/FAIL/ALTER

Block Format Keyword An advanced nonlinear stress-based failure criteria for glass applications such as a windshield.

The failure stress is described by parameters defining micro-cracks and crack propagation speed. With the X-FEM approach, the stress is set to zero perpendicular to the crack direction.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/ALTER/mat_ID/unit_ID
Exp_n V0 Vc Ncycles Irate Iside mode
Cr_foil Cr_air Cr_core Cr_edge grsh4N grsh3N
KIC KTH Rlen Tdelay Iout  
Kres1 Kres2        
Eta1 Beta1 Tau1 Area_ref    
Eta2 Beta2 Tau2        
Sig0 P_scale P_switch        
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)

 
Exp_n Crack growth exponent for subcritical crack growth.

Default = 16.0 (Real)

 
V0 Crack growth velocity V 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaaIWaaabeaaaaa@37B8@ for subcritical crack growth at KIC.

Default = 0.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
Vc Maximum crack propagation velocity glass.

Default = 0.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
Ncycles Stress filtering period in cycles. Only used when Irate=0. 2
= 1 (Default)
No filtering.

(Integer)

 
Irate Stress rate filtering method.
= 0
Exponential moving average using Ncycles.
= 1
Arithmetic average using the last 50 cycles.

(Integer)

 
Iside Strain rate dependency option.
= 0 (Default)
Strain rate dependency only on air (outwards oriented) side.
= 1
Strain rate dependency on both sides of the shell.
(Integer)
 
mode Flag to switch failure propagation models between neighbor elements.
= 0 (Default)
No failure info propagation.
= 1
xfem failure propagation.
= 2
Isotropic frontwave propagation.
= 3
Directional propagation through element edges.
= 4
Directional propagation through edges and diagnosis.

(Integer)

 
Cr_foil Crack depth at bottom surface.

Default = 0.0 (Real)

[ m ]
Cr_air Crack depth at top surface.

Default = 1.0 (Real)

[ m ]
Cr_core Crack depth in between bottom and surface integration points.

Default = 1.0 (Real)

[ m ]
Cr_edge Crack depth at the edge elements of windshield.

Default = 1.0 (Real)

[ m ]
grsh4N (Optional) Group identifier for 4 node edge shell elements.

Default = 0 (Integer)

 
grsh3N (Optional) Group identifier for 3 node edge shell elements.

Default = 0 (Integer)

 
KIC Fracture toughness.

Default = 0.0 (Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaakaaabaGaamyBaaWcbeaaaOGaay5waiaaw2faaaaa @3AB8@
KTH Fatique threshold.

Default = 0.0 (Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca WGqbGaamyyamaakaaabaGaamyBaaWcbeaaaOGaay5waiaaw2faaaaa @3AB8@
Rlen Reference length.

Default = 1.0 (Real)

[ m ]
Tdelay Relaxation time before removing elements.

Default = 0.0 (Real)

[ s ]
Iout Activate exhaustive failure flag in Engine output file.
= 0 (Default)
No additional output.
= 1
Activate extended output.

(Integer)

 
Kres1 Residual tensile stress scale factor in first crack direction.

Default = 0.0 (Real)

 
Kres2 Residual tensile stress scale factor in second crack direction.

Default = 0.0 (Real)

 
Eta1 Distribution parameters η 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaigdaaeqaaaaa@388A@ on bottom surface. 10

(Real)

[ Pa ]
Beta1 Distribution parameters β 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS baaSqaaiaaigdaaeqaaaaa@387F@ on bottom surface. 10

(Real)

 
Tau1 Distribution parameters τ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiaaigdaaeqaaaaa@38A3@ on bottom surface. 10

(Real)

[ Pa ]
Area_ref Reference element surface area.

(Real)

[ m 2 ]
Eta2 Distribution parameters η 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdG2aaS baaSqaaiaaigdaaeqaaaaa@388A@ on top surface. 10

(Real)

[ Pa ]
Beta2 Distribution parameters β 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS baaSqaaiaaigdaaeqaaaaa@387F@ on top surface. 10

(Real)

 
Tau2 Distribution parameters τ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiaaigdaaeqaaaaa@38A3@ on top surface. 10

(Real)

[ Pa ]
Sig0 Initial stress at glass surface.

