/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

General formulation (Iform=12). Formulations Iform=0, 1, 10, 11 are obsolete as of 2023 version.
Table 1. Material Law
Formulation Number of Sub-materials Plasticity Explosive
Iform = 12 (Default) 4 Johnson-Cook

Drucker-Prager

Jones-Wilkins-Lee
Outlet formulation (Iform=3) is obsolete as of 2018.0 version. It is replaced by new Non-Reflecting-Frontier (Iform = 6).
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)

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,

K 1 = ρ 0 c 2
K 2 = ρ 0 c 2 ( 2 S 1 )
K 3 = ρ 0 c 2 ( S 1 ) ( 3 S 1 )

Where,
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 :

    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.