/EOS/POLYNOMIAL

Block Format Keyword Describes the linear polynomial equation of state P ( ρ , E ) .

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/POLYNOMIAL/mat_ID/unit_ID
eos_title
C0 C1 C2 C3  
C4 C55 E0 Psh ρ 0

Definitions

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)

  
C0 Hydrodynamic pressure law coefficient

(Real)

 [ Pa ]
C1 Hydrodynamic pressure law coefficient

(Real)

 [ P ]
C2 Hydrodynamic pressure law coefficient

(Real)

 [ Pa ]
C3 Hydrodynamic pressure law coefficient

(Real)

 [ Pa ]
C4 Energy pressure law coefficient

(Real)

  
C5 Energy pressure law coefficient

(Real)

  
E0 Initial internal energy per unit reference volume

(Real)

 [ J m 3 ]
Psh Pressure shift

(Real)

 [ Pa ]
ρ 0 Reference density

Default = material density (Real)

 [ kg m 3 ]

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW20/1
steel (unit: g_cm_mus)
#        BLANK CARD                     

#  mat_ID1   mat_ID2                                     IC1       IC2 Idiscrete
         8         9                                       0         0         0
#             Alpha1              Alpha2
                0.82                0.18
/ALE/MAT/1
#     Modif. factor.
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/8
steel
#              RHO_I               RHO_O
           7.8899999                   0
#                 E                   nu
           2.0999999           .30000001
#                  A                   B                   n              epsmax              sigmax
                .011              .00275           .36000001                   0                   0
#               Pmin
               1E-10
#                  C           EPS_DOT_0                   M               Tmelt                Tmax
                .022                1E-6                   1                1811                2000
#              RHOCP                                                         T_r
        3.5699999E-5                                                           0
/EOS/POLYNOMIAL/8
steel
#                 C0                  C1                  C2                  C3
                   0           1.6900001           3.0999999                   0
#                 C4                  C5                  E0                 Psh               RHO_0
                1.83                1.83                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/9
tungstene
#              RHO_I               RHO_O
                17.6                   0
#                 E                   nu
           3.5999999           .30000001
#                  A                   B                   n              epsmax              sigmax
              .01506              .00177                 .12                   0                   0
#               Pmin
               1E-10
#                  C           EPS_DOT_0                   M               Tmelt                Tmax
          .016000001                1E-6                   1                3400                3400
#              RHOCP                                                         T_r
             2.36E-5                                                           0
/EOS/POLYNOMIAL/9
tungstene
#                 C0                  C1                  C2                  C3
                   0           2.8199999                   2               -1.37
#                 C4                  C5                  E0                 Psh               RHO_0
                1.54                1.54                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

  1. Pressure is defined by the linear polynomial:(1)
    P = C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 + ( C 4 + C 5 μ ) E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9iaadoeadaWgaaWcbaGaaGimaaqabaGccqGHRaWkcaWGdbWaaSba aSqaaiaaigdaaeqaaOGaeqiVd0Maey4kaSIaam4qamaaBaaaleaaca aIYaaabeaakiabeY7aTnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa doeadaWgaaWcbaGaaG4maaqabaGccqaH8oqBdaahaaWcbeqaaiaaio daaaGccqGHRaWkdaqadaqaaiaadoeadaWgaaWcbaGaaGinaaqabaGc cqGHRaWkcaWGdbWaaSbaaSqaaiaaiwdaaeqaaOGaeqiVd0gacaGLOa GaayzkaaGaamyraaaa@51AC@
    with (2)
    μ = ρ ρ 0 − 1

    and E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraaaa@36C0@ being the internal energy per unit reference volume.

  2. If μ < 0 , then C 2 μ 2 = 0 .
  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)