/MAT/LAW22 (DAMA)

Block Format Keyword This law is identical to Johnson-Cook material (/MAT/LAW2), except that the material undergoes damage if plastic strains reach a user-defined value ( ε d a m ). This law can be applied to both shell and solid elements.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW22/mat_ID/unit_ID or /MAT/DAMA/mat_ID/unit_ID
mat_title
ρ i                
E ν            
a b n ε p m a x σ max 0
c ε ˙ 0 ICC          
ε d a m Et            

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 ]
ν Poisson's ratio.

(Real)

 
a Yield stress - should be strictly positive.

(Real)

[ Pa ]
b Hardening parameter.

(Real)

[ Pa ]
n Hardening exponent.

(Real)

 
ε p m a x Failure plastic strain.

Default = 1030 (Real)

 
σ max 0 Maximum stress.

Default = 1030 (Real)

[ Pa ]
c Strain rate coefficient.
= 0
No strain rate effect

Default = 0.00 (Real)

 
ε ˙ 0 Reference strain rate.

If ε ˙ ε ˙ 0 , no strain rate effect.

(Real)

[ 1 s ]
ICC Strain rate computation flag. 2
= 0 (Default)
Set to 1
.
= 1
Strain rate effect on σ max .
= 2
No strain rate effect on σ max .

(Integer)

 
ε d a m Damage model starts at ε d a m .

Default = 0.15 (Real)

 
Et Softening damage slope ( E < E t 0 ).

Default = 0.00 (Real)

[ Pa ]

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/DAMA/1/1
Alu
#              RHO_I
               .0027                   
#                  E                  Nu
               70000                  .3
#                  a                   b                   n             Eps_max          SIGMA_max0
                 100                   0                   1                  .2                 100
#                  c           Eps_dot_0       ICC
                   0                   0         0
#            Eps_dam                 E_t
                  .1               -2000
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Damage is isotropic, its effect are the same in tension and compression.
    (1)
    σ = ( a + b ε p n ) ( 1 + c ln ε ˙ ε ˙ 0 )
    Where,
    ε p
    Plastic strain
    ε ˙
    Strain rate
  2. ICC is a flag of the strain rate effect on material maximum stress σ max .


    σ = σ y ( 1 + c ln ( ε ˙ ε ˙ o ) ) σ = σ y ( 1 + c ln ( ε ˙ ε ˙ o ) )
    σ max = σ max 0 ( 1 + c ln ( ε ˙ ε ˙ o ) ) σ max = σ max 0
    Figure 1.
  3. The damage appears in the material when the strain is larger than a maximum value ε d a m :(2)
    0 δ 1

    If ε < ε d a m δ = 0 , Law 22 is identical to law /MAT/LAW2.

    If ε ε d a m E d a m = ( 1 δ ) E and ν dam = 1 2 δ+( 1δ )ν

    clip0053
    Figure 2.
  4. For solid elements, the damage law can only be applied to the deviatoric stress tensor sij and G d a m = E d a m 2 ( 1 + ν d a m ) .
  5. When ε p reaches ε p m a x in one integration point, then based on the element type:
    • Shell elements: The corresponding shell element is deleted.
    • Solid elements: The deviatoric stress of the corresponding integral point is permanently set to 0, however, the solid element is not deleted.