/FAIL/LAD_DAMA

Block Format Keyword Describes the Ladeveze failure model for delamination (interlaminar fracture).

This failure model is available for orthotropic solids and thick shells. It could also be used with Plyxfem in shell property /PROP/TYPE17 as an interplay material failure model. This failure model is compatible with /MAT/LAW12 (3D_COMP), /MAT/LAW14 (COMPSO) and /MAT/LAW25 (COMPSH) and /MAT/LAW1 (ELAST) (only when used with Plyxfem).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/LAD_DAMA/mat_ID/unit_ID
K1 K2 K3 γ 1 γ 2
Y 0 Y c k a τ max
Ifail_sh Ifail_so                
Optional Line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fail_ID                  

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier.

(Integer, maximum 10 digits)

 
K1 Interlaminar stiffness in direction 1.

Default = 1030 (Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
K2 Interlaminar stiffness in direction 2.

Default = 1030 (Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
K3 Interlaminar stiffness in direction 3.

Default = 1030 (Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
γ 1 Coupling factor between delamination Mode I and Mode II.

Default = 0 (Real)

 
γ 2 Coupling factor between delamination Mode I and Mode III.

Default = 0 (Real)

 
Y 0 Yield energy damage for delamination start.

Default = 1030 (Real)

 
Y c Critical energy damage parameter for full delamination.

Default = 2 Y 0 (Real)

 
k Crack propagation velocity time constant.

Default = 0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
a Crack propagation velocity multiplier.

Default = 1030 (Real)

 
τ max Dynamic time relaxation. 3

Default = 1030 (Real)

[ s ]
Ifail_sh Shell failure flag.
= 1 (Default)
Shell is deleted, if damage criterion is reached for one layer.
= 2
Shell is deleted, if damage criterion is reached for all shell layers.

(Integer)

 
Ifail_so Solid failure flag.
= 1 (Default)
Solid is deleted, if damage criterion is reached for one integration point.
= 3
Out-of-plane stress is set to zero, if damage is reached for one integration point of solid ( σ 33 = σ 23 = σ 13 = 0 ).

(Integer)

 
fail_ID Failure criteria identifier. 2

(Integer, maximum 10 digits)

 

Example (Composite)

#RADIOSS STARTER
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSH/1/1
composite example
#              RHO_I
             .001506
#                E11                 E22                NU12     Iform                           E33
              144000               10000                 .25         0                         20000
#                G12                 G23                 G31              EPS_f1              EPS_f2
                4200                4200                4200                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax
                   0                   0                   0                   0                   0
#              Wpmax               Wpref      Ioff                         ratio
             1000000                   0         0                             0
#                  b                   n                fmax
                   0                   0             1000000
#            sig_1yt             sig_2yt             sig_1yc             sig_2yc               alpha
               10100               10100               10100               10100                   0
#           sig_12yc            sig_12yt                c_12          Eps_rate_0       ICC
               10068               10068                   0                   0         0
#          GAMMA_ini           GAMMA_max               d3max
                   0                   0                   0
#  Fsmooth                Fcut
         0                   0
/FAIL/LAD_DAMA/1/1
#                 K1                  K2                  K3              Gamma1              Gamma2
                2000                2000                2000               1E-20               1E-20
#                 Y0                  YC                   K                   A             Tau_max
                  40                 160              100000                   1                 .01
# Ifail_sh  Ifail_so                                                                               
         1         3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The Ladeveze failure damage model for delamination:(1)
    Y d 3 = E D d 3 | σ = cst = 1 2 σ 33 2 K 3 ( 1 d 3 ) 2 Mode I
    (2)
    Y d 1 = E D d 1 | σ = cst = 1 2 σ 31 2 K 1 ( 1 d 1 ) 2 Mode II
    (3)
    Y d 2 = E D d 2 | σ = cst = 1 2 σ 32 2 K 2 ( 1 d 2 ) 2 Mode III

    fail_lad-dama_delam1A
    Figure 1.
    2

    For Quad 2D element, only Mode II and Mode III are available.

    Where, d i is the internal damage parameters associated with its fracture mode.

    The damage evolution law is controlled by equivalent damage energy release rate.

    Y = Y d 3 + γ 1 Y d 1 + γ 2 Y d 2 with Y d i | t = sup Y d i | τ t

    The evolution of the damage parameters is strongly coupled with coupling factor γ 1 and γ 2 . These two material parameters come from delamination tests.

    For the present failure model, consider that d 1 = d 2 = d 3 = d .

    Damage value d increases at certain velocity:(4)
    d ˙ = k a [ 1 exp ( a w ( Y ) d ) ]

    if d < 1 .

    Otherwise, d = 1

    While,

    a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DD@ is a measure of the failure ductility, the lower the value the more ductile the failure.

    a k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGHbaabaGaam4Aaaaaaaa@37DD@ is the minimum failure duration. The duration of the energy between Y 0 and Y c should be at least equal to a k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGHbaabaGaam4Aaaaaaaa@37DD@ .(5)
    x = { x if x > 0 0 if x < 0
    The function w ( Y ) is computed as:(6)
    w ( Y ) = Y Y 0 Y c Y 0

    If the damage parameter d 1.0 , the stresses σ 33 , σ 13 and σ 23 are decreased according to the following function:

    A relaxation technique is used by gradually decreasing the stress:(7)
    σ ( t ) = f ( t ) σ d ( t r )
    With,(8)
    f(t)=exp( t t r τ max ) and t t r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAgaciGGOaGaamiDaiaacMcacqGH9aqpciGGLbGaaiiEaiaa cchadaqadiqaaiabgkHiTmaalaaabaGaamiDaiabgkHiTiaadshada WgaaWcbaGaamOCaaqabaaakeaacqaHepaDdaWgaaWcbaGaciyBaiaa cggacaGG4baabeaaaaaakiaawIcacaGLPaaacaaMi8UaaGjcVlaabc cacaqGHbGaaeOBaiaabsgacaqGGaGaamiDaiabgwMiZkaadshadaWg aaWcbaGaamOCaaqabaaaaa@58CB@
    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
  2. 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).
  3. 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.
1 O. Allix, P. Ladevèze, “Interlaminar interface modeling for the prediction of delamination”, Composite structure 22 (1992) 235-242
2 L. Gornet, “Finite Element Damage Prediction of Composite Structures"