/MAT/LAW51 (MULTIMAT)

Block Format Keyword Up to four material laws can be defined: elasto-plastic solid, liquid, gas and detonation products. The material law is based on a diffusive interface technique to get sharper interfaces between submaterial zone (/ALE/MUSCL in Radioss Starter Input).

It is not recommended to use this law with Radioss single precision engine.

Format

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

Formulation Types

Table 1. Material Law
Formulation Number of Sub-materials Plasticity Explosive
Iform = 0 3 -- --
Iform = 1 3 Johnson-Cook --
Iform = 10 4 Johnson-Cook Jones-Wilkins-Lee
Iform = 11 4 Johnson-Cook

Drücker-Prager

Jones-Wilkins-Lee
Iform = 12 5 Johnson-Cook

Drücker-Prager

Jones-Wilkins-Lee
General formulation (Iform=12) enables to define any formulation of type: 0, 1, 10, or 11 but with a simplified input.
Table 2. Elementary Boundary Conditions
Formulation Type
Iform = 2 INLET
Iform = 4 GAS INLET (state defined from stagnation point)
Iform = 5 LIQUID INLET (state defined from stagnation point)
Iform = 6 OUTLET (non-reflective)

Outlet formulation (Iform=3) is obsolete since 2018.0 version. It is replaced by new Non-Reflecting-Frontier (Iform = 6)

Modeling Technique with Polynomial EOS

Material Hypothesis Output Modeling
C0 C1 C2 C3 C4 C5 E0 Pext Pmin
Perfect gas (Example 43) P ( μ , E )         ( γ 1 ) ( γ 1 ) P 0 γ 1    
Δ P ( μ , E ) -P0       ( γ 1 ) ( γ 1 ) P 0 γ 1 P0  
Water (Linear EOS) P ( μ , E ) P0 ρ c 2             10 30
Δ P ( μ , E )   ρ c 2           P0 -P0
Elastic Solid (Linear EOS) P ( μ , E ) P0 E 3( 12ν )              
Δ P ( μ , E )   E 3( 12ν )           P0  
Mie-Gruneisen

Γ constant

Δ P ( μ , E )   K1 K 2 Γ 2 K 1 K 3 Γ 2 K 2 Γ Γ E0 P0  
Mie-Gruneisen

Γ linear

Γ= Γ 0 a( μ 1+μ )

Δ P ( μ , E )   K1 K 2 Γ 0 2 K 1 K 3 Γ 0 2 K 2 +a K 1 Γ 0 Γ 0 a E0 P0  
Where,(1)
K 1 = ρ 0 c 2
(2)
K 2 = ρ 0 c 2 ( 2 S 1 )
(3)
K 3 = ρ 0 c 2 ( S 1 ) ( 3 S 1 )
Where,(4)
μ = ρ ρ 0 1
P ( μ , E )
Total pressure and total energy formulation
Δ P ( μ , E )
Relative pressure and total energy formulation
P ( μ , Δ E )
Total pressure and relative energy formulation
Δ P ( μ , Δ E )
Relative pressure and relative energy formulation
P0
Initial total pressure
E0
Initial total energy
γ
Perfect gas constant
E
Young's modulus
ν
Poisson coefficient
Γ
Gruneisen's gamma
a
Coefficient for first order volume correction to the Gruneisen gamma Γ 0
c
Speed of sound
ρ 0
Initial density
S
Linear Hugoniot slope coefficient

Comments

  1. Numerical diffusion can be improved using the second order method for volume fraction convection, /ALE/MUSCL. The previous /UPWIND used to limit diffusion is now obsolete.
  2. Time step for ALE material laws can be tune with Engine card /DT/ALE; by default, scale factor on time step is 0.5
  3. This law can emulate /MAT/LAW37 (BIPHAS) (liquid and gas mixture) with less diffusion. It can also replace /MAT/LAW20 (BIMAT) in 2D analysis since /MAT/LAW51 is compatible with QUAD elements.
  4. /MAT/LAW51 (MULTIMAT) is based on the equilibrium between each material present inside the element. Radioss computes and outputs a relative pressure Δ P . At each cycle: Δ P = Δ P 1 = Δ P 2 = Δ P 3 = Δ P 4
    User can deduce total pressure using output value Δ P and input parameter P e x t : (5)
    P = Δ P + P e x t
  5. Tetra 4 elements can be used for this law, but BRICK elements are currently highly recommended for better numerical solution in ALE.