/MAT/LAW73

Block Format Keyword This law describes the Thermal Hill orthotropic material and is applicable only to shell elements.

This law differs from /MAT/LAW43 (HILL_TAB) by the fact that yield stress not only depends on strain rate and plastic strain, but also on temperature (it is defined by a user table).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW73/mat_ID/unit_ID
mat_title
ρ i                
E v            
fct_IDE   Einf CE Blank
r00 r45 r90 Chard Iyield0  
ε p m a x ε t ε m        
Tab_ID   σ s c a l e ε ˙ s c a l e        
Ti Cp            

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 Initial Young's modulus.

(Real)

[ Pa ]
v 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.
= 0 (Default)
In this case the evolution of Young's 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)

 
r00 Lankford parameter 0 degree. 3

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.

(Read)

 
Iyield0 Yield stress flag.
= 0
Average yield stress input.
= 1
Yield stress in orthotropic direction 1.

(Integer)

 
ε p m a x Failure plastic strain.

Default = 1.0x1030 (Real)

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

Default = 1.0x1030 (Real)

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

Default = 2.0x1030 (Real)

 
Tab_ID Table identifier for yield stress definition.

(Integer)

 
σ s c a l e Yield stress scale factor.

Default set to 1.0 (Real)

[ Pa ]
ε ˙ s c a l e Strain rate scale factor.

Default set to 1.0 (Real)

[ 1 s ]
Ti Initial temperature.

Default set to 293K (Real)

[ K ]
C p Specific heat per mass unit.

(Real)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@

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/LAW73/1/1
steel
#              RHO_I
              0.0078
#                  E                  NU
            210000.0                 0.3
#FUNCT_IDE                          EINF                  CE
         0                             0                   0
#                R00                 R45                 R90              C_HARD   Iyield0
                 1.6                 1.6                 1.6                 0.0         0
#           EPSP_MAX              EPS_T1              EPS_T2
                   0                   0                   0
#    TABLE                  SIGMA_SCALE         EPSPT_SCALE
        10                             0                   0                                        
#                 TI                  CP
                273.                  4.
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/10
table
         3
      1011                           0.0                273.                                       
      1013                          0.02                300.                                       
      1013                          0.04                300.                                       
      1012                           0.0                300.                                       
      1012                          0.02                273.                                       
      1012                          0.04                273.                                       
/FUNCT/1011
1st
                 0.0               185.0
                 0.1               339.0
                 1.0               339.0
/FUNCT/1012
2nd
                 0.0               190.0
                 0.1               344.0
                 1.0               344.0
/FUNCT/1013
3rd
                 0.0               195.0
                 0.1               349.0
                 1.0               349.0
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This material law must be used with property set /PROP/TYPE9 (SH_ORTH) or /PROP/TYPE10 (SH_COMP).
  2. The yield stress is defined by a user function and the yield stress is compared to equivalent stress:
    (1)
    σ e q = A 1 σ 1 2 + A 2 σ 2 2 - A 3 σ 1 σ 2 + A 12 σ 12 2
  3. Angles for Lankford parameters are defined with respect to orthotropic direction 1.
    R = r 00 + 2 r 45 + r 90 4 H = R 1 + R
    A 1 = H ( 1 + 1 r 00 ) A 2 = H ( 1 + 1 r 90 )
    A 3 = 2 H A 12 = 2 H ( r 45 + 0.5 ) ( 1 r 00 + 1 r 90 )
    r 00 = A 3 2 A 1 A 3 r 45 = 1 2 ( A 12 A 1 + A 2 A 3 1 )
    r 90 = A 3 2 A 2 A 3
    The Lankford parameters r α is ratio of plastic strain in plane and plastic strain in thickness direction ε 33 .(2)
    r α = d ε α + π / 2 d ε 33

    Where, α is the angle to the orthotropic direction 1.

    This Lankford parameters r α could be determined from a simple tensile test at an angle α.

    A higher value of R means better formability.

  4. If ε p (plastic strain) reaches ε p max , in one integration point, the corresponding shell element is deleted.
  5. If largest principal strain ε 1 > ε t , stress is reduced using the following relation: (3)
    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. This law always uses iterative projection for plasticity (Iplas from the property set is ignored).
  8. This law is not available with global formulation for plasticity (N=0 in the property shell is not available).
  9. The table for yield stress definition must be a 3-dimensional table whose parameters respectively represent plastic strain, strain rate, and temperature ( ε p , ε ˙ , T ) . Values of the table are yield stress values.
  10. If ε m 1 p ε p ε m p and ε ˙ n 1 ε ˙ ε ˙ n and T q 1 T T q yield is linearly interpolated between the eight values of the table corresponding to ( ε i p , ε ˙ j , T k ) , i = m 1 , m ; j = n 1 , n ; k = q 1 , q .
  11. If ( ε p , ε ˙ , T ) falls out of the range of the table, yield stress is obtained by linear extrapolation. Thus it is necessary to input into the table the static curves corresponding to zero strain rate (entry ε ˙ = 0 should belong to the table definition).
    If the /HEAT/MAT option is not associated to the material identifier, adiabatic conditions are assumed and temperature is computed as:(4)
    Τ = T i + E i n t ρ C p ( V o l u m e )
    Where,
    E int
    Internal energy computed by Radioss,
    σ
    Volume are the current density, and volume
    C p
    Heat capacity per mass unit

    Otherwise, the finite element formulation for heat transfer must be asked for (Iform =1 in option /HEAT/MAT); initial temperature and specific heat input in the option /HEAT/MAT will then be used.

  12. If the yield stresses have been obtained in the orthotropic direction 1, define Iyield0 =1; otherwise Iyield0=0.