/EOS/OSBORNE

Block Format Keyword Describes the Osborne Equation of State from R.K. Osborne, also called the “quadratic EOS”.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/OSBORNE/mat_ID/unit_ID
eos_title
A1 A2 B0 B1 B2
C0 C1 D0 P0  
ρ 0        

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier.

(Integer, maximum 10 digits)

 
eos_title EOS title.

(Character, maximum 100 characters)

 
A1 Osborne parameter.

(Real)

[ P a 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @3A96@
A2 Osborne parameter.

(Real)

[ P a 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @3A96@
B0 Osborne parameter.

(Real)

[ Pa ]
B1 Osborne parameter.

(Real)

[ Pa ]
B2 Osborne parameter.

(Real)

[ Pa ]
C0 Osborne parameter.

(Real)

 
C1 Osborne parameter.

(Real)

 
D0 Osborne parameter.

(Real)

[ Pa ]
P0 Initial pressure.

(Real)

[ Pa ]
ρ 0 Reference density.

(Real)

[ kg m 3 ]

Table of Parameters

Here is a table of parameters for various material in unit system {g, cm, µs}
Material ρ 0 A 1 A 2 B 0 B 1 B 2 C 0 C 1 D 0
Beryllium 1.845 0.9512 0.3453 0.9269 2.9484 0.5080 0.5644 0.6204 0.8
Boron 2.34 1.8212 4.3509 0.3764 0.3287 1.0801 0.5531 0.6346 .25
Graphite 2.25 0.1608 0.1619 0.8866 0.5140 1.4377 0.5398 0.5960 0.5
Magnesium 1.735 0.5665 0.3343 2.2178 0.8710 0.4814 0.4163 0.5390 1.5
Titanium 4.51 1.9428 0.6591 1.8090 2.6115 1.7984 0.4003 0.5182 1.8
Water 1.00 0.000384 0.001756 0.01312 0.06265 0.21330 0.5132 0.6761 0.02
Plexiglas 1.18 0.006199 0.015491 0.14756 0.05619 .050504 0.5575 0.6151 0.1
Polystyrene 1.04 0.038807 0.043646 0.77420 0.03610 0.46048 0.5443 0.6071 0.5
Polyethylene 0.913 0.007841 0.009766 0.19257 0.10257 0.31592 0.5748 0.6230 0.1
Micarta 1.39 0.016164 0.023579 0.34261 0.15107 0.43434 0.0540 0.0612 0.15
Silastic 1.43 0.004794 0.04684 0.33969 0.02377 0.50767 0.4925 0.5721 0.3
Aluminum 2.702 1.1867 0.7630 3.4448 1.5451 0.96430 0.43382 0.54873 1.5
Copper 8.90 4.9578 3.6884 7.4727 11.519 5.5251 0.39493 0.52883 3.6
Iron 7.86 7.78 31.18 9.591 15.676 4.634 0.3984 0.5306 9.0
Tungsten 19.17 21.67419 14.93338 10.195827 12.263234 9.6051515 0.33388437 0.48248861 7.0
Steel 7.9 4.9578323 3.6883726 7.4727361 11.519148 5.521138 0.39492613 0.52883412 3.6
Uranium 2.806 2.4562457 3.6883726 7.47361 11.519148 5.521138 0.39492613 0.52883412 0.6

