/FAIL/SYAZWAN

Block Format Keyword This simplified failure criterion is based on a fracture surface with linear damage accumulation. It also provides the initialization of damage value using strain histories with linear strain path assumptions.

Format

Card 1 – Fracture surface parameters 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/SYAZWAN/mat_ID/unit_ID
I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ ε p f M I N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGa amOtaaqabaaaaa@3C51@      
If I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ = 1: classical input / Card 2 – Fracture surface parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
C1 C2 C3 C4 C5
C6        
If I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ = 2: plastic strain input / Card 2 – Failure plastic strains
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ε f comp MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ ε f s h e a r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ ε f t e n s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ ε f p l a n e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ ε f b i a x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@
Card 3 – Damage initialization parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Dinit Dsf Dmax
Card 4 – Instability and softening parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Inst Iform Nvalue Softexp
Card 5 – Element size scaling
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDEl El_ref Fscale_El
Card 6 - 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)

I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ Card input format flag. 3
= 1 (Default)
Fracture surface parameters input.
= 2
Plastic strain at failure input.

(Integer)

ε p f M I N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGa amOtaaqabaaaaa@3C51@ Minimum plastic strain at failure.

Default = 0.0 (Real)

C1 First constant for failure surface.

(Real)

C2 Second constant for failure surface.

(Real)

C3 Third constant for failure surface.

(Real)

C4 Fourth constant for failure surface.

(Real)

C5 Fifth constant for failure surface.

(Real)

C6 Sixth constant for failure surface.

(Real)

ε f comp MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for uniaxial compression.

(Real)

ε f s h e a r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for shearing.

(Real)

ε f t e n s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for uniaxial tension.

(Real)

ε f p l a n e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for plane strain.

(Real)

ε f b i a x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for biaxial tension.

(Real)

Dinit Damage value initialization from strain tensors flag.
= 0 (Default)
Damage is not initialized.
= 1
Damage is initialized.

(Integer)

Dsf Damage initialization scale factor.

Default = 1.0 (Real)

Dmax Damage initialization maximum value.

Default = 1.0 (Real)

Inst Necking instability flag.
= 0 (Default)
Instability is not activated.
= 1
Instability is activated.

(Integer)

Iform Necking instability formulation flag.
= 1 (Default)
Incremental formulation (loading path history).
= 2
Direct formulation (no loading path history).

(Integer)

Nvalue The N-value derived from Hollomon’s Law.

Default = 0.25 (Real)

Softexp Stress softening exponent.

Default = 1.0 (Real)

fct_IDEl Element size factor function identifier.

(Integer)

El_ref Reference element size.

Default = 1.0 (Real)

[ m ]
Fscale_El Element size factor function scale factor.

Default = 1.0

fail_ID (Optional) Failure criteria identifier.

(Integer, maximum 10 digits)

Example

/FAIL/SYAZWAN/1
#              ICARD              EPFMIN
                   2                 0.0
#           EPF_COMP           EPF_SHEAR            EPF_TENS          EPF_PLSTRN            EPF_BIAX
               3.009                0.98                 0.7                0.42                0.56
#           DAM_INIT              DAM_SF             DAM_MAX
                   
#     INST     IFORM               N_VAL             SOFTEXP
         1         2                0.25                 1.2 
#             FCT_EL              EL_REF              ELSCAL                   

/FAIL/SYAZWAN/1
#              ICARD              EPFMIN
                   1                 0.0
#                 C1                  C2                  C3                  C4                  C5
                0.65             -3.2234               -0.08              3.9031              0.2652
#                 C6
              0.5266  
#           DAM_INIT              DAM_SF             DAM_MAX
                   
#     INST     IFORM               N_VAL             SOFTEXP
         1         1                0.27                 1.2 
#             FCT_EL              EL_REF              ELSCAL

