/MAT/LAW60 (PLAS_T3)

Block Format Keyword This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve (that is, plastic strain versus stress) for different strain rates.

It is similar to LAW36, except yield stress is a nonlinear interpolation from the functions.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW60/mat_ID/unit_ID or /MAT/PLAS_T3/mat_ID/unit_ID
mat_title
ρ i                
E ν ε p m a x εt εm
Nfunct Fsmooth Chard Fcut      
fct_IDp Fscale fct_IDE Einf CE    
fct_ID1 fct_ID2 fct_ID3 fct_ID4 fct_ID5          
Read only if 6 ≤ Nfunct ≤ 10
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_ID6 fct_ID7 fct_ID8 fct_ID9 fct_ID10          
Always Read
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Fscale1 Fscale2 Fscale3 Fscale4 Fscale5
Read only if 6 < Nfunct < 10
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Fscale6 Fscale7 Fscale8 Fscale9 Fscale10
Always Read
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ε ˙ 1 ε ˙ 2 ε ˙ 3 ε ˙ 4 ε ˙ 5
Read only if 6 ≤ Nfunct ≤ 10
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ε ˙ 6 ε ˙ 7 ε ˙ 8 ε ˙ 9 ε ˙ 10

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 ]
E Young's modulus.

(Real)

[ Pa ]
ν Poisson's ratio.

(Real)

 
ε p m a x Failure plastic strain.

Default = 1.0 × 1030 (Real)

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

Default = 1.0 x 1030 (Real)

 
ε m Maximum tensile failure strain at which the element is deleted.

Default = 2.0 x 1030 (Real)

 
Nfunct Number of functions. It should be 4 < Nfunct < 10.

Default ≤ 10 (Integer)

 
Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

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

(Real)

 
Fcut Cutoff frequency for strain rate filtering. 7

Default = 1.0 × 1030 (Real)

[Hz]
fct_IDp Pressure versus yield factor function. 9

Default = 0 (Integer)

 
Fscale Scale factor for yield factor in fct_IDp.

Default = 1.0 (Real)

[ Pa ]
fct_IDE Function identifier for the scale factor of Young's modulus, when Young's modulus is function of the plastic strain. 6

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)

[ Pa ]
CE Parameter for Young's modulus evolution.

(Real)

 
fct_ID1 Yield stress function identifier 1 corresponding to strain rate ε ˙ 1 .

(Integer)

 
fct_ID2 Yield stress function identifier 2 corresponding to strain rate ε ˙ 2 .

(Integer)

 
fct_ID3 Yield stress function identifier 3 corresponding to strain rate ε ˙ 3 .

(Integer)

 
fct_ID4 Yield stress function identifier 4 corresponding to strain rate ε ˙ 4 .

(Integer)

 
fct_ID5 Yield stress function identifier 5 corresponding to strain rate ε ˙ 5 .

(Integer)

 
fct_ID6 Yield stress function identifier 6 corresponding to strain rate ε ˙ 6 .

(Integer)

 
fct_ID7 Yield stress function identifier 7 corresponding to strain rate ε ˙ 7 .

(Integer)

 
fct_ID8 Yield stress function identifier 8 corresponding to strain rate ε ˙ 8 .

(Integer)

 
fct_ID9 Yield stress function identifier 9 corresponding to strain rate ε ˙ 9 .

(Integer)

 
fct_ID10 Yield stress function identifier 10 corresponding to strain rate ε ˙ 10 .

(Integer)

 
Fscale1 Scale factor for ordinate (stress) in fct_ID1.

Default = 1.0 (Real)

[ Pa ]
Fscale2 Scale factor for ordinate (stress) in fct_ID2.

Default = 1.0 (Real)

[ Pa ]
Fscale3 Scale factor for ordinate (stress) in fct_ID3.

Default = 1.0 (Real)

[ Pa ]
Fscale4 Scale factor for ordinate (stress) in fct_ID4.

Default = 1.0 (Real)

[ Pa ]
Fscale5 Scale factor for ordinate (stress) in fct_ID5.

Default = 1.0 (Real)

[ Pa ]
Fscale6 Scale factor for ordinate (stress) in fct_ID6.

Default = 1.0 (Real)

[ Pa ]
Fscale7 Scale factor for ordinate (stress) in fct_ID7.

Default = 1.0 (Real)

[ Pa ]
Fscale8 Scale factor for ordinate (stress) in fct_ID8.

Default = 1.0 (Real)

[ Pa ]
Fscale9 Scale factor for ordinate (stress) in fct_ID9.

Default = 1.0 (Real)

[ Pa ]
Fscale10 Scale factor for ordinate (stress) in fct_ID10.

Default = 1.0 (Real)

[ Pa ]
ε ˙ 1 Strain rate 1.

(Real)

[ 1 s ]
ε ˙ 2 Strain rate 2.

