/MAT/LAW66

Block Format Keyword This law models an isotropic tension-compression elasto-plastic material law using user-defined functions for the work-hardening portion of the stress-strain (plastic strain versus stress). This law can be defined for compression and tension.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW66/mat_ID/unit_ID
mat_title
ρ i                
E υ Chard Fcut Fsmooth Iyld_rate
Pc Pt            
Read only if Iyld_rate = 0, 1 or 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDc fct_IDt Fscalec Fscalet        
ε ˙ 0 c σ y 0 VP      
Read only if Iyld_rate = 3
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDc fct_IDt Fscalec Fscalet        
Frate_IDc Frate_IDt Fscale_ratec Fscale_ratet        
Read only if Iyld_rate = 4
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
NFUNCC NFUNCT                
For each NFUNCC
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDc   ε ˙ i c Fscalec        
For each NFUNCT
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDt   ε ˙ i t Fscalet        

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 ]
υ Poisson's ratio.

(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)

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

(Integer)

 
Fcut Cutoff frequency for strain rate filtering, Appendix: Filtering.

Default = 1030 (Real)

[Hz]
Iyld_rate Rate effect on the yield stress flag.
= 1 (Default)
Using Cowper-Symonds:
1 + ( ε ˙ ε ˙ 0 ) 1 c
= 2
By using:
1 + cLn ( ε ˙ ε ˙ 0 )
= 3
By using two load curves to scale the yield stress (fct_IDc) in compression and tension (fct_IDt).
= 4
By using different functions for compression and tension for different strain rate values.

(Integer)

 
Pc Limit pressure in compression.

Default = 0 (Real)

[ Pa ]
Pt Limit pressure in tensile.

Default = 0 (Real)

[ Pa ]
fct_IDc Compression yield stress.

(Integer)

 
fct_IDt Tension yield stress.

(Integer)

 
Fscalec Scale factor for ordinate (stress) in fct_IDc.

Default = 1.0 (Real)

[ Pa ]
Fscalet Scale factor for ordinate (stress) in fct_IDt.

Default = 1.0 (Real)

[ Pa ]
c Strain rate parameter.

(Real)

 
ε ˙ 0 Reference strain rate.

Default = 1.0 (Real)

[ 1 s ]
σ y 0 Initial yield stress.

Default = 0 (Real)

[ Pa ]
VP Strain rate choice flag.
= 0
Strain rate effect on the yield stress is depending on the total strain rate.
= 1
Strain rate effect on the yield stress is depending on plastic strain rate.
In this case, there is no strain rate filtering, so Fsmooth and Fcut are not used. Only available if Iyld_rate = 1 (Cowper Symonds). 2

(Integer)

 
Frate_IDc Compression strain rate effect function identifier.

(Integer)

 
Frate_IDt Tension strain rate effect function identifier.

(Integer)

 
Fscale_ratec Scale factor for ordinate (stress) in Frate_IDc.

Default = 1.0 (Real)

[ Pa ]
Fscale_ratet Scale factor for ordinate (stress) in Frate_IDt.

Default = 1.0 (Real)

[ Pa ]
NFUNCC Number of compression function.

(Integer)

 
NFUNCT Number of tension function.

(Integer)

 
ε ˙ i c ith compression strain rate i =1,NFUNCC.

(Real)

[ 1 s ]
ε ˙ i t ith tension strain rate i=1,NFUNCT.

(Real)

[ 1 s ]

Example (Aluminum)

#RADIOSS STARTER
/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/LAW66/1/1
Aluminium
#              RHO_I
               .0027
#                  E                  Nu              C_hard               F_cut  F_smooth Iyld_rate
               60400                 .33                   0                   0         0         4
#                P_c                 P_t
                 500                 600
#   NFUNCC    NFUNCT
         2         2
#funct_IDc                    Episilon_c             Fscalec
        38                            10                   1                                                  
        40                            40                 1.6                                                  
#funct_IDt                    Episilon_t             Fscalet
        38                            10                   1                                                  
        40                            40                 1.6                                                  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/38
function_38
#                  X                   Y
                   0                  90                                                            
                 .08                 170                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/40
function_40
#                  X                   Y
                   0                  90                                                            
                 .08                 170                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This is an isotropic elastic-plastic law. The yield stress is defined by using the compression and tension yield stress versus effective plastic strain for the both (compression and tension). When exceeded, the two pressures Pt and Pc, determine if the tension yield stress or compression yield stress is used respectively.

    If the pressure is between these two values, the yield stress is given by:

    If P t P P c (1)
    σ y = α σ y t ( ε p ) + ( 1 α ) σ y c ( ε p ) α = P c P P e + P t

    If P t = P c = 0 , or the pressure is out of the two values range, the yield stress is given by:

    σ y = σ y t ( ε p ) if P 0

    σ y = σ y c ( ε p ) if P > 0

  2. Yield stress is computed as:

    If VP= 1:

    σ y ( ε p , ε ˙ p ) = σ y s ( ε p ) + σ y 0 ( ε ˙ p ε ˙ 0 ) 1 c if σ y 0 > 0

    σ y ( ε p , ε ˙ p ) = σ y s ( ε p ) [ 1 + ( ε ˙ p ε ˙ 0 ) 1 c ] if σ y 0 = 0

    If VP= 0:

    σ y ( ε p , ε ˙ p ) = σ y s ( ε p ) if σ y 0 > 0

    σ y ( ε p , ε ˙ p ) = σ y s ( ε p ) if σ y 0 = 0

    with σ y t ( ε p ) being static yield stress and σ y 0 being initial yield stress.

  3. /VISC/PRONY can be used with this material law to include viscous effects.