Comments

  1. It is highly recommended to set the value of I p l a s MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGWbGaamiBaiaadggacaWGZbaabeaaaaa@3AB2@ in /PROP/SHELL to 1. This will allow accurate calculation of the principal strain ratio β .
  2. The value of C1, C2, C3, C4, C5, and C6 is based on:(1)
    ε p f = C 1 + C 2 η + C 3 θ ¯ + C 4 η 2 + C 5 θ ¯ 2 + C 6 η θ ¯ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOGaeyypa0Jaam4qamaaBaaaleaa caaIXaaabeaakiabgUcaRiaadoeadaWgaaWcbaGaaGOmaaqabaGccq aH3oaAcqGHRaWkcaWGdbWaaSbaaSqaaiaaiodaaeqaaOGafqiUdeNb aebacqGHRaWkcaWGdbWaaSbaaSqaaiaaisdaaeqaaOGaeq4TdG2aaW baaSqabeaacaaIYaaaaOGaey4kaSIaam4qamaaBaaaleaacaaI1aaa beaakiqbeI7aXzaaraWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaam 4qamaaBaaaleaacaaI2aaabeaakiabeE7aOjqbeI7aXzaaraaaaa@55DB@
    Where,
    ε p f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzda qhaaWcbaGaamiCaaqaaiaadAgaaaaaaa@3B18@
    Plastic strain at failure.
    η
    Stress triaxiality with η = 1 3 σ x x + σ y y σ V M MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH3oaAcq GH9aqpdaWcaaqaamaalaaabaGaaGymaaqaaiaaiodaaaWaaeWaceaa cqaHdpWCdaWgaaWcbaGaamiEaiaadIhaaeqaaOGaey4kaSIaeq4Wdm 3aaSbaaSqaaiaadMhacaWG5baabeaaaOGaayjkaiaawMcaaaqaaiab eo8aZnaaBaaaleaacaWGwbGaamytaaqabaaaaaaa@499F@
    with 2 3 η 2 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGHsislda WcaaqaaiaaikdaaeaacaaIZaaaaiabgsMiJkabeE7aOjabgsMiJoaa laaabaGaaGOmaaqaaiaaiodaaaaaaa@4079@
    θ ¯ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH4oqCga qeaaaa@3932@
    Normalized Lode angle θ ¯ = 1 2 π a r cos ζ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH4oqCga qeaiabg2da9iaaigdacqGHsisldaWcaaqaaiaaikdaaeaacqaHapaC aaGaamyyaiaadkhaciGGJbGaai4BaiaacohacqaH2oGEaaa@44D6@
    with Lode angle ( θ ) parameter ζ = cos 3 θ = 27 2 η η 2 1 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH2oGEcq GH9aqpciGGJbGaai4BaiaacohadaqadaqaaiaaiodacqaH4oqCaiaa wIcacaGLPaaacqGH9aqpcqGHsisldaWcaaqaaiaaikdacaaI3aaaba GaaGOmaaaacqaH3oaAdaqadaqaaiabeE7aOnaaCaaaleqabaGaaGOm aaaakiabgkHiTmaalaaabaGaaGymaaqaaiaaiodaaaaacaGLOaGaay zkaaaaaa@4D7B@

    Where, σ V M MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamOvaiaad2eaaeqaaaaa@3B00@ is the von Mises stress.

    Figure 1 shows the example of curve fit of plane stress failure curve into failure surface criteria.


