/MAT/LAW57 (BARLAT3)

Block Format Keyword This law describes plasticity hardening by a user-defined function and can be used only with shell elements.

This is an elasto-plastic orthotropic law for modeling anisotropic materials in forming processes especially aluminum alloys. This material law must be used with property set type /PROP/TYPE9 (SH_ORTH) or /PROP/TYPE10 (SH_COMP).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW57/mat_ID/unit_ID or /MAT/BARLAT3/mat_ID/unit_ID
mat_title
ρ i                
E ν            
fct_IDE   Einf CE        
r00 r45 r90 Chard m
ε p m a x εt εm Fcut Fsmooth  
Repeat the next line for each plasticity function
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDi   Fscalei ε ˙ i        

Definition

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 ]
E Young's modulus.

(Real)

[ Pa ]
ν Poisson's ratio.

(Real)

 
fct_IDE Function identifier for the scale factor of Young's modulus, when Young's modulus is function of the plastic strain. 11

Default = 0: in this case the evolution of Young's modulus depends on Einf and CE.

(Integer)

 
Einf Saturated Young's modulus for infinitive plastic strain.

(Real)

 
CE Parameter for Young's modulus evolution.

(Real)

 
r00 Lankford parameter 0 degree.

Default = 1.0 (Real)

 
r45 Lankford parameter 45 degrees.

Default = 1.0 (Real)

 
r90 Lankford parameter 90 degrees.

Default = 1.0 (Real)

 
Chard Hardening coefficient.
= 0
Hardening is full isotropic model.
= 1
Hardening uses the kinematic Prager-Ziegler model.
= between 0 and 1
Hardening is interpolated between the two models.

(Real)

 
m Barlat parameter.
= 6.0 (Default)
For Body Centered Cubic (BCC) material.
= 8.0
For Face Centered Cubic (FCC) material.

(Real)

 
ε p m a x Failure plastic strain.

Default = 1.0 x 1030 (Real)

 
ε t Tensile failure strain at which stress starts to reduce.

Default = 1.0 x 1030 (Real)

 
ε m Maximum tensile failure damage strain at which the stress in element is set to zero.

Default = 2.0 x 1030 (Real)

 
Fcut Cutoff frequency for the strain rate filtering.

Default = 10000 Hz (Real)

[Hz]
Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.
(Integer)
 
fct_IDi Plasticity curves ith function identifier.

(Integer)

 
Fscalei Scale factor for ith function.

Default set to 1.0 (Real)

 
ε ˙ i Strain rate for ith function.

(Real)

[ 1 s ]

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW57/1/1
Steel
#              RHO_I
                .008                   
#                  E                  NU
              206000                  .3
#FUNCT_IDE                          EINF                  CE
         0                             0                   0
#                r00                 r45                 r90              C_hard                   m
                1.79                1.51                2.27                   0                   0
#           EPSP_max               EPS_T               EPS_M                Fcut  Fsmooth
                   0                   0                   0                  10        1
# funct_ID                      Fscale_i               EPS_i
         5                             0                   0                                        
         5                             0                   1                                        
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/5
function_5
#                  X                   Y
                   0                 157                                                            
                  .1                 320                                                            
                  .5                 480                                                            
                 1.2                 600                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The anisotopic yield criteria F for plane stress is defined by:(1)
    F = a | K 1 + K 2 | m + a | K 1 K 2 | m + c | 2 K 2 | m 2 σ y m = 0

