/FAIL/HASHIN

Block Format Keyword Describes the Hashin failure model. This failure model is available for Shell and Solid.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/HASHIN/mat_ID/unit_ID
Iform Ifail_sh Ifail_so ratio I_Dam Imod I_frwave    
σ 1 t σ 2 t σ 3 t σ 1 c σ 2 c
σ c σ 12 f σ 12 m σ 23 m σ 13 m
ϕ Sdel τ max ε ˙ 0 Tcut
Insert, if I_frwave=2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Soft                
Optional Line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fail_ID                  

Definitions

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
Iform Formulation flag.
= 1 (Default)
Uni-directional lamina model.
= 2
Fabric lamina model.

(Integer)

 
Ifail_sh Shell failure flag.
= 1 (Default)
Shell is deleted, if damage is reached for one layer.
= 2
Shell is deleted, if failed layer > all layer * RATIO.
= 3
Shell is deleted, if all layers (except 1) have failed.

(Integer)

 
Ifail_so Solid failure flag.
= 1 (Default)
Solid is deleted, if damage is reached for one integration point of solid.
= 2
Solid is deleted, if failed int_point > all int_point * RATIO.
= 3
Solid is deleted, if all integration points (except 1) have failed.

(Integer)

 
ratio For Isolid=2 or Ifail_sh=2: the element will be deleted, if more than ratio of the layers (or integration points) have failed.

Default= 1.0 (Real)

 
I_Dam Damage calculation flag. 6
=1 (Default)
Only forces are reduced. The stress tensor is not damaged.
=2
Stress tensor is reduced (used before version 2018)

(Integer)

 
Imod Relaxation time calculation.
= 0 (Default)
Constant relaxation time.
= 1
Relaxation time is based on the timestep.

(Integer)

 
I_frwave Failure propagation flag between neighbor elements.
= 1 (Default)
Off, option is not used.
= 2
Element's rupture criteria is reduced by factor Soft when any neighbor element fails.

(Integer)

 
σ 1 t Longitudinal tensile strength (in fiber direction).

Default = 1030 (Real)

[ Pa ]
σ 2 t Transverse tensile strength (perpendicular to the fiber direction).

Default = 1030 (Real)

[ Pa ]
σ 3 t Through thickness tensile strength.

Default = 1030 (Real)

[ Pa ]
σ 1 c Longitudinal compressive strength (in fiber direction).

Default = 1030 (Real)

[ Pa ]
σ 2 c Transverse compressive strength (perpendicular to the fiber direction).

Default = 1030 (Real)

[ Pa ]
σ c Crush strength.

Default = 1030 (Real)

[ Pa ]
σ 12 f Fiber shear strength.

Default = 1030 (Real)

[ Pa ]
σ 12 m Matrix shear strength 12.

Default = 1030 (Real)

[ Pa ]
σ 23 m Matrix shear strength 23.

Default = 1030 (Real)

[ Pa ]
σ 13 m Matrix shear strength 13.

Default = 1030 (Real)

[ Pa ]
ϕ Coulomb friction Angle for matrix and delamination < 90 degrees.

Default = 0 (Real)

[ deg ]
Sdel Delamination criteria scale factor.

Default = 1.0 (Real)

 
τ max Dynamic time relaxation. 5

Default = 1030 (Real)

[ s ]
ε ˙ 0 Reference strain rate.

Default = 10-30 (Real)

 
Tcut Strain rate cutoff period.

Default = τ max (Real)

[ s ]
Soft Reduction factor applied to failure criteria when one of neighbor elements has already failed.

Only used if, I_frwave=2.

0.0. ≤ Soft ≤ 1.0

Default = 0.0 (Real)

 
fail_ID (Optional) Failure criteria identifer. 4

(Integer, maximum 10 digits)

 

Example (Composite)

With tension and compression tests (see Figure 1) of single composite layer and pure matrix test to determine the strength and yield stress, which are used in material LAW25 and in failure model Hashin. Delamination is not considered in this example.