    Figure 1. Example of Syazwan failure criterion fit
  3. Two different parameter input card formats are available for /FAIL/SYAZWAN depending on the value of I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ .
    • If I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ = 1: you must directly input the Ci parameters
    • If I c a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaado gacaWGHbGaamOCaiaadsgaaaa@3A70@ = 2: you can specify some plastic strain at failure for several commonly tested loading conditions: uniaxial compression ε f c o m p MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ , shearing ε f s h e a r MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGZbGaamiAaiaadwgacaWGHbGaamOCaaaa aaa@3D5E@ , uniaxial tension ε f t e n s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyzaiaad6gacaWGZbaaaaaa@3C80@ , plane strain ε f p l a n e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGWbGaamiBaiaadggacaWGUbGaamyzaaaa aaa@3D5B@ and biaxial tension ε f b i a x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGIbGaamyAaiaadggacaWG4baaaaaa@3C6A@ . In that case, the Ci parameter will be automatically computed by solving the set of equations below:(2)
      C 1 1 3 C 2 C 3 + 1 9 C 4 + C 5 + 1 3 C 6 = ε f c o m p C 1 = ε f s h e a r C 1 + 1 3 C 2 + C 3 + 1 9 C 4 + C 5 + 1 3 C 6 = ε f t e n s C 1 + 1 3 C 2 + 1 3 C 4 = ε f p l a n e C 1 + 2 3 C 2 C 3 + 4 9 C 4 + C 5 2 3 C 6 = ε f b i a x C 2 18 π C 3 + 2 3 C 4 18 π 3 C 6 = 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe qaaiaadoeadaWgaaWcbaGaaGymaaqabaGccqGHsisldaWcaaqaaiaa igdaaeaacaaIZaaaaiaadoeadaWgaaWcbaGaaGOmaaqabaGccqGHsi slcaWGdbWaaSbaaSqaaiaaiodaaeqaaOGaey4kaSYaaSaaaeaacaaI XaaabaGaaGyoaaaacaWGdbWaaSbaaSqaaiaaisdaaeqaaOGaey4kaS Iaam4qamaaBaaaleaacaaI1aaabeaakiabgUcaRmaalaaabaGaaGym aaqaaiaaiodaaaGaam4qamaaBaaaleaacaaI2aaabeaakiabg2da9i abew7aLnaaDaaaleaacaWGMbaabaGaam4yaiaad+gacaWGTbGaamiC aaaaaOqaaiaadoeadaWgaaWcbaGaaGymaaqabaGccqGH9aqpcqaH1o qzdaqhaaWcbaGaamOzaaqaaiaadohacaWGObGaamyzaiaadggacaWG YbaaaaGcbaGaam4qamaaBaaaleaacaaIXaaabeaakiabgUcaRmaala aabaGaaGymaaqaaiaaiodaaaGaam4qamaaBaaaleaacaaIYaaabeaa kiabgUcaRiaadoeadaWgaaWcbaGaaG4maaqabaGccqGHRaWkdaWcaa qaaiaaigdaaeaacaaI5aaaaiaadoeadaWgaaWcbaGaaGinaaqabaGc cqGHRaWkcaWGdbWaaSbaaSqaaiaaiwdaaeqaaOGaey4kaSYaaSaaae aacaaIXaaabaGaaG4maaaacaWGdbWaaSbaaSqaaiaaiAdaaeqaaOGa eyypa0JaeqyTdu2aa0baaSqaaiaadAgaaeaacaWG0bGaamyzaiaad6 gacaWGZbaaaaGcbaGaam4qamaaBaaaleaacaaIXaaabeaakiabgUca RmaalaaabaGaaGymaaqaamaakaaabaGaaG4maaWcbeaaaaGccaWGdb WaaSbaaSqaaiaaikdaaeqaaOGaey4kaSYaaSaaaeaacaaIXaaabaGa aG4maaaacaWGdbWaaSbaaSqaaiaaisdaaeqaaOGaeyypa0JaeqyTdu 2aa0baaSqaaiaadAgaaeaacaWGWbGaamiBaiaadggacaWGUbGaamyz aaaaaOqaaiaadoeadaWgaaWcbaGaaGymaaqabaGccqGHRaWkdaWcaa qaaiaaikdaaeaacaaIZaaaaiaadoeadaWgaaWcbaGaaGOmaaqabaGc cqGHsislcaWGdbWaaSbaaSqaaiaaiodaaeqaaOGaey4kaSYaaSaaae aacaaI0aaabaGaaGyoaaaacaWGdbWaaSbaaSqaaiaaisdaaeqaaOGa ey4kaSIaam4qamaaBaaaleaacaaI1aaabeaakiabgkHiTmaalaaaba GaaGOmaaqaaiaaiodaaaGaam4qamaaBaaaleaacaaI2aaabeaakiab g2da9iabew7aLnaaDaaaleaacaWGMbaabaGaamOyaiaadMgacaWGHb GaamiEaaaaaOqaaiaadoeadaWgaaWcbaGaaGOmaaqabaGccqGHsisl daWcaaqaaiaaigdacaaI4aaabaGaeqiWdahaaiaadoeadaWgaaWcba GaaG4maaqabaGccqGHRaWkdaWcaaqaaiaaikdaaeaadaGcaaqaaiaa iodaaSqabaaaaOGaam4qamaaBaaaleaacaaI0aaabeaakiabgkHiTm aalaaabaGaaGymaiaaiIdaaeaacqaHapaCdaGcaaqaaiaaiodaaSqa baaaaOGaam4qamaaBaaaleaacaaI2aaabeaakiabg2da9iaaicdaaa Gaay5Eaaaaaa@B9A9@
    Note: The last equation imposes that the plane strain condition corresponds to a local minimum of the failure criterion.
  4. In some cases, the criterion may have negative or very low values for some loading conditions. In that case, it will be bounded by the minimum plastic strain at failure parameter ε p f M I N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGa amOtaaqabaaaaa@3C51@ that must be positive or null (by default = 0.0). All values under ε p f M I N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGa amOtaaqabaaaaa@3C51@ are then ignored.
    Figure 2 shows an example with a minimum value (orange curve) of 0.2.


