Iform = 1

Block Format Keyword This material is able to handle up to three elasto plastic materials (solid, liquid, or gas). The material law is based on a diffusive interface technique.

To get sharper interfaces between submaterial zones, refer to /ALE/MUSCL.
Note: It is not recommended to use this law with Radioss single precision engine.
LAW51 is based on equilibrium between each material present inside the element. Radioss computes and outputs a relative pressure ΔPΔP . At each cycle:(1)
ΔP=ΔP1=ΔP2=ΔP3ΔP=ΔP1=ΔP2=ΔP3
Total pressure can be calculated with external pressure:(2)
P=ΔP+PextP=ΔP+Pext
Where,
P
Positive for a compression and negative for traction.
Hydrostatic stresses are computed from Polynomial EOS:(3)
σm=ΔP=C0+C1μ+C'2μ2+C'3μ3+(C4+C5μ)E(μ)
(4)
dEint=δW+δQ=(ΔP+Pext)dV+δQ

Where, E=Eint/V0,C'2=C2δμ0andC'3=C3δμ0 means that the EOS is linear for an expansion and cubic for a compression.

By default process is adiabatic δQ=0 . To enable thermal computation, refer to 6.

Deviatoric stresses are computed with a Johnson-Cook model:(5)
σdev={Gεif in elastic domain(α+bεpn)(1+cln˙ε˙ε0)(1(TT0TmeltT0)m)others

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW51/mat_ID/unit_ID
mat_title
Blank
Iform                  
#Global Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Pext ν νvol        
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_10 ρmat_10 Emat_10 ΔPmat_1min Cmat_10
C1mat_1 C2mat_1 C3mat_1 C4mat_1 C5mat_1
Gmat_11 amat_1 bmat_1 nmat_1    
cmat_1 ˙ε0mat_1            
mmat_1 Tmat_10 Tmat_1melt Tlimmat_1 ρCmat_1v
εmat_1p,max σmat_1max Kmat_1A Kmat_1B    
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_20 ρmat_20 Emat_20 ΔPmat_2min Cmat_20
Cmat_21 Cmat_22 Cmat_23 Cmat_24 Cmat_25
Gmat_21 amat_2 bmat_2 nmat_2    
cmat_2 ˙εmat_20            
mmat_2 Tmat_20 Tmat_2melt Tmat_2lim ρCmat_2v
εmat_2p,max σmat_2max Kmat_2A Kmat_2B    
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
αmat_30 ρmat_30 Emat_30 ΔPmat_3min Cmat_30
Cmat_31 Cmat_32 Cmat_33 Cmat_34 Cmat_35
Gmat_31 amat_3 bmat_3 nmat_3    
cmat_3 ˙εmat_30            
mmat_3 Tmat_30 Tmat_3melt Tmat_3lim ρCmat_3v
εmat_3p,max σmat_3max Kmat_3A Kmat_3B    

Definition

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)

 
Iform Formulation flag.

(Integer)

 
Pext External pressure. 2

Default = 0 (Real)

[Pa]
ν Kinematic viscosity shear ν=μ/ρ . 3

Default = 0 (Real)

[m2s]
νvol Kinematic viscosity (volumetric), νvol=3λ+2μρ which corresponds to Stokes Hypothesis. 3

Default = 0 (Real)

[m2s]
αmat_i0 Initial volumetric fraction. 4

(Real)

 
ρmat_i0 Initial density.

(Real)

[kgm3]
Emat_i0 Initial energy per unit volume.

(Real)

[Jm3]
ΔPmat_imin Hydrodynamic cavitation pressure. 5

If fluid material ( Gmat_i1=0 ), then default = Pext .

If solid material ( Gmat_i10 ), then default = -1e30.

(Real)

[Pa]
Cmat_i0 Initial pressure.

(Real)

[Pa]
Cmat_i1 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i2 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i3 Hydrodynamic coefficient.

(Real)

[Pa]
Cmat_i4 Hydrodynamic coefficient.

(Real)

 
Cmat_i5 Hydrodynamic coefficient.

(Real)

 
Gmat_i1 Elasticity shear modulus.
= 0 (Default)
Fluid material

(Real)

[Pa]
amat_i Plasticity yield stress.

(Real)

[Pa]
bmat_i Plasticity hardening parameter.

(Real)

[Pa]
nmat_i Plasticity hardening exponent.

Default = 1.0 (Real)

 
cmat_i Strain rate coefficient.
= 0
No strain rate effect

Default = 0.00 (Real)

 
˙εmat_i0 Reference strain rate.

If ˙ε˙εmat_j0 , no strain rate effect

(Real)

[1s]
mmat_i Temperature exponent.

Default = 1.00 (Real)

 
Tmat_i0 Initial temperature.

Default = 300 K (Real)

[K]
Tmat_imelt Melting temperature.
= 0
No temperature effect

Default = 1030 (Real)

[K]
Tmat_ilim Maximum temperature.

Default = 1030 (Real)

[K]
ρCmat_iv Specific heat per unit of volume. 7

(Real)

[Jm3K]
εmat_ip,max Failure plastic strain.

Default = 1030 (Real)

 
σmat_imax Plasticity maximum stress.

Default = 1030 (Real)

[Pa]
Kmat_iA Thermal conductivity coefficient 1. 8

(Real)

[WmK]
Kmat_iB Thermal conductivity coefficient 2. 8

(Real)

[WmK2]

Example

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. Radioss computes and outputs a relative pressure ΔP . (6)
    ΔP=max{ΔPmin,C0+C1μ+C'2μ2+C'3μ3+(C4+C5μ)E(μ)}

    However, total pressure is essential for energy integration ( dEint=PdV ). It can be computed with the external pressure flag Pext.

    P=ΔP+Pext leads to dEint=(Pext+ΔP)dV .

    This means that if Pext = 0, the computed pressure ΔP is also the total pressure: ΔP=P .

  3. Kinematic viscosities are global and is not specific to each material. It allows computing viscous stress tensor:(7)
    τ=μ[(V)+t(V)]+λ(V)I
    Where,
    ν=μ/ρ
    Cinematic shear viscosity flag
    νvol=3(λ+2μ3)ρ
    Cinematic volumetric viscosity flag
  4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

    For each material αmat_i0 must be defined between 0 and 1.

    Sum of initial volumetric fractions 3i=1αmat_i0 must be equal to 1.

    For automatic initial fraction of the volume, refer to the /INIVOL card.

  5. ΔPmat_imin flag is the minimum value for the computed pressure ΔP . It means that total pressure is also bounded to:(8)
    Pmat_imin=ΔPmat_imin+Pext

    For fluid materials and detonation products, Pmat_imin must remain positive to avoid any tensile strength so ΔPmat_imin must be set to Pext .

    For solid materials, default value ΔPmat_imin = 1e-30 is suitable but may be modified.

  6. Heat contribution is computed only if the thermal card is associated to the material law (/HEAT/MAT).
    In this case, δQ=ρCVVdT and the parameters for thermal diffusion are read for each material:(9)
    ρCmat_iV,Kmat_iA,Kmat_iBandTmat_i0

    For solids and liquids, CνCp for perfect gas: γ=Cp/Cν

  7. The temperature evolution in the Johnson-Cook model is computed with the flag ρCmat_iV , even if the thermal card (/HEAT/MAT) is not defined.
  8. Thermal conductivity, K , is linearly dependent on the temperature:(10)
    K(T)=KA+KBT
  9. Material tracking is possible through animation files:

    /ANIM/BRIC/VFRAC (All material volumetric fractions)