/EOS/LINEAR

Block Format Keyword Describes the linear equation of state P ( μ ) = P 0 + B μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaae WaaeaacqaH8oqBaiaawIcacaGLPaaacqGH9aqpcaWGqbWaaSbaaSqa aiaaicdaaeqaaOGaey4kaSIaamOqaiabeY7aTbaa@41A6@ with initial pressure and bulk modulus.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/LINEAR/mat_ID/unit_ID
eos_title
P 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS baaSqaaiaaicdaaeqaaaaa@3923@ B 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)

  
P 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS baaSqaaiaaicdaaeqaaaaa@3923@ Initial pressure

(Real)

 [ Pa ]
B Bulk modulus

(Real)

 [ Pa ]
Psh Pressure shift

(Real)

 [ Pa ]
ρ 0 Reference density

(Real)

 [ kg m 3 ]

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW06/7/1
law06
#              RHO_I        
             2.33e-3          
#                 NU                PMIN
                0.22               -0.02
/EOS/LINEAR/7/1
linear EOS 
#                 P0                   B                 PSH                RHO0          
                   1                10.0                 0.0             2.33e-3  
/ALE/MAT/7
#               Flrd
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

  1. Linear EOS has the following form:(1)
    P ( μ ) = P 0 + B μ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaae WaaeaacqaH8oqBaiaawIcacaGLPaaacqGH9aqpcaWGqbWaaSbaaSqa aiaaicdaaeqaaOGaey4kaSIaamOqaiabeY7aTbaa@41A6@
    Where,(2)
    µ = ρ ρ 0 − 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadwlacqGH9aqpdaWcaaWdaeaapeGaeqyWdihapaqaa8qacqaH bpGCpaWaaSbaaSqaa8qacaaIWaaapaqabaaaaOWdbiabgkHiTiaaig daaaa@3F63@
    which can be derived from a polynomial EOS:(3)
    P = C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 + ( C 4 + C 5 μ ) E 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9iaadoeadaWgaaWcbaGaaGimaaqabaGccqGHRaWkcaWGdbWaaSba aSqaaiaaigdaaeqaaOGaeqiVd0Maey4kaSIaam4qamaaBaaaleaaca aIYaaabeaakiabeY7aTnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa doeadaWgaaWcbaGaaG4maaqabaGccqaH8oqBdaahaaWcbeqaaiaaio daaaGccqGHRaWkdaqadaqaaiaadoeadaWgaaWcbaGaaGinaaqabaGc cqGHRaWkcaWGdbWaaSbaaSqaaiaaiwdaaeqaaOGaeqiVd0gacaGLOa GaayzkaaGaamyramaaBaaaleaacaaIWaaabeaaaaa@5292@
    Where,
    C 0 = P 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIWaaabeaakiabg2da9iaadcfadaWgaaWcbaGaaGimaaqa baaaaa@3A6F@
    C 1 = B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaaabeaakiabg2da9iaadkeaaaa@397C@
    C 2 = C 3 = C 4 = C 5 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIYaaabeaakiabg2da9iaadoeadaWgaaWcbaGaaG4maaqa baGccqGH9aqpcaWGdbWaaSbaaSqaaiaaisdaaeqaaOGaeyypa0Jaam 4qamaaBaaaleaacaaI1aaabeaakiabg2da9iaaicdaaaa@41B6@
  2. Bulk modulus is usually estimated as:(4)
    B = ρ 0 ⋅ c 0 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9iabeg8aYnaaBaaaleaacaaIWaaabeaakiabgwSixlaadogadaWg aaWcbaGaaGimaaqabaGcdaahaaWcbeqaaiaaikdaaaaaaa@3F7E@

    Where, c 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacaaIWaaabeaaaaa@37C4@ is the initial sound speed.

  3. Psh parameter enables to shift output pressure. Output pressure will also be a relative pressure Δ P ( μ ) = P − P s h MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iuamaabmaabaGaeqiVd0gacaGLOaGaayzkaaGaeyypa0Jaamiuaiab gkHiTiaadcfadaWgaaWcbaGaam4CaiaadIgaaeqaaaaa@411E@ .
  4. Equation of states are compatible with materials LAW3, 4, 6, 10, 12, and 49.