    Figure 2. Failure criterion (blue curve) bounded by plastic strain at failure minimum value. ε p f MIN MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGa amOtaaqabaaaaa@3C51@ (orange curve) of 0.2
  5. The damage variable evolution is computed incrementally as:(3)
    D= t=0 Δ ε p ε p f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaaaaa qaaiaadshacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@4621@
  6. You may want to realize a simulation starting from existing total and plastic strains fields (after a previous forming simulation for instance). In the case where the failure criterion is not computed during the first simulation, it is possible to estimate a damage field from the total strain tensor and the plastic strain values obtained at the end of the first simulation (using .sta files). If the Dinit flag is set to 1, the damage field will be computed if the plastic strain ≠ 0. /INISHE/STRA_F, /INISHE/STRA_F, /INISHE/EPSP_F and /INISH3/EPSP_F must be present in the keywords of the status file. The initial stress tensors are not incorporated into the simulation model; thus, the stress triaxiality is derived using:(4)
    η = 1 3 1 + β 1 + β + β 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaey ypa0ZaaSaaaeaacaaIXaaabaWaaOaaaeaacaaIZaaaleqaaaaakmaa laaabaGaaGymaiabgUcaRiabek7aIbqaamaakaaabaGaaGymaiabgU caRiabek7aIjabgUcaRiabek7aInaaCaaaleqabaGaaGOmaaaaaeqa aaaaaaa@445B@
    The β value can be recovered from the stress triaxiality value using the first root of Equation 4:(5)
    β = ( 2 3 η 2 ) 3 η 2 4 9 η 2 2 3 η 2 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdiMaey ypa0ZaaSaaaeaacaGGOaGaaGOmaiabgkHiTiaaiodacqaH3oaAdaah aaWcbeqaaiaaikdaaaGccaGGPaGaeyOeI0YaaOaaaeaacaaIZaGaeq 4TdG2aaWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaaI0aGaeyOeI0Ia aGyoaiabeE7aOnaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaa WcbeaaaOqaaiaaikdadaqadaqaaiaaiodacqaH3oaAdaahaaWcbeqa aiaaikdaaaGccqGHsislcaaIXaaacaGLOaGaayzkaaaaaaaa@5156@
    Then, an initial damage value can be estimated as:(6)
    D t = 0 = ε p t = 0 ε p f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG0bGaeyypa0JaaGimaaqabaGccqGH9aqpdaWcaaqaaiab ew7aLnaaDaaaleaacaWGWbaabaGaamiDaiabg2da9iaaicdaaaaake aacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaaaaaaa@4402@
    Figure 3 shows an example of initialized damage field in one-step after a forming simulation performed without failure criterion computation. Damage field is then deduced using the plastic strain and the strain tensor as presented above.


