/MAT/LAW15 (CHANG)

Block Format Keyword This law is used to model composite shell elements, similar to LAW25. The plastic behavior is based on the Tsai-Wu criteria (/MAT/LAW25 (COMPSH) for Tsai-Wu description) and failure is based on the Chang-Chang failure criterion is used.

It is recommended to use material LAW25 in combination with a separate Chang-Chang failure criteria (/MAT/LAW25 with /FAIL/CHANG keywords), instead of material LAW15.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW15/mat_ID/unit_ID or /MAT/CHANG/mat_ID/unit_ID
mat_title
ρ i                
E11 E22 ν12        
G12 G23 G31        
b n fmax        
Wpmax Wpref Ioff          
σ 1 y t σ 2 y t σ 1 y c σ 2 y c α
σ 12 y c σ 12 y t c ε ˙ 0 ICC  
β τ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3ABC@ S1 S2 S12
Fsmooth Fcut C1 C2      

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 ]
E11 Young's modulus in direction 1.

(Real)

[ Pa ]
E22 Young's modulus in direction 2.

(Real)

[ Pa ]
ν 12 Poisson's ratio.

(Real)

 
G12 Shear modulus.

(Real)

[ Pa ]
G23 Shear modulus.

(Real)

[ Pa ]
G311 Shear modulus.

(Real)

[ Pa ]
b Hardening parameter.

(Real)

 
n Hardening exponent.

Default = 1.0 (Real)

 
fmax Maximum value of yield function. 2

Default = 1030 (Real)

[ Pa ]
W p max Maximum plastic energy per volume unit.

Default = 1030 (Real)

[ J m 3 ]
W p ref Reference plastic energy per volume unit.

Default = 1.0 (Real)

[ J m 3 ]
Ioff Total element failure criteria. 4
= 0
Shell is deleted if W p * > W p max * for one layer.
= 1
Shell is deleted if W p * > W p max * for all layers.
= 2
If for each layer, W p * > W p max * or tensile failure in direction 1
= 3
If for each layer, W p * > W p max * or tensile failure in direction 2.
= 4
If for each layer, W p * > W p max * or tensile failure in directions 1 and 2.
= 5
If for all layers: W p * > W p max * or tensile failure in direction 1
or if for all layers: W p * > W p max * or tensile failure in direction 2.
= 6
If for each layer, W p * > W p max * or tensile failure in direction 1 or 2.

(Integer)

 
σ 1 y t Composite yield stress in tension in direction 1. 2

(Real)

[ Pa ]
σ 2 y t Composite yield stress in tension in direction 2.

(Real)

[ Pa ]
σ 1 y c Composite yield stress in compression in direction 1.

(Real)

[ Pa ]
σ 2 y c Composite yield stress in compression in direction 2.

(Real)

[ Pa ]
α F12 reduction factor. 2

Default set to 1.0 (Real)

 
σ 12 y c Yield stress in shear and strain rate compression in direction 12.

(Real)

[ Pa ]
σ 12 y t Yield stress in shear and strain rate tension in direction 12.

(Real)

[ Pa ]
c Yield stress in shear and strain rate coefficient. 2
= 0
No strain rate dependency.

(Real)

 
ε ˙ 0 Yield stress in shear and strain rate reference.

(Real)

[ 1 s ]
ICC Strain rate computation flag. 2
= 1 (Default)
Strain rate effect on fmax no effect on W p max .
= 2
No strain rate effect on fmax and W p max
= 3
Strain rate effect on fmax and W p max .
= 4
No strain rate effect on fmax effect on W p max .

(Integer)

 
β Shear scaling factor. 1

(Real)

 
τ max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3ABC@ Time relaxation. 3

Default = 1030 (Real)

[ s ]
S1 Longitudinal tensile strength. 1

Default = 1030 (Real)

[ Pa ]
S2 Transverse tensile strength.

Default = 1030 (Real)

[ Pa ]
S12 Shear strength.

Default = 1030 (Real)

[ Pa ]
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.

Default = 1030 (Real)

[Hz]
C1 Longitudinal compressive strength. 1

Default = 1030 (Real)

[ Pa ]
C2 Transverse compressive strength.

