1 ρ C v mat_1
ε p,max mat_1 σ max m a t _ 1 K A m a t _ 1 K B 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 a m a t _ 2 b m a t _ 2 n m a t _ 2    
c m a t _ 2 ε ˙ 0 m a t _ 2            
m m a t _ 2 T 0 m a t _ 2 T m e l t m a t _ 2 T lim m a t _ 2 ρ C v m a t _ 2
ε p , max m a t _ 2 σ max m a t _ 2 K A m a t _ 2 K B 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 a m a t _ 3 b m a t _ 3 n m a t _ 3    
c m a t _ 3 ε ˙ 0 m a t _ 3            
m m a t _ 3 T 0 m a t _ 3 T m e l t m a t _ 3 T lim m a t _ 3 ρ C v m a t _ 3
ε p , max m a t _ 3 σ max m a t _ 3 K A m a t _ 3 K B m a t _ 3    
#Material4 Parameters (Explosive)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 0 m a t _ 4 ρ 0 m a t _ 4 E 0 m a t _ 4 Δ P min m a t _ 4 C 0 m a t _ 4
A B R1 R2 ω
D PCJ C 1 m a t _ 4     IBFRAC  

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)

 
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 3 ]
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 = -Pext

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. 9

(Real)

[ Pa ]
C 5 m a t _ i Hydrodynamic coefficient.

(Real)

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

(Real)

[ Pa ]
a m a t _ i 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 aiaaygW7caWGPbaaaaaa@4278@ 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 aiaaygW7caWGPbaaaaaa@4278@ Plasticity hardening exponent.

Default = 1.0 (Real)

 
c mat_i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4yamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaaygW7caWGPbaaaaaa@4278@ Strain rate coefficient.
= 0
No strain rate effect

Default = 0.00 (Real)

 
ε ˙ 0 m a t _ i Reference strain rate.

If ε ˙ ε ˙ 0 m a t _ i , no strain rate effect

(Real)

[ 1 s ]
m mat_i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyBamaaDaaaleaaaeaacaWGTbGaamyyaiaadshacaaMi8Uaai4x aiaaygW7caWGPbaaaaaa@4282@ Temperature exponent.

Default = 1.00 (Real)

 
T 0 m a t _ i Initial temperature.

Default = 300 K (Real)

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

Default = 1030 (Real)

[ K ]
T lim m a t _ i Maximum temperature.

Default = 1030 (Real)

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

(Real)

[ J m 3 K ]
ε p , max m a t _ i Failure plastic strain.

Default = 1030 (Real)

 
σ max m a t _ i Plasticity maximum stress.

Default = 1030 (Real)

[ Pa ]
K A m a t _ i Thermal conductivity coefficient 1. 8

(Real)

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

(Real)

[ W m K 2 ]
α 0 m a t _ 4 Initial volumetric fraction of unreacted explosive. 4

(Real)

 
ρ 0 m a t _ 4 Initial density of unreacted. explosive

(Real)

[ kg m 3 ]
E 0 m a t _ 4 Detonation energy.

(Real)

[ J m 3 ]
Δ P min m a t _ 4 Minimum pressure. 5

Default = P e x t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeyOeI0IaamiuamaaBaaaleaacaWGLbGaamiEaiaadshaaeqaaaaa @3E74@

(Real)

[ Pa ]
C 0 m a t _ 4 Initial pressure of unreacted explosive.

(Real)

[ Pa ]
A JWL EOS coefficient.

(Real)

[ Pa ]
B JWL EOS coefficient.

(Real)

[ Pa ]
R1 JWL EOS coefficient.

(Real)

 
R2 JWL EOS coefficient.

(Real)

 
ω JWL EOS coefficient.

(Real)

 
D Detonation velocity. [ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
PCJ Chapman-Jouget pressure.

(Real)

[ Pa ]
C 1 m a t _ 4 Hydrodynamic coefficient for unreacted explosive. 9

(Real)

[ Pa ]
IBFRAC Burn Fraction Calculation flag. 11
= 0
Volumetric Compression + Burning Time
= 1
Volumetric Compression only
= 2
Burning Time only

(Integer)

 

