/EOS/GRUNEISEN

Block Format Keyword Describes the Gruneisen equation of state.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/GRUNEISEN/mat_ID/unit_ID
eos_title
C S1 S2 S3  
γ 0 a E0 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)

  
C C sound speed. 1

(Real)

 [ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
S1 S1 material constant. 1

(Real)

  
S2 S2 material constant.

(Real)

  
S3 S3 material constant.

(Real)

  
γ 0 γ 0 coefficient.

(Real)

  
a a coefficient (see equation below).

Default = γ 0 (Real)

  
E0 Initial energy per unit reference volume.

(Real)

 [ J m 3 ]
ρ 0 Reference density.

Default = material density (Real)

 [ kg m 3 ]

Example (Copper)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/1/1
Copper (data from Example 46 - TNT Cylinder Expansion Test)
#              RHO_I               RHO_0
                8.96                   0
#                 E                   nu
                1.24                 .35
#                  A                   B                   n              epsmax              sigmax
                9E-4              .00292                 .31                   0               .0066
#               Pmin
               -1E30
#                  C           EPS_DOT_0                   M               Tmelt               Tmax
                .025                1E-6                1.09                1656                1E30
#              RHOCP                                                         T_r
            3.461E-5                                                           0
/EOS/GRUNEISEN/1/1
Copper
#                  C                  S1                  S2                  S3
                .394               1.489                   0                   0
#             GAMMA0               ALPHA                  E0               RHO_0
                1.97                 .47                   0                8.96
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

  1. C, S1, S2 and S3 are the coefficients of the cubic equation relating the shock velocity to the particle velocity.
  2. Let μ = ρ ρ 0 − 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd0Maey ypa0ZaaSaaaeaacqaHbpGCaeaacqaHbpGCdaWgaaWcbaGaaGimaaqa baaaaOGaeyOeI0IaaGymaaaa@3EDA@ , if μ > 0 , the pressure is given by:(1)
    P = ρ 0 C 2 μ [ 1 + ( 1 − γ 0 2 ) μ − a 2 μ 2 ] [ 1 − ( S 1 − 1 ) μ − S 2 μ 2 μ + 1 − S 3 μ 3 ( μ + 1 ) 2 ] 2 + ( γ 0 + a μ ) E
  3. If μ < 0 , the pressure is given by:(2)
    P = ρ 0 C 2 μ + ( γ 0 + a μ ) E
  4. 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)
  5. Input example with units: grams, cm, μ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBca WGZbaaaa@390D@ (micro-seconds):
    Material ρ 0 [ g c m 3 ] C   [ c m μ s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaabc cadaWadaqaamaalaaabaGaai4yaiaac2gaaeaacqaH8oqBcaGGZbaa aaGaay5waiaaw2faaaaa@3DE8@ S1 γ 0 a
    Cu 8.9 0.394 1.489 1.97 0.47
    Stainless Steel 1 7.9 0.457 1.490 2.00 0.50
    Al 2.7 0.533 1.338 2.18 0.48
    Al Alloy 2 2.7855 0.533 1.338 2.18 0.48
    Be 1.8519 0.8 1.124 1.16 0.16
    Mg Alloy 3 1.7794 0.452 1.242 1.63 0.33
    Ti 4.5249 0.47 1.146 1.3 0.20
    Ni 8.8968 0.465 1.445 2 0.50
    Pb 11.3379 0.201 1.54 2.84 0.54

1 Alloy 304, 72% Fe, 19% Cr, 9% Ni
2 Alloy 2024, 93,5% Al, 4.5% Cu, 1.5% Mg
3 Alloy AZ31B, 96%Mg, 3% Al, 1% Zn