Example (Aluminum)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDPLA/7/1
ALUMINIUM-JCOOK
#              RHO_I               RHO_0
               2.702               2.702
#                  E                  nu
                .734                0.33
#                  a                   b                   n             eps_max           sigma_max
               .0024               .0042                  .8                   0              .00680
#               Pmin                 Psh
              -.0223                   0
/EOS/OSBORNE/7/1
OSBORNE-EOS-ALUMINIUM
#                 A1                  A2                  B0                  B1                  B2          
              1.1867              0.7630              3.4448              1.5451             0.96430 
#                 C0                  C1                  D0                  P0                  
             0.43382             0.54873                 1.5                 0.1                   
#               RHO0
               2.702
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This equation of state is due to R.K. Osborne:(1)
    P ( μ , E ) = A 1 μ + A 2 μ | μ | + ( B 0 + B 1 μ + B 2 μ 2 ) E + ( C 0 + C 1 μ ) E 2 E + D 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaciiuamaabmaapaqaa8qacqaH8oqBcaGGSaGaamyraaGaayjkaiaa wMcaaiabg2da9maalaaapaqaa8qacaWGbbWdamaaBaaaleaapeGaaG ymaaWdaeqaaOWdbiabeY7aTjabgUcaRiaadgeapaWaaSbaaSqaa8qa caaIYaaapaqabaGcpeGaeqiVd02aaqWaa8aabaWdbiabeY7aTbGaay 5bSlaawIa7aiabgUcaRmaabmaapaqaa8qacaWGcbWdamaaBaaaleaa peGaaGimaaWdaeqaaOWdbiabgUcaRiaadkeapaWaaSbaaSqaa8qaca aIXaaapaqabaGcpeGaeqiVd0Maey4kaSIaamOqa8aadaWgaaWcbaWd biaaikdaa8aabeaak8qacqaH8oqBpaWaaWbaaSqabeaapeGaaGOmaa aaaOGaayjkaiaawMcaaiaadweacqGHRaWkdaqadaWdaeaapeGaam4q a8aadaWgaaWcbaWdbiaaicdaa8aabeaak8qacqGHRaWkcaWGdbWdam aaBaaaleaapeGaaGymaaWdaeqaaOWdbiabeY7aTbGaayjkaiaawMca aiaadweapaWaaWbaaSqabeaapeGaaGOmaaaaaOWdaeaapeGaamyrai abgUcaRiaadseapaWaaSbaaSqaa8qacaaIWaaapaqabaaaaaaa@682A@
    Where,
    E MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyraaaa@36D6@
    Internal energy by initial volume
    E = E i n t V 0 = ρ 0 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyraiabg2da9maalaaapaqaa8qacaWGfbWdamaaBaaaleaapeGa amyAaiaad6gacaWG0baapaqabaaakeaapeGaamOva8aadaWgaaWcba Wdbiaaicdaa8aabeaaaaGcpeGaeyypa0JaeqyWdi3damaaBaaaleaa peGaaGimaaWdaeqaaOWdbiaadwgaaaa@430A@
    μ
    ρ ρ 0 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaSaaa8aabaWdbiabeg8aYbWdaeaapeGaeqyWdi3damaaBaaaleaa peGaaGimaaWdaeqaaaaak8qacqGHsislcaaIXaaaaa@3CB0@
    A 1 , A 2 , B 0 , B 1 , B 2 , C 0 , C 1 , D 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyqa8aadaWgaaWcbaWdbiaaigdaa8aabeaak8qacaGGSaGaamyq a8aadaWgaaWcbaWdbiaaikdaa8aabeaak8qacaGGSaGaamOqa8aada WgaaWcbaWdbiaaicdaa8aabeaak8qacaGGSaGaamOqa8aadaWgaaWc baWdbiaaigdaa8aabeaak8qacaGGSaGaamOqa8aadaWgaaWcbaWdbi aaikdaa8aabeaak8qacaGGSaGaam4qa8aadaWgaaWcbaWdbiaaicda a8aabeaak8qacaGGSaGaam4qa8aadaWgaaWcbaWdbiaaigdaa8aabe aak8qacaGGSaGaamira8aadaWgaaWcbaWdbiaaicdaa8aabeaaaaa@4A73@
    Constant parameters
  2. Initial pressure is used to compute E 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyra8aadaWgaaWcbaWdbiaaicdaa8aabeaaaaa@37EA@ such that P ( 0 , E 0 ) = P 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaciiuamaabmaapaqaa8qacaaIWaGaaiilaiaadweapaWaaSbaaSqa a8qacaaIWaaapaqabaaak8qacaGLOaGaayzkaaGaeyypa0Jaamiua8 aadaWgaaWcbaWdbiaaicdaa8aabeaaaaa@3EDB@ .
  3. Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws:
    • /MAT/LAW3 (HYDPLA)
    • /MAT/LAW4 (HYD_JCOOK)
    • /MAT/LAW6 (HYDRO or HYD_VISC)
    • /MAT/LAW10 (DPRAG1)
    • /MAT/LAW12 (3D_COMP)
    • /MAT/LAW49 (STEINB)
    • /MAT/LAW102 (DPRAG2)
    • /MAT/LAW103 (HENSEL-SPITTEL)