/MAT/LAW49 (STEINB)

Block Format Keyword This law defines an elastic plastic material with thermal softening.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW49/mat_ID/unit_ID or /MAT/STEINB/mat_ID/unit_ID
mat_title
ρ i ρ 0            
E0 ν            
σ0 β n ε p m a x σ max
T0 Tm ρ C p Pmin    
b1 b2 h f    

Definitions

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)

 
ρ i Initial density.

(Real)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state).

Default = ρ 0 = ρ i (Real)

[ kg m 3 ]
E0 Initial Young's modulus.

(Real)

[ Pa ]
ν Poisson's ratio.

(Real)

 
σ 0 Plasticity initial yield stress.

No default (Real)

[ Pa ]
β Plasticity hardening parameter.

No default (Real)

 
n Plasticity hardening exponent.

No default (Real)

 
ε p m a x Maximum plastic strain.

Default = 1030 (Real)

 
σ max Plasticity maximum stress.

Default = 1030 (Real)

[ Pa ]
T0 Initial temperature.

Default = 300 (Real)

[ K ]
Tm Melting temperature.

(Real)

[ K ]
ρ C p Specific heat.

(Real)

[ kg s 2 mK ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaacUgacaGGNbaabaGaai4CamaaCaaaleqabaGaaiOmaaaa kiabgwSixlaac2gacqGHflY1caGGlbaaaaGaay5waiaaw2faaaaa@420B@
Pmin Pressure cutoff.

Default = 0.0 (Real)

[ Pa ]
b1 Law coefficient.

No default (Real)

 
b2 Law coefficient.

No default (Real)

 
h Law coefficient.

No default (Real)

 
f Law coefficient.

No default (Real)

 

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW49/1/1
Aluminum
#              RHO_I               RHO_0
                2.73                   0
#                 E0                  nu
                .734                 .33
#            sigma_0                beta                   n             EPS_max           SIGMA_max
               .0029                 125                  .1                   9               .0068
#                T_0               Tmelt              rhoC_p                Pmin
                 300                1220             2.59E-5               -.005
#                 b1                  b2                   h                   f
                 6.5                 6.5              6.2E-4                   0
/EOS/GRUNEISEN/1/1
Aluminum
#                  C                  S1                  S2                  S3
                .524                 1.5                   0                   0
#             GAMMA0               ALPHA                  E0               RHO_0
                1.97                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. When material approaches melting point, the yield strength and shear modulus diminish to zero. Melting energy is defined as:(1)
    E m = E c + ρ 0 C p T m
    Where,
    E c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWGJbaabeaaaaa@37D4@
    Cold compression energy
    T m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWGJbaabeaaaaa@37D4@
    Melting temperature supposed to be constant
    If the internal energy E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraaaa@36C0@ is less than E m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWGJbaabeaaaaa@37D4@ , the shear modulus and the yield strength are defined as:(2)
    G = G 0 [ 1 + b 1 p V 1 3 h ( T T 0 ) ] e f E E E m
    With(3)
    G 0 = E 0 2 ( 1 + ν )
    (4)
    σ y = σ 0 [ 1 + b 2 p V 1 3 h ( T T 0 ) ] e f E E E m
    Where, σ 0 is given by a hardening rule:(5)
    σ 0 = σ 0 ( 1 + β ε p ) n
    If ε p > ε p max , then(6)
    σ 0 = σ 0 [ 1 + β ε p max ] n
    The value of σ 0 is limited by:(7)
    min ( σ 0 ) σ 0 σ max
  2. If an Equation of State (/EOS) does not refer to this material, the pressure is computed as:(8)
    p = E 0 3 ( 1 2 ν ) μ

    with μ = ρ ρ 0 1

  3. When ε p reaches ε p m a x , in one integration point, the deviatoric stress of the corresponding integral point is permanently set to 0; however, the solid element is not deleted.