    Where,

    σ y is the yield stress

    K 1 = σ xx +h σ yy 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaakiabg2da9maalaaabaGaeq4Wdm3aaSbaaSqa aiaadIhacaWG4baabeaakiabgUcaRiaadIgacqaHdpWCdaWgaaWcba GaamyEaiaadMhaaeqaaaGcbaGaaGOmaaaaaaa@4341@ and K 2 = ( σ xx h σ yy 2 ) 2 + p 2 σ xy 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIYaaabeaakiabg2da9maakaaabaWaaeWaaeaadaWcaaqa aiabeo8aZnaaBaaaleaacaWG4bGaamiEaaqabaGccqGHsislcaWGOb Gaeq4Wdm3aaSbaaSqaaiaadMhacaWG5baabeaaaOqaaiaaikdaaaaa caGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaamiCam aaCaaaleqabaGaaGOmaaaakiabeo8aZnaaDaaaleaacaWG4bGaamyE aaqaaiaaikdaaaaabeaaaaa@4D4A@

  2. Angles for Lankford parameters are defined with respect to orthotropic direction 1. The material constants a, c, h, and p are obtained from the three Lankford parameters:(2)
    a = 2 2 r 00 1 + r 00 r 90 1 + r 90 c = 2 a h = r 00 1 + r 00 1 + r 90 r 90
    Material constant p is calculated by solving:(3)
    2m σ y m ( F σ xx + F σ yy ) σ 45 1 r 45 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca aIYaGaamyBaiabgwSixlabeo8aZnaaBaaaleaacaWG5baabeaakmaa CaaaleqabaGaamyBaaaaaOqaamaabmaabaWaaSaaaeaacqGHciITca WGgbaabaGaeyOaIyRaeq4Wdm3aaSbaaSqaaiaadIhacaWG4baabeaa aaGccqGHRaWkdaWcaaqaaiabgkGi2kaadAeaaeaacqGHciITcqaHdp WCdaWgaaWcbaGaamyEaiaadMhaaeqaaaaaaOGaayjkaiaawMcaaiab eo8aZnaaBaaaleaacaaI0aGaaGynaaqabaaaaOGaeyOeI0IaaGymai abgkHiTiaadkhadaWgaaWcbaGaaGinaiaaiwdaaeqaaOGaeyypa0Ja aGimaaaa@5A34@
  3. If the last point of the first (static) function equals 0 in stress, the default value of ε p m a x is set to the corresponding value of ε p .
  4. If ε p (plastic strain) reaches ε p max , in one integration point, the corresponding shell element is deleted.
  5. If the largest principal strain ε 1 > ε t , the stress is reduced using the following relation:(4)
    σ = σ ( ε m ε 1 ε m ε t )
  6. If ε 1 > ε m , the stress is reduced to 0 (but the element is not deleted).
  7. The maximum number of curves is 10.
  8. If ε ˙ ε ˙ n , the yield is interpolated between fn and fn-1.
  9. If ε ˙ ε ˙ 1 , function f1 is used.
  10. Above ε ˙ max , yield is extrapolated.

    law57
    Figure 1.
  11. The evolution of Young's modulus:
    • If fct_IDE > 0, the curve defines a scale factor for Young's modulus evolution with equivalent plastic strain, which means the Young's modulus is scaled by the function f ( ε ¯ p ) :(5)
      E ( t ) = E f ( ε ¯ p )

      The initial value of the scale factor should be equal to 1 and it decreases.

    • If fct_IDE = 0, the Young's modulus is calculated as:(6)
      E ( t ) = E ( E E i n f ) [ 1 exp ( C E ε ¯ p ) ]

      Where, E and Einf are respectively the initial and asymptotic value of Young's modulus, and ε ¯ p is the accumulated equivalent plastic strain.

      Note: If fct_IDE = 0 and CE = 0, Young's modulus, E is kept constant.
  12. The parameters Fsmooth and Fcut allows you to enable a strain-rate filtering. Three cases can be set:
    • If Fsmooth = 0 and Fcut = 0.0, the strain-rate filtering is turned off.
    • If Fsmooth = 1 and Fcut = 0.0, the strain-rate filtering uses a default cutoff frequency of 10 kHz.
    • If Fcut ≠ 0, Fsmooth is automatically set to 1 and the strain-rate filtering uses the cutoff frequency given by you.