Default = 1030 (Real)

[ Pa ]

Example (Carbon)

#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/LAW15/1/1
Carbon
#              RHO_I
              1.8E-6                   0
#                E11                 E22                nu12
                  41                 3.3                  .3
#                G12                 G23                 G31
                 5.2                 1.3                 1.3
#                  b                   n                fmax
                8E-6                   1              100000
#              Wpmax              Wpref       Ioff
              100000                   0         0
#          sigma_1yt           sigma_2yt           sigma_1yc          sigma_2yc               alpha
                .786               .1566                .786               .1566                   0
#         sigma_12yc          sigma_12yt                   c           Eps_dot_0       ICC
               .0655               .0655                   0                   0         0
#               beta                Tmax                  S1                  S2                 S12
                   1                 .01                   0                   0                   0
#  Fsmooth                Fcut                  C1                 C12
         0                   0                   0                   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. Chang-Chang failure criteria
    Six material parameters are used in the Chang-Chang failure criteria to describe the two different failure behaviors.
    • For fiber breakage, the failure criteria is:
      • Tensile fiber mode σ 11 > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdacaaIXaaabeaakiabg6da+iaaicdaaaa@3B28@
        (1)
        e f 2 = ( σ 11 S 1 ) 2 + β ( σ 12 S 12 ) 2 1.0
        0 failed < 0 elastic plastic
      • Compressive fiber mode σ 11 < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdacaaIXaaabeaakiabgYda8iaaicdaaaa@3B24@
        (2)
        e c 2 = ( σ 11 C 1 ) 2 1.0
        0 failed < 0 elastic plastic
    • For matrix cracking, the failure criteria is:
      • Tensile fiber mode σ 22 > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaikdacaaIYaaabeaakiabg6da+iaaicdaaaa@3B2A@
        (3)
        e m 2 = ( σ 22 S 2 ) 2 + β ( σ 12 S 12 ) 2 1.0
        0 failed < 0 elastic plastic
      • Compressive matrix mode σ 22 < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaikdacaaIYaaabeaakiabgYda8iaaicdaaaa@3B26@
      (4)
      e d 2 = ( σ 22 2 S 12 ) 2 + [ ( C 2 2 S 12 ) 2 1 ] σ 22 C 2 + ( σ 12 S 12 ) 2 1.0
      0 failed < 0 elastic plastic
  2. Before failed (damage parameter e f 2 , e c 2 , e m 2 , e d 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyzamaaBa aaleaacaWGMbaabeaakmaaCaaaleqabaGaaGOmaaaakiaacYcacaWG LbWaaSbaaSqaaiaadogaaeqaaOWaaWbaaSqabeaacaaIYaaaaOGaai ilaiaadwgadaWgaaWcbaGaamyBaaqabaGcdaahaaWcbeqaaiaaikda aaGccaGGSaGaamyzamaaBaaaleaacaWGKbaabeaakmaaCaaaleqaba GaaGOmaaaaaaa@43F6@ is less than 0), material is in elastic–plastic phase. The plastic behavior is based on the TSAI-WU criteria (see Tsai-Wu Formulation (Iform =0) for Tsai-Wu criterion description).
  3. After failed (damage parameter e f 2 , e c 2 , e m 2 , e d 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyzamaaBa aaleaacaWGMbaabeaakmaaCaaaleqabaGaaGOmaaaakiaacYcacaWG LbWaaSbaaSqaaiaadogaaeqaaOWaaWbaaSqabeaacaaIYaaaaOGaai ilaiaadwgadaWgaaWcbaGaamyBaaqabaGcdaahaaWcbeqaaiaaikda aaGccaGGSaGaamyzamaaBaaaleaacaWGKbaabeaakmaaCaaaleqaba GaaGOmaaaaaaa@43F6@ is greater than or equal to 0), the stresses are decreased by using an exponential function to avoid numerical instabilities.
    A relaxation technique is used by gradually decreasing the stress.(5)
    σ ( t ) = f ( t ) σ d ( t r ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4WdiaacI cacaWG0bGaaiykaiabg2da9iGacAgaciGGOaGaamiDaiaacMcacqGH flY1caWHdpWaaSbaaSqaaiaadsgaaeqaaOGaaiikaiaadshadaWgaa WcbaGaamOCaaqabaGccaGGPaaaaa@4615@

    With function of relaxation:

    f ( t ) = exp ( t t r τ max ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOzaiGacI cacaWG0bGaaiykaiabg2da9iGacwgacaGG4bGaaiiCamaabmaabaGa eyOeI0YaaSaaaeaacaWG0bGaeyOeI0IaamiDamaaBaaaleaacaWGYb aabeaaaOqaaiabes8a0naaBaaaleaaciGGTbGaaiyyaiaacIhaaeqa aaaaaOGaayjkaiaawMcaaaaa@4878@ and t t r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0bGaey yzImRaamiDamaaBaaaleaacaWGYbaabeaaaaa@3C43@

    Where,
    t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36EF@
    Time
    t r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaWGYbaabeaaaaa@3812@
    Start time of relaxation when the damage criteria is assumed
    τ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3ABB@
    Time of dynamic relaxation
    σ d ( t r ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4WdmaaBa aaleaacaWGKbaabeaakiaacIcacaWG0bWaaSbaaSqaaiaadkhaaeqa aOGaaiykaaaa@3BE4@
    Stress components at the beginning of damage
  4. If a shell has several layers with one material per layer (different materials, different Ioff), the Ioff used is the one which is associated to the shell in the shell element definition.