(Real)

[ Pa ]
P_scale Limits the definition interval of selected distribution function.

(Real, between 0.0 and 1.0)

 
P_switch Distribution function interval:
= 0
Distribution function from is defined between (0, P_scale).
= 1
Distribution function from is defined between (P_scale, 1).
(Integer)
 
fail_ID Failure criteria identifier. 9

(Integer, maximum 10 digits)

 

Example (Glass)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW36/72200103/1
Glass with linear hardening
#              RHO_I
             2.50E-9
#                  E                  NU           Eps_p_max               Eps_t               Eps_m
             70000.0                0.23                   0                   0                   0 
#  N_funct  F_smooth              C_hard               F_cut               Eps_f
         1         1                   0                1650                   0
#  fct_IDp              Fscale   fct_IDE                EInf                  CE
         0                   0         0                   0                   0
#  fct_ID1   fct_ID2   fct_ID3   fct_ID4   fct_ID5
 722001021
#           Fscale_1            Fscale_2            Fscale_3            Fscale_4            Fscale_5
                1000
#          Eps_dot_1           Eps_dot_2           Eps_dot_3           Eps_dot_4           Eps_dot_5
                   0 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FAIL/ALTER/72200103/1
#              EXP_N                  V0                  VC   NCYCLES     IRATE     ISIDE      MODE
                16.0                 6.0             1520000         6         0         0         1
#            CR_FOIL              CR_AIR             CR_CORE             CR_EDGE    GRSH4N    GRSH3N
             0.00040             0.00100             0.00500                   0         0         0
#                KIC                 KTH                RLEN                TDEL      Iout
              23.717              7.9057                 1.0                   0         0
#              KRES1               KRES2
                   0                   0
#               ETA1               BETA1                TAU1            AREA_REF
                   0                   0                   0                   0
#               ETA2               BETA2                TAU2
                   0                   0                   0
#               SIG0             P_SCALE  P_SWITCH
                   0                   0         0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/722001021
Function for glass
#                  X                   Y
                 0.0               500.0
                 1.0               550.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

  1. This failure criteria is using the maximum stress as failure criterion. It is computed based on the strength of the material determined by initial cracks and the crack propagation velocity. Depending on mode switch flag, different failure propagation models between neighbor elements may be used.
  2. When Irate=0, an exponential moving average filter is used, and the filtered stress is:(1)
    σ f ( t ) = α σ ( t ) + ( 1 α ) σ ( t Δ t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAgaaeqaaOWaaeWaaeaacaWG0baacaGLOaGaayzkaaGa eyypa0JaeqySdeMaeq4Wdm3aaeWaaeaacaWG0baacaGLOaGaayzkaa Gaey4kaSYaaeWaaeaacaaIXaGaeyOeI0IaeqySdegacaGLOaGaayzk aaGaeq4Wdm3aaeWaaeaacaWG0bGaeyOeI0IaeyiLdqKaamiDaaGaay jkaiaawMcaaaaa@4F8A@
    Where,
    σ f = filtered stress MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAgaaeqaaOGaeyypa0JaaeOzaiaabMgacaqGSbGaaeiD aiaabwgacaqGYbGaaeyzaiaabsgacaqGGaGaae4CaiaabshacaqGYb GaaeyzaiaabohacaqGZbaaaa@47A0@
    α = 2 N c y c l e s + 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0ZaaSaaaeaacaaIYaaabaGaamOtamaaBaaaleaacaWGJbGaamyE aiaadogacaWGSbGaamyzaiaadohaaeqaaOGaey4kaSIaaGymaaaaaa a@41AE@
  3. This failure model is compatible only with under-integrated shell elements (Ishell =24 and Ish3n =2 are recommended) and not compatible fully integrated shells. Also, although there is no restriction of the shell property that can be used, it is only compatible with one layer shell models.
  4. The elements defined in the groups grsh4N and grsh3N should be along the edge of the windshield and will receive specific failure weakening.
  5. This failure model is applied to shell elements that sandwich a polyvinyl butyral (PVB) solid element layer using coincident nodes. The entire assembly models a windshield.


