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/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

Drucker-Prager

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

Drucker-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Outlet formulation (Iform=3) is obsolete since 2018.0 version.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)         (γ1) (γ1) P0γ1    
ΔP(μ,E) -P0       (γ1) (γ1) P0γ1 P0  
Water (Linear EOS) P(μ,E) P0 ρc2             1030
ΔP(μ,E)   ρc2           P0 -P0
Elastic Solid (Linear EOS) P(μ,E) P0 E3(12ν)              
ΔP(μ,E)   E3(12ν)           P0  
Mie-Gruneisen

Γ constant

ΔP(μ,E)   K1 K2Γ2K1 K3Γ2K2 Γ Γ E0 P0  
Mie-Gruneisen

Γ linear

Γ=Γ0a(μ1+μ)

ΔP(μ,E)   K1 K2Γ02K1 K3Γ02K2+aK1 Γ0 Γ0a E0 P0  
Where,(1)
K1=ρ0c2
(2)
K2=ρ0c2(2S1)
(3)
K3=ρ0c2(S1)(3S1)
Where,(4)
μ=ρρ01
P(μ,E)
Total pressure and total energy formulation
ΔP(μ,E)
Relative pressure and total energy formulation
P(μ,ΔE)
Total pressure and relative energy formulation
ΔP(μ,ΔE)
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 Γ0
c
Speed of sound
ρ0
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 ΔP . At each cycle: ΔP=ΔP1=ΔP2=ΔP3=ΔP4
    User can deduce total pressure using output value ΔP and input parameter Pext : (5)
    P=ΔP+Pext
  5. Tetra 4 elements can be used for this law, but BRICK elements are currently highly recommended for better numerical solution in ALE.