/FAIL/TSAIWU

Block Format Keyword Tsai-Wu failure criterion for composite materials failure modeling. This criterion is available for solids and shells.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/TSAIWU/mat_ID/unit_ID
σ 1 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ σ 2 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ σ 1 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ σ 2 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ σ ¯ 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae badaWgaaWcbaGaaGymaiaaikdaaeqaaaaa@3972@
α MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3793@ τ max MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3AB9@ Fcut   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 (Optional) Unit identifier.

(Integer, maximum 10 digits)

σ 1 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ Longitudinal tensile strength.

Default = 1020 (Real)

[ Pa ]
σ 2 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ Transverse tensile strength.

Default = 1020 (Real)

[ Pa ]
σ 1 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ Longitudinal compressive strength.

Default = 1020 (Real)

[ Pa ]
σ 2 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ Transverse compressive strength.

Default = 1020 (Real)

[ Pa ]
σ ¯ 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae badaWgaaWcbaGaaGymaiaaikdaaeqaaaaa@3972@ Shear strength.

Default = 1020 (Real)

[ Pa ]
α MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3793@ Interaction parameter 12.

Default = 0.0 (Real)

τ max MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdq3aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3AB9@ Dynamic time relaxation. 5

Default = 1020 (Real)

[ s ]
Fcut Stress tensor filtering frequency.

Default = 0.0 (Real)

[ 1 s ]
Ifail_sh Shell failure model flag.
= 0 (Default)
Shell is never deleted and no stress softening.
= 1
Shell is deleted, if damage is reached for one layer.
= 2
Shell is deleted, if damage is reached for all shell layers.

(Integer)

Ifail_so Solid failure model flag.
= 0
Solid is never deleted and no stress softening.
= 1 (Default)
Solid is deleted, if damage is reached for one integration point of solid.
= 2
Solid is deleted, if damage is reached for all integration points.

(Integer)

fail_ID (Optional) Failure criteria identifier. 4

(Integer, maximum 10 digits)

Example

/UNIT/1
                  kg                  mm                  ms
/FAIL/TSAIWU/1/1
#           SIGMA_1T            SIGMA_2T            SIGMA_1C            SIGMA_2C            SIGMA_12
                 0.6                0.525                 0.8                0.75                0.075  
#              ALPHA             TAU_MAX                 FCUT                      IFAIL_SH  IFAIL_SO
                 0.9             0.005932                                                  2          2

Comments

  1. This failure model is available for shells and solids. It considers a composite material ply with the fibers oriented in the direction 1 (also denoted m1) and the matrix oriented in transverse direction, that is, in direction 2 (and 3 for solids). Each direction considers a critical strength value in tension and compression as;
    Figure 1.

    Where, σ 1 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ , σ 2 t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ , σ 1 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ , σ 2 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaaigdaaeaacaWG0baaaaaa@3998@ , σ ¯ 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae badaWgaaWcbaGaaGymaiaaikdaaeqaaaaa@3972@ are respectively the critical strength in tension for direction 1, in tension for direction 2, in compression for direction 1, in compression for direction 2 and in shear.