    Figure 1. Windshield finite element model


    Figure 2. Windshield model - entire assembly
  6. The shell elements using this failure model should be oriented so their normals point away the from the middle PVB.
  7. The shell elements should have an offset applied to correctly model bending. This can be done using /PROP/TYPE51 Ipos=4.
  8. The fracture limit depends on the location and the fracture state of surrounding elements. 1
  9. The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL and /PERTURB/FAIL/BIQUAD. 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 for brick and with /STATE/SHELL/FAIL for shell).
  10. Ch. Brokmann extension 2 defines additional fracture criteria for external glass surfaces only. It introduces initial stress on the glass surface, due to mechanical or chemical treatment. Statistical evaluation of micro flaws in the glass surface allows to define a probability of fracture using left-truncated Weibull stochastic distribution:
    with i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36C4@ = 1,2 for bottom and top surface (2)
    P ( σ ) = 1 exp [ ( τ i η i ) β i ( σ η i ) β i ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI cacqaHdpWCcaGGPaGaeyypa0JaaGymaiabgkHiTiGacwgacaGG4bGa aiiCamaadmaabaWaaubiaeqaleqabaGaeqOSdi2aaSbaaWqaaiaadM gaaeqaaaqdbaWaaeWaaeaadaWcaaqaaiabes8a0naaBaaaoeaacaWG Pbaabeaaa0qaaiabeE7aOnaaBaaaoeaacaWGPbaabeaaaaaaniaawI cacaGLPaaaaaGccqGHsisldaqfGaqabSqabeaacqaHYoGydaWgaaad baGaamyAaaqabaaaneaadaqadaqaamaalaaabaGaeq4WdmhabaGaeq 4TdG2aaSbaa4qaaiaadMgaaeqaaaaaa0GaayjkaiaawMcaaaaaaOGa ay5waiaaw2faaaaa@5617@
    Truncation point τ = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqNaey ypa0JaaGimaaaa@397C@ yields the well-known two-parameter Weibull distribution. The Brokmann model calculates the randomly oriented initial flaws in the glass and distributes them over all finite elements with different lengths and geometry. Crack growth may be expressed by the following differential equation: (3)
    d a = V 0 . ( Y σ π a K I C ) E x p _ n d t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadg gacqGH9aqpcaWGwbWaaSbaaSqaaiaaicdaaeqaaOGaaiOlamaavaca beWcbeqaaiaadweacaWG4bGaamiCaiaac+facaWGUbaaneaadaqada qaamaalaaabaGaamywaiabeo8aZnaakaaabaGaeqiWdaNaamyyaaGd beaaa0qaamaavababeGdbaGaamysaiaadoeaaeqaneaacaWGlbaaaa aaaiaawIcacaGLPaaaaaGccaWGKbGaamiDaaaa@4BD4@

    Where, Y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqdbaGaamywaaaa@36D8@ is a flaw geometry factor obtained using Weibull distribution.

    Integral of Equation 3 will yield actual crack size, strongly dependent on stress rate. Actual stress intensity factors can be calculated and used in the fracture criteria.

    The interest of Brokmann’s model is that depending on the distribution parameters and failure stress value, it is possible to estimate the stochastic probability of failure.


    Figure 3.
    After running a sufficient number of simulations with random initialization of glass flaws return a possibility to estimate a probability to reach a given value of the head injury criterion (HIC).


    Figure 4.
  11. Flag Irate is automatically set to 0 when Ch. Brokmann criterion is used. It is then necessary to define the number of cycles for the stress filtering interval using exponential average.
1 Alter, Christian, Stefan Kolling, and Jens Schneider. "An enhanced non–local failure criterion for laminated glass under low velocity impact." International Journal of Impact Engineering 109 (2017): 342-353.
2 Ch. Brokmann: “A Model for the Stochastic Fracture Behavior of Glass and Its Application to the Head Impact on Automotive Windscreens”, Springer Vieweg, 2022, ISBN 9783658367879