Iform = 2

Block Format Keyword This boundary material enables to impose sub-material states (density, energy, and volumetric fraction) which are also used to compute global material state. Submaterial EOS parameters must be consistent with the ones in adjacent element (from the domain).

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW51/`mat_ID`/`unit_ID`
`mat_title`
Blank Format
`I`_form

#Global Parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`Scale`_time		`P`_EXT				$V E L_{i n}$			$f c t_I D_{V E L}$

#Material1 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_1}$	$ρ_{0}^{mat_1}$	$E_{0}^{m a t_ 1}$	`fct_ID`_α1	`fct_ID`_{$ρ$ 1}	$f c t_I D_{E 1}$
$C_{1}^{m a t_1}$	$C_{2}^{m a t_1}$	$C_{3}^{m a t_1}$	$C_{4}^{m a t_1}$		$C_{5}^{m a t_1}$
$Δ P_{min}^{mat_1}$	$C_{0}^{m a t_1}$

#Material2 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_2}$	$ρ_{0}^{mat_2}$	$E_{0}^{m a t_ 2}$	`fct_ID`_α2	`fct_ID`_{$ρ$ 2}	`fct_ID`_E2
$C_{1}^{m a t_2}$	$C_{2}^{m a t_2}$	$C_{3}^{m a t_2}$	$C_{4}^{m a t_2}$		$C_{5}^{m a t_2}$
$Δ P_{min}^{mat_2}$	$C_{0}^{m a t_2}$

#Material3 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_3}$	$ρ_{0}^{mat_3}$	$E_{0}^{m a t_ 3}$	`fct_ID`_α3	`fct_ID`_{$ρ$ 3}	`fct_ID`_E3
$C_{1}^{m a t_3}$	$C_{2}^{m a t_3}$	$C_{3}^{m a t_3}$	$C_{4}^{m a t_3}$		$C_{5}^{m a t_3}$
$Δ P_{min}^{mat_3}$	$C_{0}^{m a t_3}$

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Interger, maximum 10 digits)
`mat_title`	Material title (Character, maximum 100 characters)
`I`_form	Formulation flag (Integer) =2 : Imposed state
`Scale`_time	Abscissa scale factor for input functions Default = 1 (Real)
$V E L_{i n}$	Scale factor for inlet velocity 5 (Real)	$[\frac{m}{s}]$
`fct_ID`_VEL	Optional identifier for velocity function $f_{V E L} (t)$ 5 = 0 : $f_{ρ i} (t)$ > 0 : $v (t) = V E L_{i n} \cdot f_{V E L} (t)$ (Integer)
$α_{0}^{mat_ i}$	Initial imposed volumetric fraction 2 (Real)
$ρ_{0}^{mat_ i}$	Initial imposed density (Real)	$[\frac{kg}{m^{3}}]$
$E_{0}^{m a t_ i}$	Initial imposed energy per unit volume (Real)	$[\frac{J}{m^{3}}]$
`fct_ID`_αi	Optional identifier for Volumetric fraction scaling function $f_{α i} (t)$ 3 = 0 : $α^{m a t_i} (t) = α_{0}^{m a t_i}$ > 0 : $α^{m a t_i} (t) = α_{0}^{m a t_i} \cdot f_{α_{i}} (t)$ (Integer)
`fct_ID`_{$ρ_{i}$}	Optional identifier for Density fraction scaling function $f_{ρ i} (t)$ 3 = 0 : $ρ^{m a t_i} (t) = ρ_{0}^{m a t_i}$ > 0 : $ρ^{m a t_i} (t) = ρ_{0}^{m a t_i} \cdot f_{ρ_{i}} (t)$ (Integer)
`fct_ID`_Ei	Optional identifier for density energy scaling function identifier $f_{E i} (t)$ 3 = 0: $E^{{mat}_{i}} (t) = E_{0}^{mat_i}$ > 0 : $E^{m a t_i} (t) = E_{0}^{m a t_i} \cdot f_{E_{i}} (t)$ (Integer)
$C_{1}^{m a t_i}$	Coefficient for Polynomial EOS (Real)	$[Pa]$
$C_{2}^{m a t_i}$	Coefficient for Polynomial EOS (Real)	$[Pa]$
$C_{3}^{m a t_i}$	Coefficient for Polynomial EOS (Real)	$[Pa]$
$C_{4}^{m a t_i}$	Coefficient for Polynomial EOS (Real)
$C_{5}^{m a t_i}$	Coefficient for Polynomial EOS (Real)
$Δ P_{\min}^{mat_ i}$	Cut off pressure 4 Default = -10^-30 (Real)	$[Pa]$
$C_{0}^{m a t_i}$	Coefficient for Polynomial EOS (Real)	$[Pa]$

Comments

This formulation imposes sub-material states from user data.
Volumetric fraction: (1)
$α^{m a t_i} (t)$

Density: (2)
$ρ^{m a t_i} (t)$

Density Energy: (3)
$E^{m a t_i} (t)$

This enables to compute pressure from given polynomial EOS:(4)
$Δ P (t) = \min {Δ P_{\min} , C_{0} + C_{1} μ + C_{2}^{'} μ^{2} + C_{3}^{'} μ^{3} + (C_{4} + C_{5} μ) E (t)}$

Where, $P = Δ P + P_{E X T}$ and $μ (t) = \frac{ρ (t)}{ρ_{0}} = 1, E (t) = E_{int} (t) / V_{0}, C_{2}^{'} = C_{2} δ_{μ \geq 0}, and C_{3}^{'} = C_{3} δ_{μ \geq 0}$ , which means that EOS is linear in expansion and cubic for in compression.

Then global material state is determined by:

Pressure

$Δ P = \sum_{i} α^{m a t_i} (t) \cdot Δ P^{m a t_i}$

Density

$ρ = \sum_{i} α^{m a t_i} (t) \cdot ρ^{m a t_i}$

Energy

$\frac{E_{i n t}}{V} = \sum_{i} α^{m a t_i} (t) \cdot E^{m a t_i}$
Volumetric fractions enable the sharing of elementary volume within the three different materials.
For each material $α_{0}^{mat_ i}$ must be defined between 0 and 1.

Sum of initial volumetric fractions $\sum_{i = 1}^{3} α_{0}^{mat _ i}$ must be equal to 1.

For automatic initial fraction of the volume, refer to /INIVOL.
If a function is not defined, then related quantity remains constant and set to its initial value. However, input quantity can be defined as time dependent function using provided function identifiers. Abscissa functions can also be scaled using Fscale_t parameter which leads to use $f (S c a l e_{t i m e}, t)$ , instead of $f (t)$ .
$Δ P_{\min}^{mat_ i}$ flag is the minimum value for the computed pressure.
Since $P = Δ P + P_{E X T}$ , defining $P_{E X T} = 0$ implies $Δ P = P$ and $Δ P_{\min} = P_{\min}$ .

Fluid materials pressure must remain positive to avoid any tensile strength, then,

$P_{\min} = 0$ or $Δ P_{\min} = - P_{E X T}$ .

For solid materials, default value for $Δ P_{\min}^{mat_ i}$ = 10³⁰ is suitable.
If the velocity is not defined, the user must define it using /IMPVEL with nodes. Otherwise normal velocity can be entered. The normal velocity is applied to the global material with the same velocity used for each submaterial. If only the state at the stagnation point is known, use /MAT/LAW51 with I_form=4,5 instead.