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW51/99
99.99% Water + 0.01% Air-MULTIMAT:AIR+WATER+TNT,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
        10
#---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           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                1E+5 
#              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:not defined Plastic material with Johnson-Cook Yield criteria-----------------------#
#            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           SIGMA_Y_3                BB_3                 N_3
                   0                   0                   0                   0
#               CC_3     EPSILON_DOT_0_3
                   0                   0
#               CM_3                T_30             T_3MELT            T_3LIMIT             RHOCV_3
                   0                   0                   0                   0                   0
#      EPSILON_MAX_3         SIGMA_MAX_3               K_A_3               K_B_3
                   0                   0                   0                   0
#---Material#4:TNT(JWL)----------------------------------------------------------------------------#
#            ALPHA_4             RHO_0_4               E_0_4             P_MIN_4               C_0_4
                 0.0                1590              7.0E+9               1E-30             1.0E+05
#                B_1                 B_2                 R_1                 R_2                   W
           371.20E+9            3.231E+9                4.15              0.9499                 0.3
#                  D                P_CJ                C_14                       I_BFRAC
              6930.0             2.1E+10             22.5E+5                             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@ .(7)
    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 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:(8)
    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
    Kinematic 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@
    Kinematic volumetric viscosity flag
  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:(9)
    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. By default, the process is adiabatic: δ Q = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiTdqMaamyuaiabg2da9iaaicdaaaa@3DE1@ . 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:(10)
    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 Gaam4saaaa@3A76@ , is linearly dependent on the temperature:(11)
    K ( T ) = K A + K B T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEieu0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4samaabmGabaGaamivaaGaayjkaiaawMcaaiabg2da9iaadUea daWgaaWcbaGaamyqaaqabaGccqGHRaWkcaWGlbWaaSbaaSqaaiaadk eaaeqaaOGaamivaaaa@4334@
  9.   C 1 m a t _ 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiiOaiaadoeapaWaa0baaSqaa8qacaaIXaaapaqaa8qacaWGTbGa amyyaiaadshacaGGFbGaaGinaaaaaaa@3D90@ can be estimated 1 with (12)
    C 1 m a t _ 4 =   ρ 0 m a t _ 4   ( c 0 u n r e a c t e d ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qamaaDaaaleaacaaIXaaabaGaamyBaiaadggacaWG0bGaai4x aiaaisdaaaGccqGH9aqpcaGGGcGaeqyWdi3aaSbaaSqaaiaaicdaae qaaOWaaWbaaSqabeaacaWGTbGaamyyaiaadshacaGGFbGaaGinaaaa kiabgwSixlaacckadaqadaWdaeaapeGaam4ya8aadaqhaaWcbaWdbi aaicdaa8aabaWdbiaadwhacaWGUbGaamOCaiaadwgacaWGHbGaam4y aiaadshacaWGLbGaamizaaaaaOGaayjkaiaawMcaa8aadaahaaWcbe qaa8qacaaIYaaaaaaa@5657@

    Where, c 0 u n r e a c t e d MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ya8aadaqhaaWcbaWdbiaaicdaa8aabaWdbiaadwhacaWGUbGa amOCaiaadwgacaWGHbGaam4yaiaadshacaWGLbGaamizaaaaaaa@4081@ is the speed of sound in the unreacted explosive and an estimation for TNT is 2000 m/s.

  10. Explosive material ignition is made with detonator cards, /DFS/DETPOINT or /DFS/DETPLAN.
  11. Detonation Velocity (D) and Chapman Jouget Pressure (PCJ) are used to compute the burn fraction calculation ( B f r a c [ 0 , 1 ] ). It controls the release of detonation energy and corresponds to a factor which multiplies JWL pressure.

    For a given time: P ( V , E ) = B f r a c P j w l ( V , E ) .

    A detonation time Tdet is computed by the Starter from the detonation velocity. During the simulation the burn fraction is computed as:(13)
    B f r a c = min ( 1 , m a x ( B f 1 , B f 2 ) )
    Where, the burn fraction calculation from burning time is:(14)
    B f 1 = 1 V 1 V C J = ρ 0   D 2 P C J ( 1 V )
    and the burn fraction calculation from volumetric compression is:(15)
    B f 2 = { 0 , x < 0 T T d e t 1.5 Δ x , x 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOqa8aadaWgaaWcbaWdbiaadAgacaaIYaaapaqabaGcpeGaeyyp a0Zaaiqaa8aabaqbaeqabiqaaaqaa8qacaaIWaGaaiilauaabeqabe aaaeaaaaGaamiEaiabgYda8iaaicdaa8aabaWdbmaalaaapaqaa8qa caWGubGaeyOeI0Iaamiva8aadaWgaaWcbaWdbiaadsgacaWGLbGaam iDaaWdaeqaaaGcbaWdbiaaigdacaGGUaGaaGynaiaabs5acaWG4baa aiaacYcafaqabeqabaaabaaaaiaadIhacqGHLjYScaaIWaaaaaGaay 5Eaaaaaa@4E12@

    It can take several cycles for the burn fraction to reach its maximum value of 1.00.

    Burn fraction calculation can be changed defining the IBFRAC flag:

    IBFRAC = 1: B f r a c = min ( 1 , B f 1 )

    IBFRAC = 2: B f r a c = min ( 1 , B f 2 )

  12. As of version 11.0.240, Time Histories for Detonation time and burn fraction are available through /TH/BRIC with BFRAC keyword. This allows to output a function f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOzaaaa@36F7@ whose first value is detonation time (with opposite sign) and positive values corresponds to the burn fraction evolution.(16)
    T det = f ( 0 ) B f r a c ( t ) = { 0 , f ( t ) < 0 f ( t ) , f ( t ) 0
  13. Detonation times can be written in the Starter output file for each JWL element. The printout flag (Ipri) must be greater than or equal to 3 (/IOFLAG).
  14. Material tracking is possible through animation files:

    /ANIM/BRICK/VFRAC (volumetric fractions for all materials)

1 Hayes, B. "Fourth Symposium (International) on Detonation." Proceedings, Office of Naval Research, Department of the Navy, Washington, DC (1965): 595-601