(Real)

[ 1 s ]
ε ˙ 3 Strain rate 3.

(Real)

[ 1 s ]
ε ˙ 4 Strain rate 4.

(Real)

[ 1 s ]
ε ˙ 5 Strain rate 5.

(Real)

[ 1 s ]
ε ˙ 6 Strain rate 6.

(Real)

[ 1 s ]
ε ˙ 7 Strain rate 7.

(Real)

[ 1 s ]
ε ˙ 8 Strain rate 8.

(Real)

[ 1 s ]
ε ˙ 9 Strain rate 9.

(Real)

[ 1 s ]
ε ˙ 10 Strain rate 10.

(Real)

[ 1 s ]

Example (Aluminum)

#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/LAW60/1/1
Aluminium_example
#              RHO_I
               .0027 
#                  E                  Nu           Eps_p_max               Eps_t               Eps_m
               60400                 .33                   0                   0                   0
#  N_funct  F_smooth              C_hard               F_cut                
         4         0                   0                   0                    
#  fct_IDp              Fscale   Fct_IDE                EInf                  CE
         0                   0         0                   0                   0
# Funtions
         1         2         3         4
# Scale factors          Fscale_5
                   1                 1.2                 1.4                 1.6
# Strain rates          Eps_dot_5
                   0                  20                  30                  40
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
function_36
#                  X                   Y
                   0                  90                                                            
              2.5E-4                 100                                                           
                .001                 104                                                           
                .009                 121                                                            
                .017                 136                                                            
                .021                 143                                                           
                .036                 156                                                           
                .045                 162                                                         
                .055                 165                                                           
                .072                 170                                                           
                .075                 170                                                             
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
function_36
#                  X                   Y
                   0                  90                                                            
              2.5E-4                 100                                                           
                .001                 104                                                           
                .009                 121                                                            
                .017                 136                                                            
                .021                 143                                                           
                .036                 156                                                           
                .045                 162                                                         
                .055                 165                                                           
                .072                 170                                                           
                .075                 170                                                             
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3
function_36
#                  X                   Y
                   0                  90                                                            
              2.5E-4                 100                                                           
                .001                 104                                                           
                .009                 121                                                            
                .017                 136                                                            
                .021                 143                                                           
                .036                 156                                                           
                .045                 162                                                         
                .055                 165                                                           
                .072                 170                                                           
                .075                 170                                                             
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
function_36
#                  X                   Y
                   0                  90                                                            
              2.5E-4                 100                                                           
                .001                 104                                                           
                .009                 121                                                            
                .017                 136                                                            
                .021                 143                                                           
                .036                 156                                                           
                .045                 162                                                         
                .055                 165                                                           
                .072                 170                                                           
                .075                 170                                                             
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The first point of yield stress functions (plastic strain versus stress) should have a plastic strain value of zero. If the last point of the first (static) function equals 0 in stress, default value of ε p m a x is set to the corresponding value of ε p .
  2. If ε p (plastic strain) reaches ε p m a x , in one integration point, the element is deleted.
  3. If (largest principal strain) ε 1 > ε t , stress is reduced using:(1)
    σ = σ ( ε m ε 1 ε m ε t )
  4. If ε 1 > ε m , the element is deleted.
  5. The kinematic hardening model is not available in global formulation (hardening is fully isotropic).
  6. For kinematic hardening and strain rate dependency, yield stress depends on the strain rate.
  7. Strain rate filtering input (Fcut) is only available for shell and solid elements.
  8. Strain rate filtering is used to smooth strain rates.
  9. fct_IDp is used to distinguish the behavior in tension and compression for certain materials (that is, pressure dependent yield). This is available for solid elements only. The effective yield stress is then obtained by multiplying the nominal yield stress by the yield factor corresponding to the actual pressure.


    Figure 1.
  10. If ε ˙ n ε ˙ ε ˙ n + 1 , yield stress is a cubic interpolation between functions fn-1, fn, fn+1 and fn+2.
  11. If ε ˙ ε ˙ 1 , yield stress is interpolated between functions f 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIXaaabeaaaaa@37C9@ , f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIXaaabeaaaaa@37C9@ and f 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzamaaBa aaleaacaaIXaaabeaaaaa@37C9@ .
  12. If ε ˙ Nfunc 1 ε ˙ ε ˙ Nfunc , yield is extrapolated between functions fNfunc-3, fNfunc-2, fNfunc-1 and fNfunc.
  13. If ε ˙ > ε ˙ Nfunc , yield is extrapolated between functions fNfunc-2, fNfunc-1 and fNfunc.

    mat_law60_yield
    Figure 2.
  14. Functions describing strain dependence must be defined for different strain rates values.
  15. Strain rate values must be given in strictly ascending order.
  16. 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 ) :
      • 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:(2)
        E ( t ) = E ( E E inf ) [ 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.