    Figure 3. Example of damage field “one-step” initialization after a forming simulation
  7. A controlled necking instability can be used if the flag Inst is set to 1. To trigger this instability, a criterion variable denoted f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36DF@ is computed based on the Nvalue specified by you, using:(7)
    ε 1 = 2 ( 2 α ) ( 1 α + α 2 ) 4 3 α 3 α 2 + 4 α N v a l u e ε 2 = 2 ( 2 α 1 ) ( 1 α + α 2 ) 4 3 α 3 α 2 + 4 α N v a l u e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaH1o qzdaWgaaWcbaGaaGymaaqabaGccqGH9aqpdaWcaaqaaiaaikdacaGG OaGaaGOmaiabgkHiTiabeg7aHjaacMcacaGGOaGaaGymaiabgkHiTi abeg7aHjabgUcaRiabeg7aHnaaCaaaleqabaGaaGOmaaaakiaacMca aeaacaaI0aGaeyOeI0IaaG4maiabeg7aHjabgkHiTiaaiodacqaHXo qydaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI0aGaeqySdegaaiaa d6eadaWgaaWcbaGaamODaiaadggacaWGSbGaamyDaiaadwgaaeqaaa GcbaGaeqyTdu2aaSbaaSqaaiaaikdaaeqaaOGaeyypa0ZaaSaaaeaa caaIYaGaaiikaiaaikdacqaHXoqycqGHsislcaaIXaGaaiykaiaacI cacaaIXaGaeyOeI0IaeqySdeMaey4kaSIaeqySde2aaWbaaSqabeaa caaIYaaaaOGaaiykaaqaaiaaisdacqGHsislcaaIZaGaeqySdeMaey OeI0IaaG4maiabeg7aHnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa isdacqaHXoqyaaGaamOtamaaBaaaleaacaWG2bGaamyyaiaadYgaca WG1bGaamyzaaqabaaaaaa@7B6C@
    Where, α MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3793@ ratio between the minor principal and major principal stress computed from β using:(8)
    α = 2 β + 1 2 + β MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0ZaaSaaaeaacaaIYaGaeqOSdiMaey4kaSIaaGymaaqaaiaaikda cqGHRaWkcqaHYoGyaaaaaa@3FE2@
    You can then compute an effective plastic strain at necking instability:(9)
    ε p i n s t = ε 1 4 3 1 + β + β 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaOGaeyyp a0JaeqyTdu2aaSbaaSqaaiaaigdaaeqaaOGaeyyXIC9aaOaaaeaada WcaaqaaiaaisdaaeaacaaIZaaaamaabmaabaGaaGymaiabgUcaRiab ek7aIjabgUcaRiabek7aInaaCaaaleqabaGaaGOmaaaaaOGaayjkai aawMcaaaWcbeaaaaa@4C63@

    The parameter Nvalue is the value of the instability plastic strain taken in uniaxial tension (for which η = 1 / 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaey ypa0ZaaSGbaeaacaaIXaaabaGaaG4maaaaaaa@3A34@ and θ ¯ = 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqiUdeNbae bacqGH9aqpcaaIXaaaaa@3983@ ). You can then use the relation linking β and the stress triaxiality described above to plot the instability strain evolution.

    Using the instability plastic strain, an instability criterion variable denoted f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36DF@ is either computed:
    • Incrementally (if Iform = 1) to take into account the loading history(10)
      f = t = 0 Δ ε p ε p i n s t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadMgacaWGUb Gaam4CaiaadshaaaaaaaqaaiaadshacqGH9aqpcaaIWaaabaGaeyOh IukaniabggHiLdaaaa@492A@
    • Directly (if Iform = 2) to ignore the loading path history(11)
      f = ε p ε p i n s t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9maalaaabaGaeqyTdu2aaSbaaSqaaiaadchaaeqaaaGcbaGaeqyT du2aa0baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaa aaaaa@4161@
    If the criterion is reached ( f = 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9iaaigdaaaa@38A0@ ), the instant value of the damage variable D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BC@ is saved in the value D c r i t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGJbGaamOCaiaadMgacaWG0baabeaaaaa@3AAF@ that becomes an element history variable. The necking instability can then be triggered by a stress softening whose equation is:(12)
    D = Δ D f = Δ f D c r i t = 1 while f < 1 D when f 1 σ = σ e f f 1 D D c r i t 1 D c r i t S o f t exp MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGeb Gaeyypa0Zaa8qaaeaacqGHuoarcaWGebaaleqabeqdcqGHRiI8aaGc baGaamOzaiabg2da9maapeaabaGaeyiLdqKaamOzaaWcbeqab0Gaey 4kIipaaOqaaiaadseadaWgaaWcbaGaam4yaiaadkhacaWGPbGaamiD aaqabaGccqGH9aqpdaGabaqaauaabeqaceaaaeaafaqabeqadaaaba GaaGymaaqaaiaabEhacaqGObGaaeyAaiaabYgacaqGLbaabaGaamOz aiabgYda8iaaigdaaaaabaqbaeqabeWaaaqaaiaadseaaeaacaqG3b GaaeiAaiaabwgacaqGUbaabaGaamOzaiabgwMiZkaaigdaaaaaaaGa ay5EaaaabaGaeq4WdmNaeyypa0Jaeq4Wdm3aaSbaaSqaaiaadwgaca WGMbGaamOzaaqabaGcdaqadaqaaiaaigdacqGHsisldaqadaqaamaa laaabaGaamiraiabgkHiTiaadseadaWgaaWcbaGaam4yaiaadkhaca WGPbGaamiDaaqabaaakeaacaaIXaGaeyOeI0IaamiramaaBaaaleaa caWGJbGaamOCaiaadMgacaWG0baabeaaaaaakiaawIcacaGLPaaada ahaaWcbeqaaiaadofacaWGVbGaamOzaiaadshadaWgaaadbaGaciyz aiaacIhacaGGWbaabeaaaaaakiaawIcacaGLPaaaaaaa@797B@
    Where,
    σ
    Damaged stress tensor.
    σ e f f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadwgacaWGMbGaamOzaaqabaaaaa@3AA3@
    Undamaged effective stress tensor.
    D c r i t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGJbGaamOCaiaadMgacaWG0baabeaaaaa@3AAE@
    Critical damage value that triggers stress softening.
    S o f t exp MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaad+ gacaWGMbGaamiDamaaBaaaleaaciGGLbGaaiiEaiaacchaaeqaaaaa @3CAA@
    Exponent parameter.
    For visualization purposes, the instability curve ( ε p i n s t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaaaa@3C8E@ versus η ) can be obtained from all the equations above. For instance, if the Nvalue is set to 0.175, the following curve (Figure 4) is obtained.


