/MAT/LAW6 (HYDRO or HYD_VISC)

Block Format Keyword Describes a fluid material. Pressure is computed using Equation of State provided by definition of /EOS option.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW6/mat_ID/unit_ID or /MAT/HYDRO/mat_ID/unit_ID or /MAT/HYD_VISC/mat_ID/unit_ID
mat_title
ρ i ρ 0
ν Pmin

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρ i Initial density.

(Real)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state).

Default = ρ 0 = ρ i (Real)

[ kg m 3 ]
ν Kinematic viscosity.

(Real)

[ m 2 s ]
Pmin Pressure cut-off.

Default = -1.0 x 1020 (Real)

[ Pa ]

Example (Air)

#RADIOSS STARTER
/UNIT/1
unit for mat
                  kg                   m                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDRO/4/1
AIR
#              RHO_I               RHO_0
                1.22                   0 
#                Knu                Pmin
              1.5E-5                   0
/EOS/POLYNOMIAL/4/1
AIR
#                 C0                  C1                  C2                  C3
                   0                   0                   0                   0
#                 C4                  C5                  E0                 Psh               RHO_0
                 0.4                 0.4              253300                   0                1.22
/EULER/MAT/4
#     Modif. factor.
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. S ij = 2 ρ ν eq e ˙ ij
    Where,
    ν eq = ν
    No turbulence
    S i j
    Deviatoric stress tensor
    e ˙ ij
    Deviatoric strain tensor
  2. Equation of state for hydrodynamic pressure has to be prescribed via the /EOS card.
  3. In case of a linear material with a volumetric dilatation:

    C 1 = E 3 ( 1 2 ν ) and C 4 = α ν C 1 ρ C ν T

    C 4 = C 5 = γ 1 and C 0 = C 2 = C 3 = 0

    then:

    p = C 1 μ + ( C 4 + C 5 μ ) E = C 1 μ + C 4 ( 1 + μ ) E = C 1 μ + C 4 ( 1 + μ ) ρ 0 e = C 1 μ + C 4 ( 1 + μ ) ρ 0 C ν T
    p = C 1 μ + C 4 ρ C ν T = C 1 μ + α ν T

    If p = c s t = 0 , then C 1 μ + α ν T = 0 l=; so μ = α ν T C 1

    Where,
    μ
    Dilatation coefficient
    μ < 0
    Dilatation
    In this case the parameters C2 and C3 will not be taken into account.
  4. All thermal data ( ρ 0 C p , T 0 , A , and B ) can be defined with keyword /HEAT/MAT.
  5. If using LAW6 coupled with LAW37 for liquid phase (without gas phase), the compatibility of the liquid EOS is:
    • Δ P 1 = C 1 μ for /MAT/LAW37 (BIPHAS)
    • p = C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 + ( C 4 + C 5 μ ) E for LAW6 via a polynomial EOS defined as in the Example above.

    with C 0 = C 2 = C 3 = C 4 = C 5 =E=0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGdbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0Jaam4qamaaBaaaleaacaaIYaaa beaakiabg2da9iaadoeadaWgaaWcbaGaaG4maaqabaGccqGH9aqpca WGdbWaaSbaaSqaaiaaisdaaeqaaOGaeyypa0Jaam4qamaaBaaaleaa caaI1aaabeaakiabg2da9iaadweacqGH9aqpcaaIWaaaaa@46A9@

    then, p = C 1 μ

  6. If using LAW6 coupled with LAW37 for gas phase (without liquid phase), the compatibility of the gas EOS is:
    • P V γ = c o n s t . for LAW37
    • p = ( γ 1 ) ( μ + 1 ) E for LAW6, via the /EOS/IDEAL-GAS equation of state.

    Where, E MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbaaaa@3832@ is the energy per unit volume.