fail_hashin_example
Figure 1. Fabric Lamina Model (Iform =2)
#RADIOSS STARTER
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSH/1/1
composite material
#              RHO_I
              1.5E-6
#                E11                 E22                NU12     Iform                           E33
                  42                  40                 .05         1                            .5
#                G12                 G23                 G31              EPS_f1              EPS_f2
                 3.4                   3                   3                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax
                   0                   0                   0                   0               .9999
#              Wpmax               Wpref      Ioff    IFLAWP               ratio
                   0                   0         5         0                   0
#                  c          EPS_rate_0               alpha                              ICC_global
                   0                2E-4                   0                                       1
#            sig_1yt                b_1t                n_1t           sig_1maxt                c_1t
                  .1                  25                  .1                   0                   0
#            EPS_1t1             EPS_2t1          SIGMA_rst1            Wpmax_t1
                   0                   0                   0                   0
#            sig_2yt                b_2t                n_2t           sig_2maxt                c_2t
                  .1                  20                  .1                   0                   0
#            EPS_1t2             EPS_2t2            sig_rst2            Wpmax_t2
                   0                   0                   0                   0
#            sig_1yc                b_1c                n_1c           sig_1maxc                c_1c
                .005                 800                  .5                   0                   0
#            EPS_1c1             EPS_2c1            sig_rsc1            Wpmax_c1
                 .08                 .15                  .1                   0
#            sig_2yc                b_2c                n_2c           sig_2maxc                c_2c
                .005                2000                  .5                   0                   0
#            EPS_1c2             EPS_2c2            sig_rsc2            Wpmax_c2
                   0                   0                   0                   0
#           sig_12yt               b_12t               n_12t          sig_12maxt               c_12t
                .004                  83                 .31                   0                   0
#           EPS_1t12            EPS_2t12           sig_rst12           Wpmax_t12
                .075                .085                 .05                   0
#          GAMMA_ini           GAMMA_max               d3max
                1E31                1E31               .9999
#  Fsmooth                Fcut
         0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FAIL/HASHIN/1/1
#    Iform  Ifail_sh  Ifail_so               Ratio     I_Dam      Imod   Ifrwave
         2         1         0                   0         1
#           Sigma1_T            Sigma2_T            Sigma3_T            Sigma1_C            Sigma2_C
                   2                .525                1E30                 1.7                 1.7
#            Sigma_C           SigmaF_12           SigmaM_12           SigmaM_23           SigmaM_13
                1E30                1E30                .075                1E30                1E30
#                Phi              Sdelam             Tau_max           EPS_DOT_0                Tcut
                   0                   1                 .01
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Example of ratio: if ratio=0.5, and Ifail_sh=2 (or Ifail_so=2), the element will be deleted, if more than half of the layers (or integration points) failed.
  2. The 3D material failure model:
    • Uni-directional lamina model:
      Tensile/shear fiber mode:(1)
      F 1 = ( σ 11 σ 1 t ) 2 + ( σ 12 2 + σ 13 2 σ 12 f 2 )
      Compression fiber mode: (2)
      F 2 = ( σ a σ 1 c ) 2

      with, σ a = σ 11 + σ 22 + σ 33 2

      Crush mode:(3)
      F 3 = ( p σ c ) 2

      with, p = σ 11 + σ 22 + σ 33 3

      Failure matrix mode:(4)
      F 4 = ( σ 22 σ 2 t ) 2 + ( σ 23 S 23 ) 2 + ( σ 12 S 12 ) 2
      Delamination mode:(5)
      F 5 = S d e l 2 [ ( σ 33 σ 2 t ) 2 + ( σ 23 S ˜ 23 ) 2 + ( σ 13 S 13 ) 2 ]

      Where,

      S 12 = σ 12 m + σ 22 tan ϕ S 23 = σ 23 m + σ 22 tan ϕ S 13 = σ 13 m + σ 33 tan ϕ S ˜ 23 = σ 23 m + σ 33 tan ϕ

      Note: (6)
      a = { a i f a > 0 0 i f a < 0
    • Fabric lamina model:
      Tensile/shear fiber mode:(7)
      F 1 = ( σ 11 σ 1 t ) 2 + ( σ 12 2 + σ 13 2 σ a f 2 )
      (8)
      F 2 = ( σ 22 σ 2 t ) 2 + ( σ 12 2 + σ 23 2 σ b f 2 )