    Figure 4. Example of instability curve (orange) and its position with respect to failure criterion (blue)

    The effect of instability curve is restricted to positive stress triaxiality (as necking only occurs in tension) and only has an effect when it is under the failure criterion curve.

    Figure 5 shows several instability curves obtained with different Nvalue parameter values.


    Figure 5. Instability curves obtained with different Nvalue parameters
  8. Element size scaling can be used to regularize the failure and ensure to obtain an almost constant fracture energy dissipated with different mesh sizes. This element size dependency is introduced by computing a size scale factor denoted f s i z e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaaaaa@3AD8@ defined by the function fct_IDEl. The size scaling factor evolution is given with respect to the ratio of initial element characteristic length divided by a reference size El_ref (by default = 1.0): f s i z e L e 0 L r e f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaakmaabmaabaWaaSaa aeaacaWGmbWaa0baaSqaaiaadwgaaeaacaaIWaaaaaGcbaGaamitam aaBaaaleaacaWGYbGaamyzaiaadAgaaeqaaaaaaOGaayjkaiaawMca aaaa@42F9@ . An additional scale factor Fscale_El can also be applied to the entire regularization function. The element size scale factor f s i z e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaaaaa@3AD8@ thus computed is introduced in the damage variable evolution equation (and if defined, the instability variable evolution equation) as:(13)
    D= t=0 Δ ε p ε p f f size L e 0 L ref f scale el MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaGccq GHflY1caqGMbWaaSbaaSqaaiaadohacaWGPbGaamOEaiaadwgaaeqa aOWaaeWaaeaadaWcaaqaaiaadYeadaqhaaWcbaGaamyzaaqaaiaaic daaaaakeaacaWGmbWaaSbaaSqaaiaadkhacaWGLbGaamOzaaqabaaa aaGccaGLOaGaayzkaaGaeyyXICTaaeOzamaaDaaaleaacaWGZbGaam 4yaiaadggacaWGSbGaamyzaaqaaiaadwgacaWGSbaaaaaaaeaacaWG 0bGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaaa@5F57@
  9. Alternatively, the /NONLOCAL/MAT option which is compatible with Syazwan failure criterion (Figure 6) can be used to regularize the solution according to mesh size and orientation. If the non-local regularization is used, the non-local plastic strain is used to compute the damage evolution (and the instability variable, if used). In that case, the maximum non-local length parameter LE_MAX is used instead of the initial element size if an element size scaling is defined through fct_IDEl. Also, the non-local regularization is also available with the “one-step” damage field initialization.


    Figure 6. Example of /NONLOCAL/MAT option cumulated with /FAIL/SYAZWAN on automotive DP450 steel