/MAT/LAW32 (HILL)

Block Format Keyword This law describes the Hill orthotropic plastic material. It is applicable only to shell elements. This law differs from LAW43 (HILL_TAB) only in the input of yield stress.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW32/mat_ID/unit_ID or /MAT/HILL/mat_ID/unit_ID
mat_title
ρ i                
E ν            
a ε 0 n ε p m a x σ max
ε ˙ 0 m            
r00 r45 r90     Iyield0  

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)

 
a Yield parameter.

(Real)

[ Pa ]
ε 0 Hardening parameter.

(Real)

 
n Hardening exponent.

(Real)

 
ε p m a x Failure plastic strain.

Default = 1030 (Real)

 
σ max Maximum stress.

Default = 1030 (Real)

[ Pa ]
ε ˙ 0 Minimum strain rate.

Default = 1.0 (Real)

[ 1 s ]
m Strain rate exponent.

Default = 0.0 (Real)

 
r00 Lankford parameter 0 degree. 5

Default = 1.0 (Real)

 
r45 Lankford parameter 45 degrees.

Default = 1.0 (Real)

 
r90 Lankford parameter 90 degrees.

Default = 1.0 (Real)

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

(Integer)

 

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                 kg                  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/HILL/1/1
void_steel
#              RHO_I
              7.8E-7
#                  E                  NU
                 210                  .3
#                  A           EPSILON_0                   n             EPS_max           SIGMA_max
                 .17                  .2                 .45                   0                   0
#          EPS_DOT_0                   m
                   0                   0
#                r00                 r45                 r90                       Iyield0
                 .75                   1                1.25                             0
#---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 yield stress is defined as follows:(1)
    σ y = a ( ε 0 + ε p ) n max ( ε ˙ , ε ˙ 0 ) m
    The elastic limit is given by:(2)
    σ 0 = a ( ε 0 ) n ( ε ˙ 0 ) m
    Where,
    ε p
    Plastic strain
    ε ˙
    Strain rate
  2. The yield stress is compared to the equivalent stress:(3)
    σ e q = A 1 σ 1 2 + A 2 σ 2 2 A 3 σ 1 σ 2 + A 12 σ 12 2

    mat_law32_yield_stress
    Figure 1.
  3. This material law must be used with property set type /PROP/TYPE10 (SH_COMP) or /PROP/TYPE9 (SH_ORTH).
  4. Iterative projection (Iplas =1) and radial return (Iplas =2) for shell plane stress plasticity are available.
  5. Angles for Lankford parameters are defined with respect to orthotropic direction 1.
    (4)
    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 rα is the ratio of plastic strain in plane and plastic strain in thickness direction ε 33 .(5)
    r α = d ε α + π / 2 d ε 33

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

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

    A higher value of R means better formability.

  6. If the yield stresses have been obtained in the orthotropic direction 1, define Iyield0 =1; otherwise Iyield0 =0.
  7. When ε p reaches the value of ε p m a x , in one integration point, then the corresponding shell element is deleted.