/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`
$ρ_{i}$		$ρ_{0}$
$ν$		`P`_min

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)	$[\frac{kg}{m^{3}}]$
$ρ_{0}$	Reference density used in E.O.S (equation of state). Default = $ρ_{0} = ρ_{i}$ (Real)	$[\frac{kg}{m^{3}}]$
$ν$	Kinematic viscosity. (Real)	$[\frac{m^{2}}{s}]$
`P`_min	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

$S_{ij} = 2 ρ ν_{eq} {\dot{e}}_{ij}$
Where,

$ν_{eq} = ν$

No turbulence

$S_{i j}$

Deviatoric stress tensor

${\dot{e}}_{ij}$

Deviatoric strain tensor
Equation of state for hydrodynamic pressure has to be prescribed via the /EOS card.
In case of a linear material with a volumetric dilatation:
$C_{1} = \frac{E}{3 (1 - 2 ν)}$ and $C_{4} = \frac{α_{ν} C_{1}}{ρ C_{ν} T}$

$C_{4} = C_{5} = γ - 1$ and $C_{0} = C_{2} = C_{3} = 0$

then:(1)
$\begin{array}{l} p & = C_{1} μ + (C_{4} + C_{5} μ) E \\ = C_{1} μ + C_{4} (1 + μ) E \\ = C_{1} μ + C_{4} (1 + μ) ρ_{0} e \\ = C_{1} μ + C_{4} (1 + μ) ρ_{0} C_{ν} T \end{array}$
(2)
$\begin{array}{l} p & = C_{1} μ + C_{4} ρ C_{ν} T \\ = C_{1} μ + α_{ν} T \end{array}$

If $p = c s t = 0$ , then $C_{1} μ + α_{ν} T = 0$ l=; so $μ = \frac{α_{ν} T}{C_{1}}$

Where,

$μ$

Dilatation coefficient

$μ < 0$

Dilatation

In this case the parameters C₂ and C₃ will not be taken into account.
All thermal data ( $ρ_{0} C_{p}, T_{0}, A, and B$ ) can be defined with keyword /HEAT/MAT.
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 $C_{0} = C_{2} = C_{3} = C_{4} = C_{5} = E = 0$

then, $p = C_{1} μ$
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, $E$ is the energy per unit volume.