      With σ a f = σ 12 f , σ b f = σ 12 f σ 2 t σ 1 t

      Compression fiber mode:(9)
      F 3 = ( σ a σ 1 c ) 2
      with, σ a = σ 11 + σ 33 (10)
      F 4 = ( σ b σ 2 c ) 2

      with, σ b = σ 22 + σ 33

      Crush mode:(11)
      F 5 = ( p σ c ) 2

      with, p = σ 11 + σ 22 + σ 33 3

      Shear failure matrix mode:(12)
      F 6 = ( σ 12 σ 12 m ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaI2aaabeaakiabg2da9maabmaabaWaaSaaaeaacqaHdpWC daWgaaWcbaGaaGymaiaaikdaaeqaaaGcbaGaeq4Wdm3aa0baaSqaai aaigdacaaIYaaabaGaamyBaaaaaaaakiaawIcacaGLPaaadaahaaWc beqaaiaaikdaaaaaaa@4312@
      Matrix failure mode:(13)
      F 7 = S d e l 2 [ ( σ 33 σ 3 t ) 2 + ( σ 23 S 23 ) 2 + ( σ 13 S 13 ) 2 ]

      Where,

      S 13 = σ 13 m + σ 33 tan ϕ S 23 = σ 23 m + σ 33 tan ϕ

      If the damage parameter is Fi ≥ 1.0, the stresses are decreased by using an exponential function to avoid numerical instabilities. A relaxation technique is used by decreasing the stress gradually:(14)
      σ ( t ) = f ( t ) σ d ( t r )
      With, (15)
      f ( t ) = exp ( t t r τ max )

      and t t r

      Where,
      t
      Time
      t r
      Start time of relaxation when the damage criteria is assumed
      τ max
      Time of dynamic relaxation
      σ d ( t r )
      Stress at the beginning of damage
  3. The damage value, D is 0 ≤ D ≤ 1. The status for fracture is:
    • Free, if 0 ≤ D > 1
    • Failure, if D=1

    with D = M a x ( F 1 , F 2 , F 3 , F 4 , F 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaad2eacaWGHbGaamiEamaabmaabaGaamOramaaBaaaleaacaaI XaaabeaakiaacYcacaWGgbWaaSbaaSqaaiaaikdaaeqaaOGaaiilai aadAeadaWgaaWcbaGaaG4maaqabaGccaGGSaGaamOramaaBaaaleaa caaI0aaabeaakiaacYcacaWGgbWaaSbaaSqaaiaaiwdaaeqaaaGcca GLOaGaayzkaaaaaa@4779@ for uni-directional lamina model and D = M a x ( F 1 , F 2 , F 3 , F 4 , F 5 , F 6 , F 7 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaad2eacaWGHbGaamiEamaabmaabaGaamOramaaBaaaleaacaaI XaaabeaakiaacYcacaWGgbWaaSbaaSqaaiaaikdaaeqaaOGaaiilai aadAeadaWgaaWcbaGaaG4maaqabaGccaGGSaGaamOramaaBaaaleaa caaI0aaabeaakiaacYcacaWGgbWaaSbaaSqaaiaaiwdaaeqaaOGaai ilaiaadAeadaWgaaWcbaGaaGOnaaqabaGccaGGSaGaamOramaaBaaa leaacaaI3aaabeaaaOGaayjkaiaawMcaaaaa@4C5C@ for fabric lamina model. This damage value shows with /ANIM/BRICK/DAMA or /ANIM/SHELL/DAMA.

  4. The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL. There is no default value. If the line is blank, no value will be output for failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL option).
  5. After the failure criterion is reached, the τ max value determines a period of time when the stress in the failed element is gradually reduced to zero. When the stress reaches 1% of stress value at the start of failure, the element is deleted. This is necessary to avoid instabilities coming from a sudden element deletion and a failure “chain reaction” in the neighboring elements. Even if the failure criterion is reached, the default value of τ max = 1.0 E 30 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiXdq3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccqGH9aqp caaIXaGaaiOlaiaaicdacaWGfbGaaG4maiaaicdaaaa@4413@ results in no element deletion. Therefore, it is recommended to define τ max 10 times larger than the simulation time step.
  6. The I_Dam option improves damage calculation and stability calculating damage, it is not available for shell elements and material laws N° < 29 . It is available for the /MAT/LAW25 (CRASURV) law, if using /PROP/TYPE51 or /PLY and /STACK options.
1 Hashin, Z., and Rotem, A., "A Fatigue Criterion for Fiber-Reinforced Materials," Journal of Composite Materials, Vol. 7, 1973, pp. 448-464. 9
2 Hashin, Z., "Failure Criteria for Unidirectional Fiber Composites," Journal of Applied Mechanics, Vol. 47, 1980, pp. 329-334.