  2. The failure criterion for shells is written as:(1)
    F = F 11 σ 1 2 + F 22 σ 2 2 + F 66 σ 12 2 + 2 F 12 σ 1 σ 2 + F 1 σ 1 + F 2 σ 2 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9iaadAeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaeq4Wdm3aa0ba aSqaaiaaigdaaeaacaaIYaaaaOGaey4kaSIaamOramaaBaaaleaaca aIYaGaaGOmaaqabaGccqaHdpWCdaqhaaWcbaGaaGOmaaqaaiaaikda aaGccqGHRaWkcaWGgbWaaSbaaSqaaiaaiAdacaaI2aaabeaakiabeo 8aZnaaDaaaleaacaaIXaGaaGOmaaqaaiaaikdaaaGccqGHRaWkcaaI YaGaamOramaaBaaaleaacaaIXaGaaGOmaaqabaGccqaHdpWCdaWgaa WcbaGaaGymaaqabaGccqaHdpWCdaWgaaWcbaGaaGOmaaqabaGccqGH RaWkcaWGgbWaaSbaaSqaaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqaai aaigdaaeqaaOGaey4kaSIaamOramaaBaaaleaacaaIYaaabeaakiab eo8aZnaaBaaaleaacaaIYaaabeaakiabgsMiJkaaigdaaaa@629F@
    For solids the criterion becomes:(2)
    F = F 11 σ 1 2 + F 22 σ 2 2 + F 22 σ 3 2 + F 66 σ 12 2 + F 66 σ 13 2 + 2 F 12 σ 1 σ 2 + 2 F 12 σ 1 σ 3 + F 1 σ 1 + F 2 σ 2 + F 2 σ 3 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9iaadAeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaeq4Wdm3aa0ba aSqaaiaaigdaaeaacaaIYaaaaOGaey4kaSIaamOramaaBaaaleaaca aIYaGaaGOmaaqabaGccqaHdpWCdaqhaaWcbaGaaGOmaaqaaiaaikda aaGccqGHRaWkcaWGgbWaaSbaaSqaaiaaikdacaaIYaaabeaakiabeo 8aZnaaDaaaleaacaaIZaaabaGaaGOmaaaakiabgUcaRiaadAeadaWg aaWcbaGaaGOnaiaaiAdaaeqaaOGaeq4Wdm3aa0baaSqaaiaaigdaca aIYaaabaGaaGOmaaaakiabgUcaRiaadAeadaWgaaWcbaGaaGOnaiaa iAdaaeqaaOGaeq4Wdm3aa0baaSqaaiaaigdacaaIZaaabaGaaGOmaa aakiabgUcaRiaaikdacaWGgbWaaSbaaSqaaiaaigdacaaIYaaabeaa kiabeo8aZnaaBaaaleaacaaIXaaabeaakiabeo8aZnaaBaaaleaaca aIYaaabeaakiabgUcaRiaaikdacaWGgbWaaSbaaSqaaiaaigdacaaI Yaaabeaakiabeo8aZnaaBaaaleaacaaIXaaabeaakiabeo8aZnaaBa aaleaacaaIZaaabeaakiabgUcaRiaadAeadaWgaaWcbaGaaGymaaqa baGccqaHdpWCdaWgaaWcbaGaaGymaaqabaGccqGHRaWkcaWGgbWaaS baaSqaaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaikdaaeqaaOGa ey4kaSIaamOramaaBaaaleaacaaIYaaabeaakiabeo8aZnaaBaaale aacaaIZaaabeaakiabgsMiJkaaigdaaaa@7FD3@
    Where, the F MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36BE@ coefficients are obtained with:
    • F 1 = 1 σ 1 t 1 σ 1 c F 2 = 1 σ 2 t 1 σ 2 c F 11 = 1 σ 1 t σ 1 c F 22 = 1 σ 2 t σ 2 c F 12 = α 2 F 11 F 22 F 66 = 1 σ ¯ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGgb WaaSbaaSqaaiaaigdaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa eq4Wdm3aa0baaSqaaiaaigdaaeaacaWG0baaaaaakiabgkHiTmaala aabaGaaGymaaqaaiabeo8aZnaaDaaaleaacaaIXaaabaGaam4yaaaa aaaakeaacaWGgbWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0ZaaSaaae aacaaIXaaabaGaeq4Wdm3aa0baaSqaaiaaikdaaeaacaWG0baaaaaa kiabgkHiTmaalaaabaGaaGymaaqaaiabeo8aZnaaDaaaleaacaaIYa aabaGaam4yaaaaaaaakeaacaWGgbWaaSbaaSqaaiaaigdacaaIXaaa beaakiabg2da9maalaaabaGaaGymaaqaaiabeo8aZnaaDaaaleaaca aIXaaabaGaamiDaaaakiabgwSixlabeo8aZnaaDaaaleaacaaIXaaa baGaam4yaaaaaaaakeaacaWGgbWaaSbaaSqaaiaaikdacaaIYaaabe aakiabg2da9maalaaabaGaaGymaaqaaiabeo8aZnaaDaaaleaacaaI YaaabaGaamiDaaaakiabgwSixlabeo8aZnaaDaaaleaacaaIYaaaba Gaam4yaaaaaaaakeaacaWGgbWaaSbaaSqaaiaaigdacaaIYaaabeaa kiabg2da9iabgkHiTmaalaaabaGaeqySdegabaGaaGOmaaaadaGcaa qaaiaadAeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaeyyXICTaamOr amaaBaaaleaacaaIYaGaaGOmaaqabaaabeaaaOqaaiaadAeadaWgaa WcbaGaaGOnaiaaiAdaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa fq4WdmNbaebadaWgaaWcbaGaaGymaiaaikdaaeqaaaaaaaaa@80CF@

    Here, α MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3793@ is the interaction parameter between direction 1 and 2. The criterion is considered to be reached when F=1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9iaaigdaaaa@3880@ . In fact, the damage variable corresponds to the criterion itself D=F MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaadAeaaaa@388E@ .

  3. Once the criterion is reached D = F = 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaadAeacqGH9aqpcaaIXaaaaa@3A4F@ , two behaviors can be set up:
    • If Ifail_sh = 0 or Ifail_so = 0, there is no stress softening and elements are never deleted. In this case, the failure criterion is purely visual using the output of the damage variable.
    • If Ifail_sh0 or Ifail_so0, a stress relaxation is generated to decrease the load carrying capacity of the element.(3)
      σ ( t ) = f ( t ) σ d ( t r ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4WdiaacI cacaWG0bGaaiykaiabg2da9iGacAgaciGGOaGaamiDaiaacMcacqGH flY1caWHdpWaaSbaaSqaaiaadsgaaeqaaOGaaiikaiaadshadaWgaa WcbaGaamOCaaqabaGccaGGPaaaaa@4612@

      With f ( t ) = exp t t r τ max MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaciOzaiGacIcacaWG0bGaaiykaiabg2da9iGacwgacaGG4bGaaiiC amaabmGabaGaeyOeI0YaaSaaaeaacaWG0bGaeyOeI0IaamiDamaaBa aaleaacaWGYbaabeaaaOqaaiabes8a0naaBaaaleaaciGGTbGaaiyy aiaacIhaaeqaaaaaaOGaayjkaiaawMcaaiaayIW7caaMi8oaaa@4F79@ and t t r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamiDaiabgwMiZkaadshadaWgaaWcbaGaamOCaaqabaaaaa@3EAE@ .

      Where,
      t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamiDaaaa@3ACC@
      Time.
      t r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamiDamaaBaaaleaacaWGYbaabeaaaaa@3BEF@
      Start time of relaxation when the damage criteria is assumed.
      τ max MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiXdq3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3E98@
      Time of dynamic relaxation.
      σ d t r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaC4WdmaaBaaaleaacaWGKbaabeaakmaabmGabaGaamiDamaaBaaa leaacaWGYbaabeaaaOGaayjkaiaawMcaaaaa@3FF2@
      Stress tensor when the criterion is reached.

      When the stresses reach 1% of the stress value at the beginning of the failure, the element is deleted. This is necessary to avoid instabilities coming from a sudden deletion of an element and a failure “chain reaction” in the neighboring elements. Even if the failure criterion is reached, there will be no element deletion with the default value of τ max = 1.0 E 20 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiXdq3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccqGH9aqp caaIXaGaaiOlaiaaicdacaWGfbGaaGOmaiaaicdaaaa@440F@ . Therefore, it is recommended to define a value for τ max MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqiXdq3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3E98@ 10 times larger than the simulation time step.

  4. To avoid “chain reaction” when deleting elements, you can also define a stress tensor filtering frequency Fcut. Thus, the stress tensor used to calculate the TSAIWU criterion is first be filtered according to:(4)
    σ n + 1 f i l t = α σ n + 1 + 1 α σ n f i l t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4WdmaaDa aaleaacaWGUbGaey4kaSIaaGymaaqaaiaadAgacaWGPbGaamiBaiaa dshaaaGccqGH9aqpcqaHXoqycaWHdpWaaSbaaSqaaiaad6gacqGHRa WkcaaIXaaabeaakiabgUcaRmaabmaabaGaaGymaiabgkHiTiabeg7a HbGaayjkaiaawMcaaiaaho8adaqhaaWcbaGaamOBaaqaaiaadAgaca WGPbGaamiBaiaadshaaaaaaa@506A@

    With α = 2 π F c u t Δ t 2 π F c u t Δ t + 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0ZaaSaaaeaacaaIYaGaeqiWdaNaeyyXICTaamOramaaBaaaleaa caWGJbGaamyDaiaadshaaeqaaOGaeyyXICTaeuiLdqKaamiDaaqaai aaikdacqaHapaCcqGHflY1caWGgbWaaSbaaSqaaiaadogacaWG1bGa amiDaaqabaGccqGHflY1cqqHuoarcaWG0bGaey4kaSIaaGymaaaaaa a@54D6@

    Where, Δ t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iDaaaa@3853@ is the current timestep.

    If a filtering frequency is not defined (Fcut= 0.0), the filtering effect is deactivated.

  5. 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).