/MAT/LAW52 (GURSON)

Block Format Keyword This law is based on the Gurson constitutive law, which is used to model visco-elastic-plastic strain rate dependent porous metals.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW52/mat_ID/unit_ID or /MAT/GURSON/mat_ID/unit_ID
mat_title
ρ i                
E ν12 Iflag Fsmooth Fcut Iyield  
A B N c p
q 1 q 2 q 3 SN εN
fI fN fc fF    
If Iyield > 0:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Tab_ID   XFAC YFAC        

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
Unit Identifier 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 12 Poisson's ratio.

(Real)

 
Iflag Viscoplastic flow flag. 1
= 0
von Mises criteria.
= 1
von Mises criteria.
= 2
1 + void nucleation set to zero in compression
= 3
0 + void nucleation set to zero in compression.

(Integer)

 
Fsmooth Smooth strain rate are computed.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing is active.

(Integer)

 
Fcut Cutoff frequency for strain rate filtering.

Default = 1030 (Real)

[Hz]
Iyield Flag for computing the Yield stress. 3
= 0
Using Cowper-Symond's law.
= 1
Using Yield stress table (Yield stress versus plastic strain).

(Integer)

 
A Yield stress.

(Real)

[ Pa ]
B Hardening parameter.

(Real)

[ Pa ]
N Hardening exponent.

(Real)

 
c Strain rate coefficient in Cowper-Symond's law.

(Real)

[ 1 s ]
p Strain rate exponent in Cowper-Symond's law.

(Real)

 
q 1 , q 2 , q 3 Damage material parameters.

(Real)

 
SN Gaussian standard deviation.

(Real)

[ Pa ]
ε N Nucleated effective plastic strain.

(Real)

 
fI Initial void volume fraction. 2

(Real)

 
fN Nucleated void volume fraction.

(Real)

 
fc Critical void volume fraction at coalescence. 2

(Real)

 
fF Critical void volume fraction at ductile fracture. 2

(Real)

 
Tab_ID Yield stress table identifier (stress-strain functions with correspond strain rate).

(Integer)

 
XFAC Scale factor for the first entry (plastic strain) in function which used for Tab_ID.

Default = 1.0 (Real)

 
YFAC Scale factor for ordinate (Yield stress) in function which used for Tab_ID.

Default = 1.0 (Real)

 

Example (with parameter input)

#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/LAW52/1/1
Steel
#              RHO_I
               .0078                   
#                  E               NU_12     Iflag   Fsmooth                Fcut    Iyield
              200000                  .3         0         0                   0         0
#                  A                   B                   N                   c                   p
                 200                 533                   1                 802               3.585
#                q_1                 q_2                 q_3                  SN                EpsN
                1.25                   1                2.25                  .1                  .2
#                 Fi                  FN                  Fc                  FF
                 .01                 .04                 .12                  .2
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example (with function input)

#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/LAW52/1/1
Steel
#              RHO_I
               .0078                   
#                  E               NU_12     Iflag   Fsmooth                Fcut    Iyield
              200000                  .3         0         0                   0         1
#                  A                   B                   N                   c                   p
                 200                 533                   1                 802               3.585
#                q_1                 q_2                 q_3                  SN                EpsN
                1.25                   1                2.25                  .1                  .2
#                 Fi                  FN                  Fc                  FF
                 .01                 .04                 .12                  .2
#   Tab_ID                XFAC                YFAC
      1000                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/1000
curve_list with strain rates
         2
# function                    stain rate
     10010                        1.0e-4
     10020                           1.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/10010
plastic strain vs yield stress funct dt=1.0e-4
#     plastic strain       yield stress    
              0.0000                200.
              1.0000                733.
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/10020
plastic strain vs yield stress funct dt=1.0
#     plastic strain       yield stress
              0.0000                250.
              1.0000                783.
#---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 von Mises criteria for viscoplastic flow:
    If Iflag = 0:(1)
    Ω v m = σ e q σ M 1 + q 3 f * 2 2 q 1 f * 2 cosh ( 3 q 2 σ m 2 σ M )
    If Iflag = 1:(2)
    Ω v m = σ e q 2 σ M 2 + 2 q 1 f * cosh ( 3 2 q 2 σ m σ M ) ( 1 + q 3 f 2 )

    if σ m > 0

    (3)
    Ω v m = σ e q 2 σ M 2 + 2 q 1 f ( 1 + q 3 f 2 )

    if σ m 0

    Where, σ M is the admissible stress, σ m is the trace[ σ ] (hydrostatic stress), σ e q is the von Mises stress, and q 1 , q 2 , and q 3 are the material parameter for Gurson Law,

    q 3 = q 1 2

    f * is the specific coalescence function.

    f * = f if f f c

    f * = f c + f u f c f F f c ( f f c ) if f > f c

    with

    f u = 1 q 1 corresponding to the coalescence function f u = f * ( f F )

  2. The void volume fraction parameters must be entered so that, f I < f c < f F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGjbaabeaakiabgYda8iaadAgadaWgaaWcbaGaam4yaaqa baGccqGH8aapcaWGMbWaaSbaaSqaaiaadAeaaeqaaaaa@3DD8@ .
  3. If one integration point reaches f * f F , the element is deleted.
  4. If the Iyield flag is not activated (Iyield=0), the yield stress is computed using Cowper-Symond's law:
    (4)
    σ M = ( A + B ε M N ) ( 1 + ( ε ˙ c ) 1 p )

    If the Iyield flag is activated (Iyield=1), the yield stress is computed directly from the Yield stress curves (Tab_ID).

  5. This law is available for shell and solid elements.
  6. In plot files (/TH/SHEL, /TH/SH3N and /TH/BRICK) or animation files (/ANIM), the following variables are available:
    • USR1: plastic strain ε M
    • USR2: f *
    • USR3: admissible stress σ M
    • USR4: f
    • USR5: ε