/FAIL/CHANG

Block Format Keyword Describes the Chang failure model.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/CHANG/mat_ID/unit_ID
σ 1 t σ 2 t σ ¯ 12 σ 1 c σ 2 c
β τ max Ifail_sh FAILIP
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)

σ 1 t Longitudinal tensile strength.

Default = 1020 (Real)

[ Pa ]
σ 2 t Transverse tensile strength.

Default = 1020 (Real)

[ Pa ]
σ ¯ 12 Shear strength.

Default = 1020 (Real)

[ Pa ]
σ 1 c Longitudinal compressive strength.

Default = 1020 (Real)

[ Pa ]
σ 2 c Transverse compressive strength.

Default = 1020 (Real)

[ Pa ]
β Shear scaling factor.

Default = 0 (Real)

τ max Dynamic time relaxation. 7

Default = 1020 (Real)

[ s ]
Ifail_sh Shell failure model flag.
= 1 (Default)
Shell is deleted, if damage is reached for fiber or matrix for one layer.
= 2
Shell is deleted, if damage is reached for fiber or matrix for all layers of shell.
= 3
Shell is deleted, if damage is reached only for one fiber layer of shell.
= 4
Shell is deleted, if damage is reached for all fiber layers of shell.

(Integer)

FAILIP Number of failed integration points prior to solid deletion.

Default = 1 (Integer)

fail_ID Failure criteria identifier. 6

(Integer, maximum 10 digits)

Comments

  1. This failure model is available for shell only.
  2. Where direction one is the fiber direction. The failure criteria for fiber breakage is written as:
    Tensile fiber mode: σ 11 > 0
    • For shells:
      e f 2 = σ 11 σ 1 t 2 + β σ 12 σ ¯ 12 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyzamaaBaaaleaacaWGMbaabeaakmaaCaaaleqabaGaaGOmaaaa kiabg2da9maabmaabaWaaSaaaeaacqaHdpWCdaWgaaWcbaGaaGymai aaigdaaeqaaaGcbaGaeq4Wdm3aa0baaSqaaiaaigdaaeaacaWG0baa aaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakiabgUcaRi abek7aInaabmaabaWaaSaaaeaacqaHdpWCdaWgaaWcbaGaaGymaiaa ikdaaeqaaaGcbaGafq4WdmNbaebadaWgaaWcbaGaaGymaiaaikdaae qaaaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaa@5253@
    • For solids:
      e f 2 = σ 11 σ 1 t 2 + β σ 12 σ ¯ 12 2 + σ 13 σ ¯ 12 2

    Compressive fiber mode: σ 11 < 0

    e c 2 = ( σ 11 σ 1 c ) 2

  3. For matrix cracking, the failure criterion is:
    Tensile matrix mode: σ 22 > 0
    • For shells:
      e m 2 = ( σ 22 σ 2 t ) 2 + ( σ 12 σ ¯ 12 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamyzamaaBaaaleaacaWGTbaabeaakmaaCaaaleqabaGaaGOmaaaa kiabg2da9maabmaabaWaaSaaaeaacqaHdpWCdaWgaaWcbaGaaGOmai aaikdaaeqaaaGcbaGaeq4Wdm3aa0baaSqaaiaaikdaaeaacaWG0baa aaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakiabgUcaRm aabmaabaWaaSaaaeaacqaHdpWCdaWgaaWcbaGaaGymaiaaikdaaeqa aaGcbaGafq4WdmNbaebadaWgaaWcbaGaaGymaiaaikdaaeqaaaaaaO GaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaa@50BF@
    • For solids:
      e m 1 2 = ( σ 22 σ 2 t ) 2 + ( σ 12 σ ¯ 12 ) 2
      e m 2 2 = ( σ 33 σ 2 t ) 2 + ( σ 13 σ ¯ 12 ) 2
    Compressive matrix mode: σ 22 < 0
    • For shells:
      e d 2 = ( σ 22 2 σ ¯ 12 ) 2 + [ ( σ 2 c 2 σ ¯ 12 ) 2 1 ] σ 22 σ 2 c + ( σ 12 σ ¯ 12 ) 2
    • For solids:
      e d 1 2 = ( σ 22 2 σ ¯ 12 ) 2 + [ ( σ 2 c 2 σ ¯ 12 ) 2 1 ] σ 22 σ 2 c + ( σ 12 σ ¯ 12 ) 2
      e d 2 2 = ( σ 33 2 σ ¯ 12 ) 2 + [ ( σ 2 c 2 σ ¯ 12 ) 2 1 ] σ 33 σ 2 c + ( σ 13 σ ¯ 12 ) 2
  4. If the damage parameter e f 2 , e c 2 , e m 2 , or e d 2 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:
    σ ( t ) = f ( t ) σ d ( t r )

    With, f ( t ) = exp ( t t r τ max ) and t t r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabgw MiZkaadshadaWgaaWcbaGaamOCaaqabaaaaa@3AB2@ .

    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
  5. 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 ( e f 2 , e c 2 , e m 2 , e d 2 ) . This damage value shows with /ANIM/SHELL/DAMA.

  6. The fail_ID is used with /STATE/SHELL/FAIL and /INISHE/FAIL for shell. There is no default value. If the line is blank, a value will not 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).
  7. 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.