Iform = 12

Block Format Keyword Up to 4 different sub-materials (solid, liquid, gas and explosives) can be defined by specifying a material identifier and initial volume fraction.

The following materials can be defined as sub-materials:

LAW3 (HYDPLA)
LAW4 (HYD_JCOOK)
LAW5 (JWL)
LAW6 (HYDRO)
LAW10 (DPRAG1)
LAW102 (DPRAG2)

These materials can then reference the following equations of state:

/EOS/LINEAR
/EOS/POLYNOMIAL
/EOS/IDEAL-GAS
/EOS/STIFF-GAS

Format

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

#Global Parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
		$ν$

Sub-material parameters (each sub-material one line, maximum 4 lines for 4 sub-materials)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`mat_ID`₁	$α_{0}^{m a t_ 1}$

Optional lines for up to 3 additional sub-material

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`mat_ID`₂	$α_{0}^{m a t_ 2}$
`mat_ID`₃	$α_{0}^{m a t_ 3}$
`mat_ID`₄	$α_{0}^{m a t_ 4}$

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)
`I`_form	Formulation flag = 12. (Integer)
$ν$	Kinematic viscosity in shear $ν = μ / ρ$ . 4 Default is computed from sub-material laws (Real)	$[\frac{m^{2}}{s}]$
`mat_ID`₁	Material identifier for the 1^st sub-material which must refer to LAW3, 4, 5, 6, 10, or 102. Mandatory (Integer)
$α_{0}^{m a t_1}$	Initial volumetric fraction for the 1^st sub-material. Default = 0 (Real)
`mat_ID`_i	(Optional) Material Identifier from 2^nd to 4^th sub-material which must refer to LAW3, 4, 5, 6, 10 or 102. Default = 0 (Integer)
$α_{0}^{m a t_i}$	(Optional) Initial volumetric fraction. (Real)

Example (2 Submaterials)

Example for only two submaterials.

#RADIOSS STARTER
#---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/LAW51/101/1
99.99% Water-MULTIMAT:AIR+WATER ,units {g,mm,ms}
#              RHO_I               RHO_0
             
#     IFLG
        12
#                                     NU               LAMDA
                                       0                   0
#    MAT_1             ALPHA_1
         5              0.9999
#    MAT_2             ALPHA_2
         4              0.0001   
/ALE/MAT/101/1
#     Modif. factor.
                   0	
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDRO/4/1
AIR
#              RHO_I               RHO_0
             1.22e-6                   0 
#                Knu                Pmin
                   0                   0
/EOS/IDEAL-GAS/4/1
EoS for Air at atmospheric pressure
#              GAMMA                  P0                 PSH                  T0                RHO0
                 1.4                0.10                   0               300.0             1.22E-6  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|				   
/MAT/LAW06/5/1
water
#              RHO_I        
               0.001          
#                KNU                PMIN
                   0                   0 
/EOS/STIFF-GAS/5/1
STIFF_GAS_WATER
#              GAMMA                  P0                 PSH              P_STAR                RHO0
                 6.1                0.10                   0              368.85  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

The material law is based on a diffusive interface technique. Numerical diffusion can be improved using MUSCL method for volume fraction (/ALE/MUSCL). The previous /UPWIND method for limiting diffusion is now obsolete.
The sub-materials can be listed in any order, but only one of them can be an explosive sub-material /MAT/LAW5.
If 4 sub-materials are requested, at least one of them should be an explosive sub-material /MAT/LAW5.
Kinematic viscosities are global and are not specific to each material. They are used to compute the viscous stress tensor:(1)
$τ = μ [(\nabla \otimes V) +^{t} (\nabla \otimes V)] + λ (\nabla V) I$

Where,

$ν = μ / ρ$

Kinematic viscosity in shear.

$μ$

Automatically computed from mixture sub-material definition (LAW6): $µ = \sum_{i = 1}^{N_{s u b m a t}} α_{i} µ_{i}$

If a value is input to define $μ$ , it will be applied to whatever the multi-material mixture is.

$λ$

Calculated such as $3 λ + 2 μ = 0$ (Stokes hypothesis).
Volumetric fractions enable the sharing of elementary volume within the three different materials.
For each material $α_{0}^{m a t_ i}$ must be defined between 0 and 1.

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

For automatic initial fraction of the volume, refer to the /INIVOL card.
It is not recommended to use this law with Radioss single precision engine.