/MAT/LAW6 (HYDRO or HYD_VISC)

Format

Definition

Comments

1. $S_{\mathit{ij}}=2\rho {\nu }_{\mathit{eq}}{\dot{e}}_{\mathit{ij}}$
   Where,

   ${\nu }_{\mathit{eq}}=\nu$

   No turbulence

   $S_{ij}$

   Deviatoric stress tensor

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

   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:

   $C_1=\frac{E}{3\left(1-2\nu \right)}$ and $C_4=\frac{{\alpha }_{\nu }{C}_1}{\rho C_{\nu }T}$

   $C_4=C_5=\gamma -1$ and $C_0=C_2=C_3=0$

   then:(1)

   $$\begin{array}{ll}p\hfill & =C_1\mu +(C_4+C_5\mu )E\hfill \\ \hfill & =C_1\mu +C_4(1+\mu )E\hfill \\ \hfill & =C_1\mu +C_4(1+\mu ){\rho }_{0}e\hfill \\ \hfill & =C_1\mu +C_4(1+\mu ){\rho }_0{C}_{\nu }T\hfill \end{array}$$

   (2)

   $$\begin{array}{ll}p\hfill & =C_1\mu +C_4\rho C_{\nu }T\hfill \\ \hfill & =C_1\mu +{\alpha }_{\nu }T\hfill \end{array}$$

   If $p=cst=0$ , then $C_1\mu +{\alpha }_{\nu }T=0$ l=; so $\mu =\frac{{\alpha }_{\nu }T}{C_1}$

   Where,

   $\mu$

   Dilatation coefficient

   $\mu <0$

   Dilatation

   In this case the parameters C₂ and C₃ will not be taken into account.
4. All thermal data ( ${\rho }_0{C}_p,T_0,A,\text{and}B$ ) 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:
   • $\Delta P_1=C_1\mu$ for /MAT/LAW37 (BIPHAS)
   • $p=C_0+C_1\mu +C_2{\mu }^2+C_3{\mu }^3+(C_4+C_5\mu )E$ 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, $p=C_1\mu$

6. If using LAW6 coupled with LAW37 for gas phase (without liquid phase), the compatibility of the gas EOS is:
   • $PV\gamma =const.$ for LAW37
   • $p=\left(\gamma -1\right)\left(\mu +1\right)E$ for LAW6, via the /EOS/IDEAL-GAS equation of state.

   Where, $E$ is the energy per unit volume.