/EOS/COMPACTION

Block Format Keyword Describes pressure for a porous media such as soil or foam which can be compacted and unloaded.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/COMPACTION/mat_ID/unit_ID
eos_title
C0 C1 C2 C3  
μ min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3C1C@ μ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3C1C@ 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)

  
C0 EOS parameter

(Real)

  
C1 EOS parameter

(Real)

  
C2 EOS parameter

(Real)

  
C3 EOS parameter

(Real)

  
μ min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3C1C@ Elastic limit

No compaction below μ < μ min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBcq GH8aapcqaH8oqBdaWgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3ED6@

P e = C 0 + C 1 μ min + C 2 μ min 2 + C 3 μ min 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS baaSqaaiaadwgaaeqaaOGaeyypa0Jaam4qamaaBaaaleaacaaIWaaa beaakiabgUcaRiaadoeadaWgaaWcbaGaaGymaaqabaGccqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiabgUcaRiaadoeadaWg aaWcbaGaaGOmaaqabaGccqaH8oqBdaWgaaWcbaGaciyBaiaacMgaca GGUbaabeaakmaaCaaaleqabaGaaGOmaaaakiabgUcaRiaadoeadaWg aaWcbaGaaG4maaqabaGccqaH8oqBdaWgaaWcbaGaciyBaiaacMgaca GGUbaabeaakmaaCaaaleqabaGaaG4maaaaaaa@5406@

Default = 0.0 (Real)

  
μ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3C1C@ Maximum compaction

Default = 1020 (Real)

  
B Unloading bulk modulus

(Real)

 [ Pa ]
Psh Pressure shift

(Real)

 [ Pa ]
ρ 0 Initial 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/LAW06/6/1
law06
#              RHO_I        
             2.33e-3          
#                 NU                PMIN
                0.22               -0.02
/EOS/COMPACTION/6/1
law06-compaction
#                 C0                  C1                  C2                  C3
                1E-2               0.256               0.256                   1                
#              MUMIN               MUMAX                BUNL
                 0.0               0.115                1.44
#                PSH                RHO0
                   0                2.33             
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

  1. This equation of state is used to model pressure in porous media such as soil or foam. The compaction has an elastic response when it is less than the elastic limit μ = μ min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBcq GH9aqpcqaH8oqBdaWgaaWcbaGaciyBaiaacMgacaGGUbaabeaaaaa@3ED8@ .


    Figure 1.
  2. Plastic compaction is along path defined by curve:(1)
    P = C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaey ypa0Jaam4qamaaBaaaleaacaaIWaaabeaakiabgUcaRiaadoeadaWg aaWcbaGaaGymaaqabaGccqaH8oqBcqGHRaWkcaWGdbWaaSbaaSqaai aaikdaaeqaaOGaeqiVd02aaWbaaSqabeaacaaIYaaaaOGaey4kaSIa am4qamaaBaaaleaacaaIZaaabeaakiabeY7aTnaaCaaaleqabaGaaG 4maaaaaaa@49CE@
    Where,
    P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbaaaa@383D@
    Pressure in material
    μ
    Volumetric strain with μ = ρ ρ 0 − 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd0Maey ypa0ZaaSaaaeaacqaHbpGCaeaacqaHbpGCdaWgaaWcbaGaaGimaaqa baaaaOGaeyOeI0IaaGymaaaa@3EDA@
    Unloading and reloading are made along straight line whose slope is B.
    Psh
    Pressure shift value used to model the relative pressure formulation.


    Figure 2. Pressure versus Volumetric Strain
  3. In versions prior to 2019.1, this equation of state was embedded in /MAT/LAW10 with a fixed elastic limit, μ min = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH8oqBda WgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiabg2da9iaaicdaaaa